Appendix (not for publication) Trade Costs and Business Cycles Transmission in a Multi-country, Multi-sector Model Hirokazu Ishise Boston University [email protected] November 2, 2012

Contents A.1 Additional experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3

A.1.1 Robustness results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3

A.1.2 Additional robustness checks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

5

A.2 Data and mapping from data to model . . . . . . . . . . . . . . . . . . . . . . . . . . . .

6

A.2.1 Data for the business cycle calculations . . . . . . . . . . . . . . . . . . . . . . . .

6

A.2.2 Instrumental variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

7

A.2.3 IRBC statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

7

A.3 Trade cost estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

8

A.3.1 Data for the estimations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

8

A.3.2 Reduced form gravity equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 A.3.3 Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 A.3.4 Estimation result . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 A.4 Derivations and model properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 A.4.1 Household

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

A.4.2 Final good producer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 A.4.3 Intermediate goods producer, trade cost and distribution . . . . . . . . . . . . . . 19 A.4.4 Trade related variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 A.4.5 Market clearing and and the equilibrium . . . . . . . . . . . . . . . . . . . . . . . 22 A.4.6 Planner’s problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 A.4.7 Alternative specifications of budget constraint . . . . . . . . . . . . . . . . . . . . 25 A.4.8 National account of the model economy . . . . . . . . . . . . . . . . . . . . . . . . 25 A.4.9 Detrended economy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 A.4.10Properties of the non-stochastic steady state . . . . . . . . . . . . . . . . . . . . . 29 A.4.11Calculating steady state . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 A.4.12Log-linearization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 1

List of Tables A.1 International business cycle moments . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 A.2 List of empirical variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 A.3 Average and standard deviations of 390 first stage fixed effects estimations . . . . . . 47 A.4 Estimated steady state trade costs (category specific, average over exporter-importer) 48 A.5 Estimated steady state trade cost (exporter- importer-specific, average over category) 49 A.6 Reduced form gravity equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 A.7 Variables and indices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

List of Figures A.1 Varying productivity shock . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 A.2 Varying standard deviation of trade cost shock . . . . . . . . . . . . . . . . . . . . . 52 A.3 Varying correl. of trade cost shock . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 A.4 Varying financial friction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 A.5 Varying autocorrelation of productivity shock . . . . . . . . . . . . . . . . . . . . . . 53 A.6 Varying autocorrelation of trade cost shock . . . . . . . . . . . . . . . . . . . . . . . 53 A.7 Varying CES parameter θ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 A.8 Varying CES parameter ρ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 A.9 Varying capital stock adjustment friction ηϕ . . . . . . . . . . . . . . . . . . . . . . . 54 A.10 Varying number of “rest of the world” countries . . . . . . . . . . . . . . . . . . . . . 54 A.11 G7 bilateral trade and output correlations . . . . . . . . . . . . . . . . . . . . . . . . 55 A.12 G7 bilateral trade and output correlations . . . . . . . . . . . . . . . . . . . . . . . . 55 A.13 Estimated distance elasticity of trade cost . . . . . . . . . . . . . . . . . . . . . . . . 56

2

A.1 A.1.1 A.1.1.1

Additional experiments Robustness results Standard deviation of productivity shock

The left panel of Figure A.1 shows the effect of changing the standard deviation of the productivity shocks (σ(ˆ εi,m,t )). The figure illustrates the slope coefficient of trade-comovement regression, output and consumption volatilities, and cross-country correlations of output and consumption for various sizes of productivity shock, while other parameters are fixed. The volatilities of the aggregate output and consumption critically depend on the size of the shock. The magnitude of cross-country correlations is not affected by varying the size of the productivity shock. Yet, when the standard deviation approaches zero, the cross-country correlations increase. Also, the slope coefficient increases dramatically when the standard deviation decreases. Since the model has two types (productivity and trade costs) of shocks, the cross-sectional variation of the model economy is driven by the trade cost shock if the productivity shock is extremely small. The relative size of the shock is an important determinant of the cross-sectional variation of the model economy. Finally, the slope coefficient becomes small if the shock is extremely small, because temporal changes in comparative advantage are small. A.1.1.2

Cross-country correlation of productivity shock

The right panel of Figure A.1 illustrates the effects of changing the cross-country correlation of the productivity shock (σ(ˆ εi,m,t , εˆj,m,t )). IRBC literature (for example, Baxter, 1995) suggests that the cross-country correlation of productivity shock directly affects the cross-country correlations of variables. As expected, a higher productivity correlation implies higher output and consumption correlations (they almost perfectly overlap each other). In contrast, standard deviations of output and consumption do not drastically change. Therefore, a higher degree of comovement does not necessarily imply higher volatilities of the countries. Even in the case that there is almost no cross-country correlation in productivity, the slope coefficient is positive. Hence, the model cross-sectional variation does not depend exclusively on the degree of cross-country correlation of productivity shock. This result is consistent with the finding by Arkolakis and Ramanarayanan (2009), who examined a multi-sector international real business cycle model including Ricardian trade structure, and showed that their model can generate a positive aggregate output correlation and a positive slope coefficient without imposing a positive productivity correlation. A.1.1.3

Standard deviation of trade cost shock

The two panels of Figure A.2 show the effect of changing the standard deviation of trade cost shock. In the baseline parameterization, I set the standard deviation of trade cost shock to 0.0485. This value is based on the estimated trade costs. Yet, as shown in figures in the main text, the shipping

3

cost indices based on the market price show substantially larger standard deviations. Using this level of large standard deviation significantly alters model properties. The left panel of Figure A.2 displays the slope coefficient, the standard deviation of output, and the standard deviation of consumption for various standard deviations of trade cost shock. A real world interpretation of high standard deviation is that a high standard deviation represents the period of a more volatile oil price, because the shipping costs critically depend on the oil price (Stopford, 2009). The baseline parameterization is located at around 0.05. Even if trade cost volatility is set to 0.2, the standard deviation of output is still less than two, which is in the range of corresponding data from developed countries (Backus et al., 1994). The volatility of consumption increases to a smaller extent, suggesting the effect of consumption smoothing mechanisms. The cross-country correlation of output and consumption increases to some degree (right panel of Figure A.2). In contrast, the slope coefficient sharply increases because a high volatility of trade cost shock reduces trade with remote countries and increases trade with neighboring countries. This is because the shock is a percentage deviation from the steady state, meaning the absolute changes in trade costs are larger if steady state trade costs are larger. A high volatility of trade cost shock then generates a larger comovement in the neighboring countries. As a result, the average correlation also increases. An implication is that the slope coefficient depends on the timing of the sample period. If the sample comes from a relatively volatile trade costs period (1970s and 2000s), then the slope coefficient is expected to be high. A.1.1.4

Cross-country correlation of trade cost shock

Given the significant role played by the size of a trade shock, a natural question is whether the assumption on the correlation matrix of trade cost shock also significantly alters the model statistics. The answer is no, except for the slope coefficient. For examining the effect of changing parameters in the correlation matrix of the trade cost shock while maintaining tractability, I set all the offdiagonal terms of the correlation matrix to specific values. I then vary the value from zero to one. Figure A.3 shows the model statistics for various correlations of trade cost shocks. The slope coefficient changes, but the other statistics do not change. Hence, varying the correlation of trade cost shock does not change the volatilities and cross-country correlations of output and consumption. A.1.1.5

Role of the financial market

Figure A.4 shows the effects of changing the asset trading cost parameter, η b . The horizontal axis is η b in log scale. The original motivation to introduce the asset trading cost parameter is to allow the model to have a unique steady state of the amount of asset holdings to be zero in the incomplete market setting (Ghironi and Melitz, 2005). Effectively, the parameter controls the transaction costs of asset trading. A low parameter value suggests low costs in international trade of assets. A high η b reduces the incentive to change the amount of assets. At the extreme, a high enough η b is equivalent to the “financial autarky” assumption proposed by Heathcote and Perri (2002) because 4

agents in the model do not have incentive to change the amount of assets from the steady state value (which is zero). Since the “financial autarky” model excludes the possibility of asset trading, an interpretation of the parameter is the degree of restriction imposed on the international financial trading. Tightening the financial transactions (for a high η b ) does not reduce the degree of volatility, which is consistent with the results obtained by Heathcote and Perri (2002). They found that the financial autarky assumption (which corresponds to an extremely high financial transaction cost in my model) does not significantly alter intra-country business cycle properties. They also show that the financial autarky assumption reproduces empirically comparable magnitude of output and consumption cross-country correlations. Along with their findings, Figure A.4 shows that the cross-country correlations of output and consumption are not responsive to the financial friction parameter. Reducing the financial friction does not drastically change the volatilities and crosscountry correlations. The size of the financial friction influences the slope coefficient, but the absolute change is not large. A policy implication based on the model is that tightening the international financial transaction does not eliminate the magnitude of business cycle volatilities, as well as the degree of cross-country comovement.

A.1.2

Additional robustness checks

• Figure A.5: Autocorrelation of productivity shock ρa • Figure A.6: Autocorrelation of trade cost shock ρτ • Figure A.7: CES parameter θ • Figure A.8: CES parameter ρ • Figure A.9: Capital stock adjustment friction parameter ηϕ • Figure A.10: Number of countries specified as the rest of the world. (Baseline is six.)

5

A.2 A.2.1

Data and mapping from data to model Data for the business cycle calculations

The quarterly and monthly data are filtered by approximate band path filter (Baxter and King, 1999). For the quarterly data, the cutoff parameters are (6, 32) and autoregressive order is 12. The annual data is filtered by HP filter, with λ = 6.25 (Hodrick and Prescott, 1997). The choice of the filters for annual and quarterly data does not alter basic implications. HP is employed for keeping longer observations in annual data. For the monthly data, the cutoff parameters are (2, 96) and autoregressive order is 18 for extracting trend. For the monthly data, the cutoff parameters are (18, 96) and autoregressive order is 18 for extracting business cycle component. Quarterly national accounts and labor variables are taken from “Source OECD” quarterly national account and main economic indicators. If longer data is available through country’s own source or older SNA system, main economic indicator data is extrapolated by growth rate of additional data. All the variables are quarterly and seasonally adjusted. Real values in the data set are used. Hours and employments are normalized by 2000 values (average of four quarters in 2000) separately, and then they are multiplied to obtain labor variable. Italian labor is calculated only using employment data since hours data is missing. Italian labor statistics is used for TFP calculation. Labor related statistics are based on 6 countries. Filtering is applied for the longest possible dataset, and then moments are calculated using limited sample period (1970, 1st quarter to 2006, 4th quarter). Germany and West Germany data are separately filtered. Then, statistics are obtained by pooling both Germany and West Germany. Excluding net exports, variables are in natural logs, and then applied filters. Net exports are filtered after divided by real GDP. Aggregate TFP is calculated by standard Solow accounting. After calculating autocorrelation by fitting AR1, TFP shock is calculated as residual. Sector level productivity is calculated using Historic ISIC industrial production data base (ISIC2) and ISIC industrial production data base (ISIC3) obtained from “Source OECD”. ISIC2 is used as basis and expanded by the data using growth rates of ISIC3. The sectors are manufacturing (3 in ISIC2, D in ISIC3), food (31 in ISIC2, 15/16 in ISIC3) and mining (2 in ISIC2, C in ISIC3). Seasonally adjusted production indices and labor indices (no capital stock information) are used. If data is provided only in raw series, X12 is applied. The productivity is calculated by production/labor(2/3) . After calculating autocorrelations by fitting AR1, shock components are calculated as residuals. Stopford (2009) compiles long time series of the freight cost. This freight index represents a price of the dry bulk and grain freight, based mainly on US gulf to Japan via Panama canal. The index is annual, and both nominal and inflation adjusted values are provided. The nominal index series is normalized by 1947 value, and then real value is obtained by using appropriate deflator. This paper employs real value index from 1947–2007. Baltic exchange dry index (BDI) is a price index of dry bulk, compiled by Baltic Exchange. BDI is an average made up of various sizes and routes. The price is in (nominal) US dollar.

6

The data is drawn from Datastream (Datastream code: BALTICF). The available index is daily (business dates) observations from May 1985. After taking a unweighted monthly average of the daily observations, the nominal price is adjusted by US monthly CPI (Bureau of Labor Statistics series: CUUR0000SA0).

A.2.2

Instrumental variables

As mentioned by Frankel and Rose (1998), instrumental variable methods using gravity variables as instruments for the bilateral trade intensity imply larger coefficients. Yet Baxter and Kouparitsas (2005) show gravity variables are correlated with comovement even if bilateral trade is controlled (see also Clark and Wincoop, 2001). This direct effect of the gravity variables on comovement may be a result that the gravity variables proxy some other potential omitted variables. Regardless of the mechanism, the direct correlation of the gravity variables and comovement after controlling trade suggests gravity variables do not necessarily satisfy the orthogonality condition of the instrumental variable approach. Nevertheless, I use IV methodology in the model section following the literature, but OLS and IV give similar coefficients in the model.

A.2.3

IRBC statistics

Table A.1 shows international business statistics of additional cases. All the statistics are taken from the model G7 average. • Complete market: the market assumption is complete market. The corresponding plot is the left-panel of Figure A.11. • Financial autarky: the market assumption is financial autarky. The corresponding plot is the right-panel of Figure A.11. • Same TC: Only cross-country variation is population. The corresponding plot is the left-panel of Figure A.12. • Same Pop: Only cross-country variation is trade costs. The corresponding plot is the rightpanel of Figure A.12. • Symmetric countries: Perfectly symmetric case.

