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Product Di↵erentiation, and the Composition of Trade Across Dissimilar Nations Ahmad Lashkaripour Indiana University April 23, 2015 1 / 53 Motivation 2 / 53 Background I Gravity Models I I Characterize bilateral trade volumes Do not deliver a systematic relationship between exporter/importer characteristics and the commodity composition of trade. 3 / 53 Background I Gravity Models I I I Characterize bilateral trade volumes Do not deliver a systematic relationship between exporter/importer characteristics and the commodity composition of trade. Recent developments I I Trade between dissimilar countries (e.g. rich-poor) has grown dramatically. Micro-level evidence indicate that dissimilar countries trade di↵erent goods 3 / 53 Background I Three modern facts concerning the composition of trade: 1. Rich countries have systematically higher trade-to-GDP ratios 2. Rich countries export higher price goods (within categories and at the aggregate level) 3. Distant countries trade higher price goods: The Washington Apples effect 4 / 53 Background I Three modern facts concerning the composition of trade: 1. Rich countries have systematically higher trade-to-GDP ratios 2. Rich countries export higher price goods (within categories and at the aggregate level) 3. Distant countries trade higher price goods: The Washington Apples effect I Facts 1 and 2: income per capita has a systematic e↵ect on the composition of trade. I Fact 3: geography has a systematic e↵ect on the composition of trade. 4 / 53 The Literature I All three facts are beyond the scope of standard gravity models—all three concern composition! I Three independent blocks of literature corresponding to each fact: 1. GDP per capita ⇥ Trade GDP : Markusen (1986); Waugh (2010); Fieler (2011); Caron et al. (2014) 2. GDP per capita ⇥ price composition of exports: Flam and Helpman (1987); Hallak (2006); Matsuyama (2000); Schott (2004); Fajgelbaum et al. (2011) 3. Distance ⇥ price composition of exports: Hummels and Skiba (2004); Martin (2012); Irarrazabal et al. (2014) 5 / 53 This Paper I The remaining void: a theory that accommodates all three facts. I I develop a novel view of comparative advantage that fills this void. I I abstract from existing theories: e.g. non-homothetic demand, additive trade costs. 6 / 53 This Paper I The remaining void: a theory that accommodates all three facts. I I develop a novel view of comparative advantage that fills this void. I I abstract from existing theories: e.g. non-homothetic demand, additive trade costs. I I instead relax a common assumption that is inconsistent with micro level evidence: I I allow for two types of goods, which o↵er di↵erent scopes for products di↵erentiation 6 / 53 This Paper I The remaining void: a theory that accommodates all three facts. I I develop a novel view of comparative advantage that fills this void. I I abstract from existing theories: e.g. non-homothetic demand, additive trade costs. I I instead relax a common assumption that is inconsistent with micro level evidence: I I I allow for two types of goods, which o↵er di↵erent scopes for products di↵erentiation Comparative advantage across types determines the composition of foreign trade. 