Farmers’ Subjective Valuation of Subsistence Crops: The Case of Traditional Maize in Mexico by

Aslıhan Arslan B.S. (Middle East Technical University) 2001 M.S. (University of California, Davis) 2003 DISSERTATION Submitted in partial satisfaction of the requirements for the degree of DOCTOR OF PHILOSOPHY in Agricultural and Resource Economics to the OFFICE OF GRADUATE STUDIES of the UNIVERSITY OF CALIFORNIA DAVIS Approved:

J. Edward Taylor

Steve Boucher

Lovell S. Jarvis Committee in Charge December 2007

Abstract Subsistence farmers may not respond to market incentives if their resource allocation decisions are based on shadow prices. This may seem “puzzling” from an economic point of view if shadow prices are not taken into account. Subsistence maize farmers in rural Mexico are an example with their non-response to decreasing maize prices after NAFTA. Previous research suggests that the market price may fail to represent incentives if farmers’ crops have non-market values. I explore subjective valuation of subsistence crops in the context of traditional maize in Mexico – the center of domestication and diversity of maize. I show how these values affect farmer behaviour and the design of on-farm conservation programs. My theoretical contribution extends the basic agricultural household model by combining transaction costs and an asymmetric missing market for subsistence crop. This missing market arises from the fact that the market-purchased crops lack the non-market values attached to farmer’s own crop, hence are imperfect substitutes for it. This model explains why some farmers may allocate resources in ways that cannot be explained by market prices even in the absence of transaction costs. Shadow prices predict farmers’ resource allocation better than market prices and represent incentives to maintain subsistence crops. Using nationally-representative data, I estimate production functions and shadow prices. I conclude that the value of traditional maize to subsistence farmers is significantly higher than market prices for maize. The same is not true for modern maize. I identify key farm- and farmer-specific factors correlated with shadow prices of traditional maize. Use of irrigation and producing on land with high-quality soil are negatively correlated with shadow prices; male-headed households and those of indigenous origin have above-average shadow prices for traditional maize. The latter correlation is especially true in southern and southeastern Mexico indicating high de facto incentives to maintain traditional maize in these regions. On-farm conservation programs would be more effective if targeted to communities with high shadow prices. The method I use is flexible enough to be applied to guide conservation programs for other crops in other regions.1 1 The most up to date version of this dissertation is available at http://aslihana.googlepages. com/Thesis_main.pdf.

iii

Contents List of Tables

vii

List of Figures

ix

1 Introduction/Motivation

1

2 Background 2.1 Agricultural Household Literature . . . . . . . . . . . . . . . . 2.1.1 Recursive models . . . . . . . . . . . . . . . . . . . . . 2.1.2 Non-recursive models . . . . . . . . . . . . . . . . . . . 2.1.3 Non-market values: another source of non-recursiveness 2.1.4 Empirical applications of household models . . . . . . . 2.2 Conservation of Crop Genetic Resources . . . . . . . . . . . . 2.3 Maize in Mexico . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.1 Mexican agriculture in transition . . . . . . . . . . . . 2.3.2 Previous empirical research on maize in Mexico . . . . 2.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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9 9 10 11 13 15 17 19 23 25 30

3 Theoretical Framework 3.1 Agricultural Household Model and Shadow Prices . . . . . . . . . . . 3.2 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

33 37 52

4 Empirical Analysis 4.1 The ENHRUM Data . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2 Econometric Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.1 Estimating shadow prices . . . . . . . . . . . . . . . . . . . . Is there a selection bias in the production of TVs and MVs? . Estimating production functions with commercial farmer dummy 4.2.2 What predicts high shadow prices? . . . . . . . . . . . . . . . Descriptive statistics by region . . . . . . . . . . . . . . . . . . Decomposing shadow prices . . . . . . . . . . . . . . . . . . . 4.2.3 Do shadow prices explain land allocation better than market prices? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

55 56 66 67 69 73 82 82 85

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93

4.3

Policy Implications and Conclusions . . . . . . . . . . . . . . . . . . .

5 De-bugging the Empirical Results 5.1 Missing Labor Markets and Shadow Prices . . . . . . . . . . . 5.1.1 Adding missing labor markets to the theoretical model 5.1.2 Is the labor market imperfect? . . . . . . . . . . . . . . 5.2 Risk and Liquidity Constraints? . . . . . . . . . . . . . . . . . 5.3 Bad Crop Year in 2002? . . . . . . . . . . . . . . . . . . . . . 5.4 Transaction Costs and Missing Seed Market . . . . . . . . . . 5.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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99 101 102 102 109 112 115 116 118

6 Conclusions

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A KKT Conditions for the Basic Model

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B Missing Data Methods

133

Bibliography

135

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List of Tables 2.1

Maize consumption in various countries . . . . . . . . . . . . . . . . .

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4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9 4.10 4.11 4.12 4.13 4.14 4.15 4.16 4.17 4.18

Comparison of all plots with plots mono-cropped with maize . . . . Percentage of plots under different maize types by region . . . . . . Means of household characteristics by region . . . . . . . . . . . . . Maize varieties, indigenous identity, farm income and sales by region Summary statistics for plots cultivated with TV and MV . . . . . . Summary statistics for different groups of households . . . . . . . . Heckman model results for production functions for TV and MV . Input uses of commercial and non-commercial farmers . . . . . . . . Production function estimations . . . . . . . . . . . . . . . . . . . . Tests for the validity of IVs . . . . . . . . . . . . . . . . . . . . . . Estimated shadow prices and observed market prices . . . . . . . . Are estimated shadow prices equal to observed market prices? . . . Sample means of socio-economic variables by region . . . . . . . . . Sample means of market access variables by region . . . . . . . . . Sample means of agro-ecological variables by region . . . . . . . . . Decomposition of the shadow prices . . . . . . . . . . . . . . . . . . Area share of TVs, shadow and market prices by region . . . . . . . Heckman and Tobit models for area share of TVs for non-sellers . .

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58 60 61 63 64 65 72 73 76 78 79 81 84 84 85 88 94 96

5.1 5.2 5.3 5.4 5.5

Optimal land allocation under different market scenarios . . . . Production functions to test labor market imperfections . . . . . Are estimated VMPFs equal to market wages? . . . . . . . . . . Do sellers and non-sellers differ in their labor market prospects? Loss in maize production for farmers with high shadow prices .

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107 110 111 112 115

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B.1 Production functions using different missing data methods . . . . . . 134

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List of Figures 2.1

Maize area and production in Mexico, 1990-2004 . . . . . . . . . . . .

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3.1 3.2

Transaction cost band with imperfect substitutability in consumption Optimal land allocation using market prices vs. shadow prices . . . .

47 50

4.1

Regional distribution of survey communities . . . . . . . . . . . . . .

57

5.1

Optimal labor allocation with and without labor markets under perfect output market . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106 Optimal land allocation under different market scenarios . . . . . . . 108

5.2

ix

xi

Acknowledgements There are many people without whom this dissertation could not have been possible. First of all, I would like to thank all my advisors who supported me on this big project. Thanks to Edward Taylor for his continued enthusiasm about my work which helped me go through difficult times. Special thanks to Steve Boucher for his very constructive criticism during the whole process. His role as the “devil’s advocate” prepared me to defend my story and helped me ground it in strong theory. Tu Jarvis provided very thoughtful comments, helping me think about policy implications and see the big picture. I would also like to thank Antonio Yunez Naude, George Dyer, and my assistant Illiana Gomez Valdez for making my field work in Mexico productive and fun. I gratefully acknowledge the Social Science Research Council, Jastro Shields Graduate Research Scholarship, Pacific Rim Research Program, and Gifford Scholar Fellowship for providing financial support for my field work that helped me better understand my research topic. I would also like to thank the Center on Rural Economies of the Americas and Pacific Rim (REAP) and Program for the Study of Economic Change and Sustainability in Rural Mexico (PRECESAM) for letting me use their unique data set. Warmest thanks to my dear family for always believing in me, and all my friends in Davis for making my life as a graduate student unforgettable. My office mates Emi, Tina, Hayley, and Carlo provided special support by listening to my complaints and sharing my joys. I do not know how I could have made it without the feeling of community that was built over the years. I would especially like to thank David Zetland for his continued love and support, for listening to me, for reading my papers and providing useful comments, and for all the fun diversions and travels that made this long process a great life-changing experience.

Chapter 1 Introduction/Motivation Subsistence farmers may not respond to market incentives if their resource allocation decisions are based on shadow prices. This may seem “puzzling” from an economic point of view if shadow prices are not taken into account. An example is the behaviour of subsistence maize farmers in rural Mexico, when they increased maize production in spite of decreasing prices after NAFTA. Previous research suggests that the market price may fail to represent incentives if farmers attach non-market values to their crops. I explore subjective valuation, i.e. “shadow prices,” of subsistence crops in the context of traditional maize in Mexico and show how these values affect farmers’ resource allocation decisions. These subjective values are important beyond their contribution to economic analyses of farmer behaviour. If non-market values, hence high shadow prices, play a role in subsistence farmers’ continued cultivation of maize, then shadow prices can be used in designing on-farm conservation programs for maize in Mexico. Mexico is the center of maize domestication and diversity, where farmers have selected and cross bred traditional maize varieties to meet their various needs since 7000 BC (Dowswell et al., 1996; Turrent and Serratos-Hernandez, 2004). Maize farming in Mexico is primarily done by small-scale subsistence farmers, who cultivate landraces and contribute to the conservation and creation of genetic diversity of maize (Berthaud and 1

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CHAPTER 1. INTRODUCTION/MOTIVATION

Gepts, 2004; Brush and Chauvet, 2004).1 Given the importance of on-farm conservation in complementing conservation in gene-banks, Mexico is an ideal place to study farmers’ incentives to maintain maize landraces to improve the efficiency of on-farm conservation programs. In this dissertation, I develop an agricultural household model to derive subjective values of a farmer’s crops by combining transaction costs and an asymmetric missing market for subsistence crop. This missing market arises from the fact that the market-purchased crops lack the non-market values attached to farmer’s own crop, hence are imperfect substitutes for it. Unlike conventional analyses that ignore nonmarket benefits, this model explains why some farmers allocate resources in ways that cannot be explained by market prices even in the absence of transaction costs. Shadow prices predict subsistence farmers’ resource allocation better than market prices. My empirical application in the context of subsistence maize farmers in rural Mexico provides policy implications for conservation of maize landraces and makes a case for de facto conservation in the center of diversity of this important food crop. Both the theoretical and empirical methods I use are flexible enough to be applied to guide conservation programs for other crops in other regions.

Missing markets in agricultural household models and shadow prices Ever since Chayanov (1966), economists have acknowledged the fact that farm household decisions do not match the predictions of conventional consumer and producer theories. The main reason is that farm households supply part or all of their inputs, and consume part or all of their outputs (Chihiro, 1986). Although the basic neo-classical agricultural household model explains some behavioral “irregularities” for economists, it cannot totally explain farm household behaviour since it assumes 1 A landrace is a crop cultivar that evolved with and has been genetically improved by traditional agriculturalists, but was not influenced by modern breeding practices. All components of landraces are adopted to local climate conditions, cultural practices, diseases and pests (Hoisington et al., 1999; Jarvis et al., 2000).

3 perfect markets for inputs and outputs (Singh et al., 1986). Market imperfections are common in rural areas and add another level of complexity to the analyses of farm household behaviour. More recent studies extend the theory to analyze the effects of missing markets (e.g., labor, land, credit, output) on farm household production and consumption decisions (Chihiro, 1986; Strauss, 1986; de Janvry et al., 1991; Taylor and Adelman, 2003). Missing markets for a good or service nullify the importance of market prices as a signal in economic analysis, since they introduce endogenous (subjective) shadow prices that cannot be observed (Becker, 1965). Analyses of shadow prices in the context of agricultural households provide insights into how household response to changes in economic conditions may differ from conventional expectations based on market prices (Singh et al., 1986; de Janvry et al., 1991; Taylor and Adelman, 2003). The missing markets considered in this literature are symmetric, such that the constrained product cannot be sold or bought in the market. Although Strauss (1986) mentions the possibility of a “partly absent market” where the household can sell but not buy a product because home-produced and market products differ in quality, he does not explicitly model how this affects resource allocation. In my model, the asymmetric market constraint arises from non-market values of farmer’s own crop that make the purchased crop an imperfect substitute for it in consumption. Consequently, resource allocation is based on the shadow price of farmer’s own crop and depends on both production variables and farmer’s endowments. Take, for example, the resource allocation decisions of maize farmers in Mexico after NAFTA. Contrary to previous expectations, maize production and acreage increased in spite of decreasing prices prompting further research to explain this “unexpected” outcome (de Janvry et al., 1995; Dyer Leal et al., 2002; Dyer Leal and Yunez Naude, 2003). Dyer Leal et al. (2002) and de Janvry et al. (1995) both use the differences between farmer groups (i.e. subsistence, semi-subsistence or marketoriented) to explain different responses to price changes. Although Dyer Leal and

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CHAPTER 1. INTRODUCTION/MOTIVATION

Yunez Naude (2003) acknowledge the need to use shadow instead of market prices to value traditional crops with high non-market values, no previous study explicitly accounts for household-specific shadow prices.2 Understanding shadow prices of maize for subsistence farmers in Mexico provides insights into the inelastic supply response to decreasing prices. There are various reasons why farmers may not respond to market signals as expected. The literature on agricultural technology adoption provides potential explanations; e.g. risk, imperfections in insurance, credit, input or output markets, agro-ecological and information constraints (Feder, 1980; Bellon and Taylor, 1993; Smale et al., 1994).3 Farmers only partially adopt improved varieties, if at all, when traditional crops are not affected by these constraints or mitigate their effects. Even if there are no such constraints, high transaction costs of finding a perfect substitute for the farmer’s own crop create a missing market for that crop. This is because crops contain various bundles of characteristics that are valued by farmers but not necessarily by markets, such as time to harvest, ear length, taste, color, ease of shelling and processing, and suitability for specific dishes (Brush and Meng, 1998; Preibisch et al., 2002; Smale et al., 2001; Edmeades et al., 2004; Badstue et al., 2006). Some of these characteristics are too costly to recover from the market if the product gets mixed with others’ products that may have a different combination of traits. Other characteristics that are related to the ceremonial or ritual value of growing one’s own crop, farmer’s identity as a good farmer or the value of maintaining the family seed are simply impossible to obtain from the market-purchased crops. I conceptualize such non-market values using the asymmetric market constraint defined above. This specific missing market can lead to resource allocation decisions that cannot be explained by market prices (Smale et al., 2001; Dyer Leal and Yunez Naude, 2003). In such cases, we can say that farmers’ decisions are guided by household2

I use the term traditional crops interchangeably with landraces. See Feder et al. (1985) and Feder and Umali (1993) for comprehensive surveys of the literature on agricultural technology adoption. 3

5 specific shadow prices rather than market prices even if transaction costs are not binding (Becker, 1965; de Janvry et al., 1991; Jacoby, 1993). I build on the theoretical literature of agricultural households by combining transaction costs and an asymmetric market constraint in a model that allows for the derivation of household-specific shadow prices. I extend my basic model to include labor market imperfections to analyze land and labor allocation decisions and compare the results of this model with the previous research that does not account for shadow prices of subsistence crops. Using market prices leads to incorrect predictions about farmer response to changes in the economic environment in cases where there are significant non-market values attached to farmers’ own crops.

Conservation of crop genetic diversity Besides contributing to our understanding of farmer response (or the lack of it) to market signals, shadow prices provide us with a tool for targeting programs for onfarm conservation of crop genetic diversity. Shadow prices are more likely to differ from market prices in centers of crop domestication, where traditional crops play an important historical role in people’s culture and nutrition. Moreover, these centers are usually located in developing countries where the aforementioned market imperfections are prevalent, making the difference between shadow and market prices persistent.4 Traditional crops (landraces) have evolved with natural and farmer selection to suit heterogenous agro-ecological conditions and meet cultural, nutritional and economic needs (Dyer Leal, 2006; Salvador, 1997; Berthaud and Gepts, 2004; Brush and Chauvet, 2004). The result is a wider genetic variation, i.e. higher crop genetic diversity (CGD), in landraces compared to improved varieties, which is an important material input to crop breeding research (Koo et al., 2003; Bellon and Brush, 1994). Maintaining the flow of this input to crop breeding research that improves the yields 4 Some crops (center of domestication): Maize (Mexico), wheat and barley (Middle/Near East and North Africa), rice (Northern China) and potatoes (Peru). See http://veghome.ucdavis.edu/ classes/fall2003/plb12/cultiva.htm for more information.

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CHAPTER 1. INTRODUCTION/MOTIVATION

and resistances of the world’s food crops depends on the conservation of landraces. While conservation of CGD has been traditionally done in gene banks, crop breeders agree that on-farm conservation complements conservation in gene banks (Brush, 1989; Bellon and Smale, 1998). Gene banks isolate crops from their natural environments and stop their further evolution. On-farm conservation, on the other hand, allows crops to develop new traits to counteract changing ecological conditions. Given that on-farm conservation relies on farmers’ continued cultivation of traditional crops, it is crucial to understand their incentives to do so. These incentives depend on shadow prices. I use nationally-representative farm household data from rural Mexico to estimate agricultural production functions and shadow prices for maize farmers. I then use these shadow prices to econometrically identify the key variables that are correlated with the household-specific shadow prices of traditional maize. Although Taylor and Adelman (2003) define missing markets to be household-specific as opposed to the more traditional commodity-specific definition, previous empirical analyses deliver only commodity-specific shadow prices. My empirical method allows for the estimation of household-specific shadow prices. This method is developed by Jacoby (1993) and employed by others in the context of analysis of labor supply using shadow wages under imperfect labor markets (Skoufias, 1994; Barrett et al., 2005). These studies underline the importance of valuing farmer’s time appropriately when market wages fail to do so. Farmer’s output is valued at market prices in these studies, which may be inappropriate for farmers that only produce for home consumption and cannot buy a perfect substitute to their own crop due to its non-market benefits. I address this concern in my empirical application by estimating household-specific shadow prices of traditional maize for subsistence farmers in Mexico. I identify variables correlated with shadow prices, hence farmers’ incentives to maintain maize landraces, that can be used in designing and targeting programs to conserve the on-farm CGD of maize in Mexico at least cost.

7 In Chapter 2, I review the agricultural household literature and argue that non-market values of farmer’s own crops represent a heretofore unexplored source of non-separability. I then review studies of the conservation of crop genetic resources in general and conservation of maize landraces in Mexico in particular to situate my contribution within the literature. In Chapter 3, I develop my theoretical agricultural household model with an asymmetric market constraint and transaction costs. I discuss how shadow prices affect farmer’s resource allocation decisions and the implications of ignoring them when they are significantly different from market prices. I derive testable hypotheses regarding farmers’ valuation of their own crops and their resource allocation decisions. In Chapter 4, I test these hypotheses and conclude that the value of traditional maize to subsistence farmers is significantly higher than market prices for maize. The same is not true for modern maize. I use estimated shadow prices to identify the key factors that are correlated with the values farmers attach to traditional maize. I also show that shadow prices explain subsistence farmers’ land allocation decisions better than market prices. I discuss the implications for the design and targeting of on-farm conservation programs and for analyses of farmers’ resource allocation decisions in rural economies where non-market values of farmers’ own crops are significant. In Chapter 5, I identify other potential reasons that may result in the high estimated shadow prices in Chapter 4. To address the most important of these, i.e. missing labor markets, I modify my basic theoretical model to include missing labor markets and discuss the implications for the findings previously obtained. I empirically test and rule out the possibility of missing labor markets in the data. I then rule out other potential reasons and argue that the shadow prices estimated in Chapter 4 are not significantly affected by these other considerations and mainly reflect the high non-market values that subsistence farmers attach to these varieties. I conclude in Chapter 6 with a discussion of policy implications and directions for future research.

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CHAPTER 1. INTRODUCTION/MOTIVATION

Chapter 2 Background This dissertation is based on and contributes to three different lines of previous research: the agricultural household literature; the literature on the conservation of crop genetic resources; and specifically the research on maize genetic diversity in Mexico. First, I use an agricultural household framework in my theoretical model to derive household-specific shadow prices that lend themselves to econometric estimation. I then use these shadow prices to define subsistence farmers’ incentives to cultivate traditional crops.1 Traditional crops (i.e. landraces) are sources of crop genetic diversity, and there is a vast literature in anthropology, agronomy as well as economics on the conservation of these crops on farmers’ fields. Finally, my empirical application of the theoretical model to traditional maize farmers in Mexico has policy implications for the on-farm conservation of maize landraces in Mexico. This chapter provides some background on these three topics that precede and motivate this research.

2.1

Agricultural Household Literature

Agricultural household models acknowledge that farm households are both producers and consumers of agricultural output and cannot be analyzed using conventional 1 Throughout this text I use the term “subsistence farmer” to refer to small scale farmers who produce only for home consumption.

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CHAPTER 2. BACKGROUND

economic theories of consumer and firm behaviour. The dual role of an agricultural household has important implications for understanding resource allocation and production decisions (Taylor and Adelman, 2003). The literature falls into two broad categories: recursive models and non-recursive models. Recursive models assume that markets for all inputs and outputs are perfect for all households, whereas nonrecursive models allow for imperfect markets.

2.1.1

Recursive models

The key to recursive (separable) agricultural household models is that, conditional on endowments, a household first maximizes profits acting like a firm, and then makes consumption decisions based on profits generated from farm production. Thus resource allocation and profits depend only on endowments, not preferences. The research that establishes the main body of this literature was mainly neoclassical, in that all markets were assumed to be perfect, thus making the model recursive (Barnum and Squire, 1979; Singh et al., 1986). The market values of all farm products and household labor constitute “full income” which is used as the income constraint in the utility maximization problem (Becker, 1974). In a recursive model production decisions do not depend on preferences, but consumption depends on production through full income. This model explains what appears to be sluggish supply response of farmers to changing prices and the positive own-price elasticity of demand for food. The dependence of consumption decisions on exogenous prices through full income makes the income constraint endogenous, which is different from the exogenous income in consumer theory. Consequently, the conventional Slutsky equation that combines the income and substitution effects to represent the response to exogenous changes now includes an additional “farm profit” effect (Taylor and Adelman, 2003). The price response for any of the endogenous variables, Xi in an

2.1. AGRICULTURAL HOUSEHOLD LITERATURE

11

agricultural household model is given by: dXi ∂Xi ∂Xi ∂Y = + dpi ∂pi ∂Y ∂pi Y stands for full income of the farm household, which includes the profit from farming and hence is endogenous. The last term includes the effect of exogenous price changes on production, consumption and labor allocation decisions through the change in farm profits. The larger the profit effect (i.e. the larger the percentage of full income from farm profits, and the larger the expenditure elasticity of demand) the greater will be the contribution of household models to the understanding of the farm households’ responses to exogenous changes. Seven empirical studies in Singh et al. (1986) demonstrate the policy significance of employing a household model. In four of these, the own price elasticity of demand for agricultural commodity changes its sign, and in all of them labor supply becomes more elastic once the profit effect is included. Agricultural household models add more to our understanding of farmer behaviour if profits are sensitive to factor prices and constitute a large share of income, and if demand for agricultural products is sensitive to full income, as in rural economies. The perfect markets assumption of the neo-classical agricultural household models, however, is less likely to hold in rural economies in developing countries, where missing and imperfect markets are common. Non-recursive agricultural models address just that.

2.1.2

Non-recursive models

The recursiveness of the agricultural household model breaks down if there is an imperfect market for any of the inputs or outputs. Chayanov (1966) developed an agricultural household model to analyze farm households’ production and consumption decisions under the extreme case of no markets at all for inputs and outputs. However, the model becomes non-recursive even if only one market is imperfect. For

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CHAPTER 2. BACKGROUND

example, if the output market is missing, then the farmer has to produce what he wants to consume. Similarly if the labor market is missing, there is a tradeoff between farm labor and leisure that does not exist in recursive models. The implication is that production decisions depend on both endowments and preferences. Thus we can observe heterogeneity in production outcomes even when endowments are similar. Anticipating my model, for example, differences in preferences for traditional maize – coupled with an imperfect market for maize – can result in different cropping decisions for farmers with identical endowments. Missing markets were thought of as product or service specific until de Janvry et al. (1991) defined them to be household-specific and developed a detailed analysis of transaction costs (TCs). Transaction costs associated with transportation, information acquisition and/or infrastructure drive a wedge between the market price and the “effective” price paid or received by the farmer. For example, a farmer who sells maize in the market may pay ts per kilo of maize transported, thus the “effective” price he receives is p(1 − ts ). Similarly, a household seeking to buy traditional maize may spend money for transportation or significant time examining quality, so the effective price paid is p(1 + tb ). TCs thus create a “band” around the market price. If a farmer’s subjective valuation falls inside this band, then his resource allocation decisions will be much less responsive to price changes than what would be predicted by recursive models. These results essentially stem from the endogenous shadow prices of “non-tradable” goods that drive farmers’ decisions, decreasing the importance of market prices as a signaling mechanism (de Janvry et al., 1991; Taylor and Adelman, 2003; Dyer Leal et al., 2002). Analytically, the non-recursive model adds yet another term to the Slutsky equation that captures the effects of changes in endogenous prices on other prices that are no longer fixed. The new Slutsky equation is: dXi ∂Xi ∂Xi ∂Y ∂Xi ∂p = + + dpi ∂pi ∂Y ∂pi ∂p ∂pi

2.1. AGRICULTURAL HOUSEHOLD LITERATURE

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where p stands for the vector of all endogenous prices. The last term translates changes in the shadow price of one commodity into changes in other endogenous prices, which makes the overall price response ambiguous. For example, the effects of a rise in the output price on consumption and leisure demand, output supply and marketed surplus all depend on how the shadow wage changes with the output price and are indeterminate when the labor market is missing (Singh et al., 1986). Taylor and Adelman (2003) demonstrate how, compared to models with perfect markets, models with missing labor or staple markets may generate very different predictions regarding households’ responses to price changes and, consequently, lead to alternative policies to enhance rural income.