7

A.3

Trade cost estimation

A.3.1

Data for the estimations

A.3.1.1

Data set

The national accounting data employed in the estimation is Penn World Table mark 6.2 (Heston et al., 2008). Trade data is NBER-UN world trade data (Feenstra et al., 2005). The trade data spans all the world countries, four-digit Standard International Trade Classification (SITC, revision 2), from 1962 to 2000. I compress this data into 21 OECD countries, single-digit SITC (10 categories) from 1962 to 2000. As a result, 163,800 (= 21 × 20 × 10 × 39) observations are used. This data is enumerated using destination country record, in CIF (cost, insurance, freight), not FOB (free on board). Hence, the value of trade flow conceptually includes trade costs. If the value is smaller than $100,000 US dollar (in current value), the data set records this entry as missing (Feenstra et al., 2005). By aggregating into single digit SITC and focusing only on major OECD countries, many of the missing values are eliminated. Yet 3,935 (2.4%) observations are missing values. I replace these missing observations with $50,000 in current value. The exact number of the replaced value does not significantly affect the estimated trade costs.1 Before using the estimation, the original data variables are converted into model concept (e.g., the model does not have inflation). Distance variables are taken from Glick and Rose (2002) and Rose (2005). Since my focus is only OECD countries, used variables are log of the bilateral physical distance, and dummy variables. Dummies are of sharing border, of common language, of formal colonial relationship, if both in EU, if both in NAFTA, and if both in Australia-New Zealand FTA. Free trade agreement dummies are aggregated into a single dummy variable. It should be noted that if the trade costs are captured by gravity variables, the gravity variables vary with the (j, i) pair and t (e.g., period with or without regional trade agreement), but no variation is observed across m. A plausible assumption is each category has different trade cost and hence different coefficients (Hummels, 1999). Moreover, significant time variation is also expected. The following estimation is thus made for each product and time pair (m, t) samples. For each (m, t) pair, there are N (N −1) = 21×20 = 420 observations. For simplicity in presentation, the following section drops the subscripts (m, t). A.3.1.2

Data modifications

I made some modifications to data set. National accounts of Belgium and Luxembourg Since trade data treats Belgium and Luxembourg as a single country, national account data is modified. Weighted average is taken for the series for each year, where the population is used as a 1 I examine the other values {100, 1000, 100000}. The obtained estimation coefficients and trade costs are almost identical to the baseline case. Helpman et al. (2008) exploits structural model in a version of gravity equation to create exclusion variable of Tobit type estimation. Their result suggests replacement of missing values does not significantly cause the estimation bias.

8

weight. It preserve aggregate real GDP as a sum of the two economies. Distance data treats two countries as a single entry before 1996 (basically using Belgium information). After 1997, there are two separated entries. Belgium information is used as Belgium-Luxembourg entries. National accounts of Germany PWT6.2 has no German entries before 1969, except for population and nominal exchange rate. Other entries are extrapolated by using West Germany growth rate series, based on 1970 observations. The growth rate is obtained from PWT 5.6. On trade data, entire Germany is used after reunification. Before unification, West Germany data is used. In a few years around reunification, there are double entries for West Germany and Germany. According to the data appendix (Feenstra et al., 2005), they are not double counted, so that they are summed up. Imports of Canada in 1978 Canadian imports in 1978 in Feenstra et al. (2005) data set show obvious errors. Import values in 1978 are around half of 1977 and 1979 values. There is no obvious reason that there is such a huge temporal decline. The data is replaced by directly obtained data from UN comm trade data base. Population The model assumes constant population over time. The constant fraction of population to world population, πi , is calculated as follows. First, I sum up the population of the sample countries for each year using PWT. Then, I calculate population fraction of each country in each year by dividing country’s population by total of the sample countries. Finally, time series average of the fraction given period is taken. A.3.1.3

Price conversion and national accounting

The model economy has no nominal friction, inflation, etc. Also, the model economy uses world common currency. Consumption bundle price level is different across countries, reflecting their productivity. The model “purchasing power parity” price measure, Pi,t , is different from actual data counterpart in PWT. The model is CES aggregator whereas PWT employs Geary-Khamis method. The mapping between them is highly nonlinear function. Yet, within OECD economies, the discrepancy among various construction methods of world consumption basket and price index is minimal (Deaton and Heston, 2008). Given the difference, the basic strategy of conversion is following. First, I express (or use) statistics in current USD. Then, USD inflation is adjusted by USD deflator. For international consistency, inflation adjustment is by implicit US PPP deflator (obtained by fixed 2000 basket

9

Lasperyres measure) in PWT. Finally, I adjust PPP. Namely, / CULCU 1 | EXR {z } USDEF |CUUSD{z COUSD

}

PPP = COPPP EXR | {z } PPP in USD

where, for the case of GDPPC (GDP per capita), CULCU is current local currency unit GDPPC, CUUSD is current GDPPC in USD, COUSD is constant price GDPPC in USD = Pi,t Yi,t , COPPP is constant PPP adjusted GDPPC (in USD) = “RGDPL” = Yi,t , EXR is “XRAT”, nominal exchange rate (Local currency/USD), USDEF is USD deflater, calculated by “CGDP”/“RGDPL” (2000 USD = 1), PPP is “PPP”, expressed in terms of LCU by USD, and PPP/EXR is price level as if LCU is USD = Pi,t . The variabels with quotation marks are directly obtained from PWT. Given GDP statistics (RGDPL series), “RGDPL” × ( “KC” +“KG”+ “KI”) = Zi,t where KC, KI, and KG are consumption, government spending, and investment shares in PWT. The trade data is recorded in CIF, based on importing country’s report, in nominal US dollar, in current value. Let’s denote the value as CUUSD. US dollar deflator is constructed by USDEF=“CGDP”/“RGDPL” of US in PWT. Then CUUSD = exj,i,m,t = πi pj,i,m,t zj,i,m,t USDEF

A.3.2

Reduced form gravity equations

Table A.6 contains the results obtained from reduced form gravity equations. These gravity equations are estimated by pooling all the sample.

A.3.3

Estimation

I calculate the trade costs based on trade flow expression. −ρ 1−ρ

1 1−θ

(

exj,i,m,t = Pi,t πi Zi,t pj,m,t |

{z

} | {z } |

N ∑

( ) −ρ 1−ρ −1 ph,m,t υh,i τh,i,m,t −ρ 1−ρ

h=1

{z

importer exporter price income

substitution of different origin

)

θ−ρ ρ(1−θ)

(

−1 υj,i τj,i,m,t

}|

{z

) −ρ

1−ρ

. (A.1)

}

trade cost

First, the trade flow (exports) is normalized by economic size of the importer: yj,i

)) ( ( 1 / 1−θ . ≡ log exj,i Pi Zi πi

(A.2)

Then, I estimate a fixed effect model: yj,i = Γj + Λi + ν + x′j,i β + εj,i

10

(A.3)

where Γj is the indicator of fixed effect for j, Λi is the indicator of fixed effect for i, ν is the level of trade costs (which will be dropped based on the fixed effect estimation strategy), xj,i is a vector of the set of gravity variables as log of the physical distance and border dummy. εj,i is the error term orthogonal to the observable explanatory variables: E(εj,i xg,h ) = 0

for all (j, i, g, h) ∈ N 4 .

(A.4)

The error term assumption is based on the model setting. By the model construction, the trade costs consist of the steady state component and the shock component. The estimation error comes from this shock component of the trade cost. The orthogonality condition is potentially invalid, for example, by the treatment of missing observations. Namely, if distance variables predict the missing values, the error and distance variables are not orthogonal. For minimizing the possibility of this missing observation problem, I focus my sample on 21 OECD economies. The gravity variables are taken from Glick and Rose (2002) and Rose (2005). The variables included in the estimation are log of the bilateral distance, square of the log of the distance (ln(distance))2 , cube of the log distance (ln(distance))3 , indicator of the sharing national border, indicator of the colonial relationship, indicator of the common language, and indicator for being in the same regional trade agreement.2 The inclusion of the square and the cube terms aims to capture potential non-linearity in the distance coefficient suggested by, Eaton and Kortum (2002) and Anderson and van Wincoop (2004), for example. As the result, the component of the exogenous explanatory variables is expressed as x′j,i β = β1 ln distj,i + β2 (ln distj,i )2 + β3 (ln distj,i )3 + β4 borderj,i +β5 Langj,i + β6 Colonyj,i + β7 FTAj,i,t .

(A.5)

The estimation strategy exploits a variation across different exporters for a particular importer, and a variation across different importers for a particular exporter. After controlling the importers’ size, the difference in trade flow for a different destination is attributed to the difference in trade costs. The fixed effect Γj captures the contribution of the exporter- product- year-specific price (which then captures the exporter- product- year-specific productivity). That is, anything exporterspecific is attributed to the price of the goods at the origin. Anything importer-specific is attributed to the substitution effect. Then, the estimation gives the trade costs as the residual from the actual trade flow and potential explanatory variables. The strategy of obtaining trade costs as the residual is similar to Hummels (1999) and Gervais and Jensen (2009). b b ¨j , Λ ¨ i ). A two-way fixed effect estimation gives βˆ and fixed effects as deviations from the means (Γ ¯ = Γj − Γ ¨j , Λ ¯ = Λi − Λ ¨ i and ν (a potential constant term in That is, the estimation does not give Γ the true trade cost). Yet, there are N additional structural assumptions: intra-country trade costs are all unity. The basic idea of the second step is to set these three parameters so as to minimize a 2

Other common “distance” variables, e.g., the generalized system of preference, do not have enough variations across these OECD countries.

11

loss function summing the deviations of N conditions by non-linear least squares. The loss function is given by

¯ Λ) ¯ = V (Γ,

N 1∑

2

i=1

  ) 2 ( ( ) ( ) ∑ b b b ¨i + Λ ¯  . (A.6) ¨i + Γ ¯+Λ ¨i + Λ ¯ − exp θ(1 − ρ) Λ  exp (yh,i ) + exp Γ θ−ρ h̸=i

This two-step estimation is done separately for each (m, t), and hence, the estimated coefficients ˆ j,m,t , Λ ˆ i,m,t , νˆm,t . Using estimated coefficients, the trade cost is indeed depend on (m, t): βˆm,t , Γ calculated by: ( τˆj,i,m,t = exp

)) ρ−1( ′ ˆ . νˆm,t + xj,i,t βm,t + εˆj,i,m,t ρ

(A.7)

After calculating the exporter- importer- product- year-specific trade costs, the trend component of the trade costs is calculated as the mean of all of the trade costs in each period.3 Then, the steady state trade costs, specific to (j, i, m), are calculated by taking a time series average.4 ¯ Λ ¯ and ν. Yet, there are N additional structural The fixed effect estimation does not give Γ, assumptions: intra-country trade costs are all unity. The basic idea of the following estimation strategy is to set these three parameters so as to minimize the deviations of N conditions, using non-linear least squares. The structural interpretation of the terms are −ρ

exp (Γj ) = pj1−ρ ,

(A.10)

−ρ ) ( 1−ρ exp ν + x′j,i β + εj,i = τj,i ,

(A.11)

( exp (Λi ) =

N ∑

−ρ 1−ρ

ph

−ρ 1−ρ

θ−ρ ) ρ(1−θ)

τh,i

.

(A.12)

h=1

3

    / T −1 N ∑ ∑ N ∑ ∑ M M ∑ ∑ 1 1 ∑  1 (ˆ gτ ) = τˆj,i,m,t+1   τˆj,i,m,t  . T − 1 t=1 N (N − 1)M i=1 N (N − 1)M i=1 m=1 m=1 4

j̸=i

(A.8)

j̸=i

Fourth power term is to adjust model (quarterly) and data (annual) time periods. 4

τˆ ¯j,i,m =

T 1 ∑ τˆj,i,m,t / (ˆ gτ )4t . T t=1

12

(A.9)

Hence, using the assumption that τi,i = 1, it must hold ( exp

ρ(1 − θ) Λi θ−ρ

) = exp (Γi ) +

∑

( ) exp Γh + ν + x′h,i β + εh,i .

(A.13)

h̸=i

b b ¨ h + Γ, ¯ Λ is replaced by Λ ¨ i + Λ, ¯ and ν +x′ β +εj,i is replaced by ν +x′ βˆ + εˆh,i = If Γh is replaced by Γ j,i h,i ( ) i b b ¨h + Γ ¯+Λ ¨i + Λ ¯ , yh,i − Γ ( exp

)) ( ) ∑ ( ) ρ(1 − θ) ( ˆ b b ¯ ¨i + Γ ¯ + ¨i − Λ ¯ , Λi + Λ = exp Γ exp yh,i − Λ θ−ρ

(A.14)

)) ( ) ∑ θ(1 − ρ) ( b b b ¨ ¯ ¨i + Γ ¯+Λ ¨i + Λ ¯ + = exp Γ Λi + Λ exp (yh,i ) . θ−ρ

(A.15)

h̸=i

or ( exp

h̸=i

¯ and Λ. ¯ Define vi (Γ, ¯ Λ) ¯ as: There are i = 1, ..., N equations, but there are two unknowns Γ ¯ Λ) ¯ = vi (Γ,

∑ h̸=i

( ) ( )) θ(1 − ρ) ( b b b ¨ ¯ ¨ ¯ ¨ ¯ exp (yh,i ) + exp Γi + Γ + Λi + Λ − exp Λi + Λ . θ−ρ

(A.16)

Set a square distance objective function: ∑( ) ¯ Λ) ¯ 2. ¯ Λ) ¯ =1 vi (Γ, V (Γ, 2 N

(A.17)

i=1

Then, two unknowns are calculated by a minimum distance estimation (non-linear least squares): b b ¯ Λ} ¯ = argmin V (Γ, ¯ Λ). ¯ {Γ,

(A.18)

¯ Λ} ¯ {Γ,

¯ =Γ ¯ = 0 as initial values. I employ “fminunc” function of MATLAB optimization toolbox, setting Λ b b b b ¨ i . Then, ¨ j and Λ bi = Λ ¯ +Λ bj = Γ ¯+Γ Using obtained estimates, Γ νˆ =

∑∑ ∑∑ 1 1 b b ¯ − Λ. ¯ y − x′j,i βˆ − Γ j,i (N − 1)2 (N − 1)2 j

i

j

(A.19)

i

b j,m,t , Λ b i,m,t and νˆm,t . Trade cost Since these are calculated for all (m, t), the above method gives Γ is then calculated by ( τˆj,i,m,t = exp

( ))) ρ−1( b b b b ¨ ¯ ¨ ¯ yj,i,m,t − Γj,m,t + Γm,t + Λi,m,t + Λm,t . ρ

(A.20)

The transformation gives a few observations (less than 1%) with trade cost being less than one. Trade costs of these observations are set to one. 13

The steady state price is calculated, first by ( ( )) 1−ρ −ρ ˆ j,m,t pj,m,t = exp Γ ,

(A.21)

then taking time series average of the obtained prices.

