Institutional Traps Felix Várdy∗ Haas School of Business, University of California at Berkeley and International Monetary Fund, Washington, DC First draft: June, 2009 This draft: February 2010

Abstract We show how bad contract-enforcing institutions condemn a country to the production of simple goods and services in vertically integrated firms and product chains. In such a technically and organizationally simple economy, the marginal benefit of better institutions is shown to be lower than in more complex, interconnected economies. If institutional change is incremental and incentive-driven (as indeed argued by the new institutional economics literature), then economic development becomes highly path-dependent, leading to institutional traps, threshold effects, and divergence.

∗

Email: [email protected]. I would like to thank, without implicating, Laura Chioda, Allan Drazen, Burkhard Drees, John Nash, Roberto Rigobon, Emily Sinnott and, especially, Augusto de la Torre for their comments and suggestions.

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1

Introduction

How does the quality of a country’s contract-enforcing institutions affect its economic structure? And, conversely, how does a country’s economic structure affect the development of its institutions? Building on insights from the new institutional economics literature, in this paper, we develop the idea that the quality of a country’s contractenforcing institutions and the organizational complexity–or interconnectedness–of its economy are mutually reinforcing. On the one hand, this implies that countries with bad contract-enforcing institutions may be condemned to the production of relatively simple goods and services by low-skilled workers in vertically integrated firms and product chains. On the other hand, the complementarity between the quality of institutions and organizational complexity of the economy also has implications for the dynamics of institutional change. If institutional change is overwhelmingly incremental and incentive-driven (as argued by, e.g., North, 1990, 1991, 1994), then contract-enforcing institutions are more likely to improve in economies where entrepreneurs and workers stand to gain a lot from such marginal improvements than in economies where these gains are small. In the latter case, institutions are more likely to stagnate or even deteriorate over time.1 This raises the question whether the marginal benefits are higher in countries that already have good institutions, or in countries that still have to develop them. Clearly, the answer depends on whether institutional development exhibits increasing or decreasing returns. Under a standard decreasing-returns framework, the lower is a country’s “institutional capital,” the higher is the marginal benefit of improvements, and vice versa. In that case, one would expect convergence of institutional quality across countries with different initial conditions. With increasing returns, by contrast, scarcity of institutional capital makes marginal institutional change less valuable, and one would expect divergence: further improvements in advanced countries and stagnation and deterioration in the developing world. In this paper, we show that complementarity between the quality of contractenforcing institutions and the organizational complexity of the economy makes returns increasing and, hence, divergence the more likely scenario. The intuition for our results, based on Coase’s (1937) theory of the firm, is as follows.2 When a firm has to decide whether to produce an intermediate good or service 1

In the words of North (1994): “The process of change is overwhelmingly incremental. The reason is that the economies of scope, the complementarities, and the network externalities that arise from a given institutional matrix of formal rules, informal constraints, and enforcement characteristics will typically bias costs and benefits in favor of choices consistent with the existing framework.” He goes on to say that: “Deliberate institutional change will come about (...) as a result of the demands of entrepreneurs in the context of the perceived costs of altering the institutional framework at various margins. The entrepreneur will assess the gains to be derived from recontracting within the existing institutional framework compared to the gains from devoting resources to altering that framework.” 2 See, also, Williamson (1975, 1981, 1985).

