Across Markup Specialization and the Composition of Multilateral Trade

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1 Across Markup Specialization and the Composition of Multilateral Trade Ahmad Lashkaripour Indiana University April 15, / 62

2 Motivation 2 / 62

3 Background Gravity trade models Characterize aggregate trade volumes Overlook the composition margin: Do not systematically describe the type of goods a country trades. 3 / 62

4 Background Gravity trade models Characterize aggregate trade volumes Overlook the composition margin: Do not systematically describe the type of goods a country trades. Recent developments: Growing trade between dissimilar (e.g. rich-poor) countries. Micro-level evidence indicating that dissimilar countries have different export/import compositions. 3 / 62

5 Three stylized facts 1. The composition of trade is affected by geography: 1.1 Countries export high-price goods to distant markets (the Washington apples effect) 2. The composition of trade is affected by income: 2.1 Rich countries have systematically higher trade-to-gdp ratios. 2.2 Rich countries specialize in and export high-price varieties. 4 / 62

6 The Literature Standard gravity models do not accommodate these facts. One could accommodate each fact by introducing new elements into standard gravity models: 1. Distance price composition of exports: Irarrazabal et al. (2015); Feenstra and Romalis (2014); Baldwin and Harrigan (2011). 2. Income per capita Trade GDP : Waugh (2010); Fieler (2011); Caron et al. (2014). 3. Income per capita price composition of exports: Schott (2004); Hallak (2006); Fajgelbaum et al. (2011). 5 / 62

7 This Paper However, there is no unifying theory that tractably combines all three facts. Explaining the effect of geography on the composition margin requires assumptions that are strictly different from those needed to explain the role of income. To address this gap, I develop a novel view of production specialization that integrates the role of geography with income. 6 / 62

8 This Paper I construct a unified gravity model where: 1. Comparative advantage induces production specialization across low- and high-markup variates 2. Comparative advantage regulates the structure of international consumption. Production and consumption specialization pin down the composition of multilateral trade flows. = collectively explain the three highlighted facts. 7 / 62

9 Main Findings Introducing across-markup specialization into the standard gravity model 1. Improves the in-sample fit of the model by 43%. 2. Improves the out-of-sample predictive power. The unified model could reproduce the recent rise of N-S trade relative to N-N trade. 3. Magnifies the gains from trade and shifts them in favor of poor and remote nations. 8 / 62

10 Theory 9 / 62

11 The Environment There are N countries Country i is characterized by 1. Population L i 2. National Product Quality α i There are two types of goods: type H and type L Firms are homogenous and monopolistically competitive 10 / 62

12 Demand Preferences are homothetic, and described by a (three-tier) nested-ces utility The upper tier aggregates across the two types U i = z {H,L} (Ui z ) ɛ 1 ɛ ɛ ɛ 1 ɛ is the elasticity of substitution between types H and L 11 / 62

13 Demand Sub-utility Ui z of type z is a CES aggregator across national varieties N Ui z = j=1 α 1 ρz j ( Q z ji ) ρz 1 ρz αj is the National Product Quality of country j. Q z ji is the agg. quantity of type z sourced from country j [ˆ Q z ( ji = q z ) ρz ji dω ω Ω ji ] 1 ρz = M 1 ρz ji qz ji q z ji : quantity sold by a typical firm from country j to i M ji : Number of homogenous firms selling from j to i 12 / 62

14 Demand σ z = 1/ (1 ρ z ): inter-national elasticity of substitution σ z = 1/ (1 ρ z ): intra-national elasticity of substitution. The demand structure nests the Armington and Krugman models: Krugman: σ z = σ z = no national product differentiation Armington: σz = complete national product differentiation 13 / 62

15 Demand σ z = 1/ (1 ρ z ): inter-national elasticity of substitution σ z = 1/ (1 ρ z ): intra-national elasticity of substitution. The demand structure nests the Armington and Krugman models: Krugman: σ z = σ z = no national product differentiation Armington: σz = complete national product differentiation I allow for some degree of national product differentiation that is the same for both types: σ H 1 σ H 1 = σ L 1 σ L 1 η > 1 13 / 62

16 Demand Type H offers a greater scope for product differentiation than type L σ H < σ L ρ H < ρ L 14 / 62

17 Demand Type H offers a greater scope for product differentiation than type L σ H < σ L ρ H < ρ L Therefore, by definition: Demand for type L is quantity-intensive Demand for type H is quality-intensive. If σ H = σ L the model reduces to a standard gravity model. 14 / 62