A.3.4

Estimation result

Table A.3 presents the summary result of the first step estimations. Here, the mean coefficients are the mean of the coefficients over 390 (10 single-digit classifications × 39 years) different estimations. The standard deviations are variations over 390 different estimations. There are some variations in the point estimates of the gravity variables for each (m, t), suggesting variations of trade costs across categories and time. The estimated trade costs are mainly explained by the gravity variables. For decomposing the estimated trade costs into the contribution of gravity variables and other terms, I calculate a reduced form regression: ( exp

ρ τˆj,i,m,t ρ−1

)

( ) = α0 + α1 x′j,i,t βˆm,t + α2 (ˆ εj,i,m,t ) + uj,i ,

(A.22)

for each (m, t) of 390 different estimations. If I could quantify the trade costs only by the first step, and conduct this regression, then R2 of this regression would be unity because trade costs are exclusively constructed by the gravity variables. The second step introduces contributions of additional terms through estimated values of the error terms. The mean of R2 s of this estimation is 0.86. If I drop εˆj,i,m,t term from the regression, the mean of R2 s is 0.77. If I drop x′ βˆm,t term j,i,t

from the regression, the mean of

R2 s

is 0.08. Thus, the gravity variables determine a large fraction

of the estimated trade costs, but not all. According to the mean of the estimated coefficients in Table A.3, the trade flow increases if two countries share the border, or it suggests that sharing a border decreases trade costs. Two countries sharing a border have 0.04 points lower trade costs than countries do not share a border. Other gravity variables also show some effects on trade cost. Inclusion of the quadratic and cubic terms in (A.5) prevents a direct interpretation of the coefficient of the distance as the elasticity. The average elasticity of the distance is calculated by ) ∂τj,i,m,t distj,i ρ−1( = β1 + 2β2 (ln distj,i ) + 3β3 (ln distj,i )2 . ∂distj,i τj,i,m,t ρ

(A.23)

where I substitute averages of the estimated βs in Table A.3. Figure A.13 plots the implied distance elasticity of the trade costs. The distance elasticity increases in distance. The percentage increment of trade costs is higher the further the two countries are. The effect increases sharply within 2,000 kilometers—covering most pairs of European countries (e.g., the distance between Spain and Finland is 2,050 km). Within relatively near countries, additional distances increase trade costs

14

rapidly. A reason of non-linearity is that with this range, an additional increment of distance leads to switch of transportation mode. On the contrary, the curve becomes flat beyond 6,000 km (e.g., US-Japan distance is 6,225 km). In this range, trade costs increase linearly with respect to distance. For this length of separation, the trade is almost entirely done through ships (Stopford, 2009). Hence, an additional distance does affect the cost level, but does not have acceleration effects. After removing common trend components, exporter- importer- product-specific steady state trade costs are calculated by taking the time series average. The basis year of detrending is 1985, since this year is in the middle of the sample for the business cycle calculations. Tables A.4 and A.5 present the results. Trade costs are higher in agricultural products whereas lower in fuels, which is consistent with the estimation of Hummels (1999). Table A.5 shows the exporter- importerspecific trade costs, which are the averages of the categories. The countries are roughly ordered by proximity in the table. As a natural consequence, the trade costs near the diagonal are small. Isolated countries in the sample such as Japan and New Zealand generally face high trade costs whereas most of the European countries face low trade costs on average. A pair of countries separated by larger distances, as France and Australia, suffers from high trade costs. There are some differences in trade costs depending on the direction. For example, trade costs from Canada to US is smaller (1.44) than the cost from US to Canada (1.55). A potential reason is Canadian economic activities are concentrated in the US border area whereas US economic activities are scattered across countries. If Canadian exports were mainly shipped to closer areas, and Canadian imports came from all over the US, then the average trade costs would be lower for Canadian exporting.

15

A.4 A.4.1

Derivations and model properties Household

A.4.1.1

Household problem

Each representative agent living in i solves max

∞ ∑ ∑

β t Pr(st )u(Ci,t (st ), Li,t (st ))

(A.24)

t=0 st

where (

Ci,t (st )ψ (1 − Li,t (st ))1−ψ u(Ci,t (s ), Li,t (s )) = 1−γ t

)1−γ

t

(A.25)

subject to M ∑

li,m,t (st ) = Li,t (st )

(A.26)

m=1

( ki,m,t+1 (s ) = (1 − δ)ki,m,t (s t

t−1

)+ϕ

xi,m,t (st ) ki,m,t (st−1 )

) ki,m,t (st−1 )

(A.27)

where ϕ is capital adjustment friction function: x ¯i,m ϕ¯′′i,m ) ( ) ′ ¯ ¯ ¯ ϕ x ¯ /k = x ¯/k, ϕ x ¯/k = 1, − ¯ ¯′ = ηϕ , constant. ki,m ϕi,m (

(A.28)

The budget constraint is one of the following. Under the complete market, Pi,t (st )Ci,t (st ) + Pi,t (st ) [ t

= Ai,t (s , s

t−1

t

M ∑

xi,m,t (st ) +

Qt (st+1 |st )Ai,t+1 (st+1 , st )

st+1

m=1

) + Pi,t (s ) Wi,t

∑

M ∑

li,m,t +

m=1

M ∑

] t

Ri,m,t (s )ki,m,t (s

t−1

) − Gi,t (s ) . (A.29) t

m=1

where Pi,t (st ) is final good price, Wi,t (st ) is real wage, Ri,m,t (st ) is real rental rate,5 Gi,t (st ) is lump-sum tax (being equal to government expenditure), Ai,t+1 (st+1 , st ) is state contingent claim contracted after realizing st by agent in i for rewarding a unit of currency if st+1 occurs, and Qt (st+1 |st ) is the price of the claim. Transversality conditions: 0 = E0 lim

t→∞

5

t ∑ ∏

Qk (sk+1 |sk )Ai,k+1 (sk+1 , sk ).

k=0 sk+1

Since labor is instantaneously adjustable, wage is equalized across sectors. The rental rate may not.

16

(A.30)

If only available asset in the world is non-state contingent period ahead risk free claim, household budget constraint is [ Pi,t (st ) Ci,t (st ) +

M ∑

] xi,m,t (st ) + Ptb (st )Bi,t (st ) +

m=1

[

t−1

= Bi,t−1 (s

M ∑

t

) + Pi,t (s ) Wi,t

li,m,t +

m=1

M ∑

)2 ηtb b t ( b Pt (s ) Bi,t (st ) − Ti,t (st ) 2 ]

Ri,m,t (st )ki,m,t (st−1 ) − Gi,t (st ) .

(A.31)

m=1

where Ptb is world price of non-state contingent bond, Bi,t is amount of bond holdings, ηtb is bond holdings adjustment tax parameter (which is time-dependent for having stationarity in transformed b is lump-sum transfer financed by bond holding adjustment tax.6 Also, correeconomy) and Ti,t

sponding transversality condition is imposed: 0 = E0 lim

t→∞

t ∏

Pkb (sk )Bi,t (st ).

(A.32)

k=0

Period-by-period trade balance assumption restricts possibility of asset trading that is balanced: [ t

t

Pi,t (s ) Ci,t (s ) + [ = Pi,t (st ) Wi,t

M ∑

] t

xi,m,t (s )

m=1 M ∑

li,m,t +

m=1

M ∑

] Ri,m,t (st )ki,m,t (st−1 ) − Gi,t (st ) .

(A.33)

m=1

The period-by-period trade balance is a straightforward extension of “financial autarky” assumption proposed by Heathcote and Perri (2002). If there are only two countries, a country-by-country goods side balance automatically implies a period-by-period financial side balance. In the multi-country framework, however, the economies are still possible to trade asset. The asset trading may not hold country-by-country financial side balance, but a financial account of the economy is balanced in the aggregate, ensuring period-by-period financial side balance. A.4.1.2

Household maximization conditions

Given the household problem, first order conditions characterize the optimization. The intertemporal Euler equation with respect to capital investment, uC,i,t = β Pr(st+1 |st )uC,i,t+1 ϕ′i,m,t

6

(

1 − δ + ϕi,m,t+1 xi,m,t+1 Ri,m,t+1 + − ϕ′i,m,t+1 ki,m,t+1

This type of tax and transfer is based on Ghironi and Melitz (2005).

17

) (A.34)

The labor-leisure choice Wi,t = −

uL,i,t 1 − ψ Ci,t = uC,i,t ψ 1 − Li,t

(A.35)

and intertemporal Euler equation with respect to cross country asset. If complete market uC,i,t+1 /Pi,t+1 uC,j,t+1 /Pj,t+1 = uC,i,t /Pi,t uC,j,t /Pj,t

(A.36)

uC,i,t uC,j,t Pi,t = µi µj Pj,t

(A.37)

or

where µi is the initial period (steady state) asset parameter.7 If non-state contingent claim only, Ptb (st )

[ ] ( ) uC,i,t+1 /Pi,t+1 b t 1 + ηt Bi,t (s ) = βEt . uC,i,t /Pi,t

(A.38)

There is no additional condition for the financial autarky case.

A.4.2

Final good producer

A.4.2.1

Final goods producer problem

Final goods producer in i solves max Pi,t (s )Zi,t (s ) − t

t

N M ∑ ∑

pj,i,m,t (st )zj,i,m,t (st )

(A.39)

m=1 j=1

subject to 

 θ  θ1  ρ N M  ∑ ∑ ρ t ρ  t υj,i zj,i,m,t (s ) Zi,t (s ) =   m=1

(A.40)

j=1

where pj,i,m,t (st ) is the price of an intermediate product zj,i,m,t (st ) in country j. Let  qi,m,t (s ) =  t

N ∑

1

ρ

ρ υj,i zj,i,m,t (st )ρ 

(A.41)

j=1

7

Namely, µi = uc,i,0 /Pi,0 . Or in other words, µi is the lagrange multiplier to 0-period budget constraint. Also, it is the inverse of Social planner weight.

18

and

pqi,m,t

  ρ−1 ρ N −ρ ∑ ρ ρ−1 t ρ−1   . = υj,i pj,i,m,t (s )

(A.42)

j=1

A.4.2.2

Final goods producer maximization

The final good producer maximization condition is an inverse demand function ρ pj,i,m,t (st ) = Pi,t (st )Zi,t (st )1−θ qi,m,t (st )θ−ρ υj,i zj,i,m,t (st )ρ−1 .

(A.43)

Since perfect competition and constant returns to scale, it is also true that t

t

Pi,t (s )Zi,t (s ) =

M ∑

pqi,m,t (st )qi,m,t (st )

=

m=1

M ∑ N ∑

pj,i,m,t (st )zj,i,m,t (st ),

(A.44)

m=1 j=1

where pqi,m,t (st )qi,m,t (st )

=

N ∑

pj,i,m,t (st )zj,i,m,t (st )

(A.45)

j=1

Also, [ Pi,t (st ) =

M ∑

pqi,m,t

θ θ−1

] θ−1 θ ,

(A.46)

m=1

and 1−θ pqi,m,t (st ) = Pi,t (st )Zi,t qi,m,t (st )θ−1 .

(A.47)

The implied (currency unit) value of trade flow is expressed: exj,i,m,t (st ) ≡ πi pj,i,m,t (st )zj,i,m,t (st ) 1

1−θ

θ−ρ

ρ

−ρ

1−ρ = πi Pi,t (st ) 1−ρ Zi,t (st ) 1−ρ qi,m,t (st ) 1−ρ υj,i pj,i,m,t (st ) 1−ρ ρ−θ

1

ρ

−ρ

1−ρ pj,i,m,t (st ) 1−ρ . = πi Pi,t (st ) 1−θ Zi,t (st )pqi,m,t (st ) (1−ρ)(1−θ) υj,i

A.4.3

(A.48)

Intermediate goods producer, trade cost and distribution

In each country i, each intermediate producer producing (i, m) solves max pi,m,t (st )zi,m,t (st ) − Pi,t (st )Wi,t (st )li,m,t (st ) − Pi,t (st )Ri,m,t (st )ki,m,t (st )

19

(A.49)

subject to zi,m,t (st ) = ai,m,t (st )ki,m,t (st )α li,m,t (st )1−α

(A.50)

The optimization implies pi,m,t α

zi,m,t = Pi,t (st )Ri,m,t (st ) ki,m,t

pi,m,t (1 − α)

zi,m,t = Pi,t (st )Wi,t (st ) li,m,t

(A.51)

(A.52)

or two condition together implies pi,m,t αα (1 − α)1−α ai,m,t = Pi,t (st )Ri,m,t (st )α Wi,t (st )1−α

(A.53)

There is a pool of producers for each (i, m) goods. The goods are sold for any country subject to iceberg trade costs, τj,i,m,t , where a sender needs to ship τ unit of goods to reach one unit of goods to receiver. For simplicity, no trade cost for internal distribution is assumed: τi,i,m,t = 1. Hence, by arbitrage, price is equalized across destination after deducting trade costs: pi,h,m,t pi,j,m,t = = pi,i,m,t = pi,m,t τi,j,m,t τi,h,m,t

(A.54)

Also, the total goods sales is subject to resource constraints N ∑

πj τi,j,m,t zi,j,m,t (st ) = πi zi,m,t (st ).