2.1.3

Non-market values: another source of non-recursiveness

One shortcoming of TCs based household models is that they cannot account for non-market benefits farmers may derive from producing their own crops, because they assume that domestic product and market product are perfect substitutes in consumption.2 If the market crop and the domestic crop are perfect substitutes, we should not observe any farmer who produces that crop at high opportunity costs, when they could instead buy the crop in the local market with low TCs. However, if the domestic crop has non-market values that make the “same” crop purchased in the market an imperfect substitute, then some farmers will produce it at high cost even if there is a local market with small or no TCs.3 Consequently, the market constraint on the domestic crop is an asymmetric (i.e. one-sided) constraint where the farmer can sell this crop but cannot buy it. The non-market values of consuming one’s own crop can expected to be higher if 2

Throughout this dissertation I use “domestic crop” to refer to home-produced crop. Besides the prevalence of subsistence farming in spite of lively local markets in developing countries, the imperfect substitutability in consumption can also explain the rationale behind backyard gardening in developed countries. If the non-market value of growing and consuming ones own crop was not important, we would not expect a rational person to grow tomatoes in her backyard for multiple times the cost of buying it in the market. 3

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CHAPTER 2. BACKGROUND

the subsistence crop has cultural or religious connotations (Altieri, 2004). Traditional subsistence crops in their centers of domestication (such as maize in Mexico, potatoes in Peruvian highlands, rice in Philippines or wheat in Turkey) have long histories of evolution that are intertwined with the culture of the peoples who grow them. In some cases these crops are used in weddings, funerals and rituals in which purchased crop simply will not do, and are important in determining the farmer’s place in the community as a good farmer (Fussell, 1992). Akerlof and Kranton (2000) model “identity” (or the sense of self) as a way to incorporate non-pecuniary motivations into economic behaviour. If a farmer’s identity depends on the cultivation of such a crop, the market purchased crop cannot provide the same utility as the domestic crop. In this case, the market crop lacks the non-market values and is a poor substitute for the domestic crop in consumption. Consequently, market prices may not reflect the full value of non-marketed subsistence crops for the farmer. Although I do not model “identity” explicitly as do Akerlof and Kranton (2000), their study provides an intuitive way of thinking about why some subsistence farmers may produce crops at cash losses when they can buy it in the market. The effects of these non-market values on the decisions of the backyard gardener and the farmer can be conceptualized with an asymmetric market constraint for the domestic crop as described above. Strauss (1986) mentions the possibility of such a “partly absent market” in the context of commodity heterogeneity, where the separability of the agricultural household models breaks down. The non-market values of the domestic crop create a similar commodity heterogeneity and result in a non-separable model even in the absence of TCs. Lopez (1986) discusses a similar case for labor, where differential preferences for on-farm and off-farm labor can result in non-separability. He then dismisses this possibility in developing countries because he observes that farm households in developing countries have too many concerns about basic human needs “to be concerned about fine-tuning their preferences for off-farm and on-farm work” and obtains the same result using transportation costs

2.1. AGRICULTURAL HOUSEHOLD LITERATURE

15

for off-farm work. The theoretical and empirical implications for farmer decisions of an asymmetric output market constraint combined with TCs have not been discussed in previous literature and represent a primary contribution of my dissertation.

2.1.4

Empirical applications of household models

Agricultural household models have been applied to a wide range of topics in different countries.4 Early efforts in empirical applications of agricultural household models estimate commodity and input demands and output supply, or production functions using recursive models (Yotopoulos et al., 1976; Barnum and Squire, 1979). This method delivers elasticity estimates that are then compared with other studies or what would be expected from economic theory to infer the specifics about household response to exogenous changes. Applications with missing markets (e.g. insurance, labor, output, credit) analyze the effects of missing markets on production decisions and household strategies to overcome constraints (Roe and Graham-Tomassi, 1986; Lopez, 1986; de Janvry et al., 1991; Taylor and Adelman, 2003). Empirical applications of non-recursive household models with TCs are based on simulation models calibrated using household data where markets are switched on and off (de Janvry et al., 1991; Taylor and Adelman, 2003). Neither the earlier econometric applications of demand and supply systems, nor the simulation methods can capture the heterogeneity of shadow prices that are determined endogenously by the internal equilibrium for each household. Although de Janvry et al. (1991) define the missing markets and shadow prices as household-specific in their theoretical model, empirical applications did not account for it until Jacoby (1993). Jacoby (1993) develops a method to econometrically estimate individual specific shadow prices of time (i.e. shadow wages) and tests for separability of the agricultural household model under missing labor markets in the 4 See Taylor and Adelman (2003) for an excellent summary of empirical research based on agricultural household models.

16

CHAPTER 2. BACKGROUND

Peruvian highlands. This method contributes to our understanding of farmers’ labor supply decisions and has been applied to other country settings (Skoufias, 1994; Barrett et al., 2005). These papers focus on labor market imperfections and do not consider the possibility of missing output markets, as they value farmers’ products at given market prices. The imperfect substitutability between market purchased and domestic crops generates a missing market for the domestic crop in the same way as the imperfect substitutability between hired labor and household labor generates a missing market for household labor. Both cases require an understanding of household-specific shadow values for the good/service that is not traded in the market, since market prices fail to represent their value for constrained households.

The theoretical model and empirical applications in this dissertation are natural extensions of the previous literature. I develop an agricultural household model that incorporates both TCs for buying and selling the domestic crop and the imperfect substitutability between domestic and market goods. Imperfect substitutability is conceptualized with an asymmetric (one-sided) market constraint on the domestic food crop that is farmer- and crop-specific, which is different from the farmer- or market-specific definitions in the literature. In practice, this constraint will be important for crops that have significant non-market values for some farmers. I derive the shadow price of the domestic food crop that depends on both TCs and the degree to which the farmer’s own and the market product are substitutes. Using this model we can theoretically compare the shadow prices to market prices to understand the rationale behind observed land and labor allocation decisions of different groups of farmers. Empirical application of this model allows us to estimate household-specific shadow prices of domestic crops, shedding light into existence of subsistence farming, defined as producing for home consumption, in spite of “cash” losses.

2.2. CONSERVATION OF CROP GENETIC RESOURCES

2.2

17

Conservation of Crop Genetic Resources

The conservation of crop genetic resources (CGR) gained importance following the Irish potato famine (1845) and again after the Southern corn leaf blight in the United States (1970), both of which demonstrated the consequences of relying on genetically homogenous farming systems (Hoisington et al., 1999). Improving crops’ resistance to pests and diseases using wild relatives and landraces has since become one of the most important goals of crop breeding research (Rubenstein et al., 2005). Landraces are highly variable crop populations that have been selected and cultivated by farmers for millennia to adopt to heterogenous environments and needs. An important characteristic of landraces is the considerable genetic variation they display as compared to improved varieties (Bellon and Brush, 1994; Brush and Meng, 1998; Liu et al., 2003).5 Plant breeders use this variation in landraces to improve crops’ resistance to continuously evolving pests and diseases and to increase yields to meet the increasing demand for food in the World (Smale et al., 2001). Creating gene banks, where CGR is frozen and conserved, was seen as the solution to the conservation problem during the 1960’s. Finding funds for gene banks, however, proved difficult because of the public good characteristics of conservation. The possibility of free riding on others’ conservation leads to an equilibrium level of conservation below the socially optimal amount. This problem was partially addressed during the 1980’s when the World Bank and the Food and Agriculture Organization of the United Nations supported the establishment of the Consultative Group on International Agricultural Resources (CGIAR). The CGIAR still oversees the conservation of CGR in gene banks and research centers for the most important food crops in their centers of domestication.6 5 Improved varieties refer to varieties that have been created by scientists to increase their yields or to make them more resistant to a certain disease using modern breeding techniques. The term should not be taken to mean that landraces are static or not improved, because they have been improved by farmers for millennia using traditional techniques. 6 Some CGIAR centers are: CIMMYT in Mexico (maize and wheat), CIP in Peru (potatoes), IRRI in Philippines (rice), ICARDA in Syria (cereals and food legumes) and ICRISAT in India (cereals

18

CHAPTER 2. BACKGROUND Relying solely on gene banks to conserve CGR was brought under question

because of the problems faced in maintaining and utilizing the existing accessions (Wright, 1997; Koo et al., 2003). One of the most important drawbacks of gene banks is that they treat CGR as static stocks by freezing them to conserve. However, landraces form part of dynamic evolutionary processes and continue to build more genetic material as environmental conditions change. On-farm conservation of the crops in their natural environments allows the crops to build traits to contend with current ecological pressures and provides a richer genetic stock for crop breeders to work with (Bellon and Smale, 1998). The international community showed its support for in-situ (i.e. on-farm) conservation with the Convention on Biological Diversity in 1992 (UN) and the International Treaty on Plant Genetic Resources in 2001 (FAO).7 On-farm conservation, defined as “the continuous cultivation and management of a diverse set of populations by farmers in the agro-ecosystems where a crop has evolved,” is now accepted as a complement to conservation in gene banks (Jarvis et al., 2000). The centers of crop domestication and diversity have special importance for targeting on-farm conservation programs because of the wide genetic diversity contained in landraces cultivated by farmers in these locations (NRC, 1972; Bellon and Brush, 1994; Rubenstein et al., 2005). The feasibility of on-farm conservation in centers of diversity has been investigated by a variety of studies (Bellon and Smale, 1998; Doss, 2003). Most of these studies emphasize the constraints on the spread of the adoption of new crop varieties (e.g. credit constraints, transaction costs, information constraints), and predict a decline in on-farm genetic diversity as constraints are relaxed by market integration. However, these concerns did not materialize fully due to de facto conservation of landraces, especially in their centers of domestication and diversity (Brush and Meng, 1998; Dyer Leal and Yunez Naude, 2003). De-facto conservation occurs beof the semi-arid tropics). See http://www.cgiar.org/centers/index.html for more information. 7 For the texts of these treaties see: http://www.biodiv.org/convention/convention.shtml and http://www.fao.org/AG/cgrfa/itpgr.htm#text.

2.3. MAIZE IN MEXICO

19

cause farmers find it optimal to continue cultivating landraces due to their various attributes that suit farmers’ agro-ecological, social and culinary needs. For example, landraces still constitute 75% of total maize production in Mexico (Brush and Chauvet, 2004). These private benefits of CGR created hopes for decreasing the costs of on-farm conservation by targeting farmers with a higher likelihood of de facto conservation (Bellon and Smale, 1998; Brush and Meng, 1998; Brush et al., 1992; Smale et al., 2001). This dissertation focuses on the private value of CGR to farmers, because it is the private, not public, benefits that drive farmers’ decisions regarding their continued cultivation. Given the vast amount of effort and resources put into the on-farm conservation of landraces in their centers of diversity, a thorough understanding of farmers’ incentives to continue cultivating them is essential. My research contributes to the broader economic literature on farm household behaviour and conservation of genetic resources by analyzing the subjective incentives of subsistence farmers to cultivate traditional maize varieties. In an economy where subsistence farming overlaps with landrace cultivation, this research will contribute to the design and targeting of policies to conserve the genetic diversity of this important crop. On a wider scale, the theoretical and empirical methods developed here can be applied to other country/crop settings to guide conservation policies.

2.3

Maize in Mexico

Maize is the third most important food crop (after wheat and rice) in the World in terms of area harvested. It produces more food per unit of land and labor than any other cereal and has the highest total production of all grains in the world.8 Maize was domesticated from its wild relative teosinte around 7000 BC in Southern Mexico and has been evolving since then with natural and farmer selection to adopt to a wide 8 Data source: Food and Agricultural Policy Research Institute (FAPRI): http://www.fapri. iastate.edu/.

20

CHAPTER 2. BACKGROUND

Table 2.1: Maize consumption in various countries in grams and kilo calories per capita per day (2004) Maize consumption/capita/day Country Grams Calories Lesotho 244.14 1241 Mexico 308.27 1081 South Africa 293.26 1062 Malawi 318.52 1046 Zambia 221.68 944 El Salvador 258.94 895 Guatemala 246.00 869 Kenya 203.07 775 Zimbabwe 185.69 720 Tanzania 187.82 646 Honduras 176.17 591 USA 137.93 512 Source: FAOSTAT, http://faostat.fao.org

variety of soil and climate conditions, as well as satisfy farmers’ various consumption needs (Dowswell et al., 1996). This makes Mexico the most important center of diversity of maize with 59 different races (Berthaud and Gepts, 2004). Maize was “discovered” by the Spaniards during the colonial era and was introduced to the old world, where it spread quickly during the 16th century owing to its ability to adapt to a wide variety of geographical and climate conditions (Salvador, 1997). Currently maize is the main staple food in many developing countries, especially in Latin America and Africa (see Table 2.1). Mexico ranks second in the world in terms of calorie intake from maize with almost 1100 kilo calories per capita per day (more than 300 grams per capita per day). Whereas maize is mostly directly consumed by humans in Mexico and other developing countries, a large proportion is used as animal feed or an ingredient for processed foods in developed countries. Most of the maize varieties grown today – especially outside their center of diversity – are improved varieties that are derived using the wide genetic diversity of landraces (Anderson, 1946; Hoisington et al., 1999). Although there are some

2.3. MAIZE IN MEXICO

21

large-scale farmers in Mexico who cultivate improved maize varieties for commercial purposes, most farmers in rural Mexico continue to cultivate maize in traditional systems (i.e. subsistence oriented small-scale farming under rain-fed conditions with recycled seed). These small non commercial farmers contribute to the conservation and creation of genetic diversity of this important food grain (Berthaud and Gepts, 2004; Brush and Chauvet, 2004). Besides being a main food source, maize has a very special place in the cultures of Mesoamerica. According to Mayan creation myths, Gods created humankind by mixing corn dough with their blood, after unsuccessful trials with mud and wood (Salvador, 1997). The word for maize in the indigenous language of the Nahuatl means “our support/flesh” reflecting its cultural significance (Brush and Chauvet, 2004). Many case studies in Mexico find that maize cultivation is intricately connected to every aspect of daily life, from selection of seeds, sowing and harvest, to consumption, subsistence and rituals (Bellon and Brush, 1994; Rice et al., 1998; Badstue, 2006). Especially in indigenous communities, people’s identity in their community may depend on the successful cultivation and preparation of food from maize (Smale et al., 2003; Badstue, 2006). Even today, maize is considered to be the most important crop for small farmers who continue to grow it mainly for home consumption. For this group of farmers, maize is the main source of daily calories and is prepared in many types of dishes (tortillas being the most important food for daily sustenance).9 Consequently farmers choose which maize variety to cultivate based on a number of traits such as yield, softness of the dough, ease of shelling the grains, color and taste. This selection process has been underlined in a number of studies as a reason for the persistence of cultivation of landraces among subsistence farmers in Mexico (Brush and Meng, 1998; Smale et al., 2001; Dyer Leal and Yunez Naude, 2003; Berthaud and Gepts, 2004; Brush and Chauvet, 2004; Badstue et al., 2006; Dyer Leal, 2006). 9 In an exhibition at the Museo de Culturas Populares in 1982, 600 different food preparations were documented, many of which require different types of maize (Brush and Chauvet, 2004).

22

CHAPTER 2. BACKGROUND The various traits that farmers care about when selecting crops contribute to

the non-market values of the domestic crop. Especially if some of these traits are unobservable, such as processing and cooking qualities, it may be hard to find maize in the market that will be an adequate substitute. Some farmers also may want to ensure the availability of maize with certain traits if they are not sure they can find it – or the money to buy it – in the market. These conditions contribute to the subjective value of domestic maize to farmers that cannot be captured fully by market prices (Smale et al., 2001; Dyer Leal, 2006; Preibisch et al., 2002; Dyer Leal and Yunez Naude, 2003). It is not rare to find that small scale maize farmers in Mexico incur cash losses when their maize production is valued at the price of maize commercially available in local markets (and not necessarily the same variety) (Heath, 1987; Dyer Leal and Yunez Naude, 2003; Brush and Chauvet, 2004). This finding does not reflect the “irrationality” of farmers. On the contrary, it likely reflects the existence of non-market benefits that farmers get from cultivating and consuming their own maize (Dyer Leal et al., 2002). When one takes these non-market values into account, the cash losses may lose significance. It has been argued in the literature that farming in general is a way of life with non-pecuniary benefits (Vincent, 1976; Botterill, 2001). Even in developed countries farmers do not just switch in and out of farming based on monetary incentives because of the “psychic income” they get from farming. Moreover, if there are strong cultural values attached to farming, we can expect that monetary incentives will not be enough to fully explain farmers’ behaviour. Dyer Leal (2006) emphasizes the importance of shadow values (rather than market prices) in understanding the responses of subsistence maize producers to economic changes. These responses often differ from what conventional economic analyses would predict. There are no other studies to theoretically model how non-market values of a domestic crop would affect farmer behaviour and empirically analyze shadow prices for subsistence farmers – as I do in this dissertation.

2.3. MAIZE IN MEXICO

23

In summary, non-market values take two primary forms in the case of maize in Mexico: the value of solving the problem of non-observability of certain traits in purchased maize, and the direct value related to identity from cultivating maize and participating in local cultural practices centered around maize. The latter source of non-market values is the central feature of the model in this dissertation. I focus on non-market values due to “identity” which will lead to the imperfect substitutability of purchased maize for domestic maize. This dissertation fills a gap in the literature with a detailed analysis of shadow prices of domestic maize for subsistence farmers in rural Mexico.

2.3.1

Mexican agriculture in transition

Historically both producers and consumers of basic agricultural products in Mexico were subsidized by various tools and institutions. Guaranteed prices isolated the producers from world prices, while a cheap supply of basic foods by the state protected consumers (de Janvry et al., 1995). Following the economic crisis in 1982, however, Mexican agricultural policy changed its direction from protection towards liberalization of the economy and trade (Yunez-Naude, 2003). The liberalization of agricultural trade with NAFTA in 1994, therefore, was a continuation of the already ongoing restructuring of the agricultural sector (Nadal, 2000). Maize received special treatment under NAFTA given its importance in Mexican agriculture. Maize occupies 59% of agricultural land, accounts for 40% of total agricultural sector employment and provides around 20% of total agricultural product value (Brush and Chauvet, 2004). The gradual removal of subsidies from the maize sector and declining maize prices were expected to contribute to the restructuring of agriculture by shifting resources away from maize towards more productive crops such as fruits and vegetables (Levy and van Wijnbergen, 1992). The expected decrease in maize production and acreage fueled fears of losing the genetic diversity of maize maintained especially by subsistence farmers, who would be among the first to leave

24

CHAPTER 2. BACKGROUND

Maize Area and Production in Mexico 8,500

25,000

8,000 20,000

7,000

15,000

6,500 10,000

6,000

Production (1,000 tonnes)

Area hervested (1,000 ha)

7,500

5,500 5,000 5,000

Area harvested

2004

2003

2002

2001

2000

1999

1998

1997

1996

1995

1994

1993

1992

1991

0 1990

4,500

Maize produced

Figure 2.1: Maize area and production in Mexico, 1990-2004. Source: FAOSTAT maize farming (Nadal, 2000; Brush and Chauvet, 2004). Real maize prices in Mexico decreased from around 3500 Mexican pesos per tonne in 1990, to 210 pesos per ton in 2003.10 To the surprise of many, neither the production nor the acreage of maize decreased in Mexico following NAFTA (see Figure 2.1). Recent research is trying to explain this “puzzle” by accounting for previously overlooked aspects of the Mexican economy, such as heterogeneity of maize farmers and transaction costs, the changes in the prices of other crops and consumption goods, or general equilibrium effects of the decrease in maize prices (de Janvry et al., 1995; Nadal, 2000; Dyer Leal et al., 2006). Although it has been widely argued that maize has a value beyond its market price for subsistence farmers in Mexico, this fact has not been put at the center of such arguments explaining the unexpected price response of farmers (de Janvry et al., 1995; Dyer Leal and Yunez Naude, 2003; Berthaud and Gepts, 2004). Dyer Leal et al. (2006) discuss in detail how shadow values (non-market benefits) of traditional maize 10 Source: SIAP (Servico de Informacci´on Agroalimentaria y Pesquera) http://w4.siap.gob.mx/ sispro/SP_AG/sp_maiz.html. Prices are deflated using the PPI with base year 2000.

2.3. MAIZE IN MEXICO

25

will buffer subsistence farmers’ responses to changes in market prices (or income), but they do not analyze these shadow values analytically. Modeling the market crop and the domestic crop as two different goods in consumption offers a practical way of characterizing the non-market values attached to the farmer’s domestic crop. Just as a backyard gardener may continue growing tomatoes when the market price of tomatoes decreases, a farmer may continue growing maize when maize prices decrease if there are non-market benefits of growing and consuming one’s own crop. Moreover, the fact that maize has a long historical and cultural importance for subsistence farmers that adds to maize’s non-market values makes the farmers’ lack of response to market prices less of a “surprise.” I argue that any prediction about the supply response of non-commercial maize farmers in Mexico to changes in market conditions needs to consider the subjective value of maize to farmers, which is likely to be different from the market price. Ideally, to understand farmer response to any change, one would like to have panel data that provides information about maize farmers before and after the change in question. However, much can be learned about the structure of farmers’ economic decisions and subjective valuation of maize by using nationally representative data with crosssectional variation as in this dissertation.

2.3.2

Previous empirical research on maize in Mexico

It has been long established that individual farmers do not have enough incentives to conserve crop genetic diversity at the socially optimal level due to the public good nature and positive externalities of conservation (Swanson, 1994; Brush, 2002). However, if farmers are receiving private non-market benefits from maintaining diversity, they will have higher de facto incentives for conservation. Targeting farmers with high de facto incentives to maintain diversity can decrease the need for intervention and improve the efficiency of on-farm conservation (Bellon and Smale, 1998; Brush and Meng, 1998). On the other hand, if the private benefits are low but public ben-

26

CHAPTER 2. BACKGROUND

efits from on-farm conservation are high we may have to devise policies to increase farmers’ de facto incentives. Consequently, one of the main objectives of research on on-farm conservation is identifying farmer characteristics correlated with de facto incentives to maintain on-farm diversity. For the particular case of maize genetic diversity in Mexico, there has been a lot of empirical research to understand who conserves on-farm diversity where, and how they are affected by changing economic conditions. Although the previous research is mainly concerned with maize diversity, it provides insights into traditional maize farming as well given the fact that most maize farmers in rural Mexico still cultivate traditional maize on small plots (Berthaud and Gepts, 2004). The case studies in Mexico fall into three broad categories: anthropological/agronomic studies that use qualitative or descriptive data (Bellon and Brush, 1994; Perales et al., 2003; Brush and Chauvet, 2004; Badstue et al., 2006; Perales et al., 2005), economic/econometric studies that use reduced form diversity regressions or programming methods (Bellon and Taylor, 1993; Van Dusen, 2000; Van Dusen and Taylor, 2005; Dyer Leal et al., 2006), economic/anthropological studies that analyze farmers’ valuation of variety attributes (Rice et al., 1998; Smale et al., 2001; Bellon et al., 2006; Birol et al.). The studies in the first group mainly conclude that there are different needs farmers try to satisfy with their maize and these multiple needs lead to the observed on-farm diversity of maize. The studies in the second group explain farmers’ land allocation across different varieties, or diversity (measured by some type of diversity index) using farmer and farm characteristics. The third group focuses explicitly on different attributes farmers associate with different varieties and explains how different attributes (consumption and production) result in diversity. Although a common theme arises from these studies that points to market prices that may not capture the value of maize to farmers, the reasons behind it are not explicitly modeled. Unobserved quality of maize purchased in the market, transaction costs or heterogenous preferences for domestic and purchased maize are examples of reasons that can lead

2.3. MAIZE IN MEXICO

27

to the observed on-farm diversity of maize. The former creates a type of “market for lemons” and can be modeled using the asymmetric information framework as in Akerlof (1970). However, because of their significance in the current setting, I formally model the latter two reasons to identify what really may be driving farmers’ decisions to cultivate maize landraces. Regardless of the methodological differences between the three broad categories of previous research, they all seek to understand which groups of farmers contribute to maize diversity, where and why. However, as demonstrated in the excellent summary by Smale (2006), the correlation between on-farm diversity and socio-economic and agro-ecological characteristics is very case specific. Smale (2006) brings together different case studies from seven countries about on-farm diversity of different crops, two of which are about maize in Mexico. Only three household characteristics, namely household head’s education, household size and wealth, exhibit a common pattern across different case studies in Smale (2006). All of these variables are positively correlated with on-farm diversity when they are significant. If managing a more diverse set of crops requires more labor and there are imperfections in the market for labor or credit, then larger household size will make it easier to cultivate a diverse set of varieties. Similarly, wealthier households may be able to afford growing minor varieties that do not necessarily sell in the market, or that are indicators of status. However, these relationships depend on the context and should not be generalized to other cases. To illustrate, other household characteristics, such as household head’s age or experience, off-farm income and women’s participation have different effects on diversity in different countries. Working off-farm can, on one hand generate funds to relax the cash constraint allowing households to grow more diverse varieties, but it can also tighten the labor constraint causing less diversity. Similarly, women’s participation in farming may be positively correlated with maize diversity if cooking qualities are important and can be satisfied only with a diverse set of varieties, or

28

CHAPTER 2. BACKGROUND

it can be negatively correlated with diversity if women lack the skills required to manage diverse varieties. All of these three household characteristics are positively correlated with maize diversity in the case studies in Mexico. However, both studies about maize in Mexico in Smale (2006), namely Dyer Leal (2006) and van Dusen (2006), are conducted in the same region, and this finding may be different for other regions of Mexico. In terms of agro-ecological characteristics, farm size and fragmentation are the only two variables that have consistently positive correlations with diversity. Although the case studies in Mexico in Smale (2006) find that land fragmentation is not correlated with diversity, Bellon and Taylor (1993) find that fragmentation is positively associated with landrace cultivation. Soil quality and slope have differing effects across countries. Though these variables are not measured by the studies in Mexico in Smale (2006), Bellon and Taylor (1993) find that soil quality is negatively correlated with traditional maize cultivation. Although there have been a lot of claims about genetic erosion due to improved access to markets (for output, labor or inputs), the empirical literature suggests that market access is correlated to on-farm diversity in differing ways depending on the interaction of agro-ecological and market conditions in each locality. Market access has different effects on on-farm diversity of maize even within Mexico. Van Dusen and Taylor (2005) find that market integration (for labor and migration) significantly decreases on-farm diversity in Sierra Norte de Puebla. Similarly, Nadal (2000) finds that migration has a negative effect on the cultivation of landraces. In contrast, Perales et al. (2003) find that communities closer to markets have more landraces than those that are more isolated in Central Mexico. Household wealth was found to be negatively correlated with landrace cultivation by Bellon and Taylor (1993), but was uncorrelated in another study by Van Dusen (2000). These conflicting findings emphasize the importance of considering the interactions between various markets (e.g. labor, output and inputs) and other variables in each case study.

2.3. MAIZE IN MEXICO

29

As discussed in the previous section, the indigenous cultures of Mexico place high importance on the cultivation and consumption of diverse maize landraces that contribute to households’ or farmers’ place (i.e. their identity) in their community (Smale et al., 2003; Badstue et al., 2006). Regions with high ethnolinguistic diversity have been recognized as regions with high maize genetic diversity, making farmers in these regions natural targets for least cost programs for on-farm conservation of maize landraces (Bellon and Brush, 1994; Turrent and Serratos-Hernandez, 2004; Perales et al., 2005). This recommendation finds support in recent research by Brush and Perales (2007), who find that indigenous farmers in Chiapas push landraces outside of their natural habitats due to their strong preferences for landraces. In contrast, mestizos (people of Spanish origin) tend to push improved maize varieties out of their habitats. They also find that whereas agro-ecology is key, social origin and cultural pressure play important roles in determining the diversity of maize. One of the recurring findings in the literature is that small maize farmers in Mexico are producing maize at a cash loss, or that they are “inefficient” (Heath, 1987; Smale et al., 2001; Dyer Leal and Yunez Naude, 2003; Brush and Chauvet, 2004; Juarez-Torres, 2005). In most cases the explanation of producing at a loss rests on the statement that market prices do not reflect maize’s worth to farmers. Underlying this statement is the assertion that farmers value maize for multiple attributes to satisfy their multiple consumption and production needs, most of which are not captured by market prices (Smale et al., 2001; Perales et al., 2003; Brush and Chauvet, 2004; Badstue et al., 2006). If farmers cannot obtain the traits they demand by market interactions, they have to rely on their own or neighbours’ production (Smale et al., 2004). Other non-market values that are related to cultural or ethnic practices centered around maize cultivation also contribute to the value of maize to farmers (Smale et al., 2001; Dyer Leal and Yunez Naude, 2003; Berthaud and Gepts, 2004; Dyer Leal et al., 2006). Although previous studies provide intuition into the linkages between cul-

30

CHAPTER 2. BACKGROUND

tural/indigenous identity, subsistence farming and on-farm maize diversity, how these linkages factor in farmers’ decisions have not been modeled formally. One way indigenous identity may affect non-market values of maize, thus the continued cultivation of landraces, is through preferences. Farmers, for whom the cultural practices centered around maize are important (indigenous farmers in the case of Mexico), consider maize purchased in the market as an imperfect substitute to their own maize because it lacks the non-market values associated with their maize. This may deliver observed maize production patterns that cannot be explained by market prices only and call for an understanding of subjective valuation (“shadow prices”). The model I develop here can identify the subjective values of maize landraces revealed by farmers’ production decisions. These subjective values can be used to identify farmers’ real incentives to maintain maize landraces. This dissertation also provides a novel method for estimating the oft-mentioned but not measured non-market values subsistence farmers get from their maize and provides intuition into why they may produce maize at a cash loss. Another shortcoming of previous studies is that they are limited in their scale due to costly data requirements. Most of them use data from special surveys designed to understand farmer valuation, but cover small areas due to the tradeoff between survey specificity and coverage. The method I develop can be applied to conventional farm household data on a larger scale. The empirical application in this dissertation is the only one at a national scale in the empirical literature on maize diversity in Mexico.