6 / 53 This Paper (continued) I I combine the new channel of comparative advantage with national product di↵erentiation to construct a unified model of trade I Unlike gravity models, the unified model systematically pins down both the volume and the composition of foreign trade. I I estimate the unified model and compare it to a pure gravity model. I The explanatory power is substantially superior, and the gains from trade look vastly di↵erent! 7 / 53 Theory 8 / 53 The Environment I There are N countries I Country i is characterized by 1. Population Li 2. National Product Quality ↵i I There are two types of goods: type H and type L I Firms are homogenous and monopolistically competitive 9 / 53 Demand I Preferences are homothetic, and described by a (three-tier) nested-CES utility I The upper tier aggregates across the two types 2 I Ui = 4 X z2{H,L} (Uiz ) ✏ 1 ✏ 3 ✏ ✏ 1 5 ✏ the elasticity of substitution between types H and L 10 / 53 Demand I Sub-utility Uiz is a CES aggregator across national varieties of type z 2 31 ⇢z N X ⇢ 1 ⇢ z z z z Ui = 4 ↵j Qji 5 j=1 I ↵j is the national product quality of country j I Qzji is the e↵ective quantity of national variety j (of type z) Qzji = "ˆ !2⌦ji z ⇢˜z qji # ⇢˜1 z d! 1 z = Mji⇢˜z qji I z qji : quantity sold by a typical firm from country j to i I Mji : Number of homogenous firms selling from j to i 11 / 53 Demand I I I = 1/ (1 ⇢z ): the inter-national elasticity of substitution ˜z = 1/ (1 ⇢˜z ): the intra-national elasticity of substitution. z The demand structure nests the Armington and Krugman models: I Krugman: ˜z = differentiation I Armington: ˜z ! 1 =) complete national product differentiation z =) no national product 12 / 53 Demand I I I I = 1/ (1 ⇢z ): the inter-national elasticity of substitution ˜z = 1/ (1 ⇢˜z ): the intra-national elasticity of substitution. z The demand structure nests the Armington and Krugman models: I Krugman: ˜z = differentiation I Armington: ˜z ! 1 =) complete national product differentiation z =) no national product I allow for some degree of national product differentiation that is the same for both types: ˜H 1 ˜L 1 = ⌘⌘>1 1 1 H L 12 / 53 Demand I Type H o↵ers a greater scope for product di↵erentiation than type L H < L () ⇢H < ⇢L Therefore, by definition, demand for type L is quantity-intensive and demand for type H is quality-intensive. I If H I = L the model reduces to a pure gravity model. This assumption is counter-factual, but present in all standard gravity models 13 / 53 Demand I Summary of key parameters I I I ✏ governs the relative spending on type H versus L z regulates the scope for product di↵erentiation for type z ⌘ regulates the degree of national product differentiation in the economy 14 / 53 Nested-CES Demand Function I Demand in country i for varieties of type z = {H, L} produced in country j z Xji ⌘ z Mji pzji qji = ↵j ✓ Pjiz Piz ◆1 z ✓ Piz Pi ◆1 ✏ w i Li I Pi : the aggregate price index in country i I Piz : the price index of type z in country i I Pjiz : the price index of national variety j of type z 15 / 53 Supply I Firms are homogenous and monopolistically competitive I The marginal cost of producing type z in country j and selling it in country i mczji = ⌧ji wj I monopolistically competitive price: ez 1 z pji = ⌧ji wj = 1 + ⌧ji wj ez 1 ⌘ ( z 1) I I The markup is higher for type H Variable profits from exporting type z from country j to i z /M Xji ji z ⇡ji = ez 16 / 53 