(A.55)

j=1

Perfect competition in exporting ensures zero profit in exporting and intermediate goods producer: N ∑

πj pi,j,m,t (st )zi,j,m,t (st ) = πi pi,m,t (st )zi,m,t (st ).

(A.56)

j=1

A.4.4 A.4.4.1

Trade related variables Total exports and total imports

Since the set of exporting goods from country i are {zi,j,m,t }j̸=i , country i’s total exports sales value per capita is EXi,t (st ) =

1 ∑∑ πj pi,j,m,t (st )zi,j,m,t (st ). πi Pi,t m j̸=i

20

(A.57)

Similarly, country i’ total imports value is IMi,t (st ) =

1 ∑∑ πi pj,i,m,t (st )zj,i,m,t (st ). πi Pi,t m

(A.58)

j̸=i

N Xi,t (st ) = EXi,t (st ) − IMi,t (st ). A.4.4.2

(A.59)

Terms of trade

The set of exporting goods from country i are {zi,j,m,t }j̸=i . The price index of the exporting goods is the price of exports aggregated only by exporting goods and then evaluated by the aggregate price: 



 ρ−1

 ∑ ∑ ρ−1 ρ−1  E t Pi,t (s ) =  υi,j pi,j,m,t M

ρ

m=1

ρ

ρ

θ θ−1

 θ−1 θ  

/Pi,t (st ).

(A.60)

/Pi,t (st ).

(A.61)

j̸=i

Similarly, the price index of the importing goods is   I Pi,t (st ) = 

M ∑

m=1

 

∑

 ρ−1 ρ ρ−1

ρ ρ−1

ρ

υj,i pj,i,m,t 

θ θ−1

 θ−1 θ  

j̸=i

The terms of trade, defined as the relative price of imports to exports, is I E t T oTi,t (st ) = Pi,t (st )/Pi,t (s ).

A.4.4.3

(A.62)

Real exchange rate

In this framework, nominal exchange rate is always unity by the assumption of common currency. Let ei,j,t (st ) be the real exchange rate measuring value of j’s consumption basket in i’s consumption basket ej,i,t (st ) =

Pj,t (st ) . Pi,t (st )

(A.63)

By construction, ej,i,t (st ) = 1/ei,j,t (st ) =

21

ej,h,t (st ) . eh,i,t (st )

(A.64)

A.4.5 A.4.5.1

Market clearing and and the equilibrium Market clearing

Followings are market clearing conditions of the economy: M ∑

xi,m,t (st ) = Xi,t (st ) ∀(i, t, st )

(A.65)

li,m,t (st ) = Li,t (st ) ∀(i, t, st )

(A.66)

πj τi,j,m,t zi,j,m,t (st ) = πi zi,m,t (st ) ∀(i, m, t, st )

(A.67)

m=1

M ∑ m=1

N ∑ j=1

Country’s resource constraint: Ci,t (st ) + Xi,t (st ) + Gi,t (st ) = Zi,t (st ) ∀(i, t, st ).

(A.68)

Market clearing of claims are, for all st+1 given st , 0=

N ∑

πi Ai,t+1 (st+1 , st ).

(A.69)

i=1

Non-state contingent bond case: 0=

N ∑

πi Bi,t (st ).

(A.70)

i=1

and lump-sum transfer is financed by bond holding adjustment tax: )2 ηtb b t ( b Pt (s ) Bi,t (st ) = Ti,t (st ). 2 A.4.5.2

(A.71)

Equilibrium

Definition: The competitive equilibrium of the economy given exogenous shocks is a sequence of quantities and prices which are consistent with (1) household maximization problem, (2) final goods producer maximization problem, (3) intermediate goods producer maximization problem, (4) trade arbitrage conditions, and (5) market clearing conditions. The competitive equilibrium of the economy with full state contingent claim is Pareto efficient, since markets are all competitive, there is no externality, and all the productions are constant returns to 22

scale. The competitive equilibrium of the economy with non-state contingent claim is also shown to be equivalent to the allocation obtained by a constrained social planner’s problem. Claim: The competitive equilibrium with full state contingent claim is Pareto efficient. Proof: The equilibrium conditions are coincide with conditions derived from social planner’s problem. See below. (QED) From now on, explicit history dependence of variable is dropped from the notation. Since there is one degree of freedom with respect to nominal price (across Pi,t , pi,m,t and pj,i,m,t ), PN,t = 1 for all t is assumed as a normalization. The analysis focuses on an equilibrium in which steady state net exporting is zero. Namely, imposing ¯ i = IM ¯ i EX

(A.72)

where variables with upper bar is of steady state values defined later. µi is adjusted so as to consistent with achieving the equilibrium.

A.4.6 A.4.6.1

Planner’s problem Planner’s problem

Consider a Planner’s problem with weight ωi max

∑ i

ωi πi

∞ ∑ ∑

β t Pr(st )u(Ci,t (st ), Li,t (st ))

(A.73)

t=0 st

where [

Ci,t (st )ψ [1 − Li,t (st )]1−ψ u(Ci,t (st ), Li,t (st )) = 1−γ

]1−γ (A.74)

s.t. zi,m,t = ai,m,t (st )ki,m,t (st )α li,m,t (st )1−α ( ki,m,t+1 (s ) = (1 − δ)ki,m,t (s t

  Zi,t (st ) = 

M ∑ m=1

t−1

)+ϕ

xi,m,t (st ) ki,m,t (st−1 )

(A.75)

) ki,m,t (st−1 )

  θ  θ1 ρ N ∑ ρ  t ρ  υj,i zj,i,m,t (s )   j=1

23

(A.76)

(A.77)

πi zi,m,t (st ) =

∑

πj τi,j,m,t (st )zi,j,m,t (st )

(A.78)

j

Xi,t (st ) =

M ∑

xi,m,t (st )

(A.79)

li,m,t (st )

(A.80)

m=1

Li,t (st ) =

M ∑ m=1

Resource constraint: 0 = Zi,t (st ) − Ci,t (st ) − Xi,t (st ) − Gi,t (st ). A.4.6.2

(A.81)

FOCs of planner’s problem

Dropping st from the notation for simplicity. Let the multiplier associated to production be λi,m,t and the multiplier to resource constraint be Λi,t . FOCs are: Λi,t (st ) = ωi β t Pr(st )uC,i,t (st ) uL,i,t λi,m,t zi,m,t (1 − α) =− Λi,t li,m,t uC,i,t [ ( )] uC,i,t uC,i,t+1 zi,m,t+1 x i,m,t+1 = βEt λi,m,t+1 α + 1 − δ + ϕi,m,t+1 − ϕ′i,m,t+1 ϕ′i,m,t ki,m,t+1 ϕ′i,m,t+1 ki,m,t+1 1−θ θ−ρ ρ ρ−1 πi λj,m,t τj,i,m,t = πj Λi,t Zi,t qi,m,t υj,i zj,i,m,t  1 ρ ∑ ρ ρ   qi,m,t = υj,i zj,i,m,t . j

If setting ωi = 1/µi

(A.82)

pi,m,t = λi,m,t /πi ,

(A.83)

Pi,t = Λi,t /πi ,

(A.84)

Wi,t =

λi,m,t zi,m,t (1 − α) Λi,t li,m,t

24

(A.85)

Ri,m,t =

λi,m,t zi,m,t α Λi,t ki,m,t

(A.86)

Then, FOCs are consistent with equilibrium conditions under complete contingent claims.

A.4.7

Alternative specifications of budget constraint

The complete market specification is obtained by a full history time-zero budget constraint denominated by zero-period Arrow-Debreu price: ∞ ∑ ∑

=

t=0 st ∞ ∑ ∑

[ 0 Pi,t (st ) Ci,t (st ) +

] xi,m,t (st )

m=1

[ 0 Pi,t (st )

M ∑

t

Wi,t (s )

t=0 st

M ∑

M ∑

t

li,m,t (s ) +

m=1

] t

Ri,m,t (s )ki,m,t (s

t−1

) − Gi,t (s ) . t

m=1

Another interpretation of full contingent claim world is full access to other country’s investment (but in this case, ηϕ = 0 needs to be assumed.): Pi,t (st )Ci,t (st ) + [ t

= Pi,t (s ) Wi,t

∑

Pj,t (st )

m=1

j M ∑

M ∑

xj,i,m,t (st ) ]

li,m,t − Gi,t (s ) + t

m=1

∑

Pj,t (st )

j

M ∑

Rj,m,t (st )kj,i,m,t (st−1 ).

m=1

where xj,i,m,t is investment of j’s assembly by i, and capital stock is similarly indexed.

A.4.8

National account of the model economy

Combining household budget constraint, final goods producer accounting, intermediate goods producer accounting, and resource constraint in the model leads to the aggregate accounting identity. First, This economy excludes cross country investment and labor migration, meaning no net factor income, and GDP=GNP. Also, the current account equals the net exports. Let’s denote the change in the net foreign asset (F Ai,t ) per capita as:

F Ai,t

 ∑ t t−1 t+1 t t+1 t   Ai,t (s , s ) − st+1 |st Qi,t (s |s )Ai,t+1 (s , s ) (Complete market) = (Incomplete market) Bi,t−1 − Ptb Bi,t   0 (Period-by-period TB)

(A.87)

Notice that by asset market clearing conditions, ∑

πi F Ai,t = 0.

i

25

(A.88)

Let Yi,t be the real gross domestic products per capita of country i at t in this economy. The nominal gross domestic products is the value added (production accounts): M ∑

πi Pi,t Yi,t =

πi pi,m,t zi,m,t

(A.89)

m=1

which is total factor payments (income accounts):

πi Pi,t Yi,t = πi Pi,t Wi,t

M ∑

li,m,t + πi Pi,t

M ∑

Ri,m,t ki,m,t .

(A.90)

m=1

m=1

Using the definition of the income account, household budget constraint and investment market clearing conditions: −πi F Ai,t = πi Pi,t Yi,t − πi Pi,t (Ci,t + Xi,t + Gi,t )

(A.91)

To show expenditure accounts, starting from production accounts: πi Pi,t Yi,t =

=

M ∑ m=1 M ∑ m=1

=

M ∑

πi pi,m,t zi,m,t

pi,m,t

N ∑

πj τi,j,m,t zi,j,m,t

j=1

πi pi,i,m,t zi,i,m,t +

m=1

= πi Pi,t Zi,t −

M ∑ N ∑

πj pi,m,t τi,j,m,t zi,j,m,t

m=1 j̸=i N M ∑ ∑

πi pj,i,m,t zj,i,m,t +

N M ∑ ∑

πj pi,m,t τi,j,m,t zi,j,m,t

m=1 j̸=i

m=1 j̸=i

M M ∑∑ ∑∑ = πi Pi,t (Ci,t + Xi,t + Gi,t ) − πj pi,j,m,t zi,j,m,t πi pj,i,m,t zj,i,m,t + | {z } j̸=i m=1 j̸=i m=1 Absorption {z } | {z } | Imports of inputs Exports of inputs = πi Pi,t (Ci,t + Xi,t + Gi,t ) − πi Pi,t IMi,t + πi Pi,t EXi,t (A.92)

= πi Pi,t (Ci,t + Xi,t + Gi,t ) + πi Pi,t N Xi,t .

(A.93)

Comparing two equations, the balance of payments identity can be confirmed: 0 = πi Pi,t N Xi,t + πi F Ai,t .

26

(A.94)

Namely, trade deficit (if N Xi,t < 0) is financed by capital account surplus. In the steady state, trade balance (and hence financial account balance) is assumed: 0 = πi P¯i N¯X i =

M ∑∑

πj p¯i,j,m z¯i,j,m −

j̸=i m=1

M ∑∑

πi p¯j,i,m z¯j,i,m = πi F¯Ai .

(A.95)

j̸=i m=1

Also, ¯i + G ¯ i = Z¯i . Y¯i = C¯i + X

(A.96)

The domestic absorption is financed by the domestic production. Based on the aggregate GDP, implied aggregate variables are calculated. Aggregate capital stock per capita is Ki,t =

∑

ki,m,t .

(A.97)

Yi,t . α Ki,t L1−α i,t

(A.98)

m

Then, implied aggregate TFP is T F Pi,t =

A.4.9 A.4.9.1

Detrended economy Detrending

Let variables with tilde ˜ as detrended variables. It is defined, for a case of Zi,t , Z˜i,t = Zi,t /g1t

(A.99)

Other cases are summarized in the table: Detrending factor

Value

Variables

ga

ga

ai,m,t

gτ

gτ

τi,j,m,t

gτ−1

gτ−1

g1 g2

1 1−α

ga

1 1−α

ga

−1 1−α

gτ

−α 1−α

pi,m,t Zi,t , Ci,t , Xi,t , Gi,t , xi,m,t , ki,m,t , zi,j,m,t , Bi,t , Wi,t , exj,i,m,t ,Yi,t zi,m,t

g4

gτ ψ(1−γ) g1 ψ(1−γ)−1 g1

1

–

Li,t , li,m,t , Ri,m,t , Pi,t , pi,j,m,t , ej,i,t

g3

uL,i,t Λi,t , uC,i,t

Also, let ηtb = η b g1−t .

