Quality, Variable Mark-Ups, and Welfare: A Quantitative General Equilibrium Analysis of Export Prices

Transcription

1 Quality, Variable Mark-Ups, and Welfare: A Quantitative General Equilibrium Analysis of Export Prices Haichao Fan Amber Li Sichuang Xu Stephen Yeaple Fudan, HKUST, HKUST, Penn State and NBER May 2018 Mark-Ups 05/18 1 / 35

2 Introduction Rapid growth in quantitative general equilibrium trade models Parsimonious models a la Eaton and Kortum (2002), Melitz (2003), Chaney (2008) Require few parameters Key parameter is the trade elasticity, the effect on import value of a change in ad-valorem trade costs Limited use of price data (e.g. Simonovska 2017, Arkolakis et al 2017) Allow analysis of the size of the gains from trade and the effects of policy changes, e.g. Brexit Mark-Ups 05/18 2 / 35

3 Introduction Fact: The same firm charges prices that can vary dramatically across countries. Price variation reflects the interaction of 1 Heterogeneous trade costs 2 Pricing to market 3 Quality heterogeneity across firms What does the literature miss by modeling only two of the three? Mark-Ups 05/18 3 / 35

4 Introduction We analyze a simple quantiative GE model with endogenous entry by heterogeneous firms and endogenous price and quality choice that allows for Rich Treatment of Trade costs: our setting allows for trade costs that are both ad-valorem and specific Variable Mark-ups: Non-homothetic preferences and firm heterogeneity generate price heterogeneity across firms. Washington Apples Effects: Demand for quality, specific-trade costs, and higher costs to producing quality generate quality provision differences across countries Mark-Ups 05/18 4 / 35

5 Introduction We calibrate the model to moments from Chinese firm-level data and aggregate trade data to show need for all three mechanisms to match data highlight the relationship between the nature of trade costs and quality and mark-up choice of firms analyze how the interaction between quality, variable mark-ups and trade costs affect the measurement of the gains from trade. We also derive new results on inferring the gains from trade when preferences are non-homothetic. Mark-Ups 05/18 5 / 35

6 Literature Quality Literature: Schott (2003), Hummels and Skiba (2004), Feenstra and Romalis (2015), Johnson (2012), Manova and Zhang (2012), Kugler and Verhoogen (2009, 2012); Hottman, Redding, and Weinstein (2016); Fan, Li, and Yeaple (2015), Fan, Li, and Yeaple (2018) Variable Mark-Up/Pricing to Market Literature: Simonovska (2015), Jung, Simonovska, and Weinberger (2017), Atkeson and Burstein (2008), Alessandra and Kiboski (2011) Gains from Trade Literature: Arkolakis, Costinot, and Rodriguez-Clare (2012), Arkolakis, Costinot, Donaldson, and Rodriguez-Clare (2017). Mark-Ups 05/18 6 / 35

7 Stylized Facts Established facts concerning export prices: Selection: more productive firms are more likely to export and export to a larger number of markets than less productive firms (e.g. Bernard and co-authors) Selection: More firms export to rich countries than to poor countries (e.g. Eaton, Kortum, and Kramarz, 2011) Quality v Mark-ups: More productive firms charge higher prices and earn greater revenues than less productive firms in any given market (e.g. Manova and Zhang 2012) Quality v Mark-ups: Within firms, prices charged in rich countries are higher than in poor countries (e.g. Fan et al, 2015) Washington Apples Effect: Higher priced goods tend to be shipped longer distances than lower priced goods (e.g. Hummels and Skiba, 2004). Mark-Ups 05/18 7 / 35

8 Model Countries and Endowments I countries indexed by i and j Country i is endowed with measure L i of consumers Each consumer is endowed with one unit of labor that is mobile within a country but is not mobile across countries. Mark-Ups 05/18 8 / 35

9 Model Preferences Consumers have generalized CES preferences: where U j = [ i ( qij (ω)xij c (ω) + x ) σ 1 σ ω Ω ij dω ] σ σ 1 q ij (ω) quality of variety ω produced in country i and sold in country j xij c (ω) quantity of ω consumed by a consumer in j and produced in i σ governs the elasticity of substitution across ω and x creates a choke price., Mark-Ups 05/18 9 / 35