2.4

Conclusion

The agricultural household literature provides a strong tool to analyze farm households’ decisions even when some markets are missing. Although the definition of missing markets has evolved from market specific to household-specific, the literature

2.4. CONCLUSION

31

mainly focuses on transaction costs that prevent households’ participation in some markets. The possibility of a “partially missing market” due to product heterogeneity has been mentioned by Strauss (1986), but it has not been modeled explicitly in the literature. While Strauss (1986) had in mind objective quality differences between domestic and market purchased food crops, subjective quality differences, or non-market values associated with the domestic crop are sufficient to create a nonrecursive model where shadow prices connect production decisions to preferences. I contribute to this literature by combining the more traditional transaction cost model with imperfect substitutability of market crops for domestic crop in consumption to understand farmers’ decisions. Non-market values of maize are frequently mentioned in the literature on the onfarm maize diversity in Mexico as a reason for the continued existence of subsistence farming in spite of monetary losses. Although the non-market values associated with ethnic or cultural identity are usually mentioned as important in determining farmers’ incentives to maintain maize landraces, they are only discussed qualitatively if at all. The model I develop here formally incorporates such non-market values as a source of non-separability of production decisions from preferences and helps to quantify them in the context of maize in Mexico. This model can also be applied to such diverse settings as backyard gardening and production of any household goods that provide non-market values, such as the value of growing one’s own food or subjective utility of consuming home-made goods. In the next chapter, I develop an agricultural household model with TCs for buying and selling of the food crop and an asymmetric market constraint for this crop to derive its subjective value (“shadow price”) to the farmer. I analyze how price bands due to TCs may be insufficient to explain cropping decisions if the non-market values of the farmer’s domestic crop are ignored. I also discuss how shadow prices can improve analyses of farmer’s resource allocation, before I turn to the empirical analysis of shadow prices of maize for farmers in rural Mexico in Chapter 4.

32

CHAPTER 2. BACKGROUND

Chapter 3 Theoretical Model: Subjective Valuation of Subsistence Crops The concept of shadow price has been used by economists to represent the value of goods or services that are not traded in markets (Becker, 1965). Specifically, the shadow price of a crop arises from the solution to the farmer’s resource allocation problem in the absence of perfect markets for that crop (i.e. he cannot buy or sell the crop). As discussed in Chapter 2, this situation results in the non-separability of farmers’ production decisions from consumption decisions, where the shadow price, rather than the market price, is the true value measure for the constrained crop (de Janvry et al., 1991; Taylor and Adelman, 2003). Conventional economic analyses may result in misleading expectations if they fail to represent the true value of these goods and services – as was the case when subsistence maize producers in Mexico “unexpectedly” increased their production in spite of decreasing prices after NAFTA. A thorough understanding of the structure and the determinants of shadow prices becomes particularly important when the non-marketed good in question is a crop that contains important genetic diversity whose conservation depends on farmers’ incentives to cultivate it (i.e. “shadow prices”), and on-farm conservation of crop genetic resources is an internationally accepted complement to conservation in gene 33

34

CHAPTER 3. THEORETICAL FRAMEWORK

banks. Using an agricultural household framework, I develop a theoretical model to derive household-specific shadow prices for “non-tradable” crops. The shadow prices I derive may arise both because of transaction costs (TCs) as in de Janvry et al. (1991), and imperfect substitutability of market purchased crops for the domestic crop. Based on the vast literature on the non-market values of maize for subsistence farmers in Mexico (most of whom are indigenous), I assume that domestic maize and market maize are two different goods that are imperfect substitutes in consumption (unlike in de Janvry et al. (1991)). I show how shadow prices may be the relevant value measure for farmer’s decisions if the private, non-market values are significant even in the absence of TCs. I also analyze how using shadow prices instead of market prices can improve our understanding of resource allocation by subsistence farmers. The standard agricultural household model acknowledges that farm households consume part or all of their products and provide part or all of their inputs (Chihiro, 1986). As mentioned in Chapter 2, early studies in the agricultural household literature assume perfect markets, but later studies allow for imperfect or missing markets, which are common in developing countries (Singh et al., 1986; Jacoby, 1993; Skoufias, 1994; de Janvry et al., 1991; Taylor and Adelman, 2003). While most of these studies use market prices to value agricultural output, both de Janvry et al. (1991) and Taylor and Adelman (2003) analyze farmer decisions under missing product markets and represent the value of the constrained food crop with a shadow price instead of market price. Missing markets in these models are farmer-specific and arise from TCs that “trap” some farmers within the TC band so that it is optimal for these farmers to neither buy nor sell their products. They assume perfect substitutability between domestic and market goods, therefore the household is indifferent between consuming either good as long as TCs are not binding. I analyze how imperfect substitutability affects the results of earlier models and show that shadow prices may differ from market prices even in the absence of TCs.

35 Another characteristic of previous studies with missing markets is that the market constraints they analyze are symmetric, i.e. constrained farmers can neither buy nor sell their products/labor. The missing market discussed in this dissertation, however, is asymmetric (one-sided) such that it allows the farmer to sell the crop, but he has to produce it if he wants to consume it. This is because the domestic crop is characterized as a different consumption good due to its unobservable consumption characteristics and non-market values. For example, a farmer in Chiapas may not be confident that the blue maize he purchases in the local market will provide the same flavor and consistence to his tortillas as the blue maize he produces on his own farm. Similarly, even if he could find an identical blue maize, there is no means of purchasing the “utility” from being publicly acknowledged as a good maize farmer or the social ties that derive from participating in the communal labor exchanges and planting and harvest ceremonies that are practiced by maize farmers. As a result, the definition of the missing market is farmer-and crop-specific, as opposed to the more general farmerspecific or market-specific definitions in the literature. The conditions under which imperfect substitutability, hence the asymmetric market constraint, can arise are discussed in detail in the next section. The endogenously determined shadow price represents the money value of the utility the farmer receives by producing and consuming the “non-tradable” crop, i.e. the crop for which the asymmetric market constraint is binding. The household’s incentives for cultivating that crop, therefore, are represented by the shadow price. These incentives can guide on-farm conservation efforts for landraces that are grown for subsistence, especially in centers of diversity. Although Dyer Leal and Yunez Naude (2003) acknowledge the need to use shadow prices instead of market prices to value traditional crops with high non-market values for subsistence farmers, there are no studies to explicitly account for household-specific shadow prices for such crops.

36

CHAPTER 3. THEORETICAL FRAMEWORK The objective of this chapter is to extend the agricultural household litera-

ture with missing markets by analytically modeling shadow prices using TCs and the imperfect substitutability in consumption that creates an asymmetric market constraint. As demonstrated in Chapter 4, these shadow prices can then be estimated for each household. The empirical application in Chapter 4 is an extension of the previous literature on missing labor markets that models and estimates householdspecific shadow wages to analyze labor supply when the labor market is imperfect for some households (Jacoby, 1993; Skoufias, 1994).1 Although they define a symmetric missing labor market, their research provides the main motivation for the modeling exercise in this dissertation. In the next section, I develop the basic model with TCs and a market constraint for one of the farm products. I show how imperfect substitutability of the market good for the domestic good affects shadow prices, and how analyses of land allocation can be improved by using shadow prices rather than market prices for these farmers. Understanding which farm and farmer characteristics influence a household’s incentives to cultivate the subsistence crop is an important step in planning and targeting on-farm conservation programs for the subsistence crop in question. The contribution of such an understanding to models of farmer’s resource allocation is especially important if the empirical focus is on rural economies where most farmers produce only for home-consumption and receive non-market benefits from their subsistence crop – as is the case with most subsistence maize farmers (especially indigenous ones) in rural Mexico.

1 Main reasons for the imperfection modeled in these studies are imperfect substitutability of household and hired labor, the rigidity in labor hours for off-farm work and different preferences for on- and off-farm work.

3.1. AGRICULTURAL HOUSEHOLD MODEL AND SHADOW PRICES

3.1

37

Shadow Prices in an Agricultural Household Model with an Asymmetric Market Constraint

In this section, I develop a model to understand a farmer’s land and labor allocation decisions between different crops (a subsistence crop and a cash crop) and activities (farm production, off-farm work, leisure) in the presence of transaction costs and a market constraint for the subsistence crop. This market constraint arises from the imperfect substitutability of market purchased crops for the domestic subsistence crop, hence the two goods enter into the utility function as separate consumption goods.2 Therefore, the market constraint for domestic crop is asymmetric, such that the farmer can sell this crop, but cannot buy an identical crop in the market.

3

For example all sold maize may be collected in a silo where different qualities of maize get mixed. Unless every farmer’s maize is of identical quality, it is impossible for the farmer to recover the same quality of his own crop from the market.4 The consumption of the domestic crop is equal to production minus sales – if any. In light of recent developments in the study of farmers’ crop choices in centers of diversity, we can think of a crop as a bundle of multiple characteristics farmers pay attention to when choosing what to cultivate. These characteristics include production attributes, consumption attributes, subjective importance farmers place on their seed which may have provided subsistence to the family for decades, as well as other non-market benefits farmers get from farm production (Brush and Meng, 1998; Smale et al., 2001, 2003; Edmeades et al., 2004; Badstue et al., 2006; Dyer Leal et al., 2002).5 All of these characteristics are convoluted for crops like maize (or wheat, 2

21 out of 30 farmers I interviewed in 2 states and 15 different communities in Mexico during July 2005 said that the quality of the maize they buy in the market is not as good as their own maize, and they use the two different maize types for different purposes. This suggests that for the majority of farmers these two maize types are imperfect substitutes for each other in consumption. 3 My model is thus similar in spirit to the “partly absent market” defined by Strauss (1986). 4 There could exist different silos for each maize quality, however, this would be very costly and in practice few farmers have access to such finely differentiated market for maize quality. 5 Small maize farmers in Mexico value maize for traditional, ceremonial, ritual values, as well as different tastes and cooking qualities (Salvador, 1997; Dyer Leal, 2006; Berthaud and Gepts, 2004;

38

CHAPTER 3. THEORETICAL FRAMEWORK

rice, potatoes, etc.) where the seed is also the consumption good. The following discussion mainly refers to maize, but can be extended to other crops with similar characteristics. Although production attributes (e.g. plant strength, resistance to pests and disease, ear length, flowering time, adaptability to certain environments) are important in shaping farmers’ variety choices, I do not focus on them in this dissertation. The technology adoption literature covers a wide variety of production attributes that affect farmers’ variety selection, such as risk, agro-ecological conditions and information constraints (Feder, 1980; Just and Zilberman, 1983; Bellon and Taylor, 1993). How other production attributes mentioned above affect farmers’ decisions can be analyzed using the tools developed by this literature. In contrast, I analyze how consumption attributes and non-market values affect subsistence farmer’s resource allocation decisions. Subsistence-oriented farmers in Mexico demand various consumption attributes of maize such as ease of shelling and processing, color, taste, softness of dough and suitability for certain dishes, which are found to be correlated with on-farm genetic diversity of maize landraces (Smale et al., 2003; Bellon, 1996; Bellon et al., 2006; Perales et al., 2003). Some of these attributes are unobservable and may create an imperfect market for crops with the specific bundle of traits demanded by the farmer. In this case, some farmers may prefer producing and consuming their own crop at higher costs, to ensure the supply of all the consumption traits they care about. Non-market values, such as ceremonial or ritual importance associated with cultivating and consuming the subsistence crop, lead farmers to treat this crop as a separate consumption good when making resource allocation decisions. As discussed in the previous chapter, an important non-market value of maize for indigenous maize farmers in Mexico is related to their identity as good maize farmers and members of community (Smale et al., 2003; Badstue et al., 2006; Perales et al., 2005). Another Brush and Chauvet, 2004).

3.1. AGRICULTURAL HOUSEHOLD MODEL AND SHADOW PRICES

39

motivation for cultivating traditional maize in Mexico is to maintain the health of family seed that is important in the establishment and the survival of the households. Therefore we can expect that the marginal valuation of domestic maize will be higher for farmers for whom these non-market values are significant (i.e. a smaller degree of substitutability between domestic and market crop). Consequently, some farmers may not participate in the market, even if the observable TCs (such as transportation costs) are not binding. Although this model focuses on the case of traditional maize in Mexico, similar arguments about farmer preferences have been made for other countries and crops. Indigenous farmers in the Peruvian Andes prefer cultivating traditional potato varieties that are associated with various non-market benefits (Brush, 1992). Similarly, maize in Guatemala, wheat in Turkey and rice in the Philippines have some consumption characteristics that make purchasing a close substitute in the market hard (Meng et al., 1998; Bellon et al., 1998; Isakson, 2007). Therefore, the model developed here provides intuition for farmers’ incentives for maintaining traditional crops in centers of diversity beyond subsistence farmers of maize in Mexico. Suppose that a farmer produces a cash crop and a food crop using labor and a fixed amount of land (A). The markets for the cash crop and labor are perfect, hence the farmer can buy and sell these at market prices. There are no land markets.6 The farmer divides his land between the subsistence crop and the cash crop. The cash crop, in turn, is not a consumption good and thus will not directly enter the farmer’s utility function. He also decides how to allocate labor across different crops and activities to maximize his utility. Let Qi denote the quantity produced of crop i, where i = s, c, identifying the subsistence and cash crop respectively. Xm and Xl are, respectively, the amount of market goods and leisure consumed. He also consumes part or all of his subsistence 6 Finan et al. (2005) find that land rental markets in rural Mexico are very inactive with only 5% of farmers participating in rental market using 1999 data from 25,000 households. This ratio is 7.6% of all plots in ENHRUM data used for the empirical analysis in this dissertation.

40

CHAPTER 3. THEORETICAL FRAMEWORK

crop denoted by Xsh , where the superscript h indicates that the only source of consumption of Xs is home production. Under the assumption of perfect labor market, the farmer can hire out his own labor and hire in as much labor as he likes at the market wage, w. Fi and HIi denote the amount of family labor and hired-in labor used in the production of crop i, respectively. The farmer faces per-unit transaction costs tb and ts associated with buying the market good and selling the subsistence crop, respectively. These costs create a transaction cost band around the market price as defined in de Janvry et al. (1991). Output is certain and the farmer’s decisions are: what proportion of land to cultivate with the subsistence crop; how much labor to allocate to the production of each crop and to off-farm work; how much of his subsistence crop to sell (Xss ); and how much to consume of all goods (i.e. Xsh , Xm , Xl ). Li is the total labor used in the production of crop i, and θ is the proportion of land cultivated with the subsistence crop. The market good can be a crop similar to the domestic food crop. These two consumption goods can have different degrees of substitutability depending on how important the non-market values are for the farmer (i.e. Xm can be maize bought in the market for the case of Mexico). Z represents a vector of household characteristics (demand shifters), including indigenous identity, that shape preferences. The farmer’s problem is given by: max

Xl ,Xm ,Xsh ,Xss ,θ,Fi

U (Xsh , Xm , Xl ; Z)

such that, pm (1 + tb )Xm + w(HIa + HIc ) ≤ ps (1 − ts )Xss + pc Qc + wHO + W

(3.1)

Qs = g(Ls , Aθ)

(3.2)

Qc = h(Lc , A(1 − θ))

(3.3)

HO + Xl + Fs + Fc = T¯ Fi + HIi = Li , i = s, c

(3.4) (3.5)

3.1. AGRICULTURAL HOUSEHOLD MODEL AND SHADOW PRICES

41

Xsh ≤ Qs − Xss

(3.6)

Xss ≥ 0

(3.7)

Xsh ≥ 0

(3.8)

Xm ≥ 0

(3.9)

0≤ θ

≤1

Ls ≥ 0

(3.10) (3.11)

where pj denotes the market prices of consumption goods and the cash crop identified with subscripts j = s, m, c; and W denotes exogenous transfers. U(.) is a continuously differentiable and strictly quasi-concave utility function and g(.) and h(.) are, respectively, quasi-convex production functions for the subsistence and cash crops. Equation 3.1 is the cash constraint, which indicates that the total expenditure on the market good and hired labor needs to be less than or equal to the value of marketed surplus plus labor income and exogenous transfers. Equation 3.4 is the time constraint, where T¯ is the household’s time endowment. I assume that the marginal utility of the first unit of leisure is very large (i.e. M Ul |Xl =0 = ∞), hence we are not concerned about a corner solution for Xl . Consumption of Xm can equal zero if the TCs for buying is prohibitively high (which also depends on the degree of substitutability of the market crops for the domestic crop). Consumption of Xsh , will also equal zero if the farmer does not cultivate this crop. I derive the conditions under which this would happen using the non-negativity constraint in equation 3.8. The other non-negativity constraints (i.e. constraints 3.7, 3.10 and 3.11) involve the amount sold of, the proportion of land in, and the labor used for the subsistence crop to emphasize the corner solutions related to this crop that define shadow prices. Of special interest are Constraints 3.6 and 3.7, which together define the market constraint for the farmer’s subsistence crop (Qs ). Constraint 3.6 states that the consumption of the subsistence crop has to be less than or equal to the total amount produced minus sold, since he cannot buy it in the market. Constraint 3.7 states

42

CHAPTER 3. THEORETICAL FRAMEWORK

that the marketed surplus cannot be negative, and thus characterizes the one-sided missing market. Constraint 3.6 and the non-negativity constraints together determine the different regimes the farmer may be in (e.g., all land in Qs and subsistence farmer; all land in Qs and commercial farmer; some land in Qs and subsistence farmer). This allows us to derive farmer-specific shadow prices of the subsistence crop and compare them to the market price for each case. By substituting Equations 3.4 and 3.5 into the budget constraint, we obtain the following Lagrangean: max

Xl ,Xm ,Xsh ,Xss ,θ,Li ,λ,µn

L = U (Xsh , Xm , Xl ; Z)

+λ[ps (1 − ts )Xss + pc h(Lc , A(1 − θ)) + W + w(T¯ − Xl − Ls − Lc ) − pm (1 + tb )Xm ] +µ1 [g(Ls , Aθ) − Xss − Xsh ] + µ2 Xss + µ3 Xsh + µ4 Xm + µ5 θ + µ6 (1 − θ) + µ7 Ls + µ8 Lc i = s, c n = 1, ..., 8 The first order conditions (FOC) are: F OCXl : M Ul = λw

(3.12)

F OCXm : M Um − λpm (1 + tb ) + µ4 = 0

(3.13)

F OCXsh : M Ush − µ1 + µ3 = 0

(3.14)

F OCXss : λps (1 − ts ) − µ1 + µ2 = 0

(3.15)

F OCθ : µ1 A(M P As ) − λpc A(M P Ac ) + µ5 − µ6 = 0

(3.16)

F OCLs : µ1 M P Ls − λw + µ7 = 0

(3.17)

F OCLc : λ(pc M P Lc − w) + µ8 = 0

(3.18)

Equations 3.13-3.18 are FOCs for variables that can take on zero values (i.e.

3.1. AGRICULTURAL HOUSEHOLD MODEL AND SHADOW PRICES

43

corner solutions). We need to use the Karush-Kuhn-Tucker (KKT) conditions to obtain the optimality conditions for these variables. For the KKT conditions to be sufficient for a maximum, I assume that the utility function is pseudoconcave in addition to the quasi-concavity and quasi-convexity assumptions above.7 Pseudoconcavity also implies quasi-concavity because U(.) is pseudoconcave if and only if its gradient vanishes only at the global optimum and it is quasi-concave. The KKT conditions are:8

∂L : M Um − λpm (1 + tb ) + µ4 ∂Xm ∂L : Xm ∂µ4 µ4 X m ∂L : λps (1 − ts ) − µ1 + µ2 ∂Xss ∂L : Xss ∂µ2 µ2 Xss ∂L : M Ush − µ1 + µ3 h ∂Xs ∂L : Xsh ∂µ3 µ3 Xsh ∂L : µ1 A(M P As ) − λpc A(M P Ac ) + µ5 − µ6 ∂θ ∂L :θ ∂µ5 ∂L : (1 − θ) ∂µ6 µ5 θ = 0

= 0

(3.19)

≥ 0

(3.20)

= 0

(3.21)

= 0

(3.22)

≥ 0

(3.23)

= 0

(3.24)

= 0

(3.25)

≥ 0

(3.26)

= 0

(3.27)

= 0

(3.28)

≥ 0

(3.29)

≥ 0

(3.30)

& µ6 (1 − θ) = 0

(3.31)

7 Leo Simon, ARE 211 class notes: http://are.berkeley.edu/courses/ARE211/ currentVersion/mathNPP2.pdf 8 Note that Lc is automatically zero if θ = 1. The KKT conditions for Lc do not affect the following discussion on shadow prices. I discuss and interpret them in detail in Appendix A.

44

CHAPTER 3. THEORETICAL FRAMEWORK ∂L : µ1 M P Ls − λw + µ7 = 0 ∂Ls ∂L : Ls ≥ 0 ∂µ7 µ7 Ls = 0

(3.32) (3.33) (3.34)

Equation 3.19 indicates that if a farmer is not buying the market good, Xm , the monetized value of the marginal utility from consuming it must be less than or equal to the market price plus the per-unit TCs (i.e.

M Um λ

= pm (1 + tb ) −

µ4 ). λ

In an

agricultural household model with perfect markets, the farmer equalizes the ratio of marginal utilities of each good to the ratio of market prices (i.e.

M Ui M Uj

=

pi ), pj

and the

value of marginal product of land across crops (i.e. pi M P Ai = pj M P Aj ). However, these conditions take the following forms in the current model (by Equations 3.19, 3.25 and 3.28): M Ush µ1 − µ3 = , M Um λpm (1 + tb ) − µ4 µ1 pc M P Ac = M P As , when θ > 0. λ

(3.35) (3.36)

For farmers who produce the subsistence crop and consume positive amounts of Xsh and Xm , µ3 and µ4 are equal to zero, hence

µ1 λ

takes the place of ps in the

conventional optimality conditions. Given this optimization rule, I define the “shadow price” of Xsh as follows: ρ≡

µ1 , λ

where µ1 is the marginal utility of having one more unit of Qs , and λ is the marginal utility of income.9 We can observe from Equation 3.35 that, holding everything else constant, the higher a farmer’s marginal utility from consuming the subsistence crop, the higher its shadow price. Equation 3.36 implies that the farmer equates the value of marginal product of land cultivated with the cash crop to the “shadow value of 9

We can derive the same shadow price using the FOC for leisure:

M Ush M Ul

=

µ1 −µ3 λw

3.1. AGRICULTURAL HOUSEHOLD MODEL AND SHADOW PRICES

45

marginal product” of land cultivated with the subsistence crop. We can interpret ρ as the money value of having one more unit of Qs for the household (Heckman, 1974). Let us compare this interpretation with the interpretation of shadow wage in the labor supply literature. The shadow wage is defined as ω = µλ , where µ is the shadow value of the household’s time constraint, and λ is the shadow value of income. It represents the monetized value to the household of a one unit increase in total time endowment. Similarly, the shadow price of the subsistence crop represents the amount of additional income required to increase the household’s utility by the same amount as one more unit of that crop produced at home (holding the technology and inputs constant). The shadow price is conceptually the same as the one in de Janvry et al. (1991), however, the conditions under which it arises are different. In the current model, some farmers may not participate in markets even if the TC band is not binding if the non-market benefits of the subsistence crop are significant for them. I discuss the different classes of farmers as defined by the KKT conditions in detail in Appendix A. I show that if a farmer is not producing any subsistence crop (i.e. θ∗ = 0) it must be the case that the “shadow value of marginal product” of land from subsistence crop is less than the value of marginal product of land from the cash crop. The same is true for the value of marginal product of labor. For these farmers it is not worthwhile to allocate resources to subsistence crop production because they do not value it as much, and/or they can buy a close substitute for it in the market (indicating that unobserved characteristics and non-market values are not significant for such farmers). It is not the shadow price per se, but how it compares to the market price including TCs under different cases of market participation (i.e. Xss > 0 or Xss = 0), that determines whether the farmer is constrained by the missing market or not. For farmers who have θ∗ > 0 and sell part(all) of their subsistence crop, the shadow price is equal to (less than or equal to) the market price (i.e. ρ = (≤)ps (1 − ts )). For these

46

CHAPTER 3. THEORETICAL FRAMEWORK

farmers, the shadow value is equal to the market price. If, however, the farmer is consuming all of Qs at home (i.e. Xss = 0), the shadow price is greater than or equal to the selling price he would get in the market, i.e.:10 ρ=

µ1 µ1 − µ2 ≥ = ps (1 − ts ). λ λ

(3.37)

µ2 is the multiplier associated with the non-negativity constraint for Xss and represents how much the farmer’s utility would increase if we relaxed that constraint by one unit. Given that this is a non-negativity constraint, µ2 is the utility the farmer would get if he could sell a negative amount, i.e. if he could buy an identical product in the market. Therefore, farmers constrained by the non-negativity constraint for Xss value the subsistence crop more than the market.11 The results of this model differ from the TC band model in the literature in two ways. First, the upper limit of the TC band depends on how costly it is for the farmer to find a close substitute for his domestic crop in the market. Second, the lower limit of the TC band is higher for farmers who value their domestic crops highly (i.e. representing a smaller degree of substitutability due to non-market values of the domestic crop). Figure 3.1 demonstrates how allowing for imperfect substitution affects the traditional TC band model using the graphical presentation in Taylor and Adelman (2003). I use indigenous identity (I) as an indicator for non-market values attached to domestic (subsistence) crop (i.e. I is an element of the vector of demand shifters in the utility function). I assume that the degree of substitutability between the domestic and market crops is lower for indigenous farmers, with I = 1. This is manifested in 10

For this group of farmers µ2 ≥ 0 and µ3 = 0. See Appendix A for details. Rewriting the Equation 3.15 on page 42 as µλ2 = µλ1 − ps (1 − ts ) provides more intuition about this constraint (all terms in this equation are monetized). The monetized value of relaxing the non-negativity constraint by one unit is equal to the subjective value of one more unit of production using the same inputs minus the market value of that crop. Hence the conclusion that the shadow price is greater than or equal to the market price for farmers who do not sell any subsistence crop given market prices and TCs. 11

3.1. AGRICULTURAL HOUSEHOLD MODEL AND SHADOW PRICES

47

$ Maize Supply pm(1+tb) (I=1) pm'(1+tb) (I=1) pm(1+tb) (I=0) Buy if I=0 pm' ps(1-ts)

Maize Demand Qs

Xs

Xs

$ Maize Supply

pm(1+tb)

ps'(1-ts) (I=1) ps(1-ts) (I=0)

Sell if I=0

Maize Demand (I=1) Maize Demand (I=0) Xs

Qs

Xs

Figure 3.1: Transaction cost band and imperfect substitutability in consumption due to nonmarket values of domestic crop. The top panel shows the wider TC band for I = 1 as opposed to the TC band for I = 0. The bottom panel shows the higher selling price required to enter the market by farmers with I = 1.