27

A.4.9.2

Detrended economy equilibrium conditions α ˜l1−α z˜i,m,t = a ˜i,m,t k˜i,m,t i,m,t

( ϕ˜i,m,t = ϕ

x ˜i,m,t ˜ ki,m,t

( ϕ˜′i,m,t = ϕ′

)

x ˜i,m,t ˜ ki,m,t

(A.101)

)

g1 k˜i,m,t+1 = (1 − δ)k˜i,m,t + ϕ˜i,m,t k˜i,m,t   Z˜i,t = 

M ∑

m=1

πi z˜i,m,t =

 

N ∑

(A.100)

 θ  θ1 ρ  ρ ρ  υj,i z˜j,i,m,t 

(A.102)

(A.103)

(A.104)

j=1

∑

πj τ˜i,j,m,t z˜i,j,m,t

(A.105)

j

p˜i,m,t (1 − α)

uL,i,t z˜i,m,t ˜ i,t = P˜i,t −˜ = P˜i,t W li,m,t u ˜C,i,t

( )] [ u ˜C,i,t x ˜ 1 i,m,t+1 ′ ˜ i,m,t+1 + 1 − δ + ϕ˜i,m,t+1 − ϕ˜i,m,t+1 = βg4 Et u ˜C,i,t+1 R ϕ˜′i,m,t ϕ˜′i,m,t+1 k˜i,m,t+1

q˜i,m,t

 1 ρ ∑ ρ ρ = υj,i z˜j,i,m,t 

(A.106)

(A.107)

(A.108)

j

1−θ θ−ρ ρ ρ−1 p˜j,i,m,t = P˜i,t Z˜i,t q˜i,m,t υj,i z˜j,i,m,t

˜ i,t = X

M ∑

x ˜i,m,t

m=1

28

(A.109)

(A.110)

˜ i,t = L

M ∑

˜li,m,t

(A.111)

m=1

˜ i,t − G ˜ i,t , 0 = Z˜i,t − C˜i,t − X

(A.112)

u ˜C,i,t P˜i,t /µi = u ˜C,j,t P˜j,t /µj

(A.113)

If complete market

If incomplete market, 0=

N ∑

˜i,t B

(A.114)

i=1

[ ] ( ) ˜i,t+1 u ˜ / P C,i,t+1 b ˜ ˜i,t = βg4 Et P bt 1 + η B . u ˜C,i,t /P˜i,t [ P˜i,t C˜i,t (st ) +

M ∑

] ˜i,t (st ) x ˜i,m,t (st ) + P˜b t (st )B

m=1

˜i,t−1 (s = B

t−1

(A.115)

[

˜ i,t ) + P˜i,t (s ) W t

M ∑

˜li,m,t +

m=1

M ∑

] ˜ i,m,t (s )k˜i,m,t (s R t

t−1

˜ i,t (s ) . (A.116) )−G t

m=1

If financial autarky, ˜ i,t Z˜i,t = W

M ∑ m=1

A.4.10

˜li,m,t +

M ∑

˜ i,m,t (st )k˜i,m,t (st−1 ). R

(A.117)

m=1

Properties of the non-stochastic steady state

Definition: The non-stochastic steady state of the economy is a competitive equilibrium in which there is no shock, and all detrended variables stay at some constant values. In this economy, variables in the steady state are not necessarily equalized across countries. This heterogeneity is caused by the differences in the productivity, the population and the trade costs the countries face. Moreover, the trade pattern in the steady state has complicated structure because of the multiplicity of the country and the multiplicity of the intermediate goods. The calculation of the steady state exploits two properties embedded in the model. First, the model has “the return of Ricardo” (Baxter, 1992) property; although there are two fundamental input (capital stock and labor), the steady state trade pattern is explained by Ri-

29

cardo, not Heckscher=Ohlin. The return to investment in the steady state is determined only by the subjective discounting factor, degree of capital depreciation and trend growth rates. Given return to the investment, capital stock of each intermediate production is adjusted to be consistent with the product’s steady state labor productivity. Moreover, Cobb=Douglas assumption of the intermediate production implies that the total factor productivity is the same as labor productivity, after adjusting capital stock. As a result, the only production decision problem in the steady state is allocation of labor facing production technologies, which are linear in labor. Hence, the steady state of the model is regarded as an equilibrium of a static version of a Ricardian type general equilibrium model. In addition, the CES production function of the final goods leads to no perfect specialization of the intermediate productions, and hence, the possibility of corner solutions in solving the labor allocation problem is excluded.8 Second, the equilibrium conditions characterizing a class of the Ricardian models can be reduced to a system of excess demand functions. Wilson (1980) established this excess demand approach to characterize the equilibrium of a multi-country version of the Dornbusch et al. (1977) model. Recently, Alvarez and Lucas (2007) applied this method to the Eaton and Kortum (2002) model. The corresponding excess demand approach is used to calculate steady state values of the model economy. Once the steady state values are calculated, the standard macroeconomic method, which solve rational expectation equilibrium of log-linearized system, is used to analyze dynamic property of the model. Note that there are a large number of state variables: capital stock and productivity of each intermediate in each country. Claim: The non-stochastic steady state of complete market economy with steady state zero net exporting, the non-stochastic steady state of limited asset market economy, and the non-stochastic steady state of the period-by-period trade balance economy are equivalent. Proof: Notice that the only differences are in the asset holdings Euler equation and household budget constraints. The asset holdings Euler equation in the complete market is used only for determining µi , which is assumed to be consistent with zero net exporting in the steady state. The ¯i ) = βg4 , implies B ¯i = B ¯ for all i. But the bond risk-free bond holding Euler equation, P¯ b (1 + η b B ¯i = 0 for all i. This is market clearing condition requires the summation to be zero. Hence, B consistent with zero net exporting in the steady state, assumed as in the complete market case. Period-by-period trade balance always requires zero net exporting by construction, and hence in the steady state. (QED) The bond holding Euler equation implies P¯ b = βg4 .

8

Nevertheless, the equations obtained here are similar to the Ricardian problems with perfect specialization (Eaton and Kortum, 2002; Alvarez and Lucas, 2007).

30

A.4.10.1

Normalization of the price

Setting P¯N = 1 as normalization. A.4.10.2

Rental rate and capital labor ratio

¯ =x ¯ = 1. From Euler equation, By assumption, ϕ(¯ x/k) ¯/k¯ and ϕ′ (¯ x/k) ¯ i,m = R ¯ = 1 − 1 + δ. R βg4

(A.118)

Capital-labor ratio (denoting κi , which does not depend on m) is expressed by

A.4.10.3

¯i k¯i,m α W κ ¯i = ¯ = ¯ . 1−α R li,m

(A.119)

(g1 − 1 + δ)k¯i,m = x ¯i,m ,

(A.120)

Investment

Capital accumulation implies:

but combining with capital-labor ratio, x ¯i,m = (g1 − 1 + δ)¯ κi ¯li,m

(A.121)

¯ i = (g1 − 1 + δ)¯ ¯ i, X κi L

(A.122)

¯ ¯ ¯ i = (g1 − 1 + δ) α Wi L X ¯ i, 1−α R

(A.123)

and summing up over m,

or

A.4.10.4

Absorption

From household budget constraint and resource constraint, ¯ iL ¯i + R ¯ Z¯i = W

∑

k¯i,m

m

¯ iL ¯i + R ¯ = W

∑ m

=

1 ¯ ¯ Wi Li 1−α

31

¯i α W ¯ ¯ li,m 1−α R (A.124)

With resource constraint and investment condition,

A.4.10.5

α 1 − (g1 − 1 + δ) R ¯ ¯ ¯ ¯i. Wi Li = C¯i + G 1−α

(A.125)

¯ ¯ i = 1 − ψ Ci , W ¯i ψ 1−L

(A.126)

α 1 − (g1 − 1 + δ) R ¯ ¯ ¯ ¯i. Wi Li = C¯i + G 1−α

(A.127)

Labor

Combining two equations

to obtain ¯i G + ¯ 1 − ψ Wi ¯ i = L(W ¯ i) = L ¯ 1 − (g1 − 1 + δ)α/R ψ

1−α A.4.10.6

. +

(A.128)

ψ 1−ψ

Wage and price level 1

From   P¯i = 

M ∑ m=1

  ρ−1 θ  θ−1 θ ρ θ−1 N −ρ ρ ∑ ρ−1  ρ−1   υj,i p¯j,i,m , 

(A.129)

j=1

p¯j,i,m = p¯j,m τ¯j,i,m = p¯j,m τ¯j,i,m , and ¯αW ¯ 1−α , p¯j,m αα (1 − α)1−α a ¯j,m = P¯j R j

(A.130)

¯ α α−α (1 − α)−[1−α] . Ψ≡R

(A.131)

Let

32

To obtain   P¯i = 



M ∑



m=1

N ∑

 ρ−1

) ρ −ρ ( ρ−1 ¯j W ¯ 1−α τ¯j,i,m ρ−1  P Ψ¯ a−1 υj,i j,m j

ρ

θ θ−1

 θ−1 θ  

,

(A.132)

j=1

or 

 ρ−1 θ  θ−1 θ ρ θ−1 ρ ( ) ∑ ∑ ρ−1 τ ¯   ¯ 1−α j,i,m   P¯j W P¯i = Ψ  .  j υ a ¯ j,i j,m m 

(A.133)

j

A.4.10.7

Wage and price level 2

From N¯X i = 0, πi P¯i Z¯i =

N ∑ M ∑

πi p¯j,i,m z¯j,i,m =

j=1 m=1

N ∑ M ∑

πj p¯i,j,m z¯i,j,m

(A.134)

j=1 m=1

Since 1

θ−ρ

1−θ

ρ

−ρ

1−ρ 1−ρ 1−ρ p¯i,j,m z¯i,j,m = P¯j1−ρ Z¯j1−ρ q¯j,m υi,j p¯i,j,m [ ] ρ−θ 1 θ−1 ρ ρ ρ ρ ρ 1 ∑ 1−ρ ρ−1 1−ρ ρ−1 υh,j p¯h,j,m = P¯j1−θ Z¯j υi,j p¯i,j,m

h

1 1−θ

= P¯j

Z¯j

[ ∑

ρ 1−ρ

υh,j

( ) ρ ρ−1 −1 ¯ ¯ 1−α Ψ¯ ah,m Ph Wh τ¯h,j,m

(A.135)

] ρ−θ 1

θ−1 ρ

ρ 1−ρ

υi,j

(

¯ ¯ 1−α τ¯i,j,m Ψ¯ a−1 i,m Pi Wi

)

ρ ρ−1

,

h

Also, Z¯h = =

1 ¯ ¯ Wh Lh 1−α 1 ¯ ¯ ¯ Wh L(Wh ) 1−α

(A.136) (A.137)

¯ W ¯ h ) is a function derived above. Thus where L( ¯ i L( ¯ W ¯ i) πi P¯i W θ

= Ψ θ−1

(A.138) ρ−θ 1 [ ] ) ρ θ−1 ρ ( ) ρ N ∑ M 1 ∑ ∑( ρ−1 ¯h,j,m ¯i,j,m ρ−1 1−α τ 1−θ ¯ ¯ ¯ 1−α τ ¯ ¯ ¯ ¯ ¯ πj Pj Wj L(Wj ) Pi Wi Ph Wh υh,j a ¯h,m υi,j a ¯i,m j=1 m=1

h

33

A.4.10.8

Excess demand function

For simplifying the notation, define following: ¯ 1−α , Qi = P¯i W i

(A.139)

Q = {Q1 , ..., QN }.

(A.140)

( Υi,j,m =

Ωi,m (Q) =

[ ∑( h

τ¯i,j,m υi,j a ¯i,m

¯ 1−α τ¯h,i,m P¯h W h υh,i a ¯h,m

)

ρ ρ−1

)

ρ ρ−1

(A.141)

] ρ−1

[

ρ

=

∑

ρ ρ−1

Qh

] ρ−1 ρ

Υh,i,m

(A.142)

h

 ρ−1 θ  θ−1 θ ρ θ−1 ρ ) ( ∑ ∑ ρ−1 τ¯j,i,m     Φi (Q) = P¯i /Ψ =  Qj  υ a ¯ j,i j,m m 



j

[ =

∑

] θ−1 Ωi,m (Q)

θ θ−1

θ

.

(A.143)

m

−1 ψ 1 1 ¯ i Ψ 1−α (Φi (Q)) 1−α Q 1−α ) ( 1 + G i −1 ¯ i = L(W ¯ i ) = L Q 1−α (Φi (Q)) 1−α = Li (Q) = 1 − ψ . (A.144) L i ¯ 1 − (g1 − 1 + δ)α/R ψ + 1−α 1−ψ

Then, (A.138) can be expressed as 1

−α

¯ i (Q)Q 1−α (Φi (Q)) 1−α πi L i =

N ∑ M ∑

θ−α

(A.145) 1

ρ−θ

1

ρ

¯ j (Q) (Ωj,m (Q)) θ−1 ρ−1 Q ρ−1 Υi,j,m πj (Φj (Q)) (1−θ)(1−α) Qj1−α L i

j=1 m=1 1

There are N equations for i = 1, ..., N . Regarding Q as the price of labor (since Q 1−α is basket adjusted real wage by definition), the above equation can be regarded as the reduced form labor market clearing equation. Solving this N system to obtain Qi . Then, (A.138) gives P¯i . This equation can be interpreted as supply of the labor in the left-hand-side whereas demand of the labor in the right-hand-side. Dividing both sides by Qi and define Ji ((Q)) as the difference

34

of left-hand-side and right-hand-side: Ji (Q) 1 ρ−1

= Qi

N ∑ M ∑

1

θ−α

ρ−θ

1

¯ j (Q) (Ωj,m (Q)) θ−1 ρ−1 Υi,j,m πj (Φj (Q)) (1−θ)(1−α) Qj1−α L

j=1 m=1 α

−α

¯ i (Q)Q 1−α (Φi (Q)) 1−α −πi L i

(A.146)

This function, J(Q), is homogeneous of degree zero and

∑N

i=1 Qi Ji (Q)

= 0, hence it can be inter-

preted as an excess demand function. A.4.10.9

Homogeneity

Ωi,m (Q) is homogenous of degree one. Φi (Q) is homogenous of degree one. Li (Q) is homogenous of degree zero. By straightforward calculation, Ji (Q) is homogenous of degree zero. A.4.10.10