Equilibrium Equilibrium is a vector of wages wi and a matrix corresponding to the number of firms Mji that satisfy: I Balance of payments w j Lj = N X H L Xji + Xji i=1 I Free entry condition H /M H /M Xji Xji ji ji + = wj f e eH eL 17 / 53 Volume versus Composition I The volume of trade for each type is described by a gravity relationship 1 z Xji = ↵j Mji⌘ (⌧ji wj )1 PN 1 ⌘ k=1 ↵k Mki I I z (⌧ki wk )1 Xiz z Xiz total spending in country i on type z The composition of imports is determined by the relative spending on type H versus type L: XiH = XiL ✓ PiH PiL ◆1 ✏ 18 / 53 Four Underlying Patterns 19 / 53 Pattern 1 I All else equal, countries with higher national product qualities pay higher equilibrium wages. I Consider two geographically identical countries: N (north) and S (south) ↵N > ↵S =) wN > wS I Pattern 1 follows directly from the balance of payments condition 20 / 53 Pattern 2 I High-wage countries have comparative advantage in type H I From the (type-specific) gravity equation we have ✓ ◆ H /X L Xji ⌧ji wj L H ji = H /X L ⌧ki wk Xki ki I North exports relatively more of type H than South ✓ ◆ H /X L XN wN L H i Ni = >1 H /X L wS XSi Si I N has absolute quality-advantage in both types =) higher wages in N I Higher wages in N make it comparatively disadvantaged in the less di↵erentiated type L, which is price-sensitive. 21 / 53 Pattern 2 I How does this view of comparative advantage fit with the conventional view? I Conventional view: countries have comparative advantage in a good for which they have a lower autarky relative price (Deardor↵ (1980)). I Here, comparative advantage is determined based on the autarky price index. I The autarky relative price index of type H is lower in N : ✓ PNH PNL ◆Autarky < ✓ PSH PSL ◆Autarky 22 / 53 Pattern 3 I In the trade equilibrium, the price index of type H relative to type L is lower in high-income countries I Type L is relatively cheaper in the South, and type H is relatively cheaper in the North ✓ I PNH PNL ◆Autarky PH PH < NL < SL < PN PS ✓ PSH PSL ◆Autarky Only with free trade prices will be equalized across countries with similar characteristics 23 / 53 Pattern 4: The Home Production E↵ect on Consumption I Rich countries spend relatively more on type H I Given that XiH XiL = ⇣ PiH PiL ⌘1 ✏ , then H PNH PSH XN XSH < =) > L PNL PSL XN XSL I This is the opposite of the Home market effect highlighted by Krugman (1980). I Despite homothetic preferences the consumption structure is fundamentally di↵erent across rich and poor countries. 24 / 53 The Three Stylized Facts Concerning Composition 25 / 53 Trade-to-GDP ⇥ Income per capita I Rich countries have systematically higher Trade GDP because they produce and consume relatively more of type H I 1 Type H is more tradeable: ⌧ji I H 1 ⌧ ⌧ji L Type H pays a lower e↵ective trade cost. I Economic activity in S is concentrated around type L XL ( XSS ⇡ 1) ⇥ ⇤ L (Trade/GDP)S ⇡ 1 SS ⇡ 0 I Economic activity in N is concentrated around type H XL ( XN ⇡ 1) N ⇥ (Trade/GDP)N ⇡ 1 H NN ⇤ ⇡1 1+ 1 X 1+ ⌘1 ↵N ⌘ / ↵k k ! 