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in-house or buy it from another firm, it faces a trade-off between the advantages of specialization and the costs of transacting in the market. Specialization favors buying from another firm, while transaction costs favor in-house production. Bad (formal or informal) contract-enforcing institutions raise the cost of transacting in the market and, hence, make in-house production relatively more attractive. As a result, the economic structure of a country with bad institutions is more likely to be characterized by vertically integrated product chains and firms that transact little with each other. The relative paucity of inter-firm transactions makes that, marginally, such a “granular” economy benefits relatively little from better institutions. In a country with good contract-enforcing institutions, by contrast, firms optimally choose to be highly specialized and transact a lot with other firms to acquire intermediate goods and services. A further marginal improvement of the country’s institutions positively affects all of these many existing transactions. Hence, it is the country that already has good contract-enforcing institutions–and, as a result, is highly interconnected–that benefits more from a marginal improvement of its institutions than the country with bad institutions. Finally, if institutional change is “demand-driven” and incremental, it is good institutions that are likely to get better and bad institutions that are likely to get worse (up to a point). This analysis suggests that countries stuck in a trap of bad institutions and underdevelopment may not be able to rely on incremental change to lift themselves out of poverty. Instead, a more radical break with the past–i.e., a “big push”–may be necessary to create the conditions for self-sustaining economic development. Obviously, our paper is closely related to the literature on poverty traps, which identifies mechanisms that make underdevelopment self-sustaining. (See Azariadis and Stachurski , 2005, for an overview.) Primary among those are various forms of market failures. These market failures originate in phenomena such as increasing returns technologies, coordination problems, asymmetric information, credit constraints, externalities, et cetera. Moreover, the different mechanisms can interact and reinforce each other. In this paper, the trap is of an institutional kind. The issue is that, unless the net gains from better institutions are sufficiently large, winners may not be able to adequately compensate the losers. And because the people in power are likely to be among the losers, the reforms will be blocked. In addition to the papers already mentioned, technically, this paper is closely related to Kremer’s (1993) “O-ring” theory of development. We build on the “O-ring” model by introducing a trade-off between the benefit of specialization and the cost of transacting in the market. This introduces a natural measure of organizational complexity, or interconnectedness, into the model, in addition to the measure of technical complexity that is already present. We show that higher levels of both organizational and technical complexity arise in response to an improvement in contract-enforcing institutions. On the other hand, only organizational complexity, but not technical complexity, raises the marginal benefit of better institutions. The remainder of the paper is organized as follows. The model is presented in 3

Section 2 and analyzed in Section 3. Section 4 contains a discussion of the main results, while Section 5 concludes. Finally, the Appendix studies some alternative replicator dynamics for institutional change.

2

Model

The model consists of two parts. The first part describes how the quality of contractenforcing institutions affects economic structure–i.e., the organizational complexity of product chains, the technical complexity of products, and the skill levels and wages of workers. The second part describes how economic structure affects the marginal benefits of better institutions. The variables in the first part of the model are determined directly, and in a straightforward manner, by the individual choices of entrepreneurs and workers in the economy. Hence, we use a standard neoclassical optimization framework to describe them. Institutional change, on the other hand, is the result of a myriad of collective decisions, interacting in extremely complicated ways. Obviously, this is hard to model in detail, while maintaining necessary parsimony. To circumvent this problem, we take a rather “minimalist” approach and limit attention to the following question: If institutional change is incremental and incentive-driven, how conducive are different economic structures to institutional improvement? To answer this question, we determine the marginal benefit of an improvement in contract enforcement and feed this into a simple replicator dynamic. The replicator only assesses whether, on balance, the collective benefits of–and, by extension, pressure for–institutional change is large or small. If these benefits are sufficiently large, contract-enforcing institutions improve over time; otherwise, they stagnate or even deteriorate.

2.1

From Institutions to Economic Structure

We extend Kremer’s (1993) “O-ring” model of economic development to study the effect of institutions on economic structure. The interested reader may want to consult the original paper for details. Let  ∈ N denote the number of steps or tasks needed to produce some good or service, . We interpret  as a measure of technical complexity. Each step 1   in the production process is executed by a worker of skill  ,  ∈ {1  }, where  is the probability that worker  does his job properly. If a worker screws up, the product is assumed to become worthless and the production effort wasted. If all steps are done in-house, i.e., within one vertically integrated firm making up the whole product chain, then the expected value, , of the finished product is  = Π=1    () Here, the parameter  is an element of (0 1] and  () is some factor valuing technical ˜ () = complexity. To ensure that our problem is well-behaved, we assume that  4

˜ 00 ()  0. To ensure that technical complexity   () is strictly concave in , i.e.,  ˜ ˆ () = () has value, we also assume that  is strictly increasing in . (Else,  = 1  would be trivially optimal; see below.) Specialized firms focusing on fewer tasks are assumed to deliver a better product than vertically integrated firms executing many different tasks. Abstracting for the moment from market transaction costs, we model this as follows. If  is produced through the collaboration of firms 1  , 1 ≤  ≤ , where firm 1 takes on the first 1 production steps, firm 2 the next 2 steps, et cetera, such that 1 +  +  = , then the value  of the final product is  = Π=1  ((1 ) +  + ( ) )  ()  Π=1    () We interpret , the number of firms collaborating to produce , as a measure of the organizational complexity, or interconnectedness, of the economy. We interpret  as a measure of the value of specialization. Note that the closer  is to 1, the smaller is the value of specialization. An entrepreneur controlling the product chain optimally chooses  and . Product chains do not consist of  =  firms, each specialized in a single task, because transacting between firms is assumed to be costly. This cost is affected by the quality of a country’s contract-enforcing institutions.3 With good institutions, transaction costs are relatively low. If institutions are ineffective, however, transacting with other firms is risky and expensive. For analytical convenience, we assume that transaction costs are of the “iceberg” variety. This corresponds to a situation where, each time an intermediate product is shipped from one firm to another, some fraction “melts.” Alternatively, there is some probability that the good is expropriated, lost, stolen, or destroyed. We denote the iceberg cost by 1 −   ∈ (0 1). Hence, high  corresponds to low transaction costs, i.e., good institutions, and vice versa. The (expected) value of a final product of technical complexity  produced collaboratively by  firms is then4  = Π=1    ((1 ) +  + ( ) )  () Total production in the economy is  , where  denotes the number of production chains. With a labor force of size  we have = 3

