# Specialization Patterns in International Trade

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5 ensures that cross-country differences in the Gini are solely due to differences in the shape of the export revenues distributions and do not depend on the level or unit of export sales. The Principle of Population (doubling the sample population does not change the index) minimizes the impact of the aggregation bias due to product classification standards in the trade data, in particular proportional changes in the level of disaggregation do not change the concentration index. 3 Differences in the concentration index between countries can stem from two underlying mechanisms. Either a country exports more products relative to another (i.e. differences in the extensive margin) or, given that two countries export the same number of products, the distribution of export revenues of one country is more skewed in comparison to another country (differences in the intensive margin). 4 Because the Gini index does not allow for this distinction, we use the Theil index as an alternative concentration measure. To capture differences in the intensive product margin, we define the intensive Theil as follows: Tix Int = 1 N ix r N ix ik ln r k=1 ix ( rik r ix ) (2) where N ix denotes the number of exported products by country i and r ix = N ix k=1 r ik represents the mean export revenue of country i. The intensive Theil index measures the concentration in export sales by a weighted average of the log distance from the mean. In addition, we define the extensive Theil of country i as follows: T Ext ix ( ) N = ln N ix where N ix denotes the number of products exported and N the total number of products in the world. Thus, the concentration between two countries may simply differ because one country exports more products. To assess the relative importance of each margin in terms of overall concentration, we sum the extensive and the intensive component to get the total Theil index, which is equal to: T ix = T Int ix + T Ext ix = 1 N N k=1 ( ) r ik rik ln R ix R ix where R ix = 1 N N k=1 r ik represents the mean export revenue over all products N. 5 (3) (4) The total Theil index takes the value of zero in the case of complete diversification, i.e. exporting all products (N ix = N) and export revenues are equal for all products, ( R ix = r ik, k). In the case of complete specialization, one product generates all export revenues, (N ix = 1, r ik = r ik, R ik = r ik /N ) 3 In the appendix we show that our results are robust to different levels of aggregation (4 digit versus 6 digit) and different classification systems (SITC versus HS). 4 The Weak Principle of Transfers ensures that if the export revenue of a low selling product increases by the same amount a high selling product decreases its revenue, then the export revenue distribution becomes less skewed and concentration decreases. 5 In the appendix, we show that the sum of the intensive and the extensive component indeed imply the total Theil index given in equation 4. 5

8 Export Concentration Gini index HS 6 digit Mean of the index from KWT AGO BDI BOL BHR AZE BEN BGD CMR CPV COD CAF ECU ISL ARM BFA CHL CRI DOM KAZ GHA HND NGAETH JAM QAT FJI PRYMWI RWA TKM GMB LAO GNB MDG GEO MLT KGZ MRT NERSTP TCD TTO UZB YEM VENPER MUS TZAUGA SEN NPL SAU URY OMN MAR ALB BLR GTM IRL SLV LKA IRNMDA PHL BIH KEN SYR PAK CYP EGY COL ARG JOR NZL TUN HRV FIN ISR LBN LTUMEX CAN AUS EST LVA VNM PAN RUS UKR MYS SGP ROU ZAF NOR SVK BRA BGRGRC HUN KOR PRT IDN THA SVN SWE TUR CHE JPN HKG POL DNK CZE IND AUT CHN ESPBEL GBR NLD USA FRA GER ITA Import Concentration LCA BRN GAB MDV KNA TJK Export Concentration Total Theil index HS 6 digit Mean of the index from AGO BDI NER CAF COD JAMDV MRT TJK KNA GMB GABBRN TCD GNB TTO GHA KWT CMR CPV RWA BFA BEN ISLETH UGAQATKGZ ARM STP BOL CHL ECU BHR LCA PER NGA TZA PRY SEN YEM MWI UZB LAO MLT TKM CRI SAU MUS JOR KAZ MDGAZE NPL IRN HND LBN FJI GEO SGP CYP ARG VENDOM BGD ALB CAN GTM IRL MDA AUSKEN ISR BIH HKG OMN URY SLV PHL PAN MAR LVA MEX GRC NZL TUN MYS COL BLR HRVHUN FIN NOR EGY LTU