Walras’ law

The multiplying by Qi and the switching the summation order gives: N ∑

Qi Ji (Q)

i=1

=

N ∑

1

Qi Qiρ−1

=

θ−α

1

ρ−θ

1

¯ j (Q) (Ωj,m (Q)) θ−1 ρ−1 Υi,j,m πj (Φj (Q)) (1−θ)(1−α) Qj1−α L

j=1 m=1

i=1

−

N ∑ M ∑

N ∑

α

−α

¯ i (Q)Q 1−α (Φi (Q)) 1−α Q i πi L i

i=1 N ∑

M ∑

1

θ−α

¯ j (Q) πj (Φj (Q)) (1−θ)(1−α) Qj1−α L

ρ−θ

m=1

j=1

1

(Ωj,m (Q)) θ−1 ρ−1

N ∑

ρ

Qiρ−1 Υi,j,m

|i=1

{z

}

(Ωj,m (Q))ρ/(ρ−1)

− =

N ∑

i=1 N ∑

1

−α

¯ i (Q)Q 1−α (Φi (Q)) 1−α πi L i

πj (Φj (Q))

−α 1−α

1 1−α

Qj

¯ j (Q) − L

j=1

N ∑

1

−α

¯ i (Q)Q 1−α (Φi (Q)) 1−α = 0 πi L i

i=1

(A.147)

A.4.11 A.4.11.1

Calculating steady state Feeding productivities

After feeding all the parameters in the model, the above excess demand function is used for calcu¯ i is calculated. Using W ¯ i and Q ¯ i, L ¯ i is lating Qi . Then, P¯i is calculated using (A.133). Then, W 35

calculated. Then, the rest shares the next case. A.4.11.2

Feeding price estimates

The empirical estimation gives τ¯j,i,m and p¯j,m , but not a ¯j,m . Hence, when using empirical values, calculation procedure is following. • Step 1: Using τ¯j,i,m and p¯j,m to obtain P¯i by (A.129). • Step 2: Solving the system of modified version of (A.138), but in this case, Z¯i is calculated: πi P¯i Z¯i =

N ∑

1 1−θ

πj P¯j

Z¯j

[ M ∑ ∑ m=1

j=1

] ρ−θ 1 (¯ τh,j,m p¯h,m )

ρ ρ−1

θ−1 ρ

ρ

(¯ τi,j,m p¯i,m ) ρ−1

(A.148)

h

Employing a notation that [ M ∑ ∑

˜ i,j = Υ

m=1

] ρ−θ 1 (¯ τh,j,m p¯h,m )

θ−1 ρ

ρ ρ−1

ρ

(¯ τi,j,m p¯i,m ) ρ−1

(A.149)

h

¯ = [Z¯1 ... Z¯N ]′ and vector Z  ¯  π1 P1  0 =   0

0 ..

. πN P¯N





1

˜ 1,1 π1 P¯ 1−θ Υ 1   .. − .    1 ˜ N,1 π1 P¯ 1−θ Υ 1

··· .. . ···

 1 ˜ 1,N πN P¯ 1−θ Υ N   ¯ ..  Z .  1 1−θ ˜ ¯ ΥN,N πN PN

(A.150)

or ¯ 0 = AZ

(A.151)

Note that the system is linearly dependent due to “Walras law” in the excess demand property of the equation as discussed in the last subsection. Z¯1 is normalized to be unity. The actual calculation is implemented by solving linear system: 

  a1,1 a1,2 · · ·  .   . .. .   . 0= .  . + . a1,N aN,2 · · · where ai,j is (i, j) element of the matrix A. ¯ i and L ¯ i is obtained. • Step 3: W • Step 4: a ¯j,m is calculated by (A.130).

36

 a1,N Z¯2   ..   .. .  . aN,N Z¯N

   

(A.152)

A.4.11.3

Consumption and absorption

¯ i and L ¯ i, Given W

A.4.11.4

ψ ¯ ¯ i ), Wi (1 − L 1−ψ ¯ iL ¯i = (1 − α)W

C¯i =

(A.153)

Z¯i

(A.154)

Capital-labor ratio, marginal utility, absorption

κ ¯i =

¯i α W ¯ . 1−α R

(A.155)

¯ i = (g1 − 1 + δ)¯ ¯ i, X κi L

(A.156)

ψ(1−γ)−1 ¯ i ](1−ψ)(1−γ) , u ¯C,i = ψ C¯i [1 − L

(A.157)

¯ i, u ¯L,i = −¯ uC,i W

(A.158)

¯i + G ¯ i. Z¯i = C¯i + X

(A.159)

Check

A.4.11.5

Budget constraint multiplier ∑ After normalizing to i µi = 1, u ¯C,i P¯i µ−1 ¯C,j P¯j µ−1 i =u j

(A.160)

gives µ1 , ..., µN . A.4.11.6

Goods production, exporting, and relative price

The price of goods m in j is p¯j,m =

1 ¯ j P¯j . a ¯−1 κ ¯ −α W 1 − α j,m j

(A.161)

Then, the price at country i is p¯j,i,m = p¯j,m τ¯j,i,m .

37

(A.162)

Using price aggregator,

θ−1 Z¯i1−θ q¯i,m

[ ( ) ρ ] ρ−1 −ρ p¯qi,m p¯j,i,m ρ−1 ρ ρ−1 = ¯ = υj,i , Pi P¯i

(A.163)

implying  q¯i,m

1 1−θ

= P¯i

Z¯i 

∑

 ρ−1 1 −ρ ρ−1

θ−1 ρ

ρ ρ−1

υj,i p¯j,i,m 

(A.164)

j

and then [

z¯j,i,m A.4.11.7

θ−ρ ρ −1 = P¯i Z¯i1−θ q¯i,m υj,i p¯j,i,m

]

1 1−ρ

.

(A.165)

Output and investment z¯i,m =

∑

πj τ¯i,j,m z¯i,j,m /πi

(A.166)

j

¯li,m = (1 − α) z¯i,m p¯i,m ¯ i P¯i W

(A.167)

k¯i,m = κ ¯ i ¯li,m

(A.168)

x ¯i,m = (g1 − 1 + δ)k¯i,m

(A.169)

Y¯i = Z¯i

(A.170)

¯ i = k¯i,m K

(A.171)

T F¯ P i = A.4.11.8

Y¯i ¯ αL ¯ 1−α K i i

(A.172)

Trade values ex ¯ j,i,m = πi p¯j,i,m z¯j,i,m

38

(A.173)

∑∑ ¯ i= 1 ex ¯ j,i,m /P¯i IM πi m

(A.174)

∑∑ ¯ i= 1 EX ex ¯ i,j,m /P¯i πi m

(A.175)

j̸=i

j̸=i

  P¯iI = 



M ∑



m=1

  P¯iE = 

M ∑ m=1

A.4.12

∑

 ρ−1 −ρ

ρ

ρ

θ θ−1

ρ−1 ρ−1  υj,i p¯j,i,m

 θ−1 θ  

/P¯i ,

(A.176)

  ρ−1 θ  θ−1 θ ρ θ−1 −ρ ρ ∑ ρ−1  ρ−1   υi,j p¯i,j,m /P¯i 

(A.177)

j̸=i

j̸=i

Log-linearization

The economy’s dynamics is analyzed by first order log-linearized economy. • # number of equations • ♡ combining to reduce number of variables • ♢ redundant conditions (not used) ˆi,t is log-deviations from the stead state, e.g., All the variables excluding B Cˆi,t = log(Ci,t /C¯i )

(A.178)

Bond holding is linear approximation (not log-linear approximation):

A.4.12.1

ˆi,t = Bi,t − B ¯i = Bi,t . B

(A.179)

¯i L ˆ (#N ) : 0 = −ˆ uC,i,t + (ψ(1 − γ) − 1)Cˆi,t − (1 − ψ)(1 − γ) ¯ i Li,t 1−L

(A.180)

HH problem

ˆ i,t + Cˆi,t + (#N ) : 0 = −W

39

¯i L ˆ ¯ i Li,t 1−L

(A.181)

( ) (#N M ) : 0 = −ˆ uC,i,t − ηϕ x ˆi,m,t − kˆi,m,t

( ) ¯ tR ˆ i,m,t+1 + βg4 ηϕ g1 Et x +Et u ˆC,i,t+1 + βg4 RE ˆi,m,t+1 − kˆi,m,t+1 (A.182)

xi,m,t (#N M ) : 0 = −g1 kˆi,m,t+1 + (1 − δ)kˆi,m,t + (g1 − 1 + δ)ˆ A.4.12.2

(A.183)

Final goods producer (#N ) : 0 = −Z¯iθ Zˆi,t +

∑

θ q¯i,m qˆi,m,t

(A.184)

ρ ρ υj,i z¯j,i,m zˆj,i,m,t

(A.185)

m

ρ (#N M ) : 0 = −¯ qi,m qˆi,m,t +

∑ j

(#N ♢) : 0 = −P¯i Pˆi,t − Z¯i Zˆi,t +

∑∑ m

θ θ−1

(#N ♢) : 0 = −P¯i

Pˆi,t +

( ∑ ∑ m

p¯j,i,m z¯j,i,m (ˆ pj,i,m,t + zˆj,i,m,t )

−ρ ρ−1

ρ ρ−1

)

υh,i p¯h,i,m

θ−ρ ρ(1−θ)

∑

−ρ

ρ

ρ−1 ρ−1 υj,i p¯j,i,m pˆj,i,m,t

(A.187)

j

h

(#N 2 M ♡) : 0 = −ˆ pj,i,m,t + Pˆi,t + (1 − θ)Zˆi,t + (θ − ρ)ˆ qi,m,t + (ρ − 1)ˆ zj,i,m,t A.4.12.3

(A.186)

j

(A.188)

Intermediate goods producer and trade (#N M ) : 0 = −ˆ zi,m,t + a ˆi,m,t + αkˆi,m,t + (1 − α)ˆli,m,t

(A.189)

ˆ i,t − Pˆi,t + pˆi,m,t + zˆi,m,t − ˆli,m,t (#N M ) : 0 = −W

(A.190)

ˆ i,m,t − Pˆi,t + pˆi,m,t + zˆi,m,t − kˆi,m,t (#N M ) : 0 = −R

(A.191)

(#N M ) : 0 = −πi z¯i,m zˆi,m,t +

∑

πj τ¯i,j,m z¯i,j,m (ˆ zi,j,m,t + τˆi,j,m,t )

(A.192)

j

(#N 2 M ♡) : 0 = −ˆ pi,j,m,t + pˆi,m,t + τˆi,j,m,t

40

(A.193)

∑

(#N M ♢) : 0 = −πi p¯i,m z¯i,m (ˆ pi,m,t + zˆi,m,t ) +

πj p¯i,j,m z¯i,j,m (ˆ pi,j,m,t + zˆi,j,m,t )

(A.194)

j

A.4.12.4

Resource constraints ¯ iL ˆ i,t + (#N ) : 0 = −L

∑

¯li,m ˆli,m,t

(A.195)

x ¯i,m x ˆi,m,t

(A.196)

m

¯iX ˆ i,t + (#N ) : 0 = −X

∑ m

ˆ i,t ˆ i,t − G ¯iG ¯iX (#N ) : 0 = Z¯i Zˆi,t − C¯i Cˆi,t − X A.4.12.5

A.4.12.6

A.4.12.7

(A.197)

Price normalization (#1) : 0 = PˆN,t

(A.198)

(#N − 1) : 0 = −ˆ uC,i,t + Pˆi,t + u ˆC,j,t − Pˆj,t

(A.199)

Complete market case

Incomplete market case ( ) ˆi,t Et u ˆC,i,t+1 − u ˆC,i,t − Et Pˆi,t+1 + Pˆi,t − η b P¯ b B ( ) ˆj,t + Et u ˆC,j,t+1 − u ˆC,j,t − Et Pˆj,t+1 + Pˆj,t − η b P¯ b B

(A.200)

ˆi,t + B ˆi,t−1 (#N ) : 0 = − P¯i Z¯i Zˆi,t − P¯ b B ( ) ( ) ∑ ¯ iL ¯i W ˆ i,t + L ˆ i,t + P¯i R ¯ ˆ i,m,t + kˆi,m,t + P¯i W k¯i,m R

(A.201)

(#N − 1) : 0 = −

m

(# : 1♢) : 0 =

∑

ˆi,t πi B

(A.202)

i

A.4.12.8

Financial autarky case

(One of N equation is not used.) ( ) ( ) ∑ ¯ iL ¯i W ˆ i,t + L ˆ i,t + P¯i R ¯ ˆ i,m,t + kˆi,m,t .(A.203) (#N − 1(+1♢)) : 0 = −P¯i Z¯i Zˆi,t + P¯i W k¯i,m R m

41

A.4.12.9

A.4.12.10

Shock process 2 ˆ i,t ∼ N (0, σG (#N ) : G )

(A.204)

(#N M ) : a ˆi,m,t = ρa a ˆi,m,t−1 + σε εi,m,t

(A.205)

(#N M ) : εi,m,t ∼ N (0, 1)

(A.206)

(#N 2 M ) : τˆi,j,m,t = ρτ τˆi,j,m,t−1 + σϵ ϵi,j,m,t

(A.207)

(#N 2 M ) : ϵi,j,m,t ∼ N (0, 1)

(A.208)

# of state variables, equations, and total variables

• State variables (#2N M + N 2 M ): kˆi,m,t , a ˆi,m,t , τˆi,j,m,t • # of equations: 9N + 8N M + 2N 2 M − (2N + N M + N 2 M ) • # of variables: 7N + 7N M + 2N 2 M − (N 2 M ) ˆ i,t , X ˆ i,t , Zˆi,t , W ˆ i,t , Pˆi,t • (#N × 7) : u ˆC,i,t , Cˆi,t , L ˆ i,m,t , • (#N M × 7) : ˆli,m,t , x ˆi,m,t , kˆi,m,t , qˆi,m,t , zˆi,m,t , pˆi,m,t , R • (#N 2 M × (2 − 1)) : zˆi,j,m,t , pˆi,j,m,t (by ♡, pˆi,j,m,t is dropped.) ˆ i,t • Exogenous shocks: a ˆi,m,t , τˆi,j,m,t , εˆi,m,t , ϵi,j,m,t , G ˆi,t , N additional equations. • Incomplete market case: N additional state variables, B Remarks • One of the #N equations is redundant. • pˆj,i,m,t can be dropped from the system. A.4.12.11