48

CHAPTER 3. THEORETICAL FRAMEWORK

higher transaction costs associated with buying a substitute for the domestic crop compared to non-indigenous farmers. In the upper panel, a farmer with I = 0 will produce Qs and buy maize equal to the difference between demand and supply of domestic maize (i.e. Xs − Qs ) at the market price pm and the unit transaction cost tb . However, a farmer with I = 1 will not buy at the given prices because the transaction costs associated with finding a good substitute for the domestic good are higher. This is represented by the wider TC band with the bold dashed upper limit of the TC band. Holding the observable TCs constant, we may observe that some farmers (I = 1) do not buy this crop in the market even though it seems like they face the same TCs as others who buy in the same community. Farmers who have higher unobserved TCs will start buying in the market only if the market price and/or observable TCs were lower than p0m (1 + tb ), corresponding to a lower market price p0m . Therefore, the “inelastic response” of farmers to market signals may be observed more than what the traditional TC band model would suggest. The bottom panel of Figure 3.1 depicts the demand for maize by an indigenous and a non-indigenous farmer. The higher valuation of the subsistence crop by the indigenous farmer is represented by the higher willingness to pay for the same amount of domestic maize. Given the market price, ps , and transaction (transportation) costs for selling in the market,ts , the non-indigenous farmer will produce Qs and sell the difference between Qs and Xs . Even though the indigenous farmer is facing the same transaction costs, he will not sell at these prices because his subjective valuation is higher than the market price. He will start selling only if the selling price minus TCs is above p0s (1 − ts ). For farmers within the TC band defined as above, production decisions are affected by µ1 and λ, which in turn depend on household characteristics that would not affect production under perfect markets. We can interpret the decision criteria for optimal labor allocation of a farmer who produces some subsistence crop (i.e.

3.1. AGRICULTURAL HOUSEHOLD MODEL AND SHADOW PRICES

49

µ5 = µ6 = 0) using the Equation 3.17: µ1 M P Ls = λw

(3.38)

The left hand side of Equation 3.38 represents the marginal benefit the farmer receives (in utility terms) from allocating the last unit of labor into the production of subsistence crop. The right hand side represents the marginal cost of that last unit of labor (in utility terms), because λ is the marginal utility of income and it is multiplied by the wage the farmer pays for labor. Although µ1 and λ are not observable, we can define an estimable expression for ρ as follows: ρ≡

µ1 w = . λ M P Ls

(3.39)

As we can see from Equation 3.36 and Figure 3.2 on the next page, the land allocated to the subsistence crop by a subsistence farmer depends on (and increases with) its shadow price. Ignoring shadow prices and using market prices to value the subsistence crop would make farmers seem to allocate “irrationally” high amounts of land to this crop. However, by capturing the non-market values associated with the subsistence crop, shadow prices can explain the rationality of farmers’ behaviour. Because of this, using estimated shadow prices in econometric analysis is likely to improve our models of land allocation by subsistence farmers. To understand how the optimal land allocated to the subsistence crop changes with total farm size (i.e.

∂θ∗ ), ∂A

I use the Implicit Function Theorem (IFT) on the

FOC for θ (for θ∗ > 0 and Xss = 0). Under reasonable assumptions, namely that the Jacobian of the Lagrangean is non-singular, we can write θ as a continuously differentiable function of A (i.e. θ∗ = θ(A∗ ) (Simon and Blume (1994), Ch.15).12 We 12 See also Leo Simon: mathCompStat3.pdf.

http://are.berkeley.edu/courses/ARE211/currentVersion/

50

CHAPTER 3. THEORETICAL FRAMEWORK VMPA s

VMPA c VMPA s = *MPA s

VMPA c = p c *MPA c

VMPA s = p s *MPA s


*

0


0

A=1

Figure 3.2: Optimal land allocation using market prices vs. shadow prices for subsistence crop. θ∗ is the proportion of land that would be allocated to Qs using the market price (ps ) and θ0 is the proportion of land that is allocated to Qs using the shadow price (ρ).

can calculate the direction of change in θ when A changes as follows:

2

2

∂ρ ∂ g ∂ h M P As + ρ ∂A 2 θ − pc ∂A2 (1 − θ) ∂θ∗ ∂A s c = − ∂ρ 2 ∂2g ∂A M P As + ρ 2 A + pc ∂ h2 A ∂θ

∂As

(3.40)

∂Ac

The denominator is unambiguously negative, therefore the sign of the change in θ∗ depends on the numerator. The sign of the numerator depends on how the shadow price changes with farm size, and which one of the marginal product curves is flatter. Assume that the shadow price is constant and does not change with land size (i.e.

∂ρ ∂A

= 0). In this case, how the extra land will be allocated between the two crops

will depend on how the curvature of the marginal product of land from subsistence crop compares with that of the cash crop. If they have the same curvature, then the incremental land will be equally divided between the two crops. If the curvatures differ, the crop with a flatter marginal product curve will get a larger share of the incremental land. Therefore θ∗ may increase if the marginal product of land from subsistence crop is diminishing more slowly.

3.1. AGRICULTURAL HOUSEHOLD MODEL AND SHADOW PRICES

51

The shadow price, however, is not constant and it changes with land size. To sign how ρ changes with A, we can use the fact that ρ =

w M P Ls

because this

relationship has to hold at any optimum (for farmers who are constrained by the asymmetric market constraint). Holding everything else constant, if we increase total land size, the marginal product of labor will increase, therefore conclude that

∂θ∗ ∂A

∂ρ ∂A

< 0. We can

< 0, if one of the following holds:

1. the marginal product of land has the same curvature for both crops. 2. the marginal product of land from the subsistence crop is steeper. 3. the marginal product of land from the subsistence crop is flatter and the decrease in ρ offsets the difference in the changes in marginal products. On the other hand, the case where

∂θ∗ ∂A

> 0 is also possible, if the marginal

product of land from the subsistence crop is very flat as compared to that from the cash crop, and the shadow price does not decrease by a lot, resulting in more of the extra land to be allocated to the subsistence crop. The sign of the comparative statics of θ∗ with respect to land, ultimately, is an empirical question, that I investigate in the next chapter. Given Equation 3.39 on page 49 and using an empirical method similar to Jacoby (1993) and Skoufias (1994), we can econometrically estimate household-specific shadow prices by estimating the production function to derive the marginal product of labor for each household. We can also test whether shadow prices are statistically different from market prices and empirically analyze the determinants of this difference – which would shed light into whether shadow prices arise due only to TCs, or also non-market values of home produced subsistence crop. Moreover, using shadow prices instead of market prices for non-market producers can improve our analyses of farmers’ crop choice and land allocation decisions, as well as help us explore farmers’ incentives to cultivate traditional crops associated with on-farm conservation of genetic diversity.

52

3.2

CHAPTER 3. THEORETICAL FRAMEWORK

Conclusion

Farmers make resource allocation decisions based on the value of different crops or activities given market conditions. If a crop (activity) has non-market values that are not captured by market prices, its value to the subsistence farmer (i.e. shadow price) exceeds its market price. Therefore, the farmer will not find it optimal to sell this crop at market prices. The model developed in this chapter contributes to the agricultural household literature by deriving conditions under which shadow prices of domestic (“non-marketed”) products are relevant even if there are no TCs. Although there are a number of studies to calculate shadow wages for farmers who do not supply labor at market wages, there are no studies that calculate shadow prices to value subsistence farmers’ output. Just as we need to calculate shadow wages for farmers that do not supply labor to evaluate the value of their time, so too do we need to calculate the shadow prices of the products that are not sold in the market. Especially in cases where there are non-market values associated with a crop, shadow prices are likely to reflect farmers’ incentives better than market prices and thus are likely to better explain farmers’ resource allocation decisions related to subsistence crops. Based on this theoretical model, in the next chapter, I estimate householdspecific shadow prices of maize in Mexico, using nationally representative farm household data. I test whether estimated shadow prices are different from market prices and identify the determinants of shadow prices of traditional maize in order to explain farmers’ subjective valuation of these varieties that are important for the conservation of maize genetic resources. I also test whether and how the knowledge of shadow prices improves models of farmer’s land allocation. Finally, I investigate what other reasons may cause high estimated shadow prices and test whether they may have affected the empirical analysis. I claim that in rural economies such as those of Mexico, where most farmers produce for home consumption (subsistence) and the subsistence crop has non-market benefits, it is crucial to understand whether market prices represent the true sub-

3.2. CONCLUSION

53

jective value of farmers’ products. It is also important to understand whether the shadow prices emerge just due to TCs or non-market benefits associated with producing one’s own crop. This understanding will improve our models and predictions of farmer response to market signals, especially in centers of crop domestication – where subsistence crops are likely to provide various non-market benefits to farmers. This analysis also offers insights into the puzzling inelasticity of maize production in Mexico in response to a sharp decrease in maize prices after NAFTA (Nadal, 2000; Dyer Leal et al., 2002; Dyer Leal and Yunez Naude, 2003). If farmers’ decisions are guided by a shadow price that exceeds the market price, then it is not surprising that a decrease in the market price would not decrease production. Finally, it contributes toward understanding the opportunity cost of on-farm conservation and improving the efficiency of programs targeted at creating incentives for on-farm conservation of crop genetic resources.

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CHAPTER 3. THEORETICAL FRAMEWORK

Chapter 4 Empirical Analysis This chapter includes the empirical application of the theoretical model developed in the previous chapter. In the first section, I introduce the agricultural household data from the Mexican National Rural Household Survey (ENHRUM) with descriptive statistics. In the second section, I first estimate production functions for both traditional and improved maize varieties to derive shadow prices of maize for farmers. I show that they are significantly higher than market prices for subsistence farmers of traditional maize and cannot be explained by transaction costs only. This means that the cultivation of traditional maize by subsistence farmers may continue de facto in spite of changes in market conditions that are unfavorable for on-farm conservation of TVs. The answer to the question of “what farmer and farm characteristics in which regions are correlated with high shadow prices” can therefore provide information for targeting on-farm conservation programs. I answer this question using regression analysis and variables that affect the cultivation and valuation of traditional crop varieties. After understanding the determinants of shadow prices, I explore whether we can improve on models of farmers’ land allocation between different crop varieties using the estimated shadow prices rather than market prices for subsistence farmers. I conclude that, using shadow prices rather than market prices for subsistence farmers we can better predict the proportion of land allocated to TVs. This takes 55

56

CHAPTER 4. EMPIRICAL ANALYSIS

the “surprise” out of Mexican maize farmers’ inelastic supply response to decreasing market prices after NAFTA.

4.1

The ENHRUM Data

The ENHRUM data were collected in January-February 2003 and cover 1782 households in 80 villages, 14 states and 5 census regions in Mexico. The survey was designed and implemented by the National Institute of Statistics, Geography and Informatics (INEGI) to be regionally and nationally representative of 80% of the rural Mexican population. Rural Mexico is defined as communities that have between 500 and 2,500 inhabitants. The following is a non-exhaustive list of variables included in the survey: household demographics; plot level information on land, labor, fertilizer, animals and machinery used for agricultural production in 2002; total production; marketing and consumption of products; maize diversity; migration history; off-farm income sources; credit market participation and other assets.1 Figure 4.1 on the next page shows the regional distribution of the communities surveyed by the ENHRUM. The survey covers all agricultural activities in two crop cycles (Spring-Summer and Autumn-Winter) during 2002. 573 households who cultivated at least some maize on 897 plot-cycles, 73% of which are in the South-Southeast and Central regions. 223 of the 573 maize growing households in the publicly available data had some missing values and/or outliers in their production variables. I conducted a thorough cleaning for these problems by correcting the typographical errors using the actual survey forms.2 This cleaning process decreased the means and standard deviations of the production variables significantly (e.g. yield, seed, labor, fertilizers and pesticides per hectare). Ideally we would like to have input and output data at the variety level to be 1

For more details and the ENHRUM data see: http://precesam.colmex.mx Specifically, I have updated the following variables: total production, plot area, the expenditures on fertilizers and pesticides, and seed, labor, machinery and animal hours used. 2

4.1. THE ENHRUM DATA

57

Figure 4.1: Regional Distribution of the communities in the Mexican National Rural Household Survey (ENHRUM 2003)

able to estimate the production function and shadow prices for each variety. However, the production module does not differentiate between maize varieties, nor does it differentiate between different crops on the same plot. Therefore, the input data are only at the plot level, which makes the estimation of a production function for maize difficult for plots with multiple crops. Therefore, in what follows I use a subsample consisting of the plots that are cultivated only with maize. This subsample constitutes 25% of all plots, 63% of all maize plots and 67% of maize growing households in the sample (see Table 4.1). These groups are very similar to each other in terms of key variables. Two-sided t-tests fail to reject the hypothesis that the means of the two samples are equal to each other for all variables but three (indicated by ∗ ). Therefore, using the subsample of mono-cropped maize plots in the following empirical analysis should not create a significant bias. Maize varieties are grouped in two categories in the ENHRUM data: traditional

58

CHAPTER 4. EMPIRICAL ANALYSIS

Table 4.1: Means of plot level and household level variables for all and mono-cropped maize plots Variable

Whole sample Plot Level Variables Yield (kg./ha.) 1087.17 Seed amount/ha. 24.88 Plot area (ha.) 1.91 Irrigation dummy 0.14 Soil quality (1: Bad, 2: Regular, 3: Good) 2.28 Slope (1: Plain, 2: Sloped, 3: Very steep) 1.54 Walking time from the parcel to the com38.99 munity center (mins.) Total labor (days/ha.) 73.66 Total input cost/ha. 677.42 Total machinery hours/ha. 5.83 Total animal hours/ha. 18.79 Number of observations 868 Household Level Variables Wealth index 2.31 Gender of household head(=1 if male) 0.90 Indigenous language dummy 0.36 Total land owned (ha.) 7.15 Number of plots cultivated 1.78 Number of plots owned 1.45 Total farm income ($MX) 8707.04 % land cultivated with maize 0.74 % maize production sold 0.14 Maize purchase dummy (=1 if bought) 0.47 Off-farm income dummy 0.48 Maize sale dummy (=1 if sold) 0.25 Number of observations 557 ∗

Subsample 1140.53 19.69 2.14 0.15 2.31 1.53 39.01 55.58∗ 497.64 4.46∗ 14.52 551 2.28 0.91 0.40 7.09 1.87 1.52 9066.55 0.88∗ 0.14 0.43 0.45 0.25 374

indicates that the difference of the sample means is statistically significant at 5% level using a two-sided t-test.

4.1. THE ENHRUM DATA

59

and modern. Of all the plots in this subsample, 86% are cultivated with traditional maize varieties (Table 4.2 on the following page). Traditional maize here refers to maize identified as “criollo” by the farmer. The categorization of maize into distinct groups is subject to discussion in the literature, because farmers may refer to maize that has been acquired from another region or a store and adapted to local farming conditions as “criollo” (Brush and Chauvet, 2004; Louette, 1997; Bellon et al., 2006). Maize is an open pollinated variety and introducing new material helps farmers to enhance their seed stocks and add some desired traits from different varieties. This process is called “criolization.” Criolization seems to be widespread among farmers, because they seek new seed if they see their maize deteriorating or just want to experiment with new varieties. They usually prefer receiving seed from their neighbours because they can observe how it grows and can trust the seed, as opposed to seed purchased from a store “in a bag” (Bellon et al., 2006). The continuous recycling of maize seed combined with the open pollinated nature of maize plant makes the definition of distinct maize categories difficult. However, we need a classification to be able to analyze farmer decisions related to maize varieties. Farmers’ definitions of varieties have been used in the literature because farmers make decisions based on their own perceptions of the usefulness of different varieties. When asked, they often refer to seed that came from “a bag” as “h´ıbrido” (hybrid) even if it is criolized (e.g. “h´ıbrido criollo”) (Bellon et al., 2006). The ENHRUM questionnaire asked farmers whether the seed they used on a certain plot was hybrid or criollo. I use the answers to this question to classify maize varieties in this dissertation. If they answered “criollo,” I classify the maize on that plot as traditional maize (TV). The definition of “hybrid” also needs clarification, because farmers call all varieties that are not criollo “hybrid” regardless of whether they can be reproduced from seed or not. They may also use the term “mejorado” (improved) to refer to hybrids. “Improved variety” is a term conventionally used in analysis of crop diver-

60

CHAPTER 4. EMPIRICAL ANALYSIS Table 4.2: Percentage of plots under different maize types by region

Region South-Southeast Central Western Cent. Northwest Northeast Total

% of Maize types Modern Traditional 8 92 7 93 22 78 85 15 20 80 14 86

sity to indicate crops that have been improved using modern techniques in labs. This term, however, may create confusion if taken to imply that traditional varieties are not improved. Farmers have been selecting and improving the traditional varieties for centuries using traditional methods (Badstue, 2006). I use the more general term of “modern varieties” (MV) to refer to “hybrid” maize as identified by farmers. How these two categories of maize map to genetic diversity is important when it comes to on-farm conservation of landraces. Ideally we would like to have maize samples from all surveyed households and use molecular markers to identify the genetic diversity contained in them. However, such a study on a sample at this scale is prohibitively expensive and time consuming. Most empirical research on maize diversity in Mexico uses similar farmer categories to those defined here. Given the fact that farmers’ decisions depend on their own perceptions, it makes sense to use their classifications to understand and identify ways to affect their decisions related to maize varieties. Most of the maize identified as criollo by farmers is landraces (originating in that village or adopted from other villages), that display considerable genetic variation as compared to improved varieties (Bellon and Brush, 1994; Brush and Meng, 1998; Liu et al., 2003). Criollos, however, may include some criolized varieties that are well adopted to farmers’ growing conditions and satisfy their consumption needs. Although this fact in and of itself may indicate that the criolized varieties defined as criollo by farmers have a greater genetic variation compared to

4.1. THE ENHRUM DATA

61

Table 4.3: Means of household characteristics by region Wealth Index (q-tile) South-Southeast Central Western Cent. Northwest Northeast Total

1.63 2.03 3.46 4.85 2.95 2.28

EduTotal cation land (years) cult. (ha.) 3.72 6.52 3.43 1.65 2.70 7.48 4.54 11.88 4.65 24.11 3.60 7.09

Irrigated land (%) 9.57 21.06 17.21 61.54 7.09 15.85

Nr. of plots

Nr. of maize plots

2.87 2.03 2.91 2.38 1.97 2.51

1.35 1.15 1.02 1.08 1.00 1.19

Offfarm inc. (%) 39 48 44 46 59 45

hybrids, we cannot separate these two groups from each other. The lack of one-toone mapping from farmer classifications to genetic diversity is a caveat that should be kept in mind when interpreting what follows. Table 4.3 gives summary statistics of some household variables indicating significant differences across regions. Wealth Index is a variable created using Principal Component Analysis based on the characteristics of households’ primary residence, access to utilities, and ownership of a television and refrigerator.3 South-Southeast is the region with the lowest wealth index followed by the Central region. Most of the households in the sample do not have access to irrigation except in the Northwest region, where 61% of an average household’s total area is irrigated (as opposed to 16% for all households). The sample differences in household characteristics across regions reflect more aggregate regional differences in some economic indicators in Mexico. Southern Mexico includes the poorest states with high indigenous populations, whereas Northern states have higher GDP per capita, large scale farming and industrial production (Chiquiar, 2005). These fundamental differences create a need to control for regional variation when analyzing data on a national level. The structure of maize farming and its importance for households also differ across regions (Table 4.4 on page 63). Around 90% of all maize farmers in both South3 I report the quintiles of the wealth index to give an idea of the distribution of wealth in the sample.

62

CHAPTER 4. EMPIRICAL ANALYSIS

Southeast and Central regions cultivate only TVs, as opposed to only 15% for the Northwest region. Table 4.4 suggests a positive correlation between traditional maize cultivation and indigenous population, confirming similar findings in the previous literature (Perales et al., 2005; Turrent and Serratos-Hernandez, 2004; Bellon and Brush, 1994).4 The percentage of maize production sold in the market ranges from 7% in the Central Region to 83% in the Northwest Region, with a mean of only 14% for the whole sample. Given that maize production is seen as a traditional subsistence activity rather than a business among small scale farmers, we can expect that market prices will fail to represent the value of farmers’ maize. In a series of informal interviews with 35 maize farmers in 2 states (Puebla and Oaxaca) and 15 different communities in Mexico during July 2005, I found that most farmers prefer the traditional maize they produce for consumption; do not like modern varieties (either because they do not have the perfect growing conditions for them, or they do not like the tortillas made with modern maize); think that maize production is not an income generating activity; and attach different consumption and production attributes to different varieties. These observations suggest two different categories of maize for farmers, home-produced maize that is mostly TV and purchased maize that is mostly MV. They also support the asymmetric market constraint for home produced maize that is due to non-market values and unobserved consumption characteristics, as defined in Chapter 3. The production technologies of these two types of maize are different. MVs require irrigation and regular application of fertilizers and pesticides, whereas TVs are usually grown on rain-fed land with little or no fertilizers. TVs are seen as more resistant to pests and diseases during storage, which makes them preferable for subsistence farmers who save their own seed (Bellon et al., 2006). Some of these differences can be observed in Table 4.5 on page 64. There is a three-fold difference 4 Indigenous identity is defined as a dummy variable that equals to one if the household head can speak an indigenous language very well.

4.1. THE ENHRUM DATA

63

Table 4.4: Maize varieties, indigenous identity, farm income and sales by region

South-Southeast Central Western Cent. Northwest Northeast Total

Only TV (%)

Only MV (%)

92 91 75 15 76 85

8 8 21 77 24 14

Both TV& MV (%) 0 1 4 8 0 1

IndiTotal genous farm (%) inc. ($MX) 74 2,105 29 7,572 2 12,705 0 124,596 3 8,260 40 9066.55

Maize inc. (%)

Maize sold (%)

22 14 27 99 14 21

9 7 31 83 13 14

between the yields of the two types of maize. TVs are produced on smaller plots, with more labor, less fertilizer and less investment. 69% of traditional maize plots are cultivated with saved seed, as opposed to 13% of modern maize plots (or 97% of the plots cultivated with saved seed are traditional maize plots). This table is based on unconditional means and does not control for other variables that may explain the differences. In the next section, I control for other variables that may affect production by estimating production functions for both maize types. In addition the differences in plot characteristics, household characteristics also show differences depending on which maize varieties are cultivated (Table 4.6). Households that cultivate only TVs have lower wealth, less education, less farm income and are more likely to belong to an indigenous community as compared to the households that cultivate only MVs. They sell only 9% of their maize production on average as opposed to 43% for households that cultivate MVs. Given that traditional maize farmers grow maize mainly for home consumption, market prices are less likely to reflect the value of maize for these farmers. We can expect that the household-specific shadow prices of TVs would be higher than market prices capturing the non-market benefits farmers receive from them. If this is true, identifying the observable characteristics of farmers with higher likelihoods to preserve TVs will prove useful in targeting on-farm conservation programs. Moreover, using market prices to predict

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CHAPTER 4. EMPIRICAL ANALYSIS

Table 4.5: Summary statistics for plots cultivated with TV and MV Variable name yieldpha noryieldpha land seedpha irrigD soilq slope droughtD m1400 walktime famlabpha hirelabpha totlabpha machpha animpha fertpha pestpha inpcostpha investpha ownseedD N

Definition TV MV Yield (kg./ha.) 875.71 2821.24 Yield in a normal year 1471.31 3914.08 Plot area (ha.) 1.94 3.41 Seed amount (kg./ha.) 19.36 21.77 Irrigation dummy 0.11 0.37 Soil quality (1: Bad, 2: Regular, 3: Good) 2.33 2.20 Slope (1: Plain, 2: Sloped, 3: Very steep) 1.55 1.41 Drought dummy 0.33 0.39 Dummy=1 if plot is > 1400 masl. 0.76 0.63 Walking time from the parcel to the com39.04 38.41 munity center (mins.) Total family labor (days/ha.) 49.53 34.43 Total hired labor (days/ha.) 9.29 4.65 Total labor (days/ha.) 58.93 39.08 Total machinery hours/ha. 6.42 25.03 Total animal hours/ha. 15.62 7.53 Fertilizer cost/ha. 354.67 497.83 Pesticide cost/ha. 119.40 997.63 Total input cost/ha. 474.83 642.25 Total fixed investment in plot ($MX/ha.) 73.84 365.94 Dummy=1 if used own seed 0.69 0.13 Number of observations 476 75

4.1. THE ENHRUM DATA

65

Table 4.6: Summary statistics for different groups of households Variable windex hhsize age educ gender indiglang totown totpar ownpar maizpar frag m1400 biganim smanim totremit totlabpha inpcostpha totfarminc maizincshare maizareash maizsold totbuyD offarmD N

Households that cultivate Definition only TV only MV both Wealth index 2.07 3.42 3.75 Household size 5.05 4.65 5.75 Age of household head 50.61 51.06 59.25 Education of household head 3.47 4.19 5.75 (years) Gender of household head(=1 0.91 0.9 1 if male) Indigenous language dummy 0.45 0.12 0 Total land owned (ha.) 6.98 7.86 5.83 Total number of plots 1.86 1.83 3.75 Number of plots owned 1.51 1.56 2 Number of maize plots 1.21 1.08 1.25 Fragmentation index† 0.17 0.16 0.56 Dummy=1 if plot is > 1400 0.76 0.63 0.56 masl. Total number of big animals 5.12 6.77 11.75 owned Total number of small ani12.14 10.98 27 mals owned Total remittances received in 2,564.31 5,427.25 7,777.5 2002 ($MX) Total labor days/ha. (average 63.39 38.96 34.87 over plots) Total input cost/ha. (average 489.82 650.72 988.36 over plots) Total farm income ($MX) 4,588.35 35,138.04 25,555.75 % of income from maize 18 44 28 % land cultivated with maize 87 93 73 % maize production sold 8.74 40.37 19.12 Dummy=1 if purchased maize 0.44 0.37 0.25 in 2002 Dummy=1 if had off-farm in0.43 0.52 0.50 come Number of observations 318 52 4

†

Fragmentation index is the Simpson Index that indicates increasing levels of fragmentation in the P 2 i ai P range [0,1]. Simpson Index= 1 − ( ai )2 , where ai is the area of plot i. i

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CHAPTER 4. EMPIRICAL ANALYSIS

subsistence farmers’ responses to market changes may be misleading, and we can improve our analyses by using shadow prices instead. I test these hypotheses with detailed econometric analysis in the following section.

4.2

Econometric Analysis

I test the following hypotheses in this section:

1. Household-specific shadow prices of traditional maize are higher than market prices for subsistence farmers.

2. Farmers’ shadow prices can not be explained by TCs only, due to the imperfect substitutability in consumption.

Testing the first hypothesis requires generating estimates of farmer-specific shadow prices. I do so in section 4.2.1, by estimating production functions for maize and using the value of marginal product of labor to derive shadow prices.5 I discuss whether the traditional TC model can explain estimated shadow prices, or if imperfect substitution in consumption also plays a role in their determination. In section 4.2.2, I regress the estimated shadow prices on socio-economic and agro-ecological variables that are found to be correlated with farmers’ incentives to maintain landraces in the literature. I identify the key variables that are correlated with estimated shadow prices, hence are indicators of de facto incentives to maintain TVs. Lastly, in section 4.2.3, I compare estimations of subsistence farmers’ land allocation using market prices versus shadow prices and show that shadow prices predict land allocation better. 5

I use Stata 9 for the econometric analysis in this dissertation.