LKA EST PAK PRT RUS ZAF VNM UKR SYR SVK ESP BRA ROU KOR POL FRA SVN TUR DNK SWE BGRTHA CZE AUT IDN GBR BEL CHE IND JPN NLDUSA GER CHN ITA Import Concentration (a) Gini coefficient (b) Theil index Export concentration index HS 6 digit Mean of the index from Import concentration index HS 6 digit Mean of the index from Extensive Theil index GNBTCD BDI STPRWA CPV AGO BEN GMB MDV KNA CAF MWI LCA BFA COD ETH GAB MRT TKM YEMUGA BRN NER AZENGA LAOQAT ARM BOL KWT GHA CMR JAMTJK SEN PRY TZA OMN ALB FJIGEO MDGBHRISL KGZ CYP KAZ UZB TTO LBN ECU BIH DOM BGD GRC GTM HND JOR MLT SLV VEN SAU MUS NPL MDA KEN URY PAN IRN CRI CHL HRV LKA LVA EGY LTU MAR PER SYR EST COL NOR TUN BLRNZL HKG AUSARG ROU BGR CAN ISR DNK HUN PAK FINMEX IRL PHL POL PRT VNM RUS AUT SVN SGP SVK UKR TUR BEL CZE IDN CHE ESP BRA MYS NLDGBR SWE ZAF THA FRAKOR USA ITA IND GER CHN JPN Extensive Theil index STP GNB TCD CAF LAO RWA ARM COD BDI TKM GMB CPV KGZMRT NER NPL MWI UZB BFA GEO BEN FJI AZE AGO MDA BIH YEM ALB UGA CMR BLR CHNBHR EST ETH SEN QAT TJK SYR KAZ MDG TZA GHA GER LVA BGRDOM HND ITA JAM JPN KNA LTU MUS PAK KEN IND CYP FRA CZE IDN BOL BGD CRI ISL KOR IRN KWT LCA LKA JOR ARG AUT BRA BEL BRN ESPEGY GTM FIN CAN CHE CHL COL DNK ECU GBR GAB HRV AUS HUN LBN MDV PRYOMN MLT SVN URY UKR VNM SLV TTO USA NGANLD ROU POL MAR PER SWE SVK THA TUR TUN RUS ZAF IRL ISR MYS PHL PRT VEN MEX NOR NZL GRC SGP SAU HKG PAN Intensive Theil index Intensive Theil index (c) Export Concentration (d) Import Concentration Figure 1: Average export versus import concentration for the period 1995 to 2011 for 130 countries concentration is mainly due to the fact that countries export few and import many products. These result also holds for the majorities of countries, see Figures 1(a) and 1(b). In case of the United States, China, Germany, Hong Kong, India, Italy and Panama export and import concentration are almost equal. Fact 2: Extensive product margin is more important for exports and the intensive product margin for imports Turning to the decomposition, Table 1 shows that for exports the main driver of concentration is the extensive product margin with a share of 55 percent. Thus, export concentration is more sensitive to changes in the number of products exported rather than to changes in export revenues. This result is in line with existing evidence on the importance of the extensive product margin on the level of export revenues, see Hummels and Klenow (2005) for product and Eaton et al. (2011) for firm level evidence. On the other hand, for imports the intensive product margin has a higher share with 60 percent in terms of overall concentration. Countries import a wide range of products, thus changes in the import expenditure are the main contributor to changes in overall import concentration. However, there are significant cross country differences in the relative importance of each margin, see 1(c) and 1(d). 8

9 Fact 3: Concentration declines with income and size In terms of cross-country differences, the empirical evidence shows that richer and larger countries diversify more than smaller ones. Table 1 states the estimated coefficients when regressing the log of GDP per capita and the log of population onto the concentration indexes. The Gini as well as the Theil index of both, exports and imports, decrease as GDP per capita and size increase, i.e. smaller and poorer countries are more specialized. This relationship is equally pronounced for exports and for imports, with an R square of 0.63 and 0.66 respectively. Turning the attention to the decomposition reveals that the main driver of the negative relationship is the extensive product margin. The R square for exports is 0.76 and for imports Thus, richer and larger countries are more diversified because they export and import more products. These results differ from Cadot et al. (2011) in two important ways. They find that (1) the intensive Theil dominates the extensive Theil, and (2) the extensive Theil is decreasing in income until GDP per capita reaches a certain level after which the index starts to increase. The underlying reason for the