18 Demand Summary of key parameters: ɛ governs the relative spending on type H versus L σ z regulates the degree of within-product differentiation for type z η regulates the degree of national product differentiation in the economy 15 / 62

19 Nested-CES Demand Function Demand in country i for varieties of type z = {H, L} produced in country j X z ji M ji p z jiq z ji = α j ( P z ji P z i ) 1 σz ( ) P z 1 ɛ i w i L i P i P i : the aggregate price index in country i Pi z : the price index of type z in country i Pji z : the price index of national variety j of type z 16 / 62

20 Supply Firms are symmetric and monopolistically competitive The marginal cost of producing type z in country j and selling it in country i mc z ji = τ ji w j 17 / 62

21 Supply Firms are symmetric and monopolistically competitive The marginal cost of producing type z in country j and selling it in country i σ z σ z 1 τ jiw j = mc z ji = τ ji w j Monopolistically competitive price: [ p z ji = 1 + The markup is higher for type H 1 η (σ z 1) ] τ ji w j 17 / 62

22 Supply Firms are symmetric and monopolistically competitive The marginal cost of producing type z in country j and selling it in country i σ z σ z 1 τ jiw j = mc z ji = τ ji w j Monopolistically competitive price: [ p z ji = 1 + The markup is higher for type H 1 η (σ z 1) ] τ ji w j Variable profits from exporting type z from country j to i π z ji = Xz ji /M ji σ z 17 / 62

23 Equilibrium Equilibrium is a vector of wages w i and a matrix corresponding to the number of firms M ji that satisfy: 18 / 62

24 Equilibrium Equilibrium is a vector of wages w i and a matrix corresponding to the number of firms M ji that satisfy: Balance of payments w j L j = N ( X H ji + Xji) L i=1 Free entry condition X H ji /M ji σ H + XH ji /M ji σ L = w j f e 18 / 62

25 Trade Volume and Trade Composition The (within-type) volume of trade is described by a gravity equation X z i 1 η Xji z α j Mji = (τ jiw j ) 1 σz 1 X N k=1 α η kmki (τ kiw k ) 1 σz total spending in country i on type z z i 19 / 62

26 Trade Volume and Trade Composition The (within-type) volume of trade is described by a gravity equation X z i 1 η Xji z α j Mji = (τ jiw j ) 1 σz 1 X N k=1 α η kmki (τ kiw k ) 1 σz total spending in country i on type z z i The composition of imports is determined by the relative spending on type H versus type L: Xi H Xi L = ( ) P H 1 ɛ i Pi L 19 / 62

27 General Overview There are two types of goods 1. The high-markup (low-σ) type, H 2. The low-markup (high-σ) type, L Type H has a higher price: 1. It exhibits a higher markup. Type H is more tradable: 1. Lower trade elasticity = less-affected by variable trade costs 20 / 62

28 General Overview There are two types of goods 1. The high-markup (low-σ) type, H 2. The low-markup (high-σ) type, L Type H has a higher price: 1. It exhibits a higher markup. 2. High-markup goods tend to have higher production costs Type H is more tradable: 1. Lower trade elasticity = less-affected by variable trade costs 2. Higher profit margin = less-affected by fixed exporting costs I purposely shut down the channels highlighted in blue for exposition purposes. But they could be easily reintroduced. 20 / 62

29 Four Equilibrium Outcomes 21 / 62

30 Outcome 1 All else equal, countries with higher National Product Qualities pay higher equilibrium wages. Consider two geographically identical countries: N (North) and S (South) α N > α S = w N > w S Pattern 1 follows directly from the balance of payments condition 22 / 62

31 Outcome 2 High-wage countries have comparative advantage in type H The (within-type) gravity equation implies that X H ji /XL ji X H ki /XL ki ( τji w j = τ ki w k ) σl σ H North exports relatively more of type H than South X H Ni /XL Ni X H Si /XL Si = ( wn w S ) σl σ H > 1 N has absolute quality-advantage in both types = N pays a higher wage = N is comparatively disadvantaged in the low-markup type L that is price-sensitive. 23 / 62