10 Demand Utility maximization implies that the demand for variety ω in country j is [ x ij (ω) xij c (ω)l j = L ( ) j w j + xp j pij (ω) σ q ij (ω) Pjσ 1 σ x], q ij (ω) where w j is the wage earned by a consumer in country j and and P jσ = P j = p ij (ω)/q ij (ω) dω i ω Ω ij { i are aggregate price indexes. ω Ω ij (p ij (ω)/q ij (ω)) 1 σ dω } 1 1 σ Mark-Ups 05/18 10 / 35

11 Demand Define quality-adjusted prices, and quality-adjusted choke price so demand becomes x ij (ω) = p ij (ω) p ij (ω) /q ij (ω) p ij = ( ) 1 σ w j + xp j xp jσ 1 σ [( ) σ L j x p ij (ω) q ij (ω) p ij 1]. Mark-Ups 05/18 11 / 35

12 Optimal pricing For a firm from i selling variety ω to j Marginal cost: c ij (ω) Quality-adjusted marginal cost: c ij (ω) = c ij (ω) /q ij (ω). Profits: π ij (ω) = max p ij (ω) xl j [ p ij (ω) c ij (ω)] [( ) σ p ij (ω) p j 1]. Assume monopolistic competition (firm cannot affect p j ) If c ij (ω) p j, optimal p ij (ω) is the solution to σ c ij (ω) p j = ( ) σ+1 p ij (ω) p j + (σ 1) p ij (ω) p j. Mark-Ups 05/18 12 / 35

13 Quality and Production All costs incurred in exporting country. One unit of quality q requires a firm with productivity ϕ to use labor l = qη ϕ, η > 1. Across firms in country i productivity is distributed G i (ϕ) = 1 b i ϕ θ, θ > 1. Note that higher b i raises country productivity. Trade costs for a firm from i that sells in country j: Iceberg-type τ ij 1 (τ ij units shipped for one to arrive) Specific T ij (in terms of country i labor) Mark-Ups 05/18 13 / 35

14 Quality Provision For a firm from i with productivity ϕ, the quality-adjusted marginal cost for providing quality q ij to country j is τ ij ϕ qη ij c ij (ϕ) c ij (ϕ) = T ij + w i. q ij q ij Cost minimization implies ( Tij ϕ q ij (ϕ) = (η 1) τ ij and where γ is a constant and c ij (ϕ) = γ w i δ ij, ϕ 1 η ) 1 η is average trade cost. δ ij = (T ij ) 1 1 η (τ ij ) 1 η Mark-Ups 05/18 14 / 35

15 Competition and Selection The choke price determines the productivity cutoff, ϕij, for entry ) ( ) p ij (ϕ ij = c ij ϕ ij = p j or ϕ ij ( γ w i δ ij p j ) η. Measure of exporters from i to j increases as p j rises δ ij = T 1 1 η ij 1 η τij falls Mark-Ups 05/18 15 / 35

16 Closing the Model Free entry pay f in local labor get variety draw with productivity ϕ N i endogenously turns out to be linear in L i and b i Labor market is perfectly competitive Countries are on their budget constraint (trade balances): X j = X ij i Mark-Ups 05/18 16 / 35

17 Qualitative Implications More productive firms charge higher prices and higher quality adjusted mark-ups earn larger sales revenue Consumers in richer countries Pay higher import prices Enjoy greater access to variety Choke price, p j, transmits heterogeneous country characteristics into heterogeneous outcomes. Mark-Ups 05/18 17 / 35

18 Gains from Trade, Gravity, and Comparative Statics Preferences and equilibrium conditions imply indirect utility function can be written ( ) σ σ 1 w j U j = β u p j where β u is a constant. Define expenditure share of i in j, λ ij to be λ ij = X ij i X i j where X ij is the total value of exports from country i to country j. Shifts in p j mediate i) extensive margin, ii) distribution of mark-ups, and iii) distributions of market shares. Mark-Ups 05/18 18 / 35

19 Define the value of variable x in an alternative equilibrium as x and the change across equilbria x = x /x. The change in welfare in country j due to a trade shock is Û j = ( λ jj ) σ σ 1 where the change in expenditure share is 1 1+ηθ, λ jj = (ŵ j ) ηθ [ ] i λ ij T η 1 θ ij τ ij (ŵi ) ηθ and wages changes, ŵ j, solve ŵ i = j ( ) λ ij w j L j T η 1 θ ij τ ij (ŵi ) ηθ ( ) w i L i i λ i j T η 1 θ ŵ j i j τ i j (ŵi ) ηθ Mark-Ups 05/18 19 / 35