difference in the importance of the extensive versus the intensive margin comes from the fact this study is build on net trade flows rather than gross trade flows as in Cadot et al. (2011). Table 12 in the appendix replicates Table 1 for gross trade flows and the results are similar to Cadot et al. (2011). However, there are key differences: (1) I focus on the cross section rather than on the panel and (2) I include the log of population as an additional regressor in Table 1. The reason I am focusing on the cross section is that the model I am assessing has implications on cross-country differences but no dynamic implications. Including population as a control variable allows me to look at the functional relationship between GDP per capita and concentration by controlling for size effects. Figure 2 shows that this relation is negative log-linear rather than a hump shape as in Cadot et al. (2011). However, in line with Cadot et al. I also find that extensive product margin is at the origin of this relationship, 2(c) and 2(d). In general, the theoretical explanation of why larger countries export more products are based on the Armington assumptions, see Hummels and Klenow (2005) and Koren and Tenreyro (2013). However, in these type of models, by assumption tradable goods are differentiated by location of production and each country is the sole producer of a good. In contrast, in the EK model all countries potentially supply the same good and consumer purchase the good from the cheapest supplier only. The next section presents the relevant parts of the Alvarez and Lucas (2007) extension of the Eaton-Kortum framework and highlights the key features that allows the model to reproduce the stylized facts. 9

10 Export Concentration COD Total Theil index HS 6 digit Mean of the index from AGO BDI NER CAF ETH TCD TJK NGA MRT BFA RWA UGA GHA CMR JAM GMB TZA BEN YEM UZB MWI GNB NPL SEN BGD KGZ BOL ARM ECU PER GAB MDG LAO PRY MDV IRNCHL PHL TKM PAN TTO KWT KAZ SAU CPV AZE LCA BRN KEN HND VNM PAKGEO JOR IND STP GTM MAR DOM KNA VEN ARG QAT MEX LBN ZAF CRI RUS SLV MDA ALB EGY BRA BHR MYS ISL HKG SGP CAN AUS UKRCOL MUS MLT SYR FJI LKABIH IDN CHN TUN THA URY OMN ISR BLR GRC IRL TUR KOR LVA NZL ESP ROU POL HUN FRA CYP PRT FIN GBR NOR JPN USA LTU HRV SVK BGR SWE EST CZE DNKGER BEL CHE AUT SVN ITA NLD Log of GDP per capita coef = , (robust) se = , t = Import Concentration COD GNB Total Theil index HS 6 digit Mean of the index from STP TCD ARM IND CAF NER TJK BEN PHL BDI BFA RWA GMB MRT LAO MWI NPL KGZ GEO TKM YEM AGO UZB CHN CPV AZE MYS MLT USA SEN ETHMDGTZA UGA CMR KEN BGD PAK OMN ITA GER GHA NGA MDA SYR VNM PRY ALB THA HND FJI BIH LCA KAZ IDN SLV BOL JOR LKA EGY MDVUKR DOM KNA JAM LBN IRN ZAF BRA BHR HKG JPN QAT ISR RUS KOR ECU GAB COL GTM MAR PER TUN CRI MUS VEN BGR BLR TTO URY LVA LTUTUR MEX HUN IRL BRN KWT NLD SGP GBR SAU EST ARG SVK ROUCHLPOL HRV SVN PRT CZE GRC BEL CHE NZL ISL FIN ESP DNK SWE AUT FRA AUS CAN NOR CYP Log of GDP per capita coef = , (robust) se = , t = 6.62 PAN (a) Overall concentration of exports (b) Overall concentration of imports Extensive Theil index HS 6 digit Mean of the index from Extensive Theil index HS 6 digit Mean of the index from Export Concentration COD TCD BDI RWA AGO ETH GNB CAF MWI BFA BENNGA UGA NER YEM GMB TZA MRT CPV STP GHA CMR TKM SEN MDG BGD LAO BOL AZE UZB MDV GAB NPL TJK ARM PRYJAM KEN KGZ GEO EGY VEN KAZ IRN SAU KWT SLV MDA HND VNM PAK JOR IND LKA GTM MAR ALB PHLLCA PER DOM BRN QAT KNA LBN COL FJI BIH IDN CHNBRA TTO CHLMEX OMN ARGRUS GRC UKR TUNCRI PAN MUS ZAF BHR BLR ROU TUR AUS THA HRVPOL CYPISL LVA LTU MYS MLT PRT ESP HKG CAN USA NZL BGR HUN ISRKORFRA GBR NOR JPN ESTSVK CZE FIN IRL ITA SGP GER DNK SWE BEL AUT NLD CHE SVN Import Concentration COD GNB STP TCD CAF LAO RWA BDI ARM NER GMB MWI NPLMRT TKM KGZ BFA BEN UZB CPV GEO YEM AGO FJIAZE CHN ETH UGA MDGTZA SEN TJK CMR MDA IND BIH NGA KEN GHA SYR PAK ALB GER KAZ BGD VNM BLR ITA JPN USA IDN UKR HND SLV BOL PRY LKA DOM JOR PHL GTM MAR JAM EGY ECU PER TUN LBN ZAF BGR THA IRN BRA LVA LTU EST COL CRI MUS URY TUR ROU TTO MYS ARG MDV LCA KNAVEN MLT MEX OMN POL