Additional variables of interests ( ) ( ) ∑ ¯ iL ¯i W ˆ i,t + L ˆ i,t + R ¯ ˆ i,m,t + kˆi,m,t Y¯i Yˆi,t = W k¯i,m R

(A.209)

m

ec xi,j,m,t = pˆi,j,m,t + zˆi,j,m,t 42

(A.210)

∑∑ 1 ex ¯ i,j,m ec xi,j,m,t − Pˆi,t ¯ i πi P¯i EX m

(A.211)

∑∑ 1 ex ¯ j,i,m ec xj,i,m,t − Pˆi,t ¯ i πi P¯i IM m

(A.212)

d i,t d i,t − IM ¯ i − IM ¯ i IM ¯ i + EX ¯ i EX EX d N X i,t = Y¯i + Y¯i Yˆi,t

(A.213)

d i,t = EX

j̸=i

d i,t = IM

j̸=i

I Pˆi,t

  θ−ρ ρ(1−θ) θ ∑ ( ) −ρ ρ −ρ ρ ∑ ρ−1 ∑ ρ−1 ρ−1 θ − 1 ¯I ¯ 1−θ ρ−1  = Pi Pi υh,i p¯h,i,m  υj,i p¯j,i,m pˆj,i,m,t − Pˆi,t θ m h̸=i

E Pˆi,t

(A.214)

j̸=i

  θ−ρ ρ(1−θ) θ ∑ −ρ ρ ρ −ρ ∑ ρ−1 ∑ ρ−1 θ − 1 ( ¯E ¯ ) 1−θ ρ−1 ρ−1  υi,h p¯i,h,m  = Pi Pi pˆi,j,m,t − Pˆi,t υi,j p¯i,j,m θ m h̸=i

(A.215)

j̸=i

I E Td oT i,t = Pˆi,t − Pˆi,t

(A.216)

∑ ˆ i,t = 1 K k¯i,m kˆi,m,t ¯i K m

(A.217)

ˆ i,t − (1 − α)L ˆ i,t T[ F P i,t = Yˆi,t − αK

(A.218)

43

References Alvarez, Fernando and Robert E., Jr., Lucas (2007) “General Equilibrium Analysis of the EatonKortum Model of International trade,” Journal of Monetary Economics, Vol. 54, No. 6, pp. 1726–1768, September. Anderson, James E. and Eric van Wincoop (2004) “Trade Costs,” Journal of Economic Literature, Vol. 42, No. 3, pp. 691–751, September. Arkolakis, Costas and Ananth Ramanarayanan (2009) “Vertical Specialization and International Business Cycle Synchronization,” Scandinavian Journal of Economics. forthcoming. Backus, David K., Patrick J. Kehoe, and Finn E. Kydland (1994) “Dynamics of the Trade Balance and the Terms of Trade: The J-Curve?” American Economic Review, Vol. 84, No. 1, pp. 84–103, March. Baxter, Marianne (1992) “Fiscal Policy, Specialization, and Trade in the Two-Sector Model: The Return of Ricardo?” Journal of Political Economy, Vol. 100, No. 4, pp. 713–744, August. (1995) “International Trade and Business Cycles,” in Gene M. Grossman and Kenneth Rogoff eds. Handbook of International Economics, Vol. 3 of Handbooks in Economics, Amsterdam: North-Holland, Chap. 35, pp. 1801–1864. Baxter, Marianne and Robert G. King (1999) “Measuring Business Cycles: Approximate BandPass Filters for Economic Time Series,” Review of Economics and Statistics, Vol. 81, No. 4, pp. 575–593, November. Baxter, Marianne and Michael A. Kouparitsas (2005) “Determinants of business cycle comovement: a robust analysis,” Journal of Monetary Economics, Vol. 52, No. 1, pp. 113–157, January. Clark, Todd E. and Eric van Wincoop (2001) “Borders and business cycles,” Journal of International Economics, Vol. 55, No. 1, pp. 59–85, October. Deaton, Angus and Alan Heston (2008) “Understanding PPPs and PPP-Based National Accounts,” NBER working paper, Vol. 14499. Dornbusch, Rudiger, Stanley Fischer, and Paul A. Samuelson (1977) “Comparative Advantage, Trade, and Payments in a Ricardian Model with a Continuum of Goods,” American Economic Review, Vol. 67, No. 5, pp. 823–839, December. Eaton, Jonathan and Samuel Kortum (2002) “Technology, Geography, and Trade,” Econometrica, Vol. 70, No. 5, pp. 1741–1779, September. Feenstra, Robert C., Robert E. Lipsey, Haiyan Deng, Alyson C. Ma, and Hengyong Mo (2005) “World Trade Flows: 1962-2000,” NBER Working paper 11040, January.

44

Frankel, Jeffrey A. and Andrew K. Rose (1998) “The Endogeneity of the Optimum Currency Area Criteria,” Economic Journal, Vol. 108, No. 449, pp. 1009–1025, July. Gervais, Antoine and J. Bradford Jensen (2009) “Are Services Tradable? Evidence from US Microdata,” mimeo, July. Ghironi, Fabio and Mark J. Melitz (2005) “International Trade and Macroeconomic Dynamics with Heterogeneous Firms,” Quarterly Journal of Economics, Vol. 120, No. 3, pp. 865–915, August. Glick, Reuven and Andrew K. Rose (2002) “Does a currency union affect trade? The time-series evidence,” European Economic Review, Vol. 46, No. 6, pp. 1125–1151, June. Heathcote, Jonathan and Fabrizio Perri (2002) “Financial autarky and international business cycles,” Journal of Monetary Economics, Vol. 49, No. 3, pp. 601–627, April. Helpman, Elhanan, Marc Melitz, and Yona Rubinstein (2008) “Estimating Trade Flows: Trading Partners and Trading Volumes,” Quarterly Journal of Economics, Vol. 123, No. 2, pp. 441–487, May. Heston, Alan, Robert Summers, and Bettina Aten (2008) “Penn World Table version 6.2,” Center for International Comparisons at the University of Pennsylvania (CICUP). Hodrick, Robert J. and Edward C. Prescott (1997) “Postwar US Business Cycles: An Empirical Investigation,” Journal of Money, Credit and Banking, Vol. 29, No. 1, pp. 1–16, February. Hummels, David (1999) “Toward a Geography of Trade Costs,” mimeo, January. Rose, Andrew K. (2005) “Does WTO Make Trade More Stable?” Open Economies Review, Vol. 16, No. 1, pp. 7–22, January. Stopford, Martin (2009) Maritime Economics, London and New York: Routledge, 3rd edition. Wilson, Charles A. (1980) “On the general structure of Ricardian models with a continuum of goods: applications to growth, tariff theory, and technical change,” Econometrica, Vol. 48, No. 7, pp. 1675–1702, November.

45

46

0.41 0.21 0.23 0.23 −0.02 0.10

0.42 0.72 −0.32 0.97 0.19 – 7.02 5.93

Cross country correl. Output (Y ) Consumption (C) Investment (X) Labor (L) Net exports (N X) Aggregate TFP shock

Correl. to output Exports (EX) Imports (IM ) Net exports (N X)

Ave. bilat. trade int. (%) Agg. Trade-GDP ratio Trade cost

Slope (× 100) SE (×100)

– –

0.46 0.04 1.76

0.28 0.29 −0.05

0.20 0.16 0.14 0.25 −0.17 0.14

5.18 0.58

1.35 0.14 1.74

0.32 0.32 −0.01

0.28 0.22 0.22 0.33 −0.11 0.23

2.92 0.62

1.35 0.14 1.74

0.65 −0.19 0.90

0.13 0.58 0.07 −0.08 −0.10 0.08

4.82 0.58

1.35 0.14 1.74

0.32 0.32 –

0.27 0.25 0.30 0.37 −0.10 0.31

8.49 0.50

0.71 0.09 1.72

0.28 0.28 −0.01

0.24 0.19 0.19 0.39 −0.09 0.19

Table A.1: International business cycle moments G7 Baseline Complete Financial Same Mean US G7 market autarky TC

4.71 0.44

1.45 0.13 1.74

0.32 0.32 −0.01

0.28 0.22 0.22 0.34 −0.10 0.23

Same pop

– –

0.80 0.10 1.72

0.28 0.28 −0.02

0.24 0.19 0.19 0.40 −0.09 0.19

Symmetric countries

Table A.2: List of empirical variables Notation j i m t

Explanation Exporter country index Importer country index Product (sector) index Year index

Data source

exj,i,m,t

Trade flow from j to i of category m at t

Feenstra et al. (2005)

Zi,t Pi,t πi lnDistj,i Borderj,i Langj,i Colonyj,i FTAj,i,t

Absorption per capita PPP price Population Bilateral log distance Sharing a border dummy Common language dummy Formal colonial relationship dummy Indicator of j and i are in the same FTA at t

PWT6.2. PWT6.2. PWT6.2. Rose (2005) Rose (2005) Rose (2005) Rose (2005) Rose (2005)

Table A.3: Average and standard deviations of 390 first stage fixed effects estimations Mean SD Implied effect lnDistj,i 9.21 8.92 2 (lnDistj,i ) −1.27 1.33 (lnDistj,i )3 0.05 0.06 Borderj,i 0.36 0.22 −0.04 Langj,i 0.87 0.32 −0.10 Colonyj,i 0.15 0.21 −0.02 FTAj,i,t 0.15 0.33 −0.02 There are 390 category-time specific fixed effects estimations. Mean and SD are mean and standard deviations of 390 different estimations. “Implied elast.” is implied trade cost elasticity with respect to the variables. For the distance, see Figure A.13. The implied effect shows how much trade cost decreases. Sharing a border, for example, makes 0.04 points lower iceberg trade costs.

47

Table A.4: Estimated steady state trade costs (category specific, average over exporter-importer) SITC1 Description Mean SD 0 Food and live animals chiefly for food 2.24 0.48 1 Beverages and tobacco 1.72 0.26 2 Crude materials, inedible, except fuels 1.61 0.30 3 Mineral fuels, lubricants and related materials 1.59 0.35 4 Animals and vegetable oils, fats and waxes 1.72 0.37 5 Chemicals and related products, N.E.S. 1.78 0.30 6 Manufactured goods classified chiefly by material 1.77 0.30 7 Machinery and transport equipment 1.68 0.32 8 Miscellaneous manufactured articles 1.49 0.33 9 Commodities and trans. 1.67 0.27 Iceberg (the required units of goods to deliver one unit of the good) trade cost. The steady state costs are average (1962–2000), after adjusting common growth component. Basis year is 1985.

48

49

1.44

2.02 1.95 1.49 1.64 1.63 1.61 1.53 1.50 1.68 1.72 1.70 1.74 1.52 1.59 1.32 1.33 1.24 2.09 2.05 1.78 2.24 2.07 2.07 2.12 2.02 2.02 2.24 2.36 2.34 2.29 2.26 2.42 2.28 2.30 2.38

Finland

Australia

1.94 1.92 1.93 1.95 1.98 2.01 1.97 1.92 2.11 2.03 2.20 2.04 2.00 1.94 2.01 2.01 2.06 2.05 2.10 2.20

2.09 2.18 1.81 2.03 2.26 2.22 2.17 2.23 2.34 2.32 2.30 2.31 2.20 2.30 2.21 2.40 2.48 2.31 1.72

Steady state costs are calculated by taking time series average (1962–2000) after adjusting common growth component, in which 1985 is set to basis.

1.86

1.60 1.71

2.23 2.42 2.18

1.30 2.05 2.21 2.09

Iceberg (the required units of goods to deliver one unit of the good) trade cost, based on the estimation. Internal trade costs are unity.