 

For example, North (1990, p.66) writes: “the cost of transacting reflects the overall complex of institutions–formal and informal–that make up an economy or, on an even greater scale, a society.” 4 We write   instead of  −1 to assure that even a completely integrated product chains (i.e.,  = 1) is, at least somewhat, affected by the quality of institutions, . This seems realistic, as even a fully integrated chain has to transact with final consumers.

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As in Kremer (1993), firms are wage-takers, facing a wage schedule  (). That is,  () is the cost of hiring a worker of skill . Workers also take  () as given. They acquire skill level  at a cost  (), where  is some (sufficiently) convex function of .

2.2

From Economic Structure to Institutions

Following the new institutional economics literature, we assume that institutional change is incremental and incentive-driven. (See, e.g., North, 1990.) We take incrementality to mean that  is a continuous function of time. We take “incentive-driven” to mean that the drift of  is a (strictly) increasing function, , of the benefit of marginal improvements in . Here, “benefit” is interpreted as the percentage increase in the total production,  , in the economy. The replicator dynamic for  is then characterized by the differential equation5 µ ¶   (ln ()) =   While total production is always increasing in , the gains from a marginal increase in  may be large or small depending on the structure of the economy. When the gains are small, society may not be able to overcome or adequately compensate vested interests and solve the potentially sizable collective-action problems associated with institutional change. In that case, institutions will stagnate or get worse over time. To operationalize this, we assume that   0 when the marginal benefit of better  institutions is at its global minimum. Formally, µ ¶  (ln ( )) 0 inf    If, on the other hand, the collective benefit of a marginal improvement in  is sufficiently large, presumably, vested interests and collective-action problems can be overcome one way or another. Hence, we assume that there exists an   0 such that for all 0  ,  (0 )  0.

3

Analysis

3.1

Effect of Institutions on Economic Structure

Recall that the production function is  = Π=1    ((1 ) +  + ( ) )  () 5

In the Appendix, we consider variants of this replicator dynamic. The conclusions of the model do not change substantially.

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 and note that  is maximized only if 1 = 2 =  =  =  . That is, all production  chains with  6=  ,  ∈ {1  }, are a priori inefficient and will be competed out of the market. We may therefore restrict attention to “symmetric” production chains of the form ³  ´  = Π=1      ()  ˜ () = Π=1    1− 

˜ () =   ()  where  The necessary first-order condition for  to be optimal is ¢ ¡  ˜ () = Π=1   (1 − ) − + 1−  ln   

which simplifies to,

1− − ln  For this , we have to check the second-order condition =

¢  ¡ 2 −  + ( ln  + +1 − 2)  ln  0  +1

The sign of the left-hand side (LHS) of this expression is determined by the second factor. Substituting for , we get 2 −  + ( ln  + 1 − 2)  ln  µ ¶ 1− 1− 2 =  −+ ln  + 1 − 2 ln  − ln  − ln  = ( − 1)  0 Taking into account that 1 ≤  ≤ , the optimal  is then ⎧ ⎪  ≤ −(1−) ⎨ 1 if 1− −1 if −(1−)   ≤ −  ∗ = ln  ⎪ 1− ⎩  if −    ≤ 1

Note that ∗ is (weakly) increasing in . That is, the better are a country’s contract-enforcing institutions, the more specialized are its firms. Also, and for obvious reasons, ∗ is decreasing in ; i.e., the smaller is the advantage of specialization, the less firms specialize. Recall that firms face a wage schedule  (). Supermodularity of  and  ,  6= , implies sorting. All firms in the product chain choose workers with the same skill level  =  =  for all   ∈ {1  }. (See Kremer, 1993, for a detailed argument.) 7