BHR QAT RUS KORFRA SVK HUN SVN CZE ESP KWT NLD GBR GAB CHL HRV PAN CYP SAU PRT ISR SWE BEL GRC NZL ISL FIN DNK AUT CHE IRLAUS CAN HKG BRN SGP NOR Log of GDP per capita coef = , (robust) se = , t = Log of GDP per capita coef = , (robust) se = , t = 8.7 (c) Extensive product margin of exports (d) Extensive product margin of imports Intensive Theil index HS 6 digit Mean of the index from Intensive index HS 6 digit Mean of the index from Export Concentration COD TJK PAN NER JAM AGO PER TTO CHL SGP PHL CAF MRTCMR KGZ ECU ZAF MYS GHA LCA ARG MLT NPL MDG GMB TZA SEN BGD HND VNM PAK BOL ARM UZB CRI IRN ISL ISR IRL HKG BRN KWT CAN JOR IND PRY KNA GAB MUS MDV UGANGA BDI KEN LAO MDA GEO UKR LBNTHA KAZ MEX BHR RUS KOR AUS BRA SAU QAT ETHBFASLV YEM SYR FJI GTM URY MAR TUN DOM BLR LVA HUN NZLFIN FRA BIH IDN COL CHN VEN SVK ESP JPN SWE LKAAZE ALB EGY BGR BEN TKM ROU LTU EST TUR CYP PRT OMN POLSVN CZE GRCDNK GBR CHE BELGER NOR USA HRV AUT NLD MWI TCD RWA CPV ITA GNB STP Import Concentration COD PHL TJK IND MLT MYS HKG LCA BRN SGP MDV OMN ISR IRL USA TCD GNB BEN NER ETHMDG BFASLV TZA NGA KEN SEN BGD YEM STPUGA GHA CMR MRT HND AGO PAK VNM ARM PRY KNA GAB BOL GEO JOR EGY LBNTHA SAU ECU LKA GTM BDI MWI GMB SYR MAR JAM AZE IDN UZB PER TUN ALB UKR DOM COL ZAF CHN VEN CRI IRN BRA TTO BHR MEX HUN GRC NZL MUS KAZ CHL CAF RWA NPL KGZ CPV TKMBGR URY ROU LTU ARG TUR SVK RUSPRT ISL KOR FIN LVAEST HRV CZE DNK BEL ITA KWT CHE NLD QAT AUS GBR ESP SWE AUT CAN GER NOR JPN POLSVN FRA MDA BIH BLR CYP LAO FJI PAN Log of GDP per capita coef = , (robust) se = , t = Log of GDP per capita coef = , (robust) se = , t = 3.6 (e) Intensive product margin of exports (f) Intensive product margin of imports Figure 2: Average export and import concentration versus GDP per capita across 130 countries. Note: Each point in the scatter plots represents the difference from the average concentration index and the log of GDP per capita relative to the United States. The data have been adjusted to remove country size (population) effects. 10

11 3 Model The Eaton Kortum model is Ricardian, with a continuum of goods produced under a constantreturns technology. In this paper, I focus on the Alvarez and Lucas (2007) model and include capital as in Waugh (2010). Next, I derive the relevant theoretical predictions on the pattern of trade and evaluate the importance of the key model parameters for import and export specialization. Consider a world economy with I countries, where each country produces tradable intermediate goods as well as non-tradable composite and final goods. Following Alvarez and Lucas (2007), I define x = (x 1,..., x I ) as a vector of technology draws for any given tradable good and refer to it as good x with x R I +. The production of an intermediate good in country i is defined by: q i (x i ) = x θ i [k α i s1 α i ] β q 1 β mi. Technology x i differs between goods and is drawn independently from a common exponential distribution with density φ and a country specific technology parameter λ i, i.e. x i exp(1/λ i ). I denote the interest rate by r i, the wage by w i and the price of the intermediate aggregate good by p m,i. The intermediate good sector is perfectly competitive. Producers of the intermediate good minimize input costs and sell the tradable intermediate good at price p i (x i ) = Bxi θ[rα i w1 α i ] β p 1 β mi. The continuum of intermediate input good x goes into the production of the composite good q i symmetrically with a constant elasticity of substitution (η > 0) [ˆ η/(1 η) q i = q(x) φ(x)dx] 1 1/η. 0 The aggregate output of intermediate good q i can then be allocated at no cost to the production of final goods or can be used as an input in the production of other intermediate goods. Similarly, capital and labor can be used either to produce intermediate or final goods. Finally, consumers draw utility linearly from the final good. All markets are perfectly competitive. Since these features are not central to the implications I derive in this paper, I omit them. I refer interested readers to Alvarez and Lucas (2007) for a full description of the model. 3.1 General equilibrium Once a country opens up to international goods markets, intermediate goods are the only goods traded. Final goods are not traded and capital and labor are immobile between countries. Trading intermediate goods between countries is costly. We define Iceberg transportation costs for good x from country i to country j by κ ij where κ ij < 1 i = j and κ ii = 1 i. As in Alvarez and Lucas (2007), we also consider tariffs. ω ij is the tariff levied by country i on goods imported 11