4.2. ECONOMETRIC ANALYSIS

4.2.1

67

Estimating shadow prices

According to the theoretical model in Chapter 3, we can express the household-specific shadow price of maize as follows (Equation 3.39 on page 49):

ρ=

w pI = . M P La M P Ia

(4.1)

Intuitively, this means that the farmer will stop allocating labor (or other inputs) to the production of this crop when the marginal cost of using labor (other inputs) equals to the “shadow value of marginal product” of that input. I first estimate a production function, that yields an estimate of the marginal product of labor (MPL), and then use the estimated MPL to derive the farmer-specific shadow prices. I use the log of a Cobb-Douglas specification for production functions, which provides good approximations for general input elasticities when the focus is not on the production structure. Jacoby (1993) and Skoufias (1994) both use Cobb-Douglas functional forms to estimate the MPL in their analysis of labor supply using shadow wages. The estimation of primal production functions (i.e. yield as a function of inputs) faces a potential endogeneity problem because farmers may adjust variable inputs in response to shocks, such as pest infestations, that are unobservable to the econometrician. Although estimating dual functions (cost or profit) solves the endogeneity problem, it may make the results less robust (Mundlak, 2000). Moreover, in rural settings where few modern inputs are used and prices show a lot of variation (as in rural Mexico), dual estimation may be subject to serious measurement error problems (Barrett et al., 2004). The interpretation of the primal production functions estimated here should be made with the input endogeneity caveat in mind. There is one issue one has to address when using a log Cobb-Douglas production function. If some farmers do not use some of the variable inputs, then the logarithm

68

CHAPTER 4. EMPIRICAL ANALYSIS

of that input will be undefined. This issue arises often with agricultural household data from developing countries, where there are a lot of farmers who do not use hired labor or modern inputs. A conventional way of “fixing” this problem is to add 1 to inputs that have some zero values to make the logarithm defined (Jacoby, 1993; Skoufias, 1994). I tested the effects of adding a range of small values like 0.01, 0.1 or 1 on the regression results. The results were robust to the choice of constant. I report the results where a constant of 1 is added to zero inputs because it sets the logarithm of the variable to zero, hence is less disruptive to the structure of data.6 Another problem that arises with survey data is how to deal with missing data. Missing data can be ignored if there are enough observations and the missingness does not depend on the missing data (i.e. missing at random). If, however, these two conditions are not satisfied, we need to use other methods to avoid biased estimates with missing data. Mean or median imputation is used widely, but both of these methods may result in biased point estimates. They also decrease the variation in data, hence bias downward the standard deviations. Data augmentation methods, such as multiple imputation, provide unbiased and efficient estimates by preserving the joint distributions of variables in the data (Schafer and Graham, 2002; Wayman, 2003). Many households in the ENHRUM data set do not use some variable inputs (other than labor). Most of these cases are plausible given the structure of small farm agriculture in rural Mexico. A few households, however, report producing maize without any labor, which indicates missing data. Although the number of households that have such missing values is small (4 observations), I compare three different methods in my estimations: dropping observations with missing data (“casewise deletion”), median imputation and multiple imputation. My estimations are robust to different 6 I have also estimated a translog production function, which is a more flexible functional form, for TVs. The translog specification did not produce any significant results, yielded negative marginal products for some inputs and were not robust. We cannot estimate translog function for MVs because of the lack of enough degrees of freedom. The Cobb-Douglas functional form, on the other hand, provides robust results to different specifications for both TVs and MVs.

4.2. ECONOMETRIC ANALYSIS

69

methods of dealing with missing data, mainly because of the small number of missing values. Consequently, I report the results of the simplest method, i.e. “casewise deletion.”7

Is there a selection bias in the production of TVs and MVs? In an ideal world, where farmers who cultivate TV and MV of maize are randomly distributed across the population, we could simply estimate the production functions for these two different maize varieties by regressing output on inputs. However, if there is an unobserved variable that affects farmers’ variety selection and is correlated with any of the covariates in the production function, the standard regression results will be biased. In the current context, if farmers who are more motivated and open to innovation cultivate MVs, and they are also more likely to invest in their land to improve soil quality (or know the best proportions of modern inputs to apply), the results of the production function estimations will be biased and we may overestimate the effect of soil quality (or modern inputs). Alternatively, if indigenous farmers’ identity as a good farmer depends on the cultivation of TVs (Badstue et al., 2006), they will be more likely to cultivate TVs. If the unobserved importance of identity is also correlated with other production variables (input use, fragmented land holdings, age or education), then we are likely to have a bias in the estimated coefficients of the production function if we do not control for selection into TVs. Various econometric methods can control for selection. If we had repeated observations from the same farmers over time, we could use panel data econometrics methods to control for unobserved farmer characteristics that are time invariant. Another option would be to use a method similar to Barrett et al. (2004) that requires data from farmers who cultivate both types of maize at the same time. In the current data, only 4 of the 374 households cultivate both TVs and MVs, making it impossible to use their method. Given the cross-sectional nature of the data, I control for 7

Complete results of all three methods are reported in the Appendix B.

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CHAPTER 4. EMPIRICAL ANALYSIS

selection bias using a Heckman selection model. The identification of a Heckman selection model depends on the availability of good identifying instruments (i.e. variables that directly affect variety choice but have no effect on yield except through their effect on variety choice). I use six exogenous variables as identifying instruments (variable names in parentheses): the percentage of plots in the same village that are cultivated with TVs/MVs excluding the farmer’s own plots (percTVloc and percMVloc), the percentage of the village maize production that is marketed excluding the farmer’s sales (vilmaizsales), the percentage of households in the village that had off-farm income from employment in other parts of Mexico and in the US in 1980 (percoff80mx and percoff80us respectively), whether the farmer speaks an indigenous language very well (indiglang) and whether he/she has saved any maize seed for longer than 2 years at the time of the survey (oldseedD). The first two instruments are proxies for farmer’s access to information and network effects. The percentage of village plots cultivated with TV/MV may affect farmers’ variety selection if there are network effects. For example a farmer may be more likely to cultivate TVs if most of the village plots are cultivated with TVs. This can be either due to the availability of seed for TVs, or the existence of common preferences in the village. Holding all else constant, however, it should not affect farmers’ productivity. The percentage of maize that is sold in the village characterizes the market environment that may affect farmer’s crop choice depending on market demand. If most farmers in the village market their maize, this may give the farmer an incentive to cultivate the maize demanded by the market. However, this variable should not affect productivity except through its effect on selection. The historical off-farm income variables are constructed using answers to the work history module in the household survey and represent the effects of local and international migration on preferences towards maize varieties. If contact with migrants affects preferences, households that live in villages with many migrants in other parts of Mexico (mainly big cities) or in the US, may be more or less likely to prefer

4.2. ECONOMETRIC ANALYSIS

71

MVs. Alternatively, if off-farm income relaxes cash constraints, households may be more likely to cultivate TVs that cannot be sold as easily to generate cash. However, we cannot use the amount of off-farm income or remittances received by the household during the survey year because they are endogenous (e.g. they will also affect productivity through their effect on input use and households may receive more remittances in a bad crop year). The percentage of households with off-farm income in 1980 will affect current preferences (hence variety selection), but it is so far back in time that we can expect it to be exogenous (pre-determined) to the production equation making it a good identifying instrument. The last two instruments (speaking an indigenous language and having saved some seed for more than 2 years) are proxies for indigenous identity and/or preferences that may affect variety selection. Being an indigenous farmer and saving seed are likely to be correlated with preferences towards TVs, but they should not affect productivity. Table 4.7 on the following page shows per hectare production function estimations using these instruments in the Heckman model.89 The regressions are weighted to account for the fact that farmers have different numbers of plots, and are clustered around Rural Development Districts (DDR) to control for possible error correlation between the plots in the same DDR (due to unobserved variables that affect production such as rainfall or climate).10 Although most of the identifying instruments are significant in the selection equation for TVs, only the indigenous language dummy is significant for MVs. The Inverse Mills Ratio is not significant for both maize types and we cannot reject the 8

Soil quality and slope variables are transformed to take on values (-1,0,1) instead of (1,2,3) for the production function. It is generally more preferable to create two dummy variables for the three categories, however this creates convergence problems for the instrumental variables regressions in the following section. To maintain comparability, I report the results with these transformed variables. 9 A Box-Cox test confirms that the log-log specification, i.e. Cobb Douglas, provides the best way of transforming the data. 10 Rural Development Districts are districts defined by SAGARPA (Secretary of Agriculture, Ranching, Rural Development, Fisheries, and Food Supply) that have similar production potentials. See http://www.cem.itesm.mx/derecho/nlegislacion/federal/35/index.html, Capitulo 6, 7 and 8.

72

CHAPTER 4. EMPIRICAL ANALYSIS Table 4.7: Heckman model results for production functions for TV and MV Variable

Coefficient

(p-value)

Coefficient

ln(yieldpha) TV (N=425)

ln(land) ln(totlabpha) ln(seedpha) ln(inpcostpha) ln(machpha) ln(animpha) droughtD soilq† slope† irrigD frag age educ totsellD South-Southeast Central Western Central Northwest Intercept

-0.32∗∗∗ 0.18∗∗∗ 0.20∗∗∗ 0.11∗∗∗ 0.13∗∗ 0.04 -0.07 0.25∗∗∗ 0.07 0.29∗∗ -0.02 -0.01 -0.03 0.69∗∗∗ -0.62 -0.31 -0.2 3.45∗∗∗ 5.11∗∗∗

percTV/MVloc vilmaizsales percoff80mx percoff80us indiglang oldseedD soilq slope irrigD frag age educ South-Southeast Central Western Central Intercept

0.81∗

(0.00) (0.01) (0.00) (0.00) (0.01) (0.15) (0.67) (0.01) (0.60) (0.02) (0.96) (0.15) (0.27) (0.00) (0.24) (0.58) (0.69) (0.00) (0.00)

-0.32 0.17 0.55 0.04 0.52 -0.08 -0.63 0.51 -0.17 0.2 -0.34 -0.01 0.01 0.47 0.6 -0.25 -0.42 0.61 5.84

p(TV)

Lambda (IMR) p-Wald test (rho=0) †

0.16 0.48

(0.44) (0.74) (0.36) (0.70) (0.81) (0.94) (0.83) (0.67) (0.95) (0.89) (0.82) (0.95) (0.98) (0.73) (0.91) (0.98) (0.77) (0.79) (0.30) p(MV)

(0.09) (0.04) (0.95) (0.56) (0.00) (0.00) (0.26) (0.69) (0.01) (0.13) (0.23) (0.56) (0.48) (0.07) (0.01) (0.52)

-0.01∗∗ 0 -0.02 0.90∗∗∗ 0.68∗∗∗ 0.19 0.06 -0.76∗∗ -0.49 0.01 0.02 0.26 0.81∗ 0.74∗∗ -0.53

(p-value)

ln(yieldpha) MV (N=66)

0.83 0.01 -0.01 0.04 -0.97∗∗∗ -0.57 -0.1 0.04 0.78∗∗∗ 0.38 -0.01 -0.01 -0.45 -0.94 -0.91 -0.23

(0.84) (0.86) (0.95) (0.85) (0.00) (0.72) (0.82) (0.87) (0.00) (0.76) (0.81) (0.95) (0.65) (0.57) (0.54) (0.87) -1.04 0.86

Soil quality and slope variables are rescaled to (-1,0,1) to prevent unnecessary imposition of a cardinal meaning to categorical variables. Significance levels: ∗ : 10% ∗∗ : 5% ∗ ∗ ∗ : 1%

4.2. ECONOMETRIC ANALYSIS

73

hypotheses that the correlations between the error terms of the selection and production equations (i.e. rho) are zero. This result is robust to different specifications with different sets of identifying instruments.11 Therefore, I conclude that controlling for all production variables, selection into TVs or MVs does not significantly bias the production function estimations. I proceed with estimating production functions separately for TVs and MVs. Estimating production functions with commercial farmer dummy Farmers who are producing maize exclusively for home consumption and those who produce it commercially may differ in their production practices such that the latter have a higher intercept. I define commercially oriented farmers as those who sold more than 30% of their maize in the survey year (% 27 of maize farmers). A glance at the differences in inputs used between commercial and non-commercial farmers shows that the differences in their use of labor and animal traction and the slope of their plots are statistically significant (Table 4.8). Table 4.8: Differences in input uses between commercial and non-commercial farmers

Sold more than 30%? No Yes Difference

Labor days/ha

Seed kg/ha

Machinery Animal hrs/ha hrs/ha

Soil quality

Slope

62.33 24.80 37.53∗

19.89 18.68 1.21

4.39 4.84 -0.45

2.31 2.31 0

1.57 1.33 0.24∗

16.36 5.18 11.18∗

∗

Indicates that the difference between the means of two groups is statistically significant at %10 level using a t-test.

Given this difference, we might use a dummy variable to identify commercial farmers in our production function estimations. However, if there are unobserved 11 The community module of the ENHRUM data has information about whether the community has participated at the Braceros (Guest worker) program before 1964. Using this variable instead of the percentage of households with off-farm income from US in 1980 gives similar results.

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CHAPTER 4. EMPIRICAL ANALYSIS

variables that are correlated with this dummy and the yield per hectare, this might create an endogeneity bias. For example, farmers who are open to innovation (an unobserved variable) may be more likely to be commercially oriented and they may also be more likely to engage in different management practices that affect their yields. In this case the unobserved “innovativeness” variable will result in bias in the estimated coefficients. Therefore, I estimate production functions controlling for the possible endogeneity of the commercial farmer dummy. I use three different methods to control for the endogeneity of the commercial farmer dummy: treatment effect regressions, two-stage least squares (2SLS) regressions with instrumental variables (IV) and two-step IV regressions with a probit model in the first step. The treatment effect model assumes that the outcome regression and the endogenous dummy (i.e. treatment) constitute a system of simultaneous equations and uses full maximum likelihood method to estimate the treatment effect. In the current case maize productivity may be affected by whether the farmer is commercially oriented or not, and vice versa. Even if a farmer is not planning to sell his maize in the market at the beginning of the crop year, he may chose to do so if he has an exceptionally good harvest. The treatment effect model offers a way to test and correct for simultaneity bias. Two-stage least squares estimation uses a linear probability model with instruments in the first step. The predicted values of the endogenous variable are then used to estimate the second stage regression. Because the first step in our model is a binary variable, we can also use a two-step IV estimation that uses a probit model in the first step. Although using a probit model for the first step may seem more intuitive when the endogenous variable is binary, this model depends on the normality assumption that may be invalid. Angrist (2000) shows that the linear probability model is consistent regardless of whether the first stage is linear, and claims that “it is safer to use a linear first stage.” I use all three methods to compare results and check the robustness of the production function estimations (Table 4.9).

4.2. ECONOMETRIC ANALYSIS

75

All of the specifications result in similar production function coefficients. The treatment effect regressions (columns 1 and 2 in Table 4.9) fail to reject the hypothesis that the two equations are independent using the Wald test for both the TVs and MVs with a p-value of 0.97 and 0.73 respectively.12 Therefore, I conclude that the two equations do not constitute a simultaneous system and use the results of the IV models in what follows. Columns (3)-(6) of Table 4.9 present the results for the IV models that instrument for the dummy variable that identifies commercial farmers as defined above. I use the following instruments to identify the production function equation with the commercial farmer dummy: percentage of the maize production that is sold in the village (excluding that household’s sales), the time it takes for the farmer to walk to the community center, percentage of households in the village that had off-farm income in 1980 from work in the same village and in other parts of Mexico, a dummy variable indicating whether someone in the household participated in The Bracero (Guest Worker) Program before 1964.13

12 The null hypothesis for the Wald test is that the correlation between the error terms of the production function and the the commercial farmer dummy equation (i.e. ρ) is zero. 13 The Bracero Program was created by the governments of Mexico and the US to bring legal agricultural workers to the US. The program started in 1942 and lasted until 1964 which brought around 4 million “braceros” to the US.

Variables ln(land) ln(totlabpha) ln(seedpha) ln(inpcostpha) ln(machpha) ln(animpha) droughtD soilq slope irrigD m1400 age educ South-Southeast Central Western Central Northwest sold30 Constant Observations

Treatment effect (1) (2) TV MV -0.286∗∗∗ -0.216 0.162∗∗ 0.223∗ ∗∗∗ 0.241 0.674∗∗ ∗∗∗ 0.126 0.063 ∗∗ 0.124 0.625∗∗ 0.021 0.063 -0.058 -0.826∗∗ ∗∗∗ 0.294 0.242 0.041 -0.625∗∗ 0.346∗∗∗ 0.562∗∗ 0.038 -0.865∗∗ -0.008 -0.029 -0.042 -0.053 -0.471 -0.538 -0.272 -1.372 -0.165 -0.632 3.635∗∗∗ 0.540 0.380 5.082∗∗∗ 5.780∗∗∗ 425 66 0.333 5.755∗∗∗ 66

0.931 5.427∗∗∗ 425

0.727 5.452∗∗∗ 425

0.304 5.684∗∗∗ 66

IV(probit) (5) (6) TV MV -0.317∗∗∗ -0.180 0.189∗ 0.215 0.196∗∗ 0.661∗∗ ∗∗∗ 0.117 0.071 ∗ 0.162 0.650∗∗ 0.033 0.053 -0.079 -0.750∗ ∗∗∗ 0.298 0.227 0.062 -0.624∗∗ 0.405 0.530∗∗∗ -0.044 -1.026∗∗∗ -0.008 -0.030∗ -0.044 -0.050 -0.739 -0.390 -0.580 -1.240∗∗∗ -0.487 0.430

IV(2SLS+Linear Prob.) (3) (4) TV MV -0.307∗∗∗ -0.170 0.178∗ 0.232∗ ∗∗ 0.194 0.676∗∗ ∗∗∗ 0.121 0.075 0.150 0.655∗∗ 0.029 0.062 -0.084 -0.755∗ ∗∗∗ 0.300 0.218 0.051 -0.617∗∗ 0.425 0.525∗∗∗ -0.036 -1.026∗∗∗ -0.008 -0.030∗ -0.043 -0.050 -0.737 -0.401 -0.559 -1.287∗∗ -0.443 -0.422

Table 4.9: Production functions controlling for the endogenous dummy for commercial maize producers (Dep. var: ln(yieldpha))

76 CHAPTER 4. EMPIRICAL ANALYSIS

Significance levels:

vilmaizsales walktime percoff80loc percoff80mx bracerohh age educ South-Southeast Central Western Central Northwes Constant Wald test (rho=0) ∗ : 10%

∗∗ : 5%

(6) 0.029∗∗∗ 0.017∗∗ 0.037∗∗ -0.009 0.522∗∗

0.019 0.490∗ 0.082

(5) 0.002∗ 0.000 -0.010∗∗∗ -0.003 0.050

-0.083 -0.058 0.059

∗ ∗ ∗ : 1%, Cluster robust p values in parentheses

(2) (3) (4) First Step Regressions: Dep.var=sold30 0.009 0.002 0.008∗∗∗ 0.000 0.004 0.000 0.001 ∗∗∗ ∗∗∗ ∗ -0.063 0.145 -0.006 0.009 -0.017 -0.086 -0.001 0.018∗ ∗ ∗∗ 0.093 -0.275∗ 0.357 1.400 0.008 -0.050∗∗ 0.001 -0.008∗∗ 0.043 -0.106 0.009 -0.024∗∗ -0.402 -8.161∗∗∗ 0.013 -0.203 0.104 -0.216 -0.181 0.200 0.544∗∗∗ 0.402 -4.359∗∗∗ -0.888 0.011 0.078 -0.063 p-val.=0.97 p-val.=0.73

(1)

4.2. ECONOMETRIC ANALYSIS 77

78

CHAPTER 4. EMPIRICAL ANALYSIS The percentage of village maize production sold in the market may affect

whether a farmer is commercially oriented through network effects or through its effect on the village market structure. However, this variable should not effect productivity except through its effect on the commercial farmer dummy. Community centers are usually where markets are, hence the time it takes to go there may be correlated with the commercial farmer dummy, but not with productivity directly. Even if there is no market at the community center, this variable can instrument for access to information about marketing opportunities that may be correlated with the commercial farmer dummy. Historical off-farm income and migration variables may be correlated with the commercial farmer dummy if living in a village where many households have off-farm employment and/or temporary migrants to the US affects farmers’ attitudes towards selling their maize or their ability to do so. However, these variables are far enough back in time that they are predetermined and should not affect the current productivity. Table 4.10 shows the results of the tests for the validity of these instruments reported by Stata’s ivreg2 command (Baum et al.). Table 4.10: Tests for the validity of instrumental variables used in the IV-2SLS model (p-values reported) Tests TV MV Underid. test: H0 =Eqn. is underidentified Anderson canonical correlation 0.009 0 Overid. tests: H0 =Overid. restrictions are valid Hansen J Statistic 0.41 0.25 Anderson-Rubin F-test 0.27 0.69 The Anderson Canonical Correlations test strongly rejects the hypothesis that the equation is underidentified.14 Overidentification tests fail to reject the hypothesis that the instruments are valid, i.e., uncorrelated with the error term and correctly excluded from the production function equation.15 Therefore, I conclude that the 14 The Anderson canonical correlations test is a likelihood-ratio test of whether the equation is identified, i.e., that the excluded instruments are “relevant,” meaning correlated with the endogenous regressors. 15 Hansen J statistic tests the joint null hypothesis is that the instruments are valid instruments,

4.2. ECONOMETRIC ANALYSIS

79

instruments are valid. All of the estimated input elasticities are positive as expected. There are some notable differences between the production functions for TVs and MVs. There are significant decreasing returns to scale to land for TVs but not the MVs. Drought, slope and elevation are correlated significantly and negatively with per hectare productivity of MVs, but the correlation is not significant for TVs. This suggests that, holding everything else constant, TVs are more resilient to sub-optimal growing conditions. The estimated coefficients do not differ significantly across specifications. Given Angrist’s suggestions (Angrist, 2000) and the fact that linear probability model provides the best fit regardless of the distribution of the error term, I use the labor elasticities estimated by the 2SLS method (Columns 3 and 4) to calculate the marginal product of labor (MPL).16 The calculated shadow prices for sellers and non-sellers of maize by different varieties re summarized in Table 4.11. Table 4.11: Summary statistics for estimated shadow prices and observed market prices

Variable Shadow price for full sample Shadow price for sellers Shadow price for non-sellers Observed market price/kg.

TV MV 48.34 13.77 20.50 5.19 58.18 25.53 1.98 1.57

As we can see from Table 4.11, estimated shadow prices for TVs are higher than those for MVs, and they are higher for non-sellers for both varieties. We can also observe that the average village level market price is lower than the shadow prices for all groups. The difference between market prices and estimated shadow i.e., uncorrelated with the error term, and that the excluded instruments are correctly excluded from the estimated equation. Under the null, the test statistic is distributed as chi-squared in the number of overidentifying restrictions. Anderson-Rubin statistic is a Wald test that is distributed as chi-squared with L2 degrees of freedom, where L2 is the number of excluded instruments. L 16 The coefficients of the production function are input elasticities given by βˆ = ∂Q ∂L Q . The MPL Q of labor is then calculated by M P L = βˆ as in Jacoby (1993) and Skoufias (1994). L

80

CHAPTER 4. EMPIRICAL ANALYSIS

prices is very big, which essentially stems from the fact that farmers are using too much labor as compared to the optimal level that can be justified by market prices. Very high shadow prices indicate that the marginal value of using one more hour of labor for maize production exceeds the marginal value of leisure (or of other uses of labor) at the optimal point implied by market prices. Therefore, farmer uses labor until its value of marginal product equals the wage rate. It could be argued that because production is uncertain and farmers are risk averse, they apply more labor to production to hedge against down-side risk. If this is the case, we would observe the estimated difference between the shadow prices of TVs and MVs only if TVs were more risky. However, in this case farmers would adjust their portfolio and switch to MVs if TVs were not valued more. Therefore, the high levels of observed labor use can be attributed to higher subjective valuation of landraces by farmers – especially for non-sellers.17 Smale (2005) also argues that labor to land ratios explain where landraces are still grown and will continue to be grown. A high labor to land ratio corresponds to a high shadow price in the current model, confirming this statement. To test whether the estimated shadow prices are statistically significantly different from market prices, I use the method in Jacoby (1993) and Skoufias (1994). I run the following regression for sellers and non-sellers of both TVs and MVs: ρˆ = α + βp + u, to test the null hypothesis of α = 0,

(4.2)

β = 1. Under the null, market prices reflect

the value of marginal product of labor to farmers. Hence we can use market prices to value farmer’s product. Rejection of H0 indicates that market prices do not reflect the subjective value of that crop to farmers and one should use estimated shadow prices 17 We could observe a similar outcome if TVs and MVs had the same riskiness but TV producers were more risk averse. If this was the case, then we should have significant selection bias in Heckman model. However, we have seen that selection is not significant for both maize types. I’ll look into the risk issue in more detail later in Chapter 5 and show that, holding everything else constant, it does not affect shadow prices significantly.

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81

to better understand farmer behaviour. I estimate Equation 4.2 using weighted least squares estimation where the weights are equal to the reciprocal of the square root of the number of maize plots each household has, to give equal representation to each household. I also use village level clusters to control for possible error correlation between the farmers in the same village. Table 4.12 summarizes the results of F-tests and t-tests to test the null hypothesis. Table 4.12: Summary of test results: Are estimated shadow prices equal to observed market prices?

Seller F-test t-tests Non-seller F-test t-tests

MV α ˆ βˆ -1.94 5.22 0.17 0.83 0.44 -15.03 40.10 0.17 0.77 0.41

TV α ˆ βˆ 21.08 0.70 0.00 0.38 0.97 52.95 2.62 0.00 0.06 0.89

For MVs, we fail to reject the null hypothesis of equality of shadow and market prices with both tests regardless of whether the farmer sold maize or not. This may be explained by the fact that MVs lack the non-market values attached to maize landraces. Maize seed that has been bought “in a bag” does not possess the attributes of landraces that have been evolving with farmer selection and are intertwined with their culture. For sellers of TVs, the F-test rejects the joint hypothesis, however, the individual t-tests fail to reject the equality of shadow and market prices. We can conclude that although the average estimated shadow price for sellers of TVs is higher than market prices, this difference is not statistically significant, hence we can use market prices to represent the value of domestic maize to a farmer who is selling it in the market. For non-sellers of TVs, however, both F-test and t-tests reject the hypothesis that the estimated shadow prices are not different from market prices. The estimated

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shadow prices are statistically significantly higher than market prices as indicated by α ˆ that is significantly different from zero at 6% level. Using market prices to understand the cropping decisions of subsistence farmers, therefore, may lead to “puzzling” results where these farmers seem to act “irrationally” by allocating more resources to maize production than can be justified by market prices. Moreover, subsistence farmers are isolated from market price shocks because their decisions are based on shadow prices, and hence may exhibit an inelastic supply response. Given that we concluded that the wedge between farmer-specific shadow prices of TVs and market prices is statistically significant, the next step is to understand which socio-economic and agro-ecological variables are correlated with this wedge. This will provide important policy implications for conservation of the genetic diversity embedded in TVs. Conservation programs can concentrate on the key variables that are correlated with the wedge between market and shadow prices to more efficiently allocate resources to on-farm and off-farm conservation. We can also better understand how different groups of farmers may/may not respond to changes in market prices. I analyze farmer- and farm-specific characteristics that may be correlated with estimated shadow prices in the following section.