Japan

New Zealand

1.99 1.85 1.54 1.60 1.61 1.56 1.51 1.53 1.65 1.63 1.65 1.74 1.49 1.52 1.25 1.26

1.23 1.38 2.23 2.32 2.03

1.97 1.85 1.39 1.63 1.57 1.58 1.47 1.46 1.71 1.65 1.63 1.76 1.59 1.60 1.23

1.23 1.24 1.36 2.19 2.23 2.02

1.47 1.56 1.54 1.55 2.04 2.13 1.83

Sweden

1.89 1.79 1.49 1.63 1.41 1.44 1.47 1.37 1.40 1.51 1.52 1.62 1.25

1.22 1.44 1.49 1.45 1.49 2.16 2.30 2.05

Norway

Switzerland

R

1.97 1.83 1.53 1.64 1.52 1.49 1.47 1.27 1.34 1.56 1.56 1.49

1.95 1.89 1.43 1.48 1.55 1.54 1.44 1.39 1.57 1.60 1.58 1.60 1.45 1.43

Austria

E

1.49 1.60 1.71 1.78 1.70 1.77 2.25 2.45 2.12

1.73 1.50 1.57 1.49 1.59 1.55 1.62 2.44 2.44 2.22

1.26 1.58 1.60 1.52 1.59 1.67 1.67 1.70 2.25 2.37 2.09

1.91 1.91 1.57 1.74 1.47 1.49 1.50 1.37 1.32 1.59 1.75

1.96 1.91 1.47 1.58 1.46 1.48 1.52 1.51 1.61 1.37

1.90 1.89 1.51 1.55 1.35 1.48 1.48 1.47 1.47

1.47 1.54 1.42 1.35 1.35 1.57 1.67 1.64 1.67 2.10 2.22 2.06

1.42 1.50 1.51 1.49 1.23 1.30 1.39 1.52 1.48 1.51 2.07 2.20 1.97

1.30 1.41 1.50 1.50 1.49 1.42 1.41 1.41 1.52 1.50 1.56 2.15 2.18 2.06

1.91 1.83 1.57 1.60 1.37 1.45 1.50 1.41

1.91 1.86 1.56 1.51 1.40 1.32 1.31

1.96 1.90 1.41 1.43 1.36 1.17

1.16 1.31 1.39 1.50 1.50 1.50 1.44 1.40 1.44 1.52 1.51 1.57 2.18 2.23 2.03

1.26 1.40 1.38 1.34 1.39 1.46 1.49 1.50 1.33 1.53 1.62 1.60 1.64 2.17 2.30 1.99

Denmark

Greece

Spain

O

T

Italy

P

Portugal

Germany

X

R

Netherlands

1.90 1.87 1.44 1.47 1.24

Belgium

E

1.88 1.83 1.49 1.50

France

1.42 1.40 1.40 1.43 1.54 1.51 1.71 1.70 1.59 1.49 1.57 1.60 1.57 1.68 2.10 2.23 1.98

1.70 1.79 1.16

Ireland

1.17 1.48 1.42 1.43 1.54 1.56 1.52 1.50 1.59 1.56 1.49 1.44 1.47 1.49 1.52 1.84 1.82 1.95

1.63 1.73 1.81 1.78 1.79 1.82 1.82 1.91 2.05 2.06 1.95 1.93 1.99 1.91 1.98 2.01 2.06 2.06 1.81

1.55 1.85 1.78 1.85 1.85 1.83 1.90 1.92 1.88 2.11 2.12 1.99 1.88 1.96 2.04 1.99 2.10 2.20 2.32 1.90

United Kingdom 1.82 1.66

Canada

United States

E R

USA CAN GBR IRL FRA BEL NLD DEU ITA ESP PRT GRC AUT CHE DNK NOR SWE FIN AUS NZL JPN

I M P O R T

Table A.5: Estimated steady state trade cost (exporter- importer-specific, average over category)

Table A.6: Reduced form gravity equations (1) (2) (3) (4) ( ) exj,i,m,t ln(exj,i,m,t ) ln(exj,i,m,t ) ln(exj,i,m,t ) ln 1/(1−θ) ln Zj,t ln Pj,t ln πj ln Zi,t ln Pi,t ln πi lnDistj,i (lnDistj,i )2 (lnDistj,i )3 Borderj,i Langj,i Colonyj,i RTAj,i,t (j, m, t) FE (i, m, t) FE (m, t) FE Restriction† Missing Observations R2

1.95∗∗∗ (0.02) 1.13∗∗∗ (0.02) 0.93∗∗∗ (0.00) 1.31∗∗∗ (0.02) 0.69∗∗∗ (0.02) 0.80∗∗∗ (0.00) 7.99∗∗∗ (0.33) −1.27∗∗∗ (0.05) 0.06∗∗∗ (0.00) 0.09∗∗∗ (0.01) 0.32∗∗∗ (0.01) 0.89∗∗∗ (0.02) 0.34∗∗∗ (0.01) no no yes no drop 159865 0.748

2.22∗∗∗ (0.06) 1.99∗∗∗ (0.06) 1.24∗∗∗ (0.01) 1.91∗∗∗ (0.06) 1.07∗∗∗ (0.06) 1.09∗∗∗ (0.01) −2.43∗∗∗ (0.90) 0.24∗ (0.13) −0.01∗∗ (0.01) −0.61∗∗∗ (0.03) 0.76∗∗∗ (0.03) 1.05∗∗∗ (0.03) 0.35∗∗∗ (0.03) no no yes no 50K 163800 0.470

Robust standard errors in parentheses. †

∗∗∗

πi Zi,t Pi,t

1.74∗∗∗ (0.05) 1.25∗∗∗ (0.05) 1.10∗∗∗ (0.01) 9.41∗∗∗ (0.98) −1.39∗∗∗ (0.14) 0.06∗∗∗ (0.01) −0.33∗∗∗ (0.03) 0.87∗∗∗ (0.03) 0.96∗∗∗ (0.04) 0.47∗∗∗ (0.03) yes no – no 50K 163800 0.576

4.62∗∗∗ (0.98) −0.72∗∗∗ (0.14) 0.03∗∗∗ (0.01) −0.27∗∗∗ (0.03) 0.91∗∗∗ (0.03) 0.96∗∗∗ (0.04) 0.47∗∗∗ (0.03) yes no – yes 50K 163800 0.534

( ln

(5) exj,i,m,t 1/(1−θ)

πi Zi,t Pi,t

2.01∗ (1.18) −0.07 (0.16) −0.02∗∗ (0.01) 0.20∗∗∗ (0.04) 0.38∗∗∗ (0.03) 1.05∗∗∗ (0.05) 0.03 (0.03) yes yes – yes 50K 163800 0.110

p < 0.01,∗∗ p < 0.05,∗ p < 0.01.

If yes, the model implied restrictions are imposed by transforming the dependent variable with θ = 1/3.

Missings are replaced by nominal $50,000. The replacement value by 1K, 10K and 100K give the same results.

50

)

i, j ∈ {1, ..., N } m ∈ {1, ..., M } t = 0, 1, ... st ∈ S st ∈ S Pr(st )

Table A.7: Variables and indices Description Indices Country index Product (sector) index Time index State of the world at t History upto t Probability realizing history st

Ci,t (st ) Li,t (st ) li,m,t (st ) Xi,t (st ) xi,m,t (st ) ki,m,t (st−1 ) Zi,t (st ) zj,i,m,t (st ) Bi,t (st ) b (st ) Ti,t

Quantities (per capita values) Consumption of final goods Total labor supply Labor supply for sector m Total investment Investment for sector m Capital stock of sector m Total final goods production = Absorption per capita Int. goods m produced in j used in i Risk free bond holdings Transfer financed by bond adjustment tax

Pi,t (st ) Wi,t (st ) Ri,m,t (st ) Ptb (st ) pj,i,m,t (st )

Prices Final goods price Real wage Real rental rate Price of risk free bond Price of (j, m) products in i

Variable

ai,m,t τj,i,m,t (st )

Exogenous shock variables Productivity of intermediate product Trade cost of product m from j to i

u(C, L) ϕ(x/k) ηtb

Functions and constant Time separable period utility function Capital adjustment friction function Bond adjustment tax rate

exj,i,m,t (st ) Yi,t EXi,t IMi,t N Xi,t

Additional variables Total flow value of product m from j to i GDP per capita Total exports per capita Total imports per capita Net exports per capita

(st )

51

Figure A.1: Varying productivity shock 12

6 Slope Y s.d. C s.d. Y correl. C correl.

10

5

8

4

6

3

4

2

2

1

0

0

0.01

0.02

0.03

0.04 0.05 0.06 0.07 S.D. of productivity shock

0.08

0.09

0

0.1

Slope Y s.d. C s.d. Y correl. C correl.

0

0.05

0.1

0.15 0.2 0.25 0.3 0.35 Correlation of productivity shock

0.4

0.45

0.5

Left panel: baseline parameterization, with varying standard deviation of productivity shock. Right panel: baseline parameterization, with varying cross-country correlation of productivity shock. “Slope” is the slope coefficient (× 100) of trade-comovement regression. “Y s.d.” and “C s.d.” are standard deviations of model GDP and consumption (mean of model G7 countries), respectively. “Y correl.” and “C correl.” are cross-country correlations of model GDP and consumption, among G7 countries, respectively.

Figure A.2: Varying standard deviation of trade cost shock 14

0.8

12

0.7

10

0.6

8

0.5

Slope Y s.d. C s.d.

6

4

0.4

0.3

2

0

0.2

0

0.05

0.1

0.15 0.2 S.D. of trade cost shock

0.25

0.1

0.3

Y correl. C correl. 0

0.05

0.1

0.15 0.2 S.D. of trade cost shock

0.25

0.3

Baseline parameterization, with varying correlation of technology shock. “Slope” is the slope coefficient (× 100) of trade-comovement regression. “Y s.d.” and “C s.d.” are standard deviations of model GDP and consumption (mean of model G7 countries), respectively. “Y correl.” and “C correl.” are cross-country correlations of model GDP and consumption, among G7 countries, respectively.

52

Figure A.3: Varying correl. of trade cost shock

Figure A.4: Varying financial friction

10

6

9 5

8 7

4 Slope Y s.d. C s.d. Y correl. C correl.

6 5 4

Slope Y s.d. C s.d. Y correl. C correl.

3

2

3 2

1

1 0

0

0.1

0.2

0.3 0.4 0.5 0.6 0.7 Correlation of trade cost shock

0.8

0.9

0

1

−6

−4

10

10

−2

0

10 Financial friction

10

Left panel: baseline parameterization, with varying correlation of trade cost shock. Right panel: baseline parameterization, with varying financial friction parameter. “Slope” is the slope coefficient (× 100) of trade-comovement regression. “Y s.d.” and “C s.d.” are standard deviations of model GDP and consumption (mean of model G7 countries), respectively. “Y correl.” and “C correl.” are cross-country correlations of model GDP and consumption, among G7 countries, respectively.

Figure A.5: Varying autocorrelation of produc- Figure A.6: Varying autocorrelation of trade cost tivity shock shock 6

6

5

5

4

4

3

Slope Y s.d. C s.d. Y correl. C correl.

3

2

2

1

1

0 0.3

0 0.4

0.5 0.6 0.7 0.8 Autocorrelation of productivity shock

Slope Y s.d. C s.d. Y correl. C correl.

0.9

0

0.1

0.2

0.3

0.4 0.5 0.6 0.7 Autocorrelation of trade cost

0.8

0.9

1

Left panel: baseline parameterization, with varying autocorrelation of productivity shock (ρa ). Right panel: baseline parameterization, with varying autocorrelation of trade cost shock (ρτ ). “Slope” is the slope coefficient (× 100) of trade-comovement regression. “Y s.d.” and “C s.d.” are standard deviations of model GDP and consumption (mean of model G7 countries), respectively. “Y correl.” and “C correl.” are cross-country correlations of model GDP and consumption, among G7 countries, respectively.

53

Figure A.7: Varying CES parameter θ

Figure A.8: Varying CES parameter ρ

7

14

6

12

5

10 Slope Y s.d. C s.d. Y correl. C correl.

4

3

8

6

2

4

1

2

0 0.3

0.4

0.5

0.6 0.7 CES parameter (θ)

0.8

Slope Y s.d. C s.d. Y correl. C correl.

0 0.3

0.9

0.4

0.5

0.6 0.7 CES parameter (ρ)

0.8

0.9

Left panel: baseline parameterization, with varying elasticity of substitution across different products (θ). Right panel: baseline parameterization, with varying elasticity of substitution across different origins (ρ). “Slope” is the slope coefficient (× 100) of trade-comovement regression. “Y s.d.” and “C s.d.” are standard deviations of model GDP and consumption (mean of model G7 countries), respectively. “Y correl.” and “C correl.” are cross-country correlations of model GDP and consumption, among G7 countries, respectively.

Figure A.9: Varying capital stock adjustment Figure A.10: Varying number of “rest of the friction ηϕ world” countries 6

6

5

5

4

4 Slope Y s.d. C s.d. Y correl. C correl.

3

2

2

1

1

0

0 0

0.1

0.2 0.3 0.4 Adjustment friction (η )

0.5

Slope Y s.d. C s.d. Y correl. C correl.

3

0.6

φ

0

1

2 3 4 Number of the rest of the world countries

5

6

Left panel: baseline parameterization, with varying elasticity of capital stock adjustment friction (ηϕ ). Right panel: baseline parameterization, with varying number of “rest of the world” countries. “Slope” is the slope coefficient (× 100) of trade-comovement regression. “Y s.d.” and “C s.d.” are standard deviations of model GDP and consumption (mean of model G7 countries), respectively. “Y correl.” and “C correl.” are cross-country correlations of model GDP and consumption, among G7 countries, respectively.

54

Figure A.11: G7 bilateral trade and output correlations 0.8

0.8 Data Data Model Model

0.7 0.6

0.6 0.5 pair output correl.

pair output correl.

0.5 0.4 0.3

0.4 0.3

0.2

0.2

0.1

0.1

0

0

−0.1 −6.5

Data Data Model Model

0.7

−6

−5.5

−5 −4.5 −4 log(pair trade intensity)

−3.5

−3

−0.1 −6.5

−2.5

−6

−5.5

−5 −4.5 −4 log(pair trade intensity)

−3.5

−3

−2.5

Left panel: Complete market case. Right panel: Financial autarky case.

Figure A.12: G7 bilateral trade and output correlations 0.8

0.8 Data Data Model Model

0.7 0.6

0.6 0.5 pair output correl.

pair output correl.

0.5 0.4 0.3

0.4 0.3

0.2

0.2

0.1

0.1

0

0

−0.1 −6.5

Left panel:

Data Data Model Model

0.7

−6

−5.5

−5 −4.5 −4 log(pair trade intensity)

−3.5

−3

−0.1 −6.5

−2.5

Symmetric trade cost case (population is different).

(trade costs are different).

55

−6

−5.5

−5 −4.5 −4 log(pair trade intensity)

Right panel:

−3.5

−3

−2.5

Symmetric population case

Figure A.13: Estimated distance elasticity of trade cost 0.2 0.18 0.16

Elasticity of trade cost

0.14 0.12 0.1 0.08 0.06 0.04 0.02 0

ln(250)

ln(500)

ln(1000) ln(2000) ln(Distance (km))

ln(4000)

ln(8000)

From trade cost estimations, average of the estimated coefficients are obtained. Then, based on these coefficients, implied distance dependent distance elasticity is calculated.

56