12 from country j. Incorporating the trade costs, composite good producers in country i will buy the intermediate good x from country j that offers the lowest price p i (x) = B min j [rα j w1 α j κ ij ω ij ] β p 1 β mj x θ j. (5) Equation 5 shows that whether country i specializes in the production of good x depends on the productivity realizations, factor prices and trade costs. If country i does not offer a good at the lowest cost in the local market, the good is imported. Following Alvarez and Lucas, the resulting price index of tradable goods in country i is p mi = (AB) I j=1 [rα j w1 α j κ ij ω ij ] β p 1 β mj 1/θ λ j θ. (6) Next, we calculate the expenditure shares for each country i. Let D ij be the fraction of country i s per capita spending p mi q i on tradables that is spent on goods from country j. Then, we can write total spending of i on goods from j as ˆ p mi q i D ij = p i (x)q i (x)φ(x)dx B ij where B ij defines the set of goods country j attains as a minimum in equation 5. Note that D ij is simply the probability that country j is selling good x in country i at the lowest price and calculated to be D ij = (AB) 1/θ [rα j w1 α j ] β p 1 β mj p mi κ ij ω ij 1/θ λ j. (7) Equation 7 shows that in this model the sensitivity of trade between countries i and j depends on the level of technology λ, trade costs ω, geographic barriers κ and the technological parameter θ (reflecting the heterogeneity of goods in production) and is independent of the elasticity of substitution η. This result is due to the assumption that η is common across countries and does not distort relative good prices across countries. Note also that, by the law of large numbers, the probability that country i imports from country j is identical to the share of goods country i imports from j. In this sense, trade shares respond to costs and geographic barriers on the extensive margin: as a source becomes more expensive or remote it exports/imports a narrower range of goods. It is important to keep in mind that the number of intermediate input industries that enter into the production of the composite good is fixed. Each country uses the whole continuum of intermediate goods to produce composite goods. There are no gains from trade due to an increased number of varieties. Welfare gains are realized through incomplete specialization. Domestic production competes with imports and countries specialize through the reallocation of resources made available by the exit of inefficient domestic producers. 12

15 Table 2: Estimation Results Summary Statistics Observations TSS SSR R E E Geographical barriers Barrier Paremeter estimate Standard error % effect on cost [0,375) % [375,740) % [750,1500) % [1500,3000) % [3000,6000) % [6000,max) % Tariff % Shared border % Note: All parameters were estimated by OLS for an estimated parameter ˆb, the implied percentage effect on costs is 100 (e θb 1) with θ = and F i is the fraction of country i spending on tradable goods net of tariff expenses. F i = I D ji ω ji j=1 The obtained equilibrium wages together with tradable good prices, determine the implied technology levels ˆλ for each country given the structural estimates of the gravity equation. Table 2 summarizes the regression outcome of the gravity equation. In terms of fitting bilateral trade flows, I obtain an R 2 of 0.82, which is slightly lower than the R 2 of 0.83 reported by Waugh. The coefficients obtained for trade costs are consistent with the gravity literature, where distance and tariffs are an impediment to trade. The magnitudes of the coefficients reported in Table 2 are similar to those in Eaton and Kortum (2002) and in Waugh (2010), which consider a similar sample of countries without tariffs. The overall size of the trade costs in percentage terms are higher than those reported in Anderson and Van Wincoop (2004) and Waugh (2010). The main reason for the higher cost effect lies in the underlying trade elasticity. Waugh (2010) uses an elasticity of 5.5 whereas this paper uses The trade elasticity equals to 1 θ, see equation 9. 15