26 / 53 Export Price ⇥ Income per capita I Rich countries have systematically higher export prices because they export relatively more of type H I Average price of exports from country j to i ! ! H L Xji X ji p¯ji = pH pL ji + ji Xji Xji L Type H exhibits a higher markup and a higher price: pH ji > pji H @ p¯ji @ Xji > 0 =) >0 L @↵j Xji @↵j 27 / 53 Export Price ⇥ Distance I Distant countries trade relatively more of type H I Average price of exports from country j to i ! ! H L Xji Xji H p¯ji = pji + pL ji Xji Xji I Remote exporters face higher trade costs and are price-disadvantaged =) sell relatively more of type H, which is price-insensitive. H @ p¯ji @ Xji > 0 =) >0 L @⌧ji Xji @⌧ji 28 / 53 A Special Case: The Pure Gravity Model I If H = model: L = the model reduces to a pure gravity 1 Xji = ↵j Mji⌘ (⌧ji wj )1 P 1 1 ⌘ k2C ↵k Mki (⌧ki wk ) Xi I The pure gravity model only charecterizes the volume of trade =) cannot explain the three stylized facts concerning composition. I When ⌘ ! 1 and f e = 0, the pure gravity model reduces to an Armington model: Xji = P ↵j (⌧ji wj )1 k2C ↵k (⌧ki wk )1 Xi 29 / 53 Estimation 30 / 53 Data I Bilateral merchandise trade flows in 2000 from the U.N. Comtrade database. I Sample of 100 countries I 95% of the world trade in 2000. I The countries are vastly dissimilar 31 / 53 Parametrizing Trade Cost I Assume a parametric relationship between trade costs and bilateral observables: ⌧ji = 1 + [const + dist distji ] border lang agreement I dist ⇥ distji : the e↵ect of distance I border : the e↵ect of sharing a border I lang : the e↵ect of a common language I agreement : the e↵ect of a trade agreement 32 / 53 Estimated Parameters I I ✏: elasticity of substitution between type H and L H: I I the scope for product di↵erentiation for type H I cannot separately identify both Normalize L = 6 L and H I ⌘: the degree of national product differentiation I Parameters corresponding to trade costs: = {border , lang , agreement , const , dist } 33 / 53 Estimation Strategy I Inner loop: fix the estimated parameters 1. Given a vector of national product qualities ↵i , solve for Mji using the free entry condition 2. Update ↵i given Mji from the previous step using the balance of payments condition 3. Iterate over steps 1 and 2 until both conditions are satisfied 4. Calculate the matrix of trade shares I Outer loop (NLLS) I Search for the parameters that minimize the distance between simulated trade shares and data. 34 / 53 Estimation Results Parameters Unified model Pure gravity Restricted gravity L (Normalized) 6 4.6 4.6 H 3.27 (0.025) 2.78 (0.011) 3.16 (0.024) 2.16 (0.017) 0.11 (0.002) 0.57 (0.01) 0.87 (0.007) 0.71 (0.013) ... ... ... ... 2.63 (0.019) 1.96 (0.020) 0.19 (0.003) 0.69 (0.013) 0.72 (0.006) 0.80 (0.013) ... 0.96 (0.027) 0.83 (0.006) 0.27 (0.009) 0.37 (0.005) 1.17 (0.011) 0.43 0.30 0.24 (Armington model) ✏ ⌘ const dist border lang agreement Goodness of fit (R-squared) 35 / 53 The unified model vs. Pure Gravity I The superior fit of the unified model comes from fitting two aspects of the trade volumes, which are beyond the scope of pure gravity models: 1. Margin 1: the systematically higher trade-to-GDP ratio of rich countries 2. Margin 2: the lower sensitivity to distance of export flows from rich countries I In the unified model import/export elasticities are endogenously determined by the composition of a nation’s trade. I In the pure gravity model import/export elasticities are the same for all countries. 