4.2.2

What predicts high shadow prices?

Descriptive statistics by region The theoretical model developed in Chapter 3 shows that the shadow price depends on household characteristics (though preferences and endowments), plot characteristics and indicators of market access. Table 4.13 on page 84 summarizes the estimated shadow prices and sample means of some socio-economic variables for the non-sellers of TVs, by region. The South-Southeast region has the highest estimated shadow prices. This region also has the lowest levels of wealth, the highest percentage of indigenous farmers and the youngest farmers as compared to other regions. There seems to be a negative correlation between these variables and the farmers’ subjective

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83

valuation of TVs. Other variables such as education, total land area and animals owned, and whether maize is used as animal feed, do not show a clear relation to shadow prices according unconditional means. Table 4.14 on the following page shows the sample means of variables that are indicators of market access. A larger percentage of farmers purchased maize from a store in the South-Southeast, Central and Western Central regions during the survey year. These regions also have the highest shadow prices. Shadow price is a marginal concept and we would expect that a farmer who produces too much maize will value the additional units of production less and less. This indicates that farmers who could not produce enough TVs for consumption (i.e. have high shadow prices), substitute the purchased maize, an imperfect substitute, to make up for the deficit. In regions with high maize purchases more farmers use maize as animal feed, thus increasing the demand for maize and yellow maize in particular that fattens animals faster as often claimed by farmers.18 Households consume both yellow and white maize, but in general they prefer white. It can be hypothesized that households use own maize for consumption and the purchased imperfect substitutes for their animals. Two other variables that characterize market access, namely the per unit transportation costs of buying maize and the time it takes for the farmer to go to the community center, do not have a clear correlation with shadow prices. Transportation costs are small and cannot justify the high observed shadow prices. Off-farm income is negatively correlated to shadow prices according to simple unconditional means. Most farmers in the Northwest and Northeast regions have some kind of offfarm income and they have the smallest shadow prices for TVs. More farmers in the Southern and Central regions use their own seed, a finding that seems to be positively correlated with shadow prices. It is not surprising that if a farmer is diligent in taking care of his seed, he would attach a high value to his maize that sets own-produced maize apart from purchased maize as indicated by high shadow prices. 18

Based on the informal interviews I conducted with maize farmers in rural Mexico.

age 45.94 49.54 59.00 61.50 54.77 50.04

educ 3.94 3.51 3.82 3.50 4.55 3.83

totown totanim 6.51 6.75 1.70 18.28 9.21 45.09 8.88 0.00 72.81 13.38 11.90 16.64

offarmD walktime ownseed 0.38 45.79 0.69 0.50 27.63 0.75 0.47 35.93 0.36 0.75 60.00 0.25 0.63 59.88 0.40 0.46 39.69 0.63

Table 4.14: Sample means of market access variables by region

ρˆ wqtile indiglang 84.95 1.50 0.72 34.25 2.06 0.26 56.72 2.95 0.02 0.18 4.75 0.00 20.05 2.88 0.00 58.18 2.07 0.38

Region totbuyD buyTCpkg South-Southeast 0.60 0.00 Central 0.59 0.02 Western Cent. 0.36 0.00 Northwest 0.00 0.00 Northeast 0.20 0.01 Total 0.52 0.01

Region South-Southeast Central Western Cent. Northwest Northeast Total

Table 4.13: Sample means of socio-economic variables by region

procampo 0.48 0.48 0.71 1.00 0.85 0.56

maizfeedD 0.72 0.75 0.82 0.00 0.65 0.73

84 CHAPTER 4. EMPIRICAL ANALYSIS

4.2. ECONOMETRIC ANALYSIS

85

Table 4.15: Sample means of agro-ecological variables by region Region South-Southeast Central Western Cent. Northwest Northeast Total

drought soilq 0.28 2.25 0.28 2.41 0.40 2.13 0.25 2.50 0.85 2.05 0.35 2.27

slope irrigD 1.70 0.06 1.64 0.16 1.22 0.07 1.00 0.75 1.45 0.05 1.58 0.10

m1400 0.66 0.82 0.93 0.25 0.95 0.78

Procampo is a direct income support program designed to help farmers to transition into the liberalized maize trade era after NAFTA that brought down maize prices. For liquidity constrained farmers, Procampo payments would relax this constraint, making it easier for them to buy inputs, machinery or invest in other income generating activities. The cultivation of MVs or fruits and vegetables require more inputs and machinery as compared to TVs. We observe that the percentage of farmers that receive Procampo increase while the average shadow price decreases from southern to northern regions. In terms of some agro-ecological variables, regions with more incidence of drought and with more irrigation have lower shadow prices (Table 4.15). The slope of the plot shows a negative correlation with shadow prices, whereas soil quality and elevation do not have a clear correlation. Tables 4.13 to 4.15 may provide some intuition into the relationships between shadow prices and the variables considered. However, these tables provide only unconditional means without controlling for other variables, hence are just descriptive. I analyze how these variables are related to shadow prices in the next section. Decomposing shadow prices I use the difference between shadow and market prices to econometrically analyze the key factors that are correlated with shadow prices, but one issue needs consideration before analyzing the “determinants” of shadow prices. The fact that ρˆ is not observed

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directly but estimated with error introduces an additional source of variance in the standard errors of the estimation where ρˆ is used as a regressand. The test statistics will not be valid unless the standard errors are corrected (Dumont et al., 2005). There are various ways of correcting standard errors in regressions with estimated regressands. One could calculate the correct standard errors as suggested by Feenstra and Hanson (1999), or by Dumont et al. (2005). The former method may result in negative variances in which case no significance tests can be done. The latter method solves this problem by calculating the unconditional variances of the estimated coefficients. Calculation of the unconditional variance, however, can be tedious. A more practical approach to correct the standard errors of sequential estimators is bootstrapping, which permits statistical inference in cases where computation of standard errors is difficult (Cameron and Trivedi, 2005). I use the bootstrapping method here, which provides asymptotically valid standard errors for hypothesis testing. The theoretical model in Chapter 3 indicates that shadow prices of farmers depend on variables that affect farmers production and other variables that are preference shifters in utility function. Using the Equation 3.39 on page 49 we can express the estimating equation for shadow price decomposition as follows: ρˆn = f (Pp , Zn ) + un . P is a vector of plot characteristics that affect production, Z is a vector of preference shifters, and p and n are indices for plots and farmers respectively. These vectors also include some market access variables that may affect production practices or preferences. I use the variables from previous studies that are shown to affect farmers’ crop choice decisions and their valuation of traditional crops (Bellon and Smale, 1998; Van Dusen, 2000; Meng, 1997; Brush and Meng, 1998; Smale, 2006). These variables are: wealth, gender, age, education, land size, animals owned, the share of maize area, migration, off-farm income, credit access, time to community center, government

4.2. ECONOMETRIC ANALYSIS

87

transfers, soil quality, slope, altitude, irrigation and regional controls. All of these variables have different correlations in different settings as reviewed in Chapter 2. One other variable often discussed in the literature that is correlated with cultivating traditional crops is indigenous identity. However, this variable is usually discussed in qualitative or descriptive studies and not used in econometric analyses (Brush and Perales, 2007; Perales et al., 2005; Preibisch et al., 2002). It is often mentioned that indigenous farmers attach various non-market values to maize (especially traditional varieties) and that’s why they continue cultivating it despite disincentives based on market prices. I include indigenous identity dummy as a preference shifter and test the following hypothesis implied by previous studies: ∂ ρˆ > 0, I = 1 if farmer speaks an indigenous language ∂I Regression results are given in Table 4.16 on the following page, where standard errors are clustered by household and village to control for possible error correlation across different plots of a household, and across households in the same village. I use three different specifications: Column (1) uses only socio-economic variables that shape farmers’ preferences, Column (2) includes variables related to farmers’ market access in addition to socio-economic variables, and Column (3) includes an interaction variable between indigenous language dummy and South-Southeast region. This interaction variable controls for the fact that most of the indigenous farmers live in this region and the indigenous dummy may have a different effect there. As discussed in Chapter 2, previous empirical studies find that wealth, household head’s education and household size are positively correlated with on farm diversity (cultivation of landraces) (Smale, 2006). Bellon and Taylor (1993) find that household wealth and the household head’s age are negatively correlated with maize landrace cultivation. However, holding everything else constant, these variables are not significantly correlated with farmer-specific shadow prices of maize landraces in the current sample. In all three specifications, male farmers value TVs higher than

88

CHAPTER 4. EMPIRICAL ANALYSIS

Table 4.16: Dep.var: (ˆ ρ − p) using ρˆ from IV-2SLS model (significance tests based on bootstrapped standard errors). (ˆ ρ − p) (1) indigR1 irrigD soilq walktime othersoffD otherscredit slope m1400 indiglang 25.76∗ gender 35.47∗∗ windex -2.99 age -0.26 educ -1.48 totown -0.05 maizareash 23.76 Bracero -16.11 South-Southeast 41.98 Central -1.46 Western Cent. 44.81 Northwest 18.72 Constant -10.80 AIC 3793 Significance levels :

∗ : 10%

(2) -39.77∗∗∗ -33.52∗∗ 0.34∗ 35.91 -18.99 -4.42 -22.06 26.57∗ 35.73∗∗ -2.83 -0.17 -1.10 -0.09 17.53 -17.62 50.33 15.73 51.89∗ 71.81 -13.66 3787 ∗∗ : 5%

∗ ∗ ∗ : 1%

(3) 77.20∗∗∗ -33.05∗∗ -33.05∗∗ 0.27 31.57 -22.01 -9.73 -24.72 -7.24 28.37∗∗ -2.91 -0.19 -0.75 -0.08 11.41 -20.14 16.66 23.23 50.45∗ 51.68 6.46 3780

4.2. ECONOMETRIC ANALYSIS

89

females. This suggests that among the non-market values, the value of being a good farmer and preserving the family seed may be more important than the consumption characteristics (e.g. culinary superiority) women tend to care more about. In addition to wealth, two other variables related to farmers’ endowments are total area and number of animals owned. Both of these variables have no significant correlation with shadow prices. The percentage of total land area that is cultivated with TVs may indicate preferences towards TVs and hence high shadow prices. Controlling for other variables, however, maize area share is not correlated with shadow prices. It has been argued that migration to US is a detriment to on farm conservation of maize landraces in Mexico (Nadal, 2000; Turrent and Serratos-Hernandez, 2004). The bracero variable identifies households that have at least one member who participated in the Bracero Program in the past. If migration affects households’ preferences by shifting preferences towards market goods, we might expect that households with migration histories will have a lower valuation for TVs. Although the bracero variable has a negative coefficient, it is not significant in any of the specifications. Another variable often found to affect a farmer’s likelihood of cultivating landraces is belonging to an indigenous group (Turrent and Serratos-Hernandez, 2004; Perales et al., 2005; Brush and Perales, 2007). The coefficient on the indigenous language dummy is significant and positive in the first two specifications. This indicates that non-market values of TVs captured in shadow prices are higher for indigenous farmers, which underlines their role as stewards of genetic diversity. Given that 78% of indigenous farmers in the current sample (i.e. non-sellers of TVs) are in the SouthSoutheast region, we may wonder whether the coefficient of the indigenous language dummy is picking up the effect of the South-Southeast regional dummy. To test whether being indigenous has a different effect in this region, I include an interaction variable between indigenous language dummy and South-Southeast region to the regression in column 3. The coefficient of this interaction term is positive, large and significant, and the indigenous language dummy loses its significance after its inclu-

90

CHAPTER 4. EMPIRICAL ANALYSIS

sion. This suggests that, controlling for other variables, being indigenous does not have an effect on shadow prices in other regions. However, it has a very strong and significant effect on farmers’ valuation of maize landraces in South-Southeast region. Four variables represent market access: the percentage of farmers in the village that have-off farm income, the percentage of farmers in the village that have some kind of credit, the time it takes for the farmer to go to the community center and a dummy variable indicating whether the farmer receives any government transfers.19 Government transfers could potentially alleviate the effect of credit market imperfections by relaxing farmers’ liquidity constraint. Neither this variable nor the credit market variable are significantly correlated to shadow prices. The results indicate that farmer valuation of TVs does not decrease with improved access to off-farm labor, credit and other markets, which restores hope for de facto conservation of maize landraces. Previous studies mostly find that the transaction cost of going to the nearest market is negatively correlated with on-farm diversity (Bellon and Taylor, 1993; Meng, 1997; Van Dusen, 2000; Smale et al., 1994). Time it takes for the farmer to go from his/her plot to the community center is a proxy for transaction costs. This variable is significantly correlated to shadow prices only in one specification (column 2). However its significance disappears when we include the interaction term (column 3). This indicates that indigenous farmers in the South-Southeast region farm in more isolated places. Therefore, controlling for this group of farmers makes the time to community center variable insignificant. For the rest of the farmers, the shadow price is independent of how far away from community center their plots are. ENHRUM data includes farmer-reported costs of transportation that they incurred to buy and/or sell maize in the market. The average transportation costs per kilo paid by farmers in the sample are negligible (0.01 Mexican pesos per kilo of maize) and cannot justify the high shadow prices observed. This confirms the theoretical point that if 19 The first two variables exclude the farmer himself/herself to remove potential endogeneity of these variables.

4.2. ECONOMETRIC ANALYSIS

91

some farmers have different preferences toward domestic maize and market purchased maize, they may make decisions based on shadow prices rather than market prices even if observable TCs do not constrain them.20 Soil quality, slope, irrigation and altitude are agro-ecological variables that affect growing conditions and productivity of both TVs and MVs. Bellon and Taylor (1993) find that cultivation of TVs is negatively correlated to high soil quality. I find that soil quality is negatively and significantly correlated with farmers’ subjective valuation of TVs, confirming the findings in Bellon and Taylor (1993). Similarly, irrigation is negatively and significantly correlated with shadow prices, indicating that farmers who farm under relatively worse growing conditions value TVs more. Perales et al. (2003) find that altitude is positively correlated with the cultivation of maize landraces in Mexico. Even if it is not significant in the current model, this does not necessarily contradict Perales et al. (2003). Altitude may make a farmer more likely to cultivate TVs, but given that a subsistence farmer is already cultivating them, his subjective valuation (i.e. incentives to cultivate TVs) does not depend on altitude. In summary, four variables are significantly correlated with farmer-specific shadow prices of TVs that are over and above observed market prices. Farmers who have plots with good soil quality and irrigation have lower shadow prices, whereas male farmers have higher shadow prices. The most important indicator of having a high shadow price is being an indigenous farmer in the South-Southeast region. Controlling for other farmer and farm variables, indigenous identity increases the demand for TVs causing higher de facto incentives for their continued cultivation. These results have important policy implications. Programs for on-farm conservation of genetic diversity of maize in Mexico will be more cost effective if targeted at communities with indigenous populations where de facto conservation is more likely. These areas represent least-cost conservation opportunities as defined by Bellon and 20

I discuss the transaction costs in more detail in Chapter 5.

92

CHAPTER 4. EMPIRICAL ANALYSIS

Smale (1998), where both the public value of diversity and the private incentives to conserve them are high. These results agree with previous research that emphasizes the link between traditional agroecosystems and on-farm conservation of traditional crop varieties (Louette et al., 1997; Peterson, 2000; Altieri, 2004). However, proposing to maintain the traditional agroecosystems as they are to ensure on-farm conservation is not feasible because there are gains to be made by promoting rural development. Rural development policies in areas where indigenous identity is strong could be accompanied with programs to raise awareness such as diversity fairs to strengthen the incentives to maintain traditional varieties. More resources and creative policy may be needed to maintain TVs on-farm in regions where the shadow prices are low but public benefits of conservation high, namely; where the indigenous identity is not strong, irrigation projects are being developed or programs to improve soil quality exist. The potential negative effects of such projects on traditional maize cultivation in areas of diversity can be counteracted with additional programs to increase farmers’ incentives to maintain traditional varieties, such as conservation payments, or programs to create niche markets to increase the market value of traditional maize varieties. These policies may also improve farmers incentives in areas where de facto incentives to maintain TVs are low (e.g areas with high soil quality, irrigation and non-indigenous farmers). However, a more effective way of allocating conservation budgets in such low-incentive areas may be prioritizing off-farm conservation rather than on-farm conservation. Most previous research finds a positive correlation between on farm diversity of landraces and household wealth (Smale, 2006). These findings suggest that conservation policies should target wealthier households to have better results. However, there is no correlation between households’ wealth and their shadow prices for TVs in the current analysis. Given that there is no tradeoff between wealth and shadow prices of TVs in rural Mexico, conservation policies should not be targeted based on wealth but should consider the non-market values of TVs for indigenous peoples in

4.2. ECONOMETRIC ANALYSIS

93

marginal growing environments. This finding does not necessarily contradict findings of previous studies. It can be the case that, controlling for other variables – especially indigenous identity – wealth does not affect the subjective valuation of landraces, but the number of varieties cultivated may be correlated with wealth given that a household already cultivates landraces. Ideally one should calculate shadow prices for each variety to better understand the non-market values attached to each variety. However, the ENHRUM data set does not allow this because the production data is not differentiated between varieties. Future studies should combine shadow prices for each variety and diversity indices to better understand which varieties are most likely to be maintained and how shadow prices relate to diversity.

4.2.3

Do shadow prices explain land allocation better than market prices?

Farmers’ land allocation decisions have long been a subject of economics. It has been studied in the concept of technology adoption, especially after the introduction of high yielding crop varieties with the Green Revolution (Feder, 1980; Just and Zilberman, 1983; Bellon and Taylor, 1993; Brush et al., 1992; Smale et al., 1994). These studies use market prices to value farmers’ output as a determinant of land allocation decision, along with socio-economic and agro-ecological variables. Smale et al. (1994) show that multiple explanations, such as input fixity, safety first behaviour, learning and portfolio selection, together determine farmers’ land allocation into HYV’s, where they value output at market prices. If, however, the land allocation decision is based on shadow prices that are different from market prices for some farmers, we may underestimate the land such farmers will allocate to TVs. In this section, I test whether we can improve land allocation models by using shadow prices instead of market prices for subsistence farmers. As discussed in Chapter 3, the percentage of land allocated to TVs depends

94

CHAPTER 4. EMPIRICAL ANALYSIS

Table 4.17: Area share of TVs, weighted average shadow prices and market prices by region Regions South-Southeast Central Western Cent. Northwest Northeast Total

TVshare 0.70 0.76 0.52 0.11 0.68 0.67

wtavrhoTV 71.64 28.68 47.17 0.18 21.39 50.17

sellprice 2.24 1.74 1.52 1.92 1.32 1.87

on shadow prices (representing farmers preferences), total land size and other production variables. We have already shown that the shadow prices of TVs are significantly higher than market prices for subsistence maize farmers in the ENHRUM data. Table 4.17 shows that farmers in the South-Southeast region allocate the largest proportion of land to TVs and have the highest estimated shadow prices. Based on these estimates, we can expect that subsistence farmers’ land allocation decisions will be based on shadow prices. I analyze land allocation using both market prices and estimated shadow prices to test this hypothesis.21 Two econometric issues arise when analyzing TVs’ area share. First, shadow prices are endogenous and will cause bias in area share regressions if not properly instrumented for. Second, area share regression includes farmers who grew no TVs at all, which may cause selection bias if there is an unobserved variable that is correlated with both selection into growing TVs and the area share. I use both the Heckman selection method and the tobit method to account for the censored nature of the area share data. For both methods, I use the predicted values of shadow prices that are obtained from a regression that uses the variables that are identified to affect shadow prices in the previous section as instruments. Table 4.18 on page 96 reports 3 specifications of both Heckman selection model and tobit model. The first specification uses only market prices, the second uses only shadow prices (instrumented) and the third 21 The analysis of area share is done at the household level. I use the area weighted averages for shadow prices, soil quality and slope variables for this analysis.

4.2. ECONOMETRIC ANALYSIS

95

uses both to explain the area share of TVs for non-seller households, i.e. the group for which we have shown that shadow prices are statistically significantly different from and higher than market prices. I use the following explanatory variables in the area share regressions: the market price or shadow prices of TVs depending on specification, total area owned by the farmer, total number of adults (ages 15-60) in the household representing household labor availability, a dummy variable indicating whether the farmer uses saved seed or not, area weighted soil quality and slope, a dummy variable indicating whether the farmer has access to irrigation, proportion of farmers that have off-farm income and credit in the same village (both excluding the farmer himself), farmer’s age, education and regional dummy variables. Shadow prices represent the effect of farmers’ preferences on area share of TVs. All other variables that affect land allocation are related to production as identified in the theoretical model ( 3.40 on page 50). A Box-Cox regression model shows that the area share model for non-sellers has a better fit if we transform the shadow prices using a logarithmic transformation. However, the model with market prices has a better fit without any transformation. Therefore, I use the log of the instrumented shadow prices and non-transformed market prices in Table 4.18. The first step in the Heckman model estimates the probability that a farmer will cultivate TVs. The variables that are significantly correlated to shadow prices identified in the previous section will affect the probability of cultivating TVs. I use the variables that are related to farmers’ preferences (indigenous identity, gender) as identifying instruments. These variables should not affect the area share of TVs except through their affect on shadow prices. The specification in column (1) ignores the shadow prices both in selection and the outcome equations and just uses market prices. We can see that even though market prices are barely significant in predicting the probability of cultivating TVs, they

96

CHAPTER 4. EMPIRICAL ANALYSIS

Table 4.18: Heckman and Tobit models for area share of TVs for non-sellers TVshare mktprice lnrhohat totown adults oldseedD wtsoilq wtslope irrigD othersoffD otherscredit age educ South-Southea. Central Western Cent. Northwest Intercept mktprice rhohat gender indiglang indigR1 wtsoilq irrigD walktime South-Southea. Central Western Cent. Northwest Intercept N IMR p-Wald test AIC Significance levels :

mkt.pr. (1) 0.029 -0.001 -0.019∗∗ -0.001 -0.059∗ -0.076∗∗ 0.023 0.115 -0.089 -0.004∗∗ -0.012∗∗ -0.122 -0.073 -0.240∗∗∗ -0.384∗ 1.335∗∗∗

Heckman ln(rhohat) (2) 0.042∗ -0.001 -0.021∗∗ 0.034 -0.04 -0.065∗ 0.095 0.057 -0.045 -0.004∗∗∗ -0.015∗∗ -0.237∗ -0.163∗∗ -0.339∗∗∗ -0.469∗∗∗ 1.306∗∗∗ p(TVshare>0)

both (3) 0.047 0.035∗∗ -0.001 -0.020∗∗ 0.028 -0.038 -0.073∗ 0.098 0.038 -0.073 -0.004∗∗∗ -0.017∗∗∗ -0.256∗∗ -0.170∗∗ -0.325∗∗∗ -0.523∗∗∗ 1.282∗∗∗

mkt.pr. (4) 0.188∗

Tobit ln(rhohat) (5)

-0.002 -0.036 0.102 0.005 -0.08 -0.059 0.177 -0.303 -0.008∗ -0.045∗∗ -0.315 -0.055 -0.285 -1.258∗∗ 1.703∗∗∗

0.219∗∗∗ -0.003∗ -0.044 0.044 0.022 -0.143 0.068 0.349 -0.246 -0.007 -0.041∗∗ -0.634∗∗∗ -0.346 -0.858∗∗∗ -0.947∗ 1.594∗∗∗

both (6) 0.063 0.212∗∗∗ -0.003∗ -0.045 0.038 0.026 -0.154 0.074 0.316 -0.269 -0.007∗ -0.042∗∗ -0.672∗∗∗ -0.354 -0.847∗∗∗ -1.028∗∗ 1.564∗∗∗

280 n.a. n.a. 534.57

280 n.a. n.a. 511.22

280 n.a. n.a. 512.779

0.524∗ 0.223

0.316 -0.492 0.004∗ 0.032 0.583∗∗ 0.681∗ -1.120∗∗ -0.844 280 0.097∗∗ 0.01 287.744 ∗ : 10%

0.504∗∗∗ -0.098 -0.800∗∗∗ 1.649∗∗∗ 0.304 -1.239∗∗∗ 0.016∗∗∗ -0.453 1.055∗∗∗ -1.181∗∗∗ 0.33 -1.989∗∗∗ 280 0.298∗∗ 0.00 175.425 ∗∗ : 5%

0.490∗∗∗ -0.149 -0.749∗∗ 1.850∗∗∗ 0.317 -1.183∗∗∗ 0.016∗∗∗ -0.603 0.947∗ -1.027∗∗∗ 0.022 -1.914∗∗∗ 280 0.297∗∗ 0.00 175.094 ∗ ∗ ∗ : 1%

4.2. ECONOMETRIC ANALYSIS

97

are not significantly correlated with the area share of TVs for these farmers. Column (2) uses instrumented shadow prices for both selection and outcome equations. The selection stage also controls for the indigenous language dummy which is shown to be strongly correlated to shadow prices. The coefficient of the indigenous language dummy is negative and significant in the selection equation. This indicates that controlling for shadow prices, indigenous farmers are less likely to cultivate TVs. The interaction variable between indigenous language dummy and the South-Southeast region is significantly positive and very large in magnitude, indicating that indigenous farmers in this region are more likely to cultivate TVs. We can see that shadow prices are very significant in predicting selection into TV cultivation and that they are significantly correlated to the area share of TVs, given selection. Total land area owned is not significantly correlated to the area share of TVs after controlling for other variables. The number of working age adults, the area weighted slope, farmer’s age and education all are negatively correlated to area shares. Farmers in all regions have smaller proportion of their land under TVs compared to the default Northeast region. Column (3) includes both market prices and shadow prices. We can see that controlling for shadow prices market prices are not significant in determining the area share of TVs. The Akaike Information Criteria shows that the specifications in columns (2) and (3) give almost exactly the same fit indicating that market prices do not add anything to the likelihood function for non-sellers.22 I also estimate the area share equations using a tobit model that controls for the censoring in the dependent variable both from above and below (Columns 4-6 in Table 4.18). Tobit model gives very similar results to the Heckman model confirming the robustness of the specifications. Although the market price variable is significant at the ten percent level in column (4), the specification in column (5) that uses shadow 22 Akaike Information Criteria (AIC) is used to select between several competing models. The model with the minimum AIC is chosen. AIC = (-2)Log(maximum likelihood) + 2(number of independently adjusted parameters within the model) (Akaike, 1974).

98

CHAPTER 4. EMPIRICAL ANALYSIS

prices provides the best fit according to the AIC. This indicates that for non-sellers the estimated shadow prices perform better than market prices in explaining the proportion of land allocated to TVs. Total land area owned by the farmer is positively correlated to the area share of TVs in tobit models with shadow prices. However, the coefficient of the land size variable is very small. Although farmers with bigger landholdings allocate more land to TVs, they do not necessarily allocate a larger proportion of their land to these maize types. Brush et al. (1992) have a similar finding about the area share of improved potato varieties in the Peruvian Andes. The only variables that are significantly correlated to the area share of TVs in the tobit model (besides regional dummies) are farmers’ age and education. Area share decreases with both of these variables.23 The variables that indicate market access, namely the percentage of farmers that have off-farm income and credit in the same village, are not significantly correlated to area share of TVs. This is similar to the result in Bellon and Taylor (1993). This section shows that by using shadow prices rather than market prices, we can better understand land allocation decisions of subsistence farmers who cultivate crops that have non-market values. In the case of maize in Mexico, shadow prices capture various non-market values subsistence farmers attach to traditional maize hence their real incentives to cultivate them. Accounting for these incentives also takes the “surprise” out of farmers’ non-response to decreasing market prices following NAFTA. The non-market values of maize were one of the oft-mentioned underlying reasons for why farmers did not respond to price signals as expected (de Janvry et al., 1995; Dyer Leal and Yunez Naude, 2003; Berthaud and Gepts, 2004). This exercise confirms this reason by formally comparing shadow prices and market prices in explaining land allocation.