32 Outcome 2 This notion of comparative advantage fits right into the conventional definition : Countries have comparative advantage in a good for which they have a lower autarky relative price (Deardorff (1980)). The autarky relative price index of type H is lower in the North: ( P H N ) Autarky ( P H < S ) Autarky P L N P L S 24 / 62

33 Outcome 3 In the trade equilibrium, the price index of type H relative to type L is lower in high-income countries Type L is relatively cheaper in the South, and type H is relatively cheaper in the North ( P H N P L N ) Autarky < P H N P L N < P H S P L S < ( P H S P L S ) Autarky Only with free trade prices will be equalized across countries. 25 / 62

34 Outcome 4: Consumption Specialization Rich countries spend relatively more on type H Given that XH i X L i = ( P H i P L i ) 1 ɛ, then PN H PN L < P H S P L S = XH N X L N > XH S X L S Consumption specialization could occur in any multi-sector gravity model with inter-sector substitutability. Here, however, consumption specialization occurs across more- and less-tradable goods = strong implications for import composition. 26 / 62

35 The Three Facts About the Composition Margin 27 / 62

36 Trade-to-GDP Income per capita Rich countries produce and consume relatively more of type H = have systematically higher Trade GDP 28 / 62

37 Trade-to-GDP Income per capita Rich countries produce and consume relatively more of type H = have systematically higher Trade GDP Type H is more tradeable: τ 1 σ H ji τ 1 σ L ji }{{} type H pays a lower effective trade cost Economic activity in S is concentrated around type L XS L ( ) Trade 1 = [ 1 λ L X S GDP SS] 0 S Economic activity in N is concentrated around type H XN L ( ) Trade 1 = [ 1 λ H ] NN 1 (α 1+ 1 η N X N GDP / N k α 1+ 1 η k ) 28 / 62

38 Export Price Income per capita Rich countries have systematically higher export prices since they export relatively more of the high-markup good. 29 / 62

39 Export Price Income per capita Rich countries have systematically higher export prices since they export relatively more of the high-markup good. Average price of exports from country j to i ( ) ( ) X H ji X L p ji = p H ji ji + X ji }{{} high-markup share X ji }{{} low-markup share p L ji Type H exhibits higher price: p H ji > pl ji α j high-markup share low-markup share > 0 = p ji α j > 0 29 / 62

40 Export Price Geography Distant countries trade relatively more of type H 30 / 62

41 Export Price Geography Distant countries trade relatively more of type H Average price of exports from country j to i ( ) ( ) X H ji X L p ji = p H ji ji + X ji }{{} high-markup share X ji }{{} low-markup share p L ji Remote exporters are price-disadvantaged = export relatively more of type H, which is price-insensitive. high-markup share τ ji low-markup share > 0 = p ji > 0 τ ji 30 / 62

42 A Special Case: The Standard Gravity Model If σ H = σ L = σ the model reduces to a standard gravity model: 1 η α j Mji X ji = (τ jiw j ) 1 σ 1 X i k C α η kmki (τ kiw k ) 1 σ The standard gravity model characterizes the export values, but overlooks variations in export composition across destinations. The Armington model is the perfectly competitive case of the standard gravity model: η, f e = 0 = X ji = α j (τ ji w j ) 1 σ k C α k (τ ki w k ) 1 σ X i 31 / 62

43 Estimation 32 / 62

44 Estimation Approach The Unified model delivers distinct predictions w.r.t. 1. Multilateral trade Volumes 2. Export prices Since data on trade values are less noisy: I evaluate the model by fitting it to bilateral trade values. Compare it to a standard gravity model fitted to the same data. The above approach is quite common: Di Giovanni and Levchenko (2009); Waugh (2010); Fieler (2011). 33 / 62

45 Data Bilateral merchandise trade flows in 2000 from the U.N. Comtrade database. Sample of 100 countries 95% of the world trade in Includes vastly dissimilar countries 34 / 62

46 Parametrizing Trade Cost Assume a parametric relationship between trade costs and bilateral observables: τ ji = 1 + [κ const + κ dist dist ji ] κ border κ lang κ agreement κdist dist ji : the effect of distance κ border : the effect of sharing a border κlang : the effect of a common language κagreement : the effect of a trade agreement 35 / 62

47 Estimated Parameters σ H σl : regulates the degree of across-markup specialization. ɛ: regulates the degree of consumption specialization. η: the degree of National Product Differentiation. Parameters corresponding to trade costs: κ = {κ border, κ lang, κ agreement, κ const, κ dist } 36 / 62