36 / 53 Trade-to-GDP in the Data Data SGP 0 MYS AGO PHL BLR BEL IRL HUN THA CZE TWN ARE SVNBHR NLD LUX QAT OMN SAU KWT CAN CHE SWE AUT LKA KOR FIN ROM IDN NGA YEM HRV MEX ECU JOR MAR CIV PRT DOM JAM YUG NZL ISR DEU DNK ISL NOR RUS CHN CYP LBY DZA CHL SYRPRY BWAPOL ZAF FRA IRN ESP GBR LBN SLV ZWE ITA TUR CMR VEN KEN GRC AUS BOL COL BGD URY SDN PAK UZB PER VNM −2 −1 UKR ETH BGR TUN KAZ LTU CRI LVA TTO TZA UGA EGY IND BRA ARG USA JPN −3 Log( trade−to−GDP ratio ) HKG SVK −6 −4 −2 0 Log( GDP per worker: US=1 ) 37 / 53 Trade-to-GDP in the unified model 0 The Unified model −1 ISL QAT IRL BEL AUT DNK CHE FIN NOR CAN HKG NLD SWE SGP −2 PRY ETH UGA SDN KENYEM UKR ZWE CMR −3 TZA UZB VNM PAK CIV AGO NGA BGD JOR YUGBLRBGR BOL SYR TUN KAZ ARE URY SVN CYP KWTFRA BHR PRT ISR DEU LVA MEX LTU GRC ESP ITA SVK CZE OMN MYS LBN HRV BWA GBR LBY HUN TTO JAM POL MAR ROM DZA RUS ECU EGY DOM SLV CRI IRN COL PER TUR VEN THA CHL LKAPHL CHN IDN IND SAU ARG NZL TWN KOR ZAF AUS USA BRA JPN −4 Log( trade−to−GDP ) LUX −6 −4 −2 0 Log( GDP per worker (US=1) ) 38 / 53 Trade-to-GDP in the pure gravity model 0 The Pure Gravity Model LUX −2 ETH JOR BEL YUG LVA TUN BOL LTU LBN URY SVNBHR YEM IRLQAT BLRBGR AUT CMR SYR CYP JAM SVK BWA HRV TTO OMN KEN ZWE ISLCHE LBY TZA MAR UKR ECU DZA KAZ FIN CZE KWT CAN CIV HUN SLV DNK ROM UZB PAK CRI PRT DOM NLD ARE GRC AGO MYS SWE EGY PER SGP VNM NGA POL ISRFRA COL HKG LKA DEU SAU CHL NOR PHL BGD ESP IRN VEN RUS TUR ITA ARG GBR THA MEX IND UGA SDN −4 IDN CHN ZAF TWN NZL BRA KOR USA AUS JPN −6 Log( trade−to−GDP ) PRY −6 −4 −2 0 Log( GDP per worker (US=1) ) 39 / 53 North vs South Export Flows – Data Data −10 −15 X ln X i Xi j j −20 −25 North South South North −30 −35 −3 −2 −1 0 1 2 3 ln( d i s t i j) 40 / 53 North vs South Export Flows – Unified model The unified model −12 −14 −18 X ln X i Xi j j −16 −20 −22 North South South North −24 −26 −3 −2 −1 0 1 2 3 ln( d i s t i j) 41 / 53 North vs South Export Flows – Pure Gravity Model The Gravity model −15 −20 X ln X i Xi j j −25 −30 −35 −40 −45 −3 North South South North −2 −1 0 1 2 3 ln( d i s t i j) 42 / 53 The Gains from Trade 43 / 53 Two Counterfactual Analyses I Welfare in country i is given by the real wage: Wi = wi Pi 1. I quantify the realized gains by comparing the counterfactual autarky real wage with the actual real wage 2. I quantify the prospective gains from marginally lowering the trade costs by 10%. 44 / 53 JPN USA BRA ARG AUS KOR CHL ZAF TWN VEN NZL IDN PER COL THA IND CHN LKA BGD CRI ECU PHL SAU IRN AGO TUR SLV VNM DOM NGA PAK BWA TZA ZWE EGY CIV GBR UZB BOL KAZ KEN LBY MYS ROM CMR YEM DZA RUS MAR URY POL TTO JAM UKR OMN ETH ISR HUN UGA SDN ITA SYR HRV LBN TUN ESP BGR SGP BLR LTU DEU ARE YUG KWT LVA HKG GRC JOR SVK CZE BHR PRY FRA PRT CYP SVN MEX NOR SWE NLD FIN CAN CHE DNK AUT QAT BEL IRL ISL LUX The Unified Model The Pure Gravity Model 0 10 20 30 40 The gains from trade relative to autarky 50 The Realized Gains from Trade Unified model vs pure gravity model The average gains from trade relative to autarky The coefficient of variation of the gains (across countries) The unified model 4.45 (per cent) 1.10 The pure gravity model 2.38 (per cent) 0.84 I The gains from trade are about 200% larger in the unified model. I The gains are also more unequally distributed across nations. 46 / 53 Why are the gains larger in the unified model? I Short answer: I the unified model combines systematic across-product specialization and within product trade. I pure gravity models focus only on within product trade. 