The first-order condition (FOC) for  to be optimal is 

 ˜ () =  −1  1−    ˜ () =  −1   1−  

Integrating over  gives all wage schedules that satisfy the FOC for all : Z  ˜ ()  +   () = −1  1−  0

   1− ˜    () +  = 

Imposing a zero-profit condition for firms implies that  (0) = 0 and, hence,  = 0. Therefore,   () =  Next, we determine the profit-maximizing technical complexity, , of product . The FOC for  to be optimal is ˜ 0 () +    1−  ˜ () ln  =  ()    1−  Substituting for  () and simplifying, the FOC reduces to ³ ˜ ´0 () 

− ln  =

˜ ()  ˆ0

 () ˆ () 

=

The second-order condition (SOC) for  to be a maximum is ³ ´ ³ ´ ˜ 00 () +  ˜ 0 () ln  +   ln ()  ˜ 0 () +  ˜ () ln   0  

This reduces to

ln2  

˜ 00 ()  ˜ () 

˜ 00 ()  0. which holds because  Next, we verify that   0. Note that   

Ã

ˆ 0 ()  ˆ () 

!

 

 0 iff

 

³ ˆ0

 () ˆ ()

ˆ ()  ˆ 00 () −  ˆ 02 ()  = ˆ 2 ()  8

´

 0. Because

ˆ 00 ()  0. Finally, it can be easily verified a sufficient condition for   0 is that   ˆ 00 ()  0 is implied by  ˜ 00 ()  0. that  Workers choose their skill levels  ,  ∈ {1  }, by optimally trading off cost  ( ) with reward  ( ). The FOC for  to be optimal is  (  − ) | =− =  ³ ´ ( − )   = | =− =  ³  ´ −1  1− ˆ   ·     () = 

 0 () =

In the unique symmetric equilibrium, ˆ ()  0 () =  −1  1−   =  or  0 () =  () As long as  0 () increases sufficiently fast, this equation always has a unique solution in  that satisfies the SOC. The optimal  is increasing in  and, hence, in . We conclude: Proposition 1 Organizational complexity , technical complexity , skill level  and wages  () are all increasing in the quality of contract-enforcing institutions .

3.2

Effect of Economic Structure on Institutions

Recall that the marginal benefit , , of better institutions is  =

 (ln ( )) 

Substituting for  and simplifying we get  =

where ∗ =

⎧ ⎪ ⎨ 1

−1 ln 

⎪ ⎩ 

if  ≤ −(1−) 1− if −(1−)   ≤ −  1− if −    ≤ 1 9

∗ 

In the following figure,

 

is drawn as a function of .

y 24 22 20 18 16 14 12 10 8 6 4 2 0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

x

Marginal benefit of better institutions Note that marginal benefits are U-shaped in . The marginal benefits of better contract-enforcing institutions are largest when institutions are either very bad, or when they are very good. In the middle they are substantially lower. The intuition is as follows. Good institutions support an organizationally complex economy in which highly specialized firms transact a lot amongst each other to produce advanced goods and services. A marginal improvement in contract-enforcing institutions, which is reflected in a marginal reduction in transaction costs, positively affects all of these many transactions. Hence, the more complex is the economy, the larger is the benefit of a marginal improvement of institutions. This explains the upward-sloping part of the marginal benefit curve to the right. When institutions deteriorate, firms respond by becoming more vertically integrated and less specialized in order to be less affected by the higher transaction costs. At some point, however,  reaches its lowest point, i.e.,  = 1, and cannot fall any further. (This happens when  ≤ −1 , which corresponds to  = 061 in the figure.) At this point, the product chain is fully integrated. As long as even a fully integrated product chain is at least somewhat affected by bad institutions–because it has to transact with final consumers, for instance–having run out of mitigation options, it will be hit harder and harder by further deteriorations in institutions. This explains the downward sloping part of the marginal benefit curve to the left. What does the U-shape of the  curve imply for institutional change? Recall

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that the replicator dynamic for  is characterized by µ ¶  (ln ())  =    µ ¶  =   is also U-shaped. The following Because  is a strictly increasing function,    figure depicts (a generic representation of)  as a function of .

dg/dt

g  

as a function of 

In this figure, the -axis cuts through points at which the forces for and against = 0. Above the -axis,  0 institutional change exactly cancel each other, i.e.,    and institutions improve, below,   0 and they deteriorate. By assumption, the  curve lies below the -axis at its minimum. Moreover, for  ↓ 0 and  ↑ 1,  goes ∗ ∗ to infinity. Hence, there are always two interior equilibria, 0      1, the first of which is stable. The phase diagram for  looks as follows: 

11

0

∗ 

∗ 

1

Phase diagram ∗ ∗ converge to  . Countries starting Countries starting out anywhere below  ∗ out above  keep improving and move towards  = 1.