23 Farm fragmentation index, when added to these specifications, is also negatively and significantly correlated with area share of TVs.

4.3. POLICY IMPLICATIONS AND CONCLUSIONS

4.3

99

Policy Implications and Conclusions

We have seen that traditional maize farmers in rural Mexico allocate more resources to the production of TVs than what market prices would justify. Especially farmers that do not sell their maize in the market have shadow prices that are significantly different from and higher than market prices. This finding indicates that the nonmarket values of TVs give most subsistence farmers incentives to maintain maize landraces even when market prices decline. However, as expected, estimated shadow prices of MVs are not different from market prices, because MVs do have perfect substitutes that can be purchased in the market. The decomposition of shadow prices has policy implications for the conservation of CGD of maize landraces in Mexico. Indigenous farmers have long been acknowledged as the stewards of on-farm genetic diversity, and this claim is confirmed by the high statistical significance of indigenous identity in determining which farmers have high shadow prices. Especially, indigenous farmers in the South-Southeast region of Mexico represent “promising candidates” for on-farm conservation programs as defined bySmale (2005). Better access to markets, education and wealth have no significant effect on shadow prices, suggesting that rural development programs can achieve these goals without hindering incentives for on-farm conservation of TVs in rural Mexico in general, and predominantly indigenous communities in particular. The current model does not explicitly incorporate some market conditions that may have an effect on determining shadow prices. In the next chapter, I consider such conditions as the potentially missing labor markets, risk and credit constraints and a bad year for maize production in the sample area, that may have contributed to the results obtained in this chapter. I discuss these conditions in detail and rule out their potential effects on empirical results using various methods in the next chapter.

100

CHAPTER 4. EMPIRICAL ANALYSIS

Chapter 5 De-bugging the Empirical Results The basic model described in Chapter 3 assumes perfect labor markets by using market wages to represent the value of farmer’s time. It also implicitly assumes perfect credit markets and no risk. These conditions interact with farmers’ production decisions, and thus with the shadow prices as derived and estimated. I now discuss how violations of these assumptions may affect farmer behaviour and the results obtained thus far. The following is a list of conditions that may have affected the shadow prices in the empirical analysis:

1. Labor market imperfection.

2. Liquidity (credit) and risk constraints.

3. The possibility that 2002 was a bad crop year for maize so that supply decreased a lot increasing the shadow prices.

4. Significant transaction costs or missing seed markets.

I discuss these conditions in detail in what follows. 101

102

CHAPTER 5. DE-BUGGING THE EMPIRICAL RESULTS

5.1

Missing Labor Markets and Shadow Prices

Off-farm labor markets may fail in isolated rural areas due to the lack of industrial enterprizes or transaction (monitoring) costs, and on-farm labor markets may fail during the harvest time when the demand for labor is high, due to out-migration of farm workers or imperfect substitutability between family labor and hired labor (unobserved characteristics of hired labor). Market wages may not reflect the true value of time under such market imperfections. I introduce a missing labor market to the basic model and analyze how it affects the results derived in Chapter 3.

5.1.1

Adding missing labor markets to the theoretical model

The market wage does not represent the proper value of the farmer’s time if he does not, or is not able to, hire in or hire out labor at that wage, or if hired labor is an imperfect substitute for household labor. This is the main motivation for previous research on labor market imperfections that explains the labor supply of agricultural households using estimated shadow wages (Jacoby, 1993; Skoufias, 1994; Barrett et al., 2005). Although these analyses improve our understanding of farmers’ labor supply decisions, they assume perfect markets for farm output and take the market prices as given. As discussed in previous chapters, market prices do not reflect the true value of farm product to subsistence farmers if they are constrained by a (partially) missing market. We have also seen that, if there are non-market values of domestic crops (that make the purchased crops an imperfect substitute for domestic crops), we may observe subsistence farming more often than what the traditional TC models would suggest. I relax the perfect output markets assumption used in previous research and build an agricultural household model with missing markets for both the farmer’s subsistence crop and labor.1 Thus, the farmer modeled in Chapter 3 now does not 1

The missing market for the subsistence crop is as defined in Chapter 3.

5.1. MISSING LABOR MARKETS AND SHADOW PRICES

103

have a choice of hiring labor in or out. There was only one variable input (i.e. labor) in the basic model for the sake of simplicity. I introduce a purchased input (I) to the model, to make clearer the interpretation of the effects of the missing labor market on resource allocation – hence shadow prices. The farmer’s problem is now given by:

max

Xl ,Xm ,Xsh ,Xss ,θ,Fi ,Ii

U (Xsh , Xm , Xl ; Z) s.t.

pm (1 + tb )Xm + pI (Is + Ic ) ≤ ps (1 − ts )Xss + pc Qc + W

(5.1)

Qs = g(Ls , Is , Aθ)

(5.2)

Qc = h(Lc , Ic , A(1 − θ))

(5.3)

Xl + Fs + Fc = T¯

(5.4)

Xsh ≤ Qs − Xss

(5.5)

Xss ≥ 0

(5.6)

Xsh ≥ 0

(5.7)

Xm ≥ 0

(5.8)

0≤ θ

(5.9)

≤1

where pI denotes the price of the purchased input, and Is and Ic denote the amount of purchased input used for the subsistence crop and the cash crop, respectively. All remaining variables are as defined in Chapter 3. Note the differences between this model and the previous one: no hired labor is used in production, and there is no off-farm income. The Lagrangean for this problem is: max

Xm ,Xsh ,Xss ,θ,Fi ,Ii ,λ,µn

L = U (Xsh , Xm , T¯ − Fs − Fc ; Z)

+λ[ps (1 − ts )Xss + pc h(Fc , Ic , A(1 − θ)) + W − pm (1 + tb )Xm − pI (Is + Ic )] +µ1 [g(Fs , Is , Aθ)−Xss −Xsh ]+µ2 Xss +µ3 Xsh +µ4 Xm +µ5 θ+µ6 (1−θ)+µ7 Ls +µ8 Is +µ9 Lc +µ10 Ic

104

CHAPTER 5. DE-BUGGING THE EMPIRICAL RESULTS i = s, c, n = 1, ..., 10 The interpretation of the KKT conditions for Xss , θ, Fc and Ic are similar to the

model in Chapter 3. To analyze the effects of missing labor markets on the shadow prices, I only focus on subsistence farmers who cultivate some of both crops (i.e. Xss = 0 and 0 < θ < 1) in this section. The FOCs are: F OCXm : M Um = λpm (1 + tb ) − µ4

(5.10)

F OCXsh : M Ush = µ1 − µ3

(5.11)

F OCXss : λps (1 − ts ) = µ1 − µ2

(5.12)

F OCFs : M Ul = µ1 M P Fs

(5.13)

F OCFc : M Ul = λpc M P Fc

(5.14)

F OCIs : µ1 M P Is = λpI

(5.15)

F OCIc : pc M P Ic = pI

(5.16)

Equations 5.13 to 5.16 imply

M P Fi M P Ii

=

M Ul λpI

not missing, this relation would be

M P Fi M P Ii

=

w . pI

for i = s, c. If the labor market was Therefore, we can define

M Ul λ

as the

“shadow wage” using the same logic as we did in deriving the shadow price of Qs in Section 3.1. The Equation 5.14 indicates that the farmer is setting the marginal cost of leisure, equal to the marginal benefit of working one more hour on his farm, i.e. shadow wage.2 The estimable expression for the shadow wage is: ω = p c M P Fc , M P Fs , ω = pI M P Is

for farmers who produce and sell cash crop,

(5.17)

for farmers who do not produce or sell cash crop.

(5.18)

This interpretation is clearer if we rewrite the Equation 5.14 as MλUl = pc M P Fc . The left hand side is the monetized value of marginal utility of labor, and the right hand side is the marginal value product of labor. 2

5.1. MISSING LABOR MARKETS AND SHADOW PRICES

105

Equation 5.17 is similar to its counterpart in Jacoby (1993) and Skoufias (1994) (i.e. ω = pi M P Fi ), but can only be used for crops whose subjective value can be measured by market prices.3 The same expression for subsistence farmers (Equation 5.18), is different because there is no exogenous market price for Xsh in the current model. Therefore, we cannot simply estimate the value of the marginal product of labor using market prices and equate it to shadow wages for subsistence farmers. We can derive the shadow price of the subsistence crop under missing labor markets using the same method as in Chapter 4: ρ≡

µ1 ω pI = = λ M P Fi M P Ii

(5.19)

Although we can no longer rely on market wages to estimate shadow prices, we can still calculate ρ by using the estimated marginal product of purchased input (M P Ii ). However, M P Ii will be different from the value it would take if the labor market was perfect, because a missing labor market leads a farmer to adjust his labor allocation to farm production. Total labor used for farm production may increase or decrease when we take out the labor market, depending on whether the household would be hiring labor in or out if the market were perfect. To better understand the effects of missing labor markets on farmer’s labor allocation and the shadow price of Qs , consider Figure 5.1 on the following page. The first panel in Figure 5.1 represents a household that would hire out labor if the labor market is perfect, because the market wage (w1 ) is higher than the shadow wage (ω) determined where the value of his marginal product of labor (V M P L) is equal to the marginal utility (M U ) of leisure. The household in the second panel would hire in labor if it could, since the market wage (w2 ) is less than ω. With a perfect labor market for both cases, farmer will work on-farm until the V M P L and the M U of leisure equal the market wage. Hence the market wage represents the 3 Jacoby (1993) and Skoufias (1994) assume that there is no market constraint for any of the farmer’s crops and use market prices to value all output.

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CHAPTER 5. DE-BUGGING THE EMPIRICAL RESULTS

VMPL

MU (Leisure)

MU of Leisure

VMPL= p *MPL

w1

0

L

HO L'

Leisure Leisure '

VMPL

T

MU (Leisure)

MU of Leisure

VMPL= p *MPL

w2 HI

0

F L' = F '

L

Leisure

T

Leisure '

Figure 5.1: Optimal labor allocation with and without labor markets when output markets are perfect. T is total hours of labor used by the household, V M P L is the value of marginal product of labor, w is market wage, ω is shadow wage, L is the labor hours used in production, F is family labor used in farm production, and HO and HI are, respectively, the labor hours hired out and hired in.

5.1. MISSING LABOR MARKETS AND SHADOW PRICES Missing(Imperfect) market None Product market Product&Labor markets If HO > 0 under perfect labor: If HI > 0 under perfect labor:

Shadow price of Qs ρ = ps ρ0 > ps

Proportion of land allocated to Qs θ∗ θ0 > θ∗

ρ1 < ρ0 ρ2 > ρ0

θ0 > θ1 > θ∗ θ2 > θ0 > θ∗

107

Table 5.1: Subsistence farmer’s optimal land allocation under different scenarios for labor and product markets. θ∗ denotes the amount of land cultivated with Qs under perfect markets, θ1 and θ2 denote, respectively, the amount of land cultivated with Qs when only product markets are missing and when both product and labor markets are missing. true value of farmer’s time, and the shadow price of Qs is given by Equation 3.39, i.e. ρ=

w . MP F

With a missing labor market, however, he will equate the V M P L to the monetized value of M U of leisure, which determines his shadow wage. Depending on how shadow wage compares with the market wage, the total amount of labor used in farm production changes in different ways. In the first panel, total labor used for farm production increases since the labor that was hired out is now trapped inside the household (L0 > L). In the second panel, total farm labor decreases since the household cannot hire in labor anymore (L0 < L). These changes in the labor use have implications on the derived shadow prices of and the land allocation to the subsistence crop when both labor and product markets are missing for the farmer. Table 5.1 summarizes the shadow prices and optimal land allocations under different market scenarios, and Figure 5.2 shows the land allocation under each scenario graphically.

As we can see from Figure 5.2, if the labor market is also missing in

addition to the product market, the farmer will adjust his labor allocation depending on the scarcity of family labor as described above. Assuming purchased inputs and labor are complements in maize production (Denbaly and Vroomen, 1993), and holding pI constant, more labor will increase the marginal product of purchased input, causing the shadow price without labor markets to be smaller than it would be with perfect labor markets (ρ1 < ρ0 ). In this case the proportion of land allocated to the

108

CHAPTER 5. DE-BUGGING THE EMPIRICAL RESULTS VMPA s

VMPA c




VMPA s = *MPA s

VMPA c = p c *MPA c

VMPA s = p s *MPA s


2)

(


0)

(


1)

(

0

*

1

0

2

A=1

Figure 5.2: Optimal land allocation using market prices vs. shadow prices for subsistence crop. θ∗ is the proportion of land that would be allocated to Qs using the market price (ps ), θ0 , θ1 and θ2 are respectively the proportion of land allocated to Qs using the shadow prices ρ0 , ρ1 and ρ2 that correspond to different scenarios considered in Table 5.1.

subsistence crop is smaller than it would be under the assumption of perfect labor markets (θ1 < θ0 ). On the other hand, if the farmer is using less labor due to missing labor markets, the marginal product of purchased input will decrease and the shadow price will be larger than it would be under perfect labor markets (ρ2 > ρ0 ). Consequently, a larger proportion of land is allocated to the subsistence crop than it would be under perfect labor markets (θ2 > θ0 ). The previous discussion demonstrates that ignoring the possibility of missing labor markets in empirical analysis may result biased estimates for the shadow price of the subsistence crop and the farmer’s land allocation. This conclusion holds for all subsistence farmers regardless of the reason for the missing output market. Even if the reason is a TC band that traps the farmer in autarky, as in de Janvry et al. (1991) (where domestic and market goods are perfect substitutes of each other), one needs to consider whether the labor market is also missing. As discussed in Chapter 3, however, the TC band may be wider for some farmers if the domestic and market

5.1. MISSING LABOR MARKETS AND SHADOW PRICES

109

goods are imperfect substitutes, increasing the prevalence of subsistence farming and the importance of correctly accounting for shadow prices. To avoid bias in estimated shadow prices for subsistence farmers, one should test for missing labor markets by using farmers’ observed labor allocation and market wage rate as in Jacoby (1993) and Skoufias (1994).4 This analysis can be extended to the allocation of other resources such as purchased inputs or labor, that ultimately depend on correct valuation of farmer’s time and output as well.

5.1.2

Is the labor market imperfect?

If the labor market is imperfect for farmers in ENHRUM data, we may have under- or overestimated the shadow prices of domestic maize depending on whether the farmer would be hiring labor in or out, respectively, if perfect labor markets existed (see Table 5.1 on page 107). We need to test for imperfections in the labor market to ensure that the high shadow prices estimated are the result of imperfect substitutability between market and domestic maize and represent subsistence farmers’ incentives to cultivate TVs. As discussed in Section 5.1, if the family labor and hired labor are imperfect substitutes (e.g. due to information asymmetries), we need to treat them as separate inputs in the production function (Jacoby, 1993; Skoufias, 1994). In this case, it will also have implications for the estimation of shadow prices for domestic crop since we cannot use the market wage as given and need to use another traded input to estimate shadow prices (see Equation 4.1). I use the method in Jacoby (1993) and Skoufias (1994) to test whether the value of marginal product of family labor is equal to market wage for local agricultural workers (i.e. whether the agricultural household model is separable or not). I estimate production functions for both TVs and MVs to derive the value of marginal product 4 This test is done by estimating the marginal value product of labor and testing whether it is equal to market wage by running the following regression: V MˆP L = γ + θw + u. The rejection of H0 : γ = 0, θ = 1 indicates that market wage does not reflect the true value of household labor and shadow wages should be used to value time instead of market wages.

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CHAPTER 5. DE-BUGGING THE EMPIRICAL RESULTS

of family labor. Table 5.2 shows production functions that treat family labor and hired labor as different inputs and are estimated using the 2SLS-IV procedure to account for endogenous commercial farmer dummy (sold30) as in Section 4.2.1. Table 5.2: Production functions for TVs and MVs to test labor market imperfections

ln(yield/ha) TV lnland -0.335∗∗∗ lntotfampha 0.104 lntothirepha 0.119∗∗ lnseedpha 0.173∗ lninpcostpha 0.121∗∗∗ lnmachpha 0.113 lnanimpha 0.005 drought -0.117 soilq 0.274∗∗∗ slope 0.052 irrigD 0.392 age -0.009∗ educ -0.045 m1400 0.021 sold30 0.672 South-Southeast -0.775 Central -0.556 Western Cent. -0.364 Intercept 5.736∗∗∗ N 425 Significance levels :

∗ : 10%

MV -0.287 0.073 0.084 0.665∗ 0.077 0.605∗∗ 0.05 -0.741∗ 0.216 -0.563∗ 0.564∗∗∗ -0.030∗ -0.04 -1.032∗∗ 0.439 -0.343 -1.190∗∗ -0.494 6.152∗∗∗ 66 ∗∗ : 5%

∗ ∗ ∗ : 1%

Around 63% of farmers in each group hired some labor, and 42%(52%) of farmers who cultivated TVs (MVs) have off-farm income. The estimated labor elasticities of family labor and hired labor are very close to each other for both groups. To check whether the rural labor market is imperfect, I calculate the VMPL using the estimated elasticities to run the following regression: V MˆP L = γ + δw + u

5.1. MISSING LABOR MARKETS AND SHADOW PRICES

111

If we reject the null hypotheses of γ = 0 and δ = 1, we can conclude that the market wage does not reflect the true value of household labor. Table 5.3 shows the results of this test. Table 5.3: Summary of test results: Are estimated VMPFs equal to market wages?

TV MV ˆ γˆ δ γˆ δˆ Coefficients -25.89 0.85 4.31 1.19 F-test 0.002 0.80 t-tests 0.40 0.73 0.96 0.83 Although the F-test rejects the hypothesis of separability for TVs, t-tests fail to reject these hypotheses for both TVs and MVs. I conclude that shadow wages are not statistically significantly different from market wages for farmers in the sample. The preceding test of separability can only be done for households that sold maize in the market, because we need a price to calculate the value of marginal product of labor (i.e. V M P L = pM P L). Both Jacoby (1993) and Skoufias (1994) value farmer’s products using market prices regardless of whether the farmer sold them or not. As we have seen in Chapter 3, this may not be correct if some farmers value their own products higher than the market (e.g. due to non-market values). I run the above test of labor market separability only for farmers who sold some maize in the market (whose shadow prices are less than or equal to the market price as derived from the theoretical model and empirically shown in Section 4.2.1). To be able to generalize the conclusion that the market wages represent the value of time for all farmers, I test whether these two groups of farmers (sellers and non-sellers) differ significantly from each other by some key characteristics that affect their labor market prospects (Table 5.4). Farmers’ age, education and the time it takes for them to walk to the community center are variables that affect their labor market prospects. Using a t-test, I find that those who sold maize and who did not do not differ significantly in terms of these

112

CHAPTER 5. DE-BUGGING THE EMPIRICAL RESULTS Table 5.4: Do sellers and non-sellers differ in their labor market prospects?

age educ walktime offfarmD Mean of non-sellers 50 3.8 39 0.46 Mean of sellers 51 3.5 37 0.36 † p-val. of t-test 0.48 0.38 0.45 0.03 † Two sided t-test of H0 = Group means are equal.

hirelabD 0.57 0.72 0.002

key variables. The last two columns of Table 5.4 show that a higher percentage of non-sellers have off-farm income and a smaller percentage use hired labor. Given that we concluded that market wages represent the value of time for sellers, if non-sellers are more likely to have off-farm employment, we can easily extend the labor market separability result to non-sellers and use market wages to value the time of the nonseller farmers as well. Moreover, non-sellers are less likely to use hired labor. If the labor market is missing and they would have hired-in labor if they could, we have shown that ignoring the missing labor market would result in an underestimation of shadow prices of domestic maize (Table 5.1 on page 107). Therefore, we can conclude that the high shadow prices estimated do not result from a missing labor market in the current sample. If anything, we may have underestimated the value of TVs for non-sellers if the labor market to hire in labor is missing for subsistence farmers.

5.2

Risk and Liquidity Constraints?

How imperfections in financial markets affect farmer’s crop choices has been discussed by the well-established literature on the adoption of new technologies embedded in high yielding crop varieties by farmers (Fafchamps, 1999; Feder, 1980; Just and Zilberman, 1983; Feder et al., 1985). The main conclusion of this literature is that constrained farmers will not behave as predicted by neo-classical models and will only adopt the high yielding crop varieties partially, if at all. To the extent that traditional crop varieties grown for subsistence alleviate some of these constraints, their

5.2. RISK AND LIQUIDITY CONSTRAINTS?

113

value to the farmer will also depend on the status of financial markets. Formally incorporating these constraints into the theoretical model developed here that already has two market constraints would complicate the model substantially with little value added. Instead, I discuss how they may affect the shadow price of farmer’s subsistence crop and how they are accounted for in the empirical analysis in Chapter 4. Insurance markets are often missing for small farmers in developing countries (Binswanger, 1980; Morduch, 1999; Rosenzweig and Wolpin, 1993; Chaudhuri and Paxson, 2001). Farmers try to minimize their exposure to risk when choosing crops. If one crop variety is more resistant to the type of risk farmer faces (e.g., pests, drought, frost, wind), he will value that variety more than others that are more vulnerable. Whereas some modern crop varieties may be resistant to some risks, empirical evidence suggests that landraces, which by definition are highly adapted to local agro-ecological conditions, show higher resistance to many local risks (Smale et al., 2001; Edmeades et al., 2004). These risk mitigating attributes are production side attributes that could be incorporated into the current model by modifying the production functions to include a stochastic shock. Such a model would give a similar result to that of the standard portfolio selection model as in Feder (1980) and Just and Zilberman (1983), where partial adoption of modern varieties is observed. The main difference would be for subsistence farmers, for whom the shadow value the traditional crop would also depend on the riskiness of crops and farmer’s risk aversion parameter.5 The empirical analysis of the determinants of shadow prices in Section 4.2.2 includes a wealth index that can be a proxy for farmers’ risk perceptions. The wealth index is not significant in any of the specifications in Table 4.16 on page 88. If risk is important in farmers’ valuation of TVs and there is decreasing absolute risk aversion, we would expect less wealthy households to have higher or lower shadow prices depending on whether TVs are more or less resistant to the risks farmers encounter. 5 A similar result can be obtained if there is uncertainty about the price of the cash crop. In this case the shadow price would depend on the price risk and the risk aversion parameter.

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CHAPTER 5. DE-BUGGING THE EMPIRICAL RESULTS

However, controlling for other variables the wealth index is not significantly correlated to estimated shadow prices. Missing credit markets may constrain farmers in their crop choices and cause partial adoption of high return technologies or high yielding crops if they require an upfront investment (Smale et al., 1994; Zeller et al., 1998; Fafchamps, 1999; Croppenstedt et al., 2003). In the agricultural household context discussed here, a farmer may face a liquidity constraint if he cannot receive enough credit to buy purchased inputs. If the traditional crop requires less cash outlay on inputs, such as fertilizers or pesticides, than the cash crop, a credit constrained farmer will be likely to cultivate more traditional crop than a farmer who is not constrained. The shadow price of the traditional crop for subsistence farmers will be higher, reflecting the fact that the liquidity constraint is less binding for the traditional crop than for the cash crop. Empirical evidence suggests that one of the reasons for de-facto conservation of traditional crop varieties is that small farmers do not have access to credit to buy seeds or modern inputs required to switch to new crops (Feder et al., 1985; Doss, 2003). If this were the only reason why farmers cultivate traditional crops, then shadow prices would be less than or equal to market prices for farmers who have access to credit. However, it is likely that other non-market benefits discussed in the basic model will still be important for subsistence farmers, creating incentives to cultivate them even if the credit market is perfect. The empirical analysis of the determinants of shadow prices in Section 4.2.2 includes the variable “otherscredit” to account for farmers’ credit access. This variable is the percentage of farmers who have some credit in the same village excluding each farmer himself to prevent endogeneity. If a farmer is living in a village where many other farmers have access to credit, we can expect that he will be less likely to face a liquidity constraint. The credit variable, however, is not significant as a determinant in shadow price decomposition or the area share of TVs models. We can conclude that credit market constraints do not play a significant role in determining the shadow

5.3. BAD CROP YEAR IN 2002?

115

price estimates in this study.

5.3

Bad Crop Year in 2002?

If the 2002 crop year was particularly bad for maize farmers in rural Mexico, the supply of maize would have contracted and the shadow prices of TVs (maize in general) would have increased to reflect the scarcity. This could confuse the scarcity value with the non-market values of TVs represented by shadow prices. I use farmer reported assessments of maize yields in 2002 as compared to a normal year to understand whether such a bad crop year caused the estimated shadow prices to be high during the survey year. Table 5.5 shows that only around 30% of TV farmers who have estimated shadow prices that are greater than market prices lost more than onethird of their normal year output in 2002. This may indicate that the estimated high shadow prices reflect the scarcity value that would be true for any crop regardless of non-market values. However, if scarcity value was the only reason why we observe high farmer valuation of TVs, we would expect that those who produced more than their normal output would have shadow prices less than or equal to market prices. On the contrary, almost all of the TV farmers who produced more than in a normal year have shadow prices that are also higher than market prices (149 out of 152), indicating that there is more to farmers’ high subjective valuation of TVs than the scarcity value. Table 5.5: Loss in maize production as compared to a normal year for farmers with high shadow prices (ˆ ρ > p) TV Lost > 1/3 161 Lost < 1/3 256

MV 22 20

Although the farmer reported losses show an average of 17% decline in maize production as compared to a normal year, aggregate statistics for rural Mexico re-

116

CHAPTER 5. DE-BUGGING THE EMPIRICAL RESULTS

ported by SIAP show that maize production decreased only by 4% from 2001 to 2002.6 Such a small decline in maize production alone cannot generate the very high shadow prices estimated here. Even if we hypothesize that this small a decrease can result in shadow prices that are more than 20 times the observed market prices, this would indicate a very steep demand for domestic TVs and support that market purchased maize is an imperfect substitute for domestic maize.

5.4

Transaction Costs and Missing Seed Market

Transaction costs Transaction costs and how they affect/create shadow prices are discussed in Chapter 3. Conventional analyses of transaction costs in agricultural household models acknowledges the fact that farmer specific transaction costs may cut farmers off the markets creating missing markets (de Janvry et al., 1991). In these models shadow prices emerge for farmers who are trapped inside the TC band hence cannot participate in market transactions. As discussed earlier these models assume perfect substitutability between domestic and market crops, which leads to the valuation of farmers’ crops at market prices when TCs are not binding. However, if there are significant non-market values attached to domestic crops by some farmers, we cannot use market prices to value these crops even if TCs are not binding. We have seen that the estimated shadow prices of traditional maize for subsistence farmers exceed market prices and the difference is statistically significant. The empirical decomposition of shadow prices included a variable “walktime” that can be a proxy for TCs. This variable is not significant in determining shadow prices. Another variable that can be a proxy for TCs is the percentage of total maize production of the village that is marketed. If most of the maize is marketed in a village this would indicate low TCs. This variable is also not significant when included in the shadow 6

Source: http://w4.siap.gob.mx/sispro/SP_AG/sp_maiz.html.