20 Calibration Use Chinese firm-level data, equation (1), and Simulated Method of Moments to identify σ and ηθ Standard deviation of observed (not quality adjusted) log price (demeaned by industry and country) Correlation between log price and log revenue Estimate θ using gravity equation and tariff data (ad valorem measure of trade cost). Mark-Ups 05/18 20 / 35

21 Calibration FOC condition for quality-adjusted price can be written ( ) 1 η ( ) σ+1 ϕ p ij (ϕ) σ ϕij = p j + (σ 1) p ij (ϕ) p j. ( ) 1 Note that ϕ/ϕij η follows a Pareto distribution with shape parameter ηθ. Since this distribution shares a common support in all countries, ( ) 1 define ξ = ϕ/ϕij η, and write FOC as ( ) σ+1 σ ξ = p ij (ξ) pj + (σ 1) p ij (ξ) pj. (1) revenues are r ij (ξ) = L j x p ij (ξ) [( ) σ p ij (ξ) p ij 1]. Mark-Ups 05/18 21 / 35

22 Calibration: Gravity The problem facing the macro elasticity? ( λ ij λ jj = J i b i J j b j ( T η 1 ij T η 1 jj τ ij w η i τ jj w η j ) θ ) θ, where J i is the measure of entrants in country i and b i is productivity. Gravity yields ( ) λij ln = S i S j ηθ log δ ij λ jj but δ ij = (T ij ) 1 1 η (τ ij ) 1 η. Tariffs are generally ad-valorem Can control for other variation in T ij and τ ij using standard controls. Then gravity identifies the trade elasticity only if η = 0, but it does identify θ. Mark-Ups 05/18 22 / 35

23 Calibration: Gravity Using standard bilateral trade data, we estimate ( ) λij log = S i S j βx ij θ log tar ij + ε ij, λ jj where ε ij is assumed to be Gaussian measurement error and X ij are standard gravity controls. Gravity estimates of all coeffi cients, combined with the equilibrium conditions of the model, and the elasticities allow us to back out Country productivities (b i ) and wages (w i ) Trade costs δ ij Price indexes Measure of entrants per market Mark-Ups 05/18 23 / 35

24 Welfare Implications: Alternative Models Benchmark GT bmark j = 1 (λ jj ) σ σ ηθ, Variable mark-ups but no Washington Apples mechanism GT Vmkup j = 1 (λ jj ) σ σ θ, Plain vanilla model GT j = 1 (λ jj ) 1 σ 1. Mark-Ups 05/18 24 / 35

25 Alternative Model Calibrations parameters BMK no WA No WA, VM σ θ NaN η 1.8 NaN NaN different trade elasticities across models allowing for correlation drives up estimate of σ Mark-Ups 05/18 25 / 35

26 Fit of Model Calibrations data bmk no WA no WA, VM std logsale corr logsale, logprice trade elasticity Mark-Ups 05/18 26 / 35

27 Gains From Trade Comparison across restricted models appropriately recalibrated Readers of ACDRC would find column 4)>column 5) strange. Fan, Li, Xu, Column and Yeaple (Fudan, 1)<Column HKUST, HKUST, 4) Penn driven Quality State by andnber) Mark-Ups appropriate calibrations of05/18 different 27 / 35

28 Prices and Trade Shocks Consider a shock to trade costs (say tariffs or customs regulations, etc) that have the effect of changing trade volumes by 5% By construction, whether these shocks are specific or ad-valorem has no impact on the size of the gains from trade They do, however, have big implications for the observed change in local import prices. Mark-Ups 05/18 28 / 35

29 Specific trade cost, Quality, Ad-valorem, Quality Price changes (not quality adjusted) amplified for specific dampened for ad-valorem. Note: also presents challenge for using price gaps between countries to calibrate models! Mark-Ups 05/18 29 / 35

30 Conclusion Washington Apples mechanism first order important to fit the facts But raises questions about calculating macro elasticities Cautions against the careless use of price data in estimation Cautions against interpreting import price changes as purely pass through Mark-Ups 05/18 30 / 35

31 Back-up Material Mark-Ups 05/18 31 / 35

32 Model Fit The model somewhat overpredicts the relationship between price and real income within firms and underpredicts the relationship between price and real income across firms. This is largely because the model underestimates Fan, variation Li, Xu, and Yeaple in entry (Fudan, HKUST, across HKUST, firms. PennQuality State andnber) Mark-Ups 05/18 31 / 35

33 Model Fit: Micro Data Price and revenue along the size distribution Model fits well for the larger, more productive firms with that are far away from the entry cutoff. Mark-Ups 05/18 32 / 35

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