16 4.1 Results Next, I feed the model with the estimated trade costs and technology levels. 12 Table 3 shows the mean concentration levels for the simulated countries. The results show that the calibrated model replicates the Fact 1, i.e. countries are more concentrated in exports than in imports on all margins. However, the levels of export concentration are almost twice as high as the ones observed in the data: mean export (import) concentration on the extensive product margin is 5.04 (0.82) compared to 2.60 (1.10) in the data. This implies that, in the simulated model, countries export (import) 0.8 (43.2) percent of the product space compared to 7.4 (33.3) percent in the data. On the hand, the simulated import levels are close to the one observed in the data. Table 3: Summary statistics of the average simulated concentration indexes for 130 countries. Concentration Gini Theil Exports Theil Imports Exports Imports Extensive Intensive Extensive Intensive Total Margin Margin Margin Margin Total Level Share of total 62% 38% 30% 70% Correlation Regression (Simulation θ = 0.25, η = 4)) log(gdppc) *** *** *** *** [0.0010] [0.0023] [0.0305] [0.0500] [0.0524] [0.0190] [0.0108] [0.0244] log(population) *** * *** *** *** *** [0.0016] [0.0034] [0.0455] [0.0747] [0.0783] [0.0283] [0.0162] [0.0364] Observations R-squared Turing the attention to the decomposition shows that consistent with Fact 2, the extensive product margin is more important for exports and the intensive product margin for imports. In quantitative terms, the share of the extensive margin of exports (imports) is 62% (30%) compared to 55% (40%) in the data. This result reflects the previous point that, in the model, countries specialize much more in the extensive margin of exports relative to the intensive margin. On the import side, the opposite is true. The lower part of Table 3 shows the simulated relationship between income per capita, size and trade concentration. The model can replicate Fact 3 (Concentration declines with income and size) for exports but not for imports. Also in line with the empirical evidence is that the negative relationship is driven by the extensive margin with a strikingly similar elasticity between income and export concentration. Next, I plot the corresponding cross-country pattern for simulated and empirically observed concentration levels against the log of GDP. Figure 4 shows the relationship between income and 12 See Table 6 at the end of the paper. 16

17 concentration conditional on population and the mean. The model replicates the empirical pattern with export concentration decreasing as income increases, see 4(a). However, the cross country differences in terms of income and concentration are much larger in the model than in the data. In the model, the difference from the mean level of concentration ranges from -2 to +2, whereas in the model from -4 to +4. The reason for the larger dispersion is the extensive margin, see 4(c). On the import side, the cross country differences in terms of concentration in the calibrated model are similar to the data, see 4(b). With regard to the intensive margin, see 4(f), the results show that, in line with the data, the model predicts no relationship between concentration and income. Overall, the calibrated model is able to replicate the qualitative pattern but produces relatively high levels of concentration compared to the data, particularly for the extensive margin of exports. A potential explanation for the excessive export concentration lies in the underlying productivity distribution. While the model reproduces the bilateral trade volumes, it fails to capture the underlying distribution of trade volumes across products. To shed light on why countries trade in too few products, I follow Haveman and Hummels (2004) and plot the empirical and simulated density of the number of exporters and importers per product. 