4

Discussion

Essentially, this paper makes two claims: 1) The quality of a country’s institutions affects its economic structure. 2) Conversely, a country’s economic structure affects the quality of its institutions. More specifically, we have formalized the following chain of arguments. First, good contract-enforcing institutions lead to vertically disintegrated product chains consisting of highly specialized firms interacting with each other through myriad market transactions. Second, the marginal benefits of improving contract-enforcing institutions are proportional to the existing level of interconnectedness of the economy. Taken together, these results imply that the marginal benefits of better institutions are greater in countries that already have good institutions than in those that still have to develop them. Finally, if institutional change is incremental and demanddriven, then divergence is the natural outcome: good contract-enforcing institutions get better, while bad ones stagnate, or get worse. Or, in more Biblical terms: “For he that hath, to him shall be given: and he that hath not, from him shall be taken even that which he hath.” (Mark 4:25).

4.1

Testable implications and empirical evidence.

The model has, at least, three testable implications. The first two correlate the quality of contract-enforcing institutions to vertical integration and to the returns to education. The third is related to the “Convergence” debate. Of these three implications, the first seems to be borne out by the data, the second may not be, while there is no consensus on the third.

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Vertical integration One testable implication of the model is that, all else equal, bad institutions are correlated with more vertically integrated firms. At least three recent papers have studies this question empirically, and all of them indeed find such a positive relationship.6 Khanna and Palepu (2000) provide evidence that companies in India are larger and more vertically integrated than in the US, and they suggest that this happens because trading at arm’s length is more costly in developing countries where contract enforcement is weaker. Fan et al. (2009) study differences in vertical integration across the various regions in China. They show that vertical integration is more common in regions where legal institutions are weaker and where regional governments are of lower quality. Finally, in a cross-country analysis of 45 developing countries, Pascali (2009) also finds that firms are more vertically integrated in countries with weak institutions. While these empirical findings are indeed consistent with the model presented in the paper, it should be noted that they do not speak to the direction of the causation (if indeed there is a causal relationship). That is, the data are consistent with all three of the following hypotheses: 1) Firms are more integrated because institutions are worse. 2) Institutions are worse because firms are more integrated. 3) All of the above (as claimed in this paper). Therefore, we have to conclude that the empirical validity of this testable implication of the model remains somewhat of an open question. Institutions and the returns to education. Our model suggests that the quality of institutions affects the returns to education: The better are a country’s contract-enforcing institutions, the higher the skill premium. There seem to be no papers in the literature that explicitly study the relationship between the quality of a country’s institutions and the skill premium. However, there are a number of studies that look at cross-country returns to education. (See, e.g., Psacharopoulos, 1985, and Trostel et al., 2002.) Generally, they find that the returns to education in developing countries are higher than in developed countries. Indeed, insofar as developed countries have better institutions than developing countries, this would seem to contract our model. Of course, there could be many reasons why educational returns are higher in the developing world, even though institutions positively affect the equilibrium skill premium, as implied by the model. For example, if people in the developing world are severely credit constrained, workers’ educational attainments will never reach the equilibrium level where marginal cost equals marginal benefit. Hence, in the data, we would be comparing equilibrium marginal returns in the developed world with out6

The finding in Rajan, Zingales and Kumsar (1999) that firms tend to be larger in countries with better institutions might seem to contradict the model’s prediction that better institutions lead to more specialized firms. However, a specialized firm focussing on single task in a long product chain and replicating that same task many times over may very well be larger than a less specialized firm executing many different tasks. Hence, firm size cannot be taken as a proxy for vertical integration.