5.4. TRANSACTION COSTS AND MISSING SEED MARKET

117

price decomposition regression. Moreover, as discussed in Section 4.2.2 the observed transportation costs are very small confirming Dyer Leal et al. (2002) who also mention that farmers in rural Mexico are not likely to face prohibitive TCs. All of these reasons combined indicate that TCs alone cannot justify the high estimated shadow prices and that shadow prices represent non-market values of traditional maize for subsistence farmers.

Missing Seed Market Another possible market imperfection that could affect shadow prices is a missing seed market. Production characteristics such as the maturity date, plant height or ear length are hard to observe from the seed, creating a missing seed market (for the seed with particular characteristics farmer demands). These characteristics can also be interpreted as high transaction costs for finding an identical seed in the market. A farmer who wants to cultivate crops with those unobservable characteristics would have to save his own seed every year. Therefore, his valuation for this crop is likely to be higher than market prices. Missing seed markets are common for landraces because they are characterized by high levels of local adaptation that makes it hard for an established seed market to exist. The effect of the missing seed market can be mitigated by repeated interactions in rural communities where farmers can buy seed from each other. However, to the extent that ensuring continued supply of a specific seed is costly to achieve by repeated interactions or community management systems, farmer’s subjective valuation of the crop will reflect the value of the production attributes of the seed. Especially for crops such as maize, for which the seed is also the consumption good, the consumption and production characteristics are intertwined and farmer’s subjective valuation will reflect both of these characteristics. Table 4.14 on page 84 shows that in the current sample 63% of TV farmers use their own seed (only 13% for MVs). We can also observe that the percentage

118

CHAPTER 5. DE-BUGGING THE EMPIRICAL RESULTS

of farmers who use their own seed is positively correlated with shadow prices. This indicates that the non-market values captured by shadow prices may also include the value of using one’s own seed or preserving the seed which contributes to farmer’s identity as a good farmer. Missing seed market is the only other reason that cannot be ruled out as a potential source of high shadow prices, but its effect is inseparable from the missing market for maize as a consumption good produced by farmer’s own seed, that creates the imperfect substitutability modeled in this dissertation.

5.5

Conclusion

Missing markets affect farmers’ production and consumption decisions regardless of the market in which they occur. We have seen that the shadow price of a domestic crop that is caused by a missing market for a perfect substitute for it is also affected by other problems in other markets. In depth modeling of an agricultural household with both missing output and labor markets show that these two interact in shaping farmer’s subjective valuation of domestic crop. Empirical analysis of ENHRUM data shows that labor market imperfections do not affect shadow prices significantly removing doubts about convoluting the effect of missing labor markets and missing output markets in estimating shadow prices of maize using this data. Other potential reasons why we may have estimated high shadow prices, such as risk, missing credit markets, a production shock in 2002 and prohibitive transaction costs are also ruled out using proxies from ENHRUM data or external data. This chapter removes potential doubts about the empirical results in the previous chapter and shows that we cannot explain observed levels of maize production even after controlling for all observable variables related to farmers’ maize production and consumption decisions. Subsistence farmers in rural Mexico make production decisions about TVs based on their subjective valuations that are significantly higher from market prices. Therefore, both understanding maize production and on-farm

5.5. CONCLUSION

119

conservation of TVs in rural Mexico requires that we pay attention to shadow prices along with changes in market conditions.

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CHAPTER 5. DE-BUGGING THE EMPIRICAL RESULTS

Chapter 6 Conclusions The contributions of this dissertation to the literature are threefold: theoretical, empirical, and policy. Theoretically, I show how farmers who attach significant nonmarket values to their own crops will allocate their productive resources in ways that cannot be explained by market prices. One implication of this is that models focusing on transaction costs may be insufficient to explain the existence of subsistence farming in such regions. Non-market values may include the ceremonial and ritual value of growing one’s own subsistence crop, the value of successfully growing the subsistence crop for the farmer’s identity in the community, or the value of maintaining the family seed that is passed from generation to generation. Although others mentioned that farmers may not respond to market signals because of non-market values, I develop the first explicit model of these values and their implications for household’s resource allocation decisions. I show that these decisions depend on shadow prices that can be significantly greater than market prices for subsistence farmers. As a consequence, production decisions are not separable from farmers’ preferences and endowments, which would not affect production if farmers valued their crops at the market price. This theoretical model also sheds light on a previously overlooked reason why we may observe an inelastic supply response in rural economies, even when other market constraints are not binding. 121

122

CHAPTER 6. CONCLUSIONS Empirically, this study is the first to estimate household-and crop-specific

shadow prices of output. Traditional models of agricultural households define shadow prices as market specific; thus the empirical applications based on programming methods yield market specific shadow prices. Although some previous studies changed our thinking about missing markets by redefining them as household-specific rather than market specific, empirical applications focused mainly on missing labor markets and resulting household-specific shadow wages to understand labor supply. While these studies contributed to our understanding of households’ labor allocation decisions, they overlooked the possibility that the value of some of the farmers’ products may not be correctly represented by market prices. This dissertation argues that market prices do not represent the value of maize for many farmers in rural Mexico because of the non-market values attached to subsistence maize production. My empirical application based on a nationally representative household data from rural Mexico shows that subsistence maize farmers’ incentives to cultivate traditional maize depend on shadow prices that are significantly higher than market prices. I also show that shadow prices perform better than market prices in predicting the land area allocated to traditional maize varieties. I then use the cross-sectional variation in the estimated shadow prices of traditional maize to analyze key socioeconomic and agro-ecological variables that are correlated with farmers’ incentives and derive policy implications for on-farm conservation of traditional maize. Indigenous households in southern and southeastern Mexico have above-average shadow prices for traditional varieties of maize. Similarly households that have less favorable growing conditions have high shadow prices. Therefore, de facto incentives to maintain traditional maize are higher for these households. The third contribution of this dissertation is related to the design and targeting of on-farm conservation programs. Previous research tried to identify what types of farmers cultivate a diverse set of crop varieties and where, including for maize in Mexico given Mexico’s importance for conserving the diversity of this important food

123 crop. The bulk of these studies are applied and conducted using data collected from a handful of communities at best. This dissertation combines a theory of farmer decision making with an empirical approach that employs nationally representative rural household data. It also provides a conceptual framework for modeling and understanding how the oft-mentioned non-market values of maize affect farmers’ resource allocation and incentives to maintain maize landraces. The method I use is flexible enough to be applied to guide conservation programs in other regions and with other crops. The empirical analysis of the determinants of high shadow prices of maize landraces, i.e. de facto incentives, reveals important policy implications. The effectiveness of on-farm conservation programs depends on both the private and the public value of the crops to be conserved as identified by Bellon and Smale (1998). The shadow prices modeled and estimated here provide a measure of the private value of maize landraces. On-farm conservation would be least costly if targeted to communities that have high shadow prices identified in this analysis. These communities are mainly ones with a high proportion of indigenous population in the south and southeast regions of Mexico. Although doing nothing may seem to be the best on-farm conservation policy in such places, we cannot be sure how incentives will change over time as market conditions change. Therefore, targeted policy action may be required even in places with high de facto incentives. Given that 67% of indigenous farmers are in the lowest wealth quintile, this has implications for poverty and equity, as well. Policy options generally suggested for on-farm conservation include cash incentives, participatory plant breeding (PPB), creation of niche markets to increase the market value of diversity (landraces), or diversity fairs to create awareness and incentives. Cash incentives may be the least preferred policy because they are hard to monitor; farmers may not change their crop choices consistent with the policy after receiving a cash transfer. PPB, niche markets and diversity fairs have the potential to contribute to farmers’ incentives to maintain diversity and decrease poverty if

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CHAPTER 6. CONCLUSIONS

targeted carefully. Communities without irrigation and of sub-optimal soil quality are also identified as potential least cost targets for on-farm conservation. However, maintaining the status-quo of these sub-optimal growing conditions in order to conserve diversity is not an appropriate development policy. Rural development policies in such regions should combine efforts to supply irrigation and improve soil quality, with the policy options identified above to prevent a potential decrease in de facto conservation incentives. PPB brings together farmers and crop breeders to develop crops that have better yields and marketability, as well as maintain the attributes valued by farmers. PPB may be one of the most effective policies if improvements in growing conditions affect the tradeoffs between the market value of cash crops and the non-market values of subsistence crops, tipping the balance in favor of cash crops. These programs have the potential to make the subsistence crops more competitive while still maintaining the non-market values of these crops to farmers. On-farm conservation in any event should be combined with off-farm conservation and cataloguing in order to be effective and accessible to plant breeders. Off-farm conservation may be the best policy in places where the private incentives to maintain on-farm diversity are very low but the public benefits are high. This dissertation is explicitly concerned with private values of landraces, which are only one essential part of conservation strategies. Given that understanding public benefits is also essential to designing effective conservation policies, future studies should combine a detailed study of private values and public benefits. One way to measure public benefits of conservation is using genetic analysis, which identifies the potential value of diversity in improving crops’ yields and resistances. The costs of such analyses (e.g. gene sequencing, molecular markers) may be very high but they would be justified if the discounted net returns from successfully conserving important landraces are high enough. Shadow prices ideally should be analyzed at variety level to better understand

125 farmers’ valuations for each variety. This exercise was infeasible due to the structure of the ENHRUM data, which despite its strengths does not provide variety-specific production data. Future research can make such a study feasible with a suitable survey design and help us better understand farmers’ incentives to maintain specific varieties on their farms. An interesting methodological extension to this dissertation is to combine the revealed preference approach employed here with a stated preference approach. This would help us understand the links between the two approaches and provide guidance for future research that tries to identify farmers’ preferences for different varieties. While leading to various interesting questions for future research, this dissertation is a major step towards a better understanding of subsistence farmers’ resource allocation decisions as well as their incentives for on-farm conservation by focusing on nonmarket values.

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CHAPTER 6. CONCLUSIONS

Appendix A Karush-Kuhn-Tucker (KKT) Conditions for the Derivation of the Shadow Price The Lagrangean for the basic model is: max

Xl ,Xm ,Xsh ,Xss ,θ,Li ,λ,µn

L = U (Xsh , Xm , Xl ; Z)

+λ[ps (1 − ts )Xss + pc h(Lc , Ic , A(1 − θ)) + W + w(T¯ − Xl − Ls − Lc ) − pm (1 + tb )Xm ] +µ1 [g(Ls , Is , Aθ) − Xss − Xsh ] + µ2 Xss + µ3 Xsh + µ4 Xm + µ5 θ + µ6 (1 − θ) + µ7 Ls + µ8 Lc i = s, c, n = 1, ..., 8. Leisure cannot be zero by assumption, hence we can use the FOC to get the optimal condition: M Ul = λw. Farmer equates the money value of his marginal utility of leisure to wage rate at the optimum. We need to use the KKT conditions for optimal choices of Xm , Xss , Xsh , θ and Li where (i = s, c) because of the possibility of corner solutions for these variables: ∂L : M Um − λpm (1 + tb ) + µ4 = 0 ∂Xm ∂L : Xm ≥ 0 ∂µ4 µ4 Xm = 0

127

(A.1) (A.2) (A.3)

128

APPENDIX A. KKT CONDITIONS FOR THE BASIC MODEL ∂L : M Ush − µ1 + µ3 = 0 ∂Xsh ∂L : Xsh ≥ 0 ∂µ3 µ3 Xsh = 0 ∂L : λps (1 − ts ) − µ1 + µ2 = 0 ∂Xss ∂L : Xss ≥ 0 ∂µ2 µ2 Xss = 0 ∂L : µ1 A(M P As ) − λpc A(M P Ac ) + µ5 − µ6 ∂θ ∂L :θ ∂µ5 ∂L : (1 − θ) ∂µ6 µ5 θ = 0 ∂L : µ1 M P Ls − λw + µ7 ∂Ls ∂L : Ls ∂µ7 µ7 Ls ∂L = λ(pc M P Lc − w) + µ8 ∂Lc ∂L = Lc ∂µ8 µ8 Lc

(A.4) (A.5) (A.6) (A.7) (A.8) (A.9)

= 0

(A.10)

≥ 0

(A.11)

≥ 0

(A.12)

& µ6 (1 − θ) = 0

(A.13)

= 0

(A.14)

≥ 0

(A.15)

= 0

(A.16)

= 0

(A.17)

≥ 0

(A.18)

= 0.

(A.19)

The Equation A.1 indicates that if a farmer is not buying the market good Xm the monetized value of the marginal utility from consuming it must be less than or equal to the market price and TC. Although the decision to buy Xm or not may provide intuition into the substitutability of market good for domestic good, the shadow price of domestic good is determined independently. This is because Xs is a different consumption good, and the production decisions depend on the tradeoffs between the cash crop and the domestic crop. In what follows, I assume interior solution for Xm , hence µ4 = 0. Let us interpret the different cases implied by the KKT conditions related to Xs : ¯ − Xss − Xsh > 0, 0 < θ < 1, µ1−8 = 0. Case 1: Xss > 0, Xsh > 0, Qa (L, A) If the sum of home consumption and sales of Xs is less than the total production market price has to be equal to zero by A.7. Therefore there will never be waste since market prices are strictly positive. For the following cases I assume there is no waste and hence µ1 > 0.

129 Case 2: Xss > 0, Xsh > 0, θ = 0, µ5 ≥ 0, µ2,3,6,7,8 = 0. This case is impossible, since the farmer has to have θ > 0 to be able to sell any Qa . For θ = 0, we can similarly rule out the cases where Xss > 0, Xsh = 0 and Xss = 0, Xsh > 0. Case 3: Xss = Xsh = 0, θ = 0, µ4 ≥ 0, µ6 = 0, µ2,3,5,7,8 ≥ 0. This case represents farmers who only grow cash crop. We can rewrite the Equation A.10 to get: µ1 µ5 M P As = pc M P Ac − . λ λA This condition indicates that the marginal (monetized) value of an extra unit of subsistence crop is worth less than the value of marginal product of land allocated to cash crop. For farmers in this group the non-market benefits and the unobservable characteristics of subsistence crop are not important. Therefore it is not worth to allocate any resources to subsistence crop production. Case 4: Xss > 0, Xsh > 0, 0 < θ < 1, Lc > 0, µ2−8 = 0. This case characterizes the farmer who sells part of Xs in the market. For this group of farmers market price equals shadow price, i.e. ρ = ps (1−ts ) = µλ1 and we can safely use market price to represent farmers’ valuation of the subsistence crop. Therefore, the optimality conditions for allocation of land, labor and input are the conventional conditions where farmer equates the value of marginal products across crops, i.e.: ps (1 − ts )M P As = pc M P Ac , pi M P Li = w, i = s, c. Case 5: Xss > 0, Xsh = 0, 0 < θ < 1, µ3 ≥ 0, µ2,5−8 = 0. Farmer is selling all his product at the market price, which is greater than or equal to the shadow price, i.e. ρ=

µ1 µ1 − µ3 ≤ = ps (1 − ts ) λ λ

This case is similar to Case 3 and we can use market prices. The case where both Xsh and Xss are equal to zero when 0 < θ < 1 is not likely to occur (given the “no-waste” assumption in Case 1), hence will not be considered here. Case 6: Xss > 0, Xsh > 0, θ = 1, Lc = 0, µ2−5 = 0, µ6−8 ≥ 0. In this case, farmer only cultivates the subsistence crop and sells part of it (hence

130

APPENDIX A. KKT CONDITIONS FOR THE BASIC MODEL ps (1 − ts ) =

µ1 λ ).

The optimality conditions for resource allocation are: ps (1 − ts )M P As −

µ6 = pc M P Ac , λA

pc M P L c = w −

µ8 . λ

According to the first condition, if the farmer allocated one unit of land to the cash crop, its value would be less than the value of marginal product of land allocated to the subsistence crop. Accordingly, the value of marginal products of the first unit of labor and purchased input to be used for the cash crop would be less than the market prices of these inputs. Therefore, the farmer does not allocate any land to the cash crop at the optimum. When θ = 1, the case of Xss > 0, Xsh = 0 is similar to Case 5, and the case of Xss = 0, Xsh = 0 is ruled out in Case 1. Case 7: Xss = 0, Xsh > 0, 0 < θ < 1, µ2 ≥ 0, µ3−8 = 0. This case characterizes subsistence farmers, who consume all of their subsistence crop at home. The market price is less than or equal to farmers’ shadow price as given by A.7 on page 128: µ1 µ1 − µ2 ≤ =ρ ps (1 − ts ) = λ λ Farmer is not selling Qa since he values it more than the market. The optimality condition for land allocation is different from the conventional condition in Case 3 above. Here the farmer equates the value of marginal product of land allocated to cash crop to the “shadow value of marginal product” of land allocated to subsistence crop, i.e.: µ1 M P As = pc M P Ac . λ The conditions for labor and purchased input for the subsistence crop set the “shadow value of marginal product” of inputs equal to market prices of these inputs: µ1 M P Ls = w λ For this group of farmers we need to estimate shadow prices to understand how they value their subsistence crop, and how they make resource allocation decisions. Case 8: Xss = 0, Xsh > 0, θ = 1, µ3−7 = 0, µ2,6,8 ≥ 0. In this case, farmer only cultivates the subsistence crop and consumes all of it at

131 home. The optimality condition for land allocation is: ρM P As −

µ6 M P As = pc M P Ac , λ

which means that if he allocated one unit of land to the cash crop, its value would be less than the “shadow value of marginal product” of land allocated the subsistence crop. The conditions for labor and purchased input are the same as in the Case 6 above, and similarly shadow prices rather than market prices should be used to understand the subjective valuation of farmers in this group.

132

APPENDIX A. KKT CONDITIONS FOR THE BASIC MODEL

Appendix B Missing Data Methods for the Estimation of Agricultural Production Functions Table B.1 summarizes the results of four different ways of dealing with missing data: casewise deletion, median imputation in two different ways and multiple imputation. Casewise deletion drops 4 observations that have no labor days reported in spite of positive production. The first median imputation imputes the village median of the per hectare total labor used for each variety for these 4 observations. When we look at different stages of production, there are 9, 17 and 25 observations with zero labor before planting, after planting and during harvest, respectively. The second median imputation imputes the village median of the per hectare labor used for each of these stages for these missing values. Multiple imputation method uses multiple imputation by chained equations to generate the values to be imputed for missing values at different stages of production. These different methods do not generate significant differences in the magnitude and statistical significance of production function coefficients. The results of the easiest method, i.e. casewise deletion, are used in the empirical application of this dissertation.

133

deletion† MV -0.17 0.232∗ 0.676∗∗ 0.075 0.655∗∗ 0.062 -0.755∗ 0.218 -0.617∗∗ 0.525∗∗∗ -1.026∗∗∗ -0.030∗ -0.05 -0.401 -1.287∗∗ -0.422 0.304 5.684∗∗∗ 66

Median Imputation I†† TV MV ∗∗∗ -0.320 -0.183 0.171 0.198∗ 0.243∗∗∗ 0.686∗∗ 0.107∗∗∗ 0.076 0.132 0.653∗∗ 0.02 0.061 -0.126 -0.742∗ 0.309∗∗∗ 0.222 0.071 -0.622∗∗ 0.422 0.541∗∗∗ -0.009 -1.032∗∗∗ -0.006 -0.031∗ -0.028 -0.051 -0.915 -0.421 -0.767 -1.318∗∗ -0.672 -0.437 0.881 0.267 5.461∗∗∗ 5.835∗∗∗ 429 66

Median Imputation II‡ TV MV ∗∗∗ -0.315 -0.152 0.192∗∗ 0.263∗ 0.261∗∗∗ 0.661∗∗ 0.108∗∗∗ 0.073 0.141 0.684∗∗ 0.025 0.048 -0.123 -0.679∗ 0.313∗∗∗ 0.169 0.083 -0.621∗∗ 0.411 0.505∗∗∗ 0.005 -0.956∗∗∗ -0.007 -0.030∗ -0.028 -0.036 -0.908 -0.325 -0.777 -1.284∗∗ -0.694 -0.359 0.901 0.292 5.343∗∗∗ 5.441∗∗∗ 429 66

Multiple Imputation‡‡ TV MV ∗∗∗ -0.310 -0.146 0.200∗ 0.296∗ 0.248∗∗∗ 0.668∗∗ 0.107∗∗∗ 0.066 0.143 0.730∗∗ 0.025 0.055 -0.12 -0.692∗ 0.312∗∗∗ 0.207 0.077 -0.628∗∗ 0.407 0.531∗∗∗ 0.004 -0.954∗∗ -0.007 -0.032∗ -0.027 -0.043 -0.895 -0.257 -0.754 -1.329∗∗ -0.673 -0.376 0.952 0.346 5.313∗∗∗ 5.373∗∗∗ 429 66

†

Significance levels: ∗ : 10% ∗∗ : 5% ∗ ∗ ∗ : 1%, Cluster robust p values in parentheses Ignores the missing values for total labor used (4 observations) †† Imputes the village median of the total labor used (per hectare) for each maize type (4 imputations) ‡ Imputes the village median of the labor used before and after planting and for harvest (9, 17 and 25 observations respectively) ‡‡ Obtained using ice and micombine commands in Stata 9.

Casewise Variables TV ln(land) -0.307∗∗∗ ln(totlabpha) 0.178∗ ln(seedpha) 0.194∗∗ ln(inpcostpha) 0.121∗∗∗ ln(machpha) 0.15 ln(animpha) 0.029 droughtD -0.084 soilq 0.300∗∗∗ slope 0.051 irrigD 0.425 m1400 -0.036 age -0.008 educ -0.043 South-Southeast -0.737 Central -0.559 Western Central -0.443 sold30 0.727 Constant 5.452∗∗∗ Observations 425

Table B.1: Production functions estimated with IV-2SLS method using different methods to deal with missing variables

134 APPENDIX B. MISSING DATA METHODS

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Index Akaike (1974), 97, 135 Akerlof and Kranton (2000), 14, 135 Akerlof (1970), 27, 135 Altieri (2004), 14, 92, 135 Anderson (1946), 20, 135 Angrist (2000), 74, 79, 135 Badstue et al. (2006), 4, 21, 26, 29, 37, 38, 69, 135 Badstue (2006), 21, 60, 135 Barnum and Squire (1979), 10, 15, 135 Barrett et al. (2004), 67, 69, 135 Barrett et al. (2005), 6, 16, 102, 135 Baum et al. (), 78, 135 Becker (1965), 3, 5, 33, 136 Becker (1974), 10, 136 Bellon and Brush (1994), 5, 17, 18, 21, 26, 29, 60, 62, 136 Bellon and Smale (1998), 6, 18, 19, 25, 86, 91, 123, 136 Bellon and Taylor (1993), 4, 26, 28, 38, 87, 90, 91, 93, 98, 136 Bellon et al. (1998), 39, 136 Bellon et al. (2006), 26, 38, 59, 62, 136 Bellon (1996), 38, 136 Berthaud and Gepts (2004), 1, 5, 20, 21, 24, 26, 29, 37, 98, 136 Binswanger (1980), 113, 136 Birol et al. (), 26, 136 Botterill (2001), 22, 136 Brush and Chauvet (2004), 2, 5, 19, 21–24, 26, 29, 37, 59, 137 Brush and Meng (1998), 4, 17–19, 21, 25, 37, 60, 86, 136 Brush and Perales (2007), 29, 87, 89, 137 Brush et al. (1992), 19, 93, 98, 137 Brush (1989), 6, 137 Brush (1992), 39, 137

Brush (2002), 25, 136 Cameron and Trivedi (2005), 86, 137 Chaudhuri and Paxson (2001), 113, 137 Chayanov (1966), 2, 11, 137 Chihiro (1986), 2, 3, 34, 137 Chiquiar (2005), 61, 137 Croppenstedt et al. (2003), 114, 137 Denbaly and Vroomen (1993), 107, 137 Doss (2003), 18, 114, 137 Dowswell et al. (1996), 1, 20, 138 Dumont et al. (2005), 86, 138 Dyer Leal and Yunez Naude (2003), 3, 4, 18, 21, 22, 24, 29, 35, 53, 98, 138 Dyer Leal et al. (2002), 3, 12, 22, 37, 53, 117, 138 Dyer Leal et al. (2006), 24, 26, 29, 138 Dyer Leal (2006), 5, 21, 22, 28, 37, 138 Edmeades et al. (2004), 4, 37, 113, 138 Fafchamps (1999), 112, 114, 138 Feder and Umali (1993), 4, 138 Feder et al. (1985), 4, 112, 114, 138 Feder (1980), 4, 38, 93, 112, 113, 138 Feenstra and Hanson (1999), 86, 138 Finan et al. (2005), 39, 138 Fussell (1992), 14, 138 Heath (1987), 22, 29, 139 Heckman (1974), 45, 139 Hoisington et al. (1999), 2, 17, 20, 139 Isakson (2007), 39, 139 Jacoby (1993), 5, 6, 15, 34, 36, 51, 67, 68, 79, 80, 102, 105, 109, 111, 139 Jarvis et al. (2000), 2, 18, 139 Juarez-Torres (2005), 29, 139 Just and Zilberman (1983), 38, 93, 112, 113, 139 Koo et al. (2003), 5, 18, 139 Levy and van Wijnbergen (1992), 23, 139

143

144 Liu et al. (2003), 17, 60, 139 Lopez (1986), 14, 15, 139 Louette et al. (1997), 92, 139 Louette (1997), 59, 139 Meng et al. (1998), 39, 140 Meng (1997), 86, 90, 140 Morduch (1999), 113, 140 Mundlak (2000), 67, 140 NRC (1972), 18, 140 Nadal (2000), 23, 24, 28, 53, 89, 140 Perales et al. (2003), 26, 28, 29, 38, 91, 140 Perales et al. (2005), 26, 29, 38, 62, 87, 89, 140 Peterson (2000), 92, 140 Preibisch et al. (2002), 4, 22, 87, 140 Rice et al. (1998), 21, 26, 140 Roe and Graham-Tomassi (1986), 15, 140 Rosenzweig and Wolpin (1993), 113, 140 Rubenstein et al. (2005), 17, 18, 141 Salvador (1997), 5, 20, 21, 37, 141 Schafer and Graham (2002), 68, 141 Simon and Blume (1994), 49, 141 Singh et al. (1986), 3, 10, 11, 13, 34, 141 Skoufias (1994), 6, 16, 34, 36, 51, 67, 68, 79, 80, 102, 105, 109, 111, 141 Smale et al. (1994), 4, 90, 93, 114, 141 Smale et al. (2001), 4, 17, 19, 21, 22, 26, 29, 37, 113, 141 Smale et al. (2003), 21, 29, 37, 38, 141 Smale et al. (2004), 29, 141 Smale (2005), 80, 99, 141 Smale (2006), 27, 28, 86, 87, 92, 141 Strauss (1986), 3, 14, 31, 37, 141 Swanson (1994), 25, 141 Taylor and Adelman (2003), 3, 6, 10, 12, 13, 15, 33, 34, 46, 142 Turrent and Serratos-Hernandez (2004), 1, 29, 62, 89, 142 Van Dusen and Taylor (2005), 26, 28, 142 Van Dusen (2000), 26, 28, 86, 90, 142 Vincent (1976), 22, 142 Wayman (2003), 68, 142 Wright (1997), 18, 142 Yotopoulos et al. (1976), 15, 142 Yunez-Naude (2003), 23, 142

INDEX Zeller et al. (1998), 114, 142 de Janvry et al. (1991), 3, 5, 12, 15, 33, 34, 40, 45, 108, 116, 137 de Janvry et al. (1995), 3, 23, 24, 98, 137 van Dusen (2006), 28, 142