13 Figure 5 shows the results. The simulated countries export their goods to too many destinations. The assumed productivity distribution generates producers that are so efficient that even firms facing high trade costs can sell their products to numerous destinations around the world. As a consequence, the number of exporting countries per product is small. In the data (in blue) more than a third of the products are exported by 25 or more countries. In the simulation (in red) no product is exported by more than 25 countries. With regard to imports, Figure 5(b) shows that, contrary to exports, the simulated distribution of the number of countries importing a product is closely related to the empirical one. 5 Policy experiments This section considers the following policy experiment: suppose a country wants to diversity its exports. This policy was advocated by many policy institutions in order to reduce the negative impact of volatility on growth, see De Ferranti et al. (2002) and IMF (2014). In order to show the model s implications of such a policy, I consider the free trade equilibrium (κ ij = w ij = 1, i, j), which is simple and can be solved by hand. Later, I will use the calibrated model to calculate precisely the policy effects for each country. Within the Alvarez and Lucas (2007), there are basically two ways to decrease export concentration. The first one is an increase in the level of technology (λ), for example through R&D investment, and the second policy is by increasing competitiveness, for example through an exchange rate depreciation. I consider a change in the level of technology as a long term effect, while a change in the exchange rate as a short run effect. 13 To get the empirical distribution of the number of exporters and importers per product, I count for each HS code the number of countries that net export or net import the product. Similarly, the model implied distribution represents the number of exporters and importers for each simulated product. 17

18 5.1 Short run (partial equilibrium) For the moment, I consider the short run equilibrium, where wages cannot adjust. Note that the Theil index of exports is defined as the sum of the extensive and the intensive component, i.e. T ix = T Ext ix + Tix Int. The extensive component is given by T Ext ix and the intensive component is given by T Int ix = 1 N ix = ln N i k=1 ( ) Nix N r ik ln r ix where r ik are export revenues of product k, r ix = N ix k=1 r ik represents the mean export revenue of country i, N ix denotes the number of exported products by country i and N is the total number of products in the world. In the free trade equilibrium, all goods a country produces are exported. Thus, the total value of exports is ( rik r ix ) X i = L j p mj q j D ji j =i and, given that the share of goods produced equals the number of goods produced, we can write the share of goods exported by country i as, n X i : n X i = D ii. In the special case of the free trade equilibrium, every country exports the same goods to all countries. Thus, the distribution of the export revenues is identical to the import expenditure distribution. In the appendix I show that the import and export concentration in the free trade equilibrium are Frechet distributed. The resulting Theil index of the intensive margin equals T Int ix = (ˆ 1 ( Γ(1 1 α ) ln u ( 1/α)) ) u ( 1/α) e u du ln (Γ(1 1α ) ) 0 (10) Concentration on the intensive margin is completely determined by the shape parameter α = 1/(θ(η 1)), which is a function of the elasticity of substitution η and the degree of comparative advantage θ. 14 To compute the Theil of the extensive component of exports, I use equation 7 and impose the free trade equilibrium to get the number of goods exported as a function of wages and 14 The integral in equation 10 cannot be solved analytically. To compute the exact Theil index implied by the shape parameter α, I approximate the integral numerically via the Gauss Laguerre procedure. The derivation can be found in the appendix. 18