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of-equilibrium marginal returns in the developing world. Higher out-of-equilibrium marginal returns could very well go hand-in-hand with lower equilibrium marginal returns. In short, it a more careful empirical study would be needed to properly evaluate this prediction of the model. Convergence / Divergence. The decreasing-returns assumptions of standard neoclassical growth models such as Solow (1956), Cass (1965), and Koopmans (1965) imply economic convergence of countries that start out at different initial conditions. In our model, returns to institutional development are initially decreasing, but become increasing thereafter. As we have seen, this implies that countries fall into two categories depending on their initial conditions of institutional development. Countries starting out below some threshold converge to a stable equilibrium characterized by an economy of low organizational and technical complexity. These countries are caught in an institutional trap. Countries starting out above the threshold, on the other hand, are in a state of continuous, self-perpetuating growth. Their levels of institutional development support economies that are so complex that the benefits of further reductions in transaction costs are sufficiently high to overcome inherent obstacles to further institutional improvement. This puts these countries in a virtuous cycle of economic and institutional growth that feed on each other. In principle, convergence versus divergence of countries is an empirically testable question. While it has received a lot of attention in the literature, no consensus has been reached as to the answer. (See Durlauf, 1996, and the references therein, for a detailed discussion of the controversy.) Moreover, even if there were a consensus that countries were diverging, one would have to test the theory of divergence developed here against various alternative theories. Presumably, this would not be an easy exercise.

4.2

Enclave industries

Enclave industries are highly vertically-integrated, export-oriented operations that have very little connections with the rest of the economy. They tend to have a bad reputation, associated as they are in people’s minds with the resource curse. (Auty, 1993, Sachs and Warner, 2001.) Famous examples from the past and present are the banana enclaves of the United Fruit Company in Central America and the Caribbean, mining enclaves in Chile and Peru, and oil enclaves in Ecuador, Mexico and Venezuela. (Lindsay-Poland, 2003). Recently, however, the resource curse hypothesis has come under critical scrutiny. (See, e.g., Wright and Czelusta, 2004, Brunnschweiler, 2008, Brunnschweiler and Bulte, 2008, and Lederman and Maloney, 2006, 2008). The critique has focused on the fact that there is often no way of telling whether countries have not grown because they are dependent on commodities, or whether they are dependent on commodities because they have not been able to grow. In other words, commodity dependence and 14

enclave industries may not be the cause but the consequence of underdevelopment. Indeed, our model provides a rationale why, in countries with bad institutions, enclave industries may be–and can continue to be over long periods of time–“the only game in town.” When institutions are bad, only highly vertically integrated product chains can be profitably operated. These operations will make an active effort to be self-sufficient and transact as little as possible with the rest of the economy. Once they have achieved that goal, the operators of these enclaves benefit little from broad improvements in the host county’s institutions. Hence, they will not push for them and things will stay pretty much as they were.

5

Conclusion

In this paper we have studied how the quality of a country’s contract-enforcing institutions affects the structure of its economy. Conversely, we have also analyzed how economic structure affects the marginal benefits of better institutions. The main insight derived from the model is that, beyond some threshold, there are increasing returns to institutional development. Hence, it is not countries with bad institutions, but rather those that already have good institutions, that benefit most from further institutional improvements. Put differently, scarcity of institutional capital makes institutions not more, but less valuable in marginal terms. If institutional change is incremental and demand-driven, then good institutions will get better and bad institutions will get worse. As a result, “convergence” remains elusive. In a possible extension of the model to two countries and two types of goods, one could compare the marginal benefit of better institutions under autarky and free trade. Under autarky, both countries produce both goods and the model proceeds roughly along the lines set out above. Under free trade, the country with the worse institutions would specialize in the production of the simpler good, “out-sourcing” the production of the more complex good to the country with superior institutions. Initially, trade liberalization would make both countries better off. However, in the country with inferior institutions, the marginal benefit of improving its institutions would suddenly drop considerably. In the long run, this could cost the country dearly, since institutional development would stagnate and could even go into reverse.

A

Alternative Replicator Dynamics

In the main text, we analyzed the replicator dynamic characterized by µ ¶  ln ()  =    µ ¶  =   15

While this replicator does indeed express the idea that  is monotone in the mar ginal benefit of an improvement in , it is clearly not the only way this idea can be expressed. Two obvious alternatives are µ ¶   () =   and

µ ¶   ln () =   ln 

In the first case,  is assumed to be monotone in the absolute–as opposed to  relative–increase in total production that a marginal improvement in  generates. In the second case,  is monotone in the relative increase in total production caused  by a relative marginal improvement in . ´ ³ ( )  The replicator  =   reduces to

while the replicator

 

µ ¶   =     ´ ³ ) reduces to =   ln( ln   =  () 

In both cases, the phase diagram looks as follows

∗

0

1

Phase diagram of alternative replicator dynamics

∗ Countries starting out below ∗ converge to 0. Countries starting out above  converge to 1.

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