48 Estimation Strategy Inner loop: fix the estimated parameters 1. Given a vector of national product qualities α i, solve for M ji using the free entry condition 2. Update α i given M ji 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 Outer loop (NLLS) Search for the parameters that minimize the distance between simulated trade shares and data. 37 / 62

49 Estimation Results Parameters Unified model Standard gravity Armington model (Perfect Competition) σ L (Normalized) σ H 3.27 (0.025) ɛ 2.78 (0.011) η 3.16 (0.024) κ const 2.16 (0.017) κ dist 0.11 (0.002) κ border 0.57 (0.01) κ lang 0.87 (0.007) κ agreement 0.71 (0.013) (0.019) 1.96 (0.020) 0.19 (0.003) 0.69 (0.013) 0.72 (0.006) 0.80 (0.013) (0.027) 0.83 (0.006) 0.27 (0.009) 0.37 (0.005) 1.17 (0.011) Goodness of fit (R-squared) / 62

50 What Derives the Improved Fit? The Unified model accommodates two additional data-margins: 1. The systematically higher trade-to-gdp of rich countries There is significantly less S-S trade than N-N trade. The standard gravity model does not distinguish between N-N and S-S trade 39 / 62

51 The Decomposition of Trade Flows Predicted vs. Data South South North South North North Unified Model Data Standard Gravity Model 40 / 62

52 Trade-to-GDP Ratios Data SGP Log( trade to GDP ratio ) ETH UGA TZA VNM LKA IDN ROM NGA YEM CIV MAR ECU JOR MEX DOM JAM HRV YUG CHN RUS DZA LBY SYR CHL PRY IRN ZAFBWAPOL ZWE SLV LBN TUR KEN CMR VEN BOL BGD COL SDN URY PAK UZB PER IND AGO UKR PHL BLR KAZ EGY THA BGR TUN LTU LVA MYS SVK CRI BRA HUN CZE TTO TWN SVNBHR OMN SAU KOR ARG PRT CYP NZL GRC ESP KWT BEL IRL ARE NLD QAT CAN CHE FIN AUT SWE ISRDEU FRA GBR ITA AUS HKG DNK ISL NOR USA JPN LUX Log( GDP per worker: US=1 ) 41 / 62

53 Trade-to-GDP Ratios Log( trade to GDP ) ETH UGA TZA The Unified model BEL IRL AUTDNK CHE FIN CAN NLD HKG NOR PRY SGP SWE URY CYP SVN FRA ARE BHR KWT PRT SDN JOR DEU MEX ISR YUGBLR LTU LVA BOL GRC BGR SVK CZE OMN ESP ITA SYR TUN MYS LBN KEN YEM UKR HRV ZWE KAZ BWA CMR HUN TTO LBY GBR JAM POL PAK MAR ROM RUS DZA VNM UZB CIV ECU EGY SAU BGD NGA AGO SLV DOM PHL IRN COL PER TUR CRI LKA ARG NZL TWN THA VEN IND CHN CHL IDN AUS KOR ZAF USA BRA ISL QAT JPN LUX Log( GDP per worker (US=1) ) 42 / 62

54 Trade-to-GDP Ratios The Standard Gravity Model Log( trade to GDP ) ETH UGA TZA PRY JOR BEL SDN YEM BOL YUG TUN AUT IRL SYR BLRBGR LTU LVA LBN CMR SVK URY SVNBHR QAT KEN ZWE JAM BWA CYP HRV TTO OMN CHE DZA LBY ISL UKR MAR KAZ ECU CIV CZE CAN FIN HUN KWT PAK UZB ROMSLV DNK DOM CRI GRC PRT NLD EGY MYS ARE VNM AGO PER SGP SWE NGA COL POL ISRFRA LKA SAU DEU HKG BGD PHL CHL NOR IRN ESP RUS TUR VEN ARG ITA THA GBR IND MEX IDN ZAF TWN NZL CHN BRA KOR AUS USA JPN LUX Log( GDP per worker (US=1) ) 43 / 62

55 Goodness of Fit The Unified model accommodates two additional data-margins: 1. The systematically higher trade-to-gdp of rich countries There is significantly less S-S trade than N-N trade. The standard gravity model does not distinguish between N-N and S-S trade 44 / 62