19 technology: ix = ln ni X = ln T Ext k αβ θ i k=1 N k αβ θ k w β θ i λ i β w θ k λ k Suppose now that a country wants to diversify its exports and decrease the Theil by 0.1 units. In the free trade equilibrium, the only way to achieve this is goal is by diversifying on the extensive margin. The diversification of exports can be achieved by reducing the local unit labor costs relative to other countries, for example by depreciating the currency (in this framework, this is equal to subsidizing production). To show how an exchange rate depreciation helps to increase exports, I express the unit costs of production in local currency by introducing country i s exchange rate vis-a-vis the US dollar 15, s i, into the free trade version of the model. In this case, the number of goods exported is given by the ratio of local unit costs of production relative to the average unit costs in the importing country and equals ix = ln ni X = ln T Ext s 1 θ i k αβ θ i N k=1 s 1 θ k w β θ i λ i k αβ θ k β w θ k λ k The resulting elasticity on the extensive margin of exports equals to T Ext ix ln s i = ln nx i ln s i = 1 θ (1 nx i ) Hence, the percentage depreciation in the exchange rate needed to increase the share of goods exported by 1 percent is ln s i = ( θ/(1 n X i ) ). The smaller the share of products exported (1 n X i ), the less depreciation is needed to diversify exports Long run (general equilibrium) The general equilibrium version of the policy experiment accounts for the endogenous response of wages. In the free trade version, the equilibrium wage is given by which can be solved to L i w i = w i = k I L j w j D ji. j=1 αβ ( ) θ (β+θ) λi (β+θ) i L i Substituting back into D ii we get the elasticity in the general equilibrium framework. 15 I chose the US dollar as international currency. Of course, I could have chosen any other currency as the common currency denominator. 19

20 (β+θ) ix = ln ni X i L = ln αβ k=1 N k T Ext and the elasticity equals to αβ β θ k (β+θ) (β+θ) i λi β θ (β+θ) (β+θ) (β+θ) k Lk λk T Ext ix ln λ i = ln nx i ln λ i = θ (β + θ) (1 nx i ) Thus, within the general equilibrium, we will have a weaker response to a technology shock in comparison to the partial equilibrium, where the elasticity is TExt ix ln λ i = (1 D ii ). The reason is that an increase in technology will also increase wages, which will partly reduce the pro-competitive effects on the export markets. If we consider now the case of an exchange rate depreciation, the market clearing conditions in US dollars becomes whereas the trade share equation equals I L i w i L j w j D ji = s i, s j=1 j ( [k D ji = (AB) 1/θ α i w i ] β p 1 β mi p mj s j s i ) 1/θ λ i. p mj s i Note that in the free trade equilibrium, prices in US dollars equalize across countries, = p m and the equilibrium wage in local currency becomes: p mi s i = w i = k αβ ( ) β (β+θ) λi (β+θ) i si L i Changes in the exchange rate lead to a one to one change in the wage. Plugging the obtained wage back into the trade share matrix (D ij ), we observe that changes in the exchange rate have no effects on trade. D ji = p β θ m k αβ (β+θ) i Note that the described effects in the partial and the general equilibrium only hold in the free trade equilibrium. Once we introduce trade costs, exchange rate changes will have real effects in the general equilibrium framework because the gain in competitiveness from an exchange rate depreciation is not uniform across countries. Still, the free trade case highlights that policies aiming to diversify in exports (1) depend on the initial share of goods exported and (2) are more effective under the assumption of rigid prices (short run) than in the case of full price flexibility (long run). Next, I show the simulation elasticities for both, the general as well as the partial equilib- λ θ β+θ i L β β+θ i 20

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