47 / 53 Why are the gains larger in the unified model? I Long Answer: Following Arkolakis et al. (2012), the gains from trade depend on ii (1 Trade GDP ) and e (trade elasticity): Gainsi ⇠ ii 1 e I The pure gravity model understates the gains for rich nations because it understates their Trade GDP . I The pure gravity model understates the gains for poor nations because it forces their trade elasticity to be the same as rich countries. I In the Unified model, poor countries are net importers of highly-di↵erentiated types =) sizable gains despite low Trade GDP 48 / 53 The Prospective Gains From Trade Rich vs Poor Countries The Unified model PRY 5 ETH UGA TZA JOR CZE YUGBLR JAM LVA POL LTU SYR BGRTUN SVK BOL YEMUKR LBN HRV DZA MAR ROM CMR PRT KEN KAZEGY HUN SVN RUS DOM UZB ZWE NGA PAK TTO SLV TUR URY PHL ECU VNM CIV GRC MYS BWA IRN COL CRI BGDIND AGO LKA LBY THA CHN OMN PER IDN ESP ZAF VEN SAU BRA CHL SDN ARG CAN BEL IRL ISL AUT QAT FIN DNK ITAFRA NLD DEU CHE GBR SWE AUS JPN USA ISR KWT KOR NZL BHR TWN CYP 0 The prospective gains from trade 10 MEX NOR ARE −5 SGP HKG −6 −4 −2 0 Log( GDP per worker (US=1) ) 15 The Pure Gravity Model 10 JOR BEL BOL YUG UGA SDN 5 ETH TZA 0 The prospective gains from trade PRY −6 YEM CMR ZWE TUN BLRBGR SYR LVA LTU JAM IRL URY LBN BWA SVK HRV TTO SVNBHR CYP OMN AUTQAT ISLCHE KEN ECU KAZ LBY UKR MAR FIN CZE SLV DZA KWT PAK CRI DNK CIV UZB PRT ROM DOM MYSHUN VNM SGP GRC HKG AGO PER ARE NLD NGA POL ISRFRASWE NOR LKAPHL EGY COL CHL BGD VEN ESP MEX IRN RUS SAUKORNZL THA TUR ARG TWN ITA IND DEU IDN GBR USA CHN ZAF BRA AUS JPN −4 −2 Log( GDP per worker (US=1) ) CAN 0 49 / 53 The Prospective Gains From Trade 30 BRA ZAF 20 CHN MEX IDN IND 10 RUS TUR IRN THA KOR POL SAU EGY PHL NGA BGD VEN LKA COL FRA GRC AGOPER PRT HUN CZE ROM VNM MYS GBR UZB PAK DOM DZA CIV CAN UKR MAR CRI SLV KAZ KEN TZA HRV BGR LBY NLDISL ECUTWN SYR SVK BLR SDN ZWE LUX CMR LBN JAM ETH LTU TTO YEM DNK TUN BWA OMN AUT YUG UGA LVASVN BEL JOR URY PRY QAT BOL SWE FIN IRL CHE BHR CYP ITAESP DEU 0 The prospective gains from trade (unified/gravity) The E↵ect of Remoteness 0 5 CHL NZL ARG 10 Remoteness 50 / 53 The Prospective Gains From Trade I Compared to the pure gravity model, the prospective gains in the unified model systematically favor poor and remote countries. I Why? 51 / 53 The Prospective Gains From Trade I Compared to the pure gravity model, the prospective gains in the unified model systematically favor poor and remote countries. I Why? I Given the existing impediments to trade, poor and remote countries are predominantly importing the highly-di↵erentiated type. I Partially removing these impediments allows poor and remote countries to import more of the highly-di↵erentiated type. I Highly-di↵erentiated varieties are not easily substitutable with domestic counter-parts, so they bring along sizable welfare gains. 51 / 53 53 / 53 Arkolakis, C., A. Costinot, and A. Rodriguez (2012). Clare, 2012, new trade models, same old gains. American Economic Review 102 (1), 94. Caron, J., T. Fally, and J. R. Markusen (2014). International trade puzzles: A solution linking production and preferences. The Quarterly Journal of Economics 129 (3), 1501–1552. Deardor↵, A. V. (1980). The general validity of the law of comparative advantage. 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