56 Goodness of Fit The Unified model accommodates two additional data-margins: 1. The systematically higher trade-to-gdp of rich countries There is significantly less S-S trade than N-N trade. The standard gravity model does not distinguish between N-N and S-S trade 2. The lower distance elasticity of exports from rich countries In the standard gravity model a common distance elasticity applies to all trade flows. 44 / 62

57 Distance Elasticity 10 Data ln Xij XiXj North South South North ln(dist ij) 45 / 62

58 Distance Elasticity 12 The unified model ln Xij XiXj North South South North ln(dist ij) 46 / 62

59 Distance Elasticity 15 The Gravity model ln Xij XiXj North South South North ln(dist ij) 47 / 62

60 Out-of-Sample Predictive Power In the past two decades the relative magnitude of N-S to N-N trade has risen dramatically (Krugman (2009); Hanson (2012)). 48 / 62

61 Out-of-Sample Predictive Power In the past two decades the relative magnitude of N-S to N-N trade has risen dramatically (Krugman (2009); Hanson (2012)). trade with poor and middle income nations trade with other rich nations.6 Data share in total trade estimation year / 62

62 Out-of-Sample Predictive Power trade with poor and middle income nations trade with other rich nations.6 Data share in total trade estimation year The Unified Model.55 Share in Total Trade International Trade Costs (mean) / 62

63 Out-of-Sample Predictive Power trade with poor and middle income nations trade with other rich nations.6 Data share in total trade estimation year The Standard Gravity Model Share in Total Trade International Trade Costs (mean) / 62

64 The Gains from Trade 51 / 62

65 First Counter-factual Analysis Shut down trade in the estimated models to quantify the realized gains from trade. 52 / 62

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67 First Counter-factual Analysis The gains from trade are four-times larger in the unified model compared to the standard gravity model. Interpreting the results from the perspective of ACR: Gains (1 Trade GDP )1 σ Rich countries have high Trade GDP s. Poor countries are net importers of low-σ goods. 54 / 62

68 Second Counter-factual Analysis Shut down comparative advantage and across-markup specialization σ H σ L 1 = Calculate the gains from comparative-advantage-driven trade 55 / 62

69 Gains from C.A. Trade vs. Income ETH % Gains from comparative advantage UGA TZA SDN BGD NGA KEN VNM YEM UZB ZWE CIV AGO CMR PAKUKR IND LKA YUG IDN BOL SYR PHLMAR KAZ BLR ECU PRY BGR JOR CHN EGY ROM IRNDZA TUN SLV RUS DOM THA COL PER JAM LTU LVA BWA SVK HRV ZAF TUR CRI LBN MYS HUN TTO POLCZE BRA VEN CHL LBY LUX MEX URY OMN USA SVN BHR CYP JPN SAU GRC ISL ARG PRT NZL KWT FRA DEU KOR ESP ITA CAN GBR TWN AUS NLD CHE BEL FIN AUT IRLQAT HKG SWE DNK ISRARE NOR SGP Log( GDP per worker (US=1) ) 56 / 62

70 Gains from C.A. Trade vs. Remoteness ETH % Gains from comparative advantage MYS MEX LUX CAN BEL FRA DEU AUT TZA SDN KEN VNMNGA BGD YEM ZWE UZB CIV CMR AGO UKR PAK IND LKA YUG SYR IDN BOL BLRMAR PHL KAZ ECU PRY JOR BGR CHNEGY ROM DZA TUN IRN SLV RUS DOM THA JAM COL PER LTULVA BWA SVK HRV LBN TUR CRIZAF HUN TTO CZEPOL LBY USA BRA VEN CHL URY SVN OMN CYP BHR JPN PRT SAU GRC ISL IRL CHE DNK ARG NOR NLD ITA ESP FIN GBR SWE KWT QAT HKG ISRARE SGP KOR TWN Remoteness UGA NZL AUS 57 / 62

71 Third Counter-factual Analysis Counterfactually lower the trade frictions in both the unified and standard gravity models. Calculate the effect of trade liberalization on international income inequality 58 / 62

72 Trade and International Income Inequality 59 / 62

73 Concluding Remarks Guided by three stylized facts, I developed a theory to characterize the composition of multilateral trade flows. The main thesis: comparative advantage induces production and consumption specialization across low- and high-markup goods. The main implication: Allowing for production and consumption specialization creates a new window for countries especially those that are poor and remote to alleviate the burden of trade costs. 60 / 62

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