. Gravity and Comparative Advantage: Estimation of Trade Elasticities for the Agricultural Sector

Transcription

1 . Gravity and Comparative Advantage: Estimation of Trade Elasticities for the Agricultural Sector Kari E.R. Heerman, Economic Research Service, USDA Ian Sheldon, Ohio State University NBER Trade and Agriculture Conference Boston, MA May 17, 2018 The analysis and views expressed are the authors and do not represent the views of the Economic Research Service or USDA.

2 Introduction Systematic Heterogeneity (SH) Gravity Model Tailored to fundamental features of agriculture & sub-sectors Holding technology constant, productivity is inextricably linked to land and climate Intra-sector variation in trade costs linked to policy and intrinsic characteristics Allows systematic influences on within-sector specialization

3 Introduction Systematic Heterogeneity (SH) Gravity Model Tailored to fundamental features of agriculture & sub-sectors Allows systematic influences on within-sector specialization Other structural gravity models Intra-sector heterogeneity independently distributed Eaton and Kortum (2002), Chaney (2008) and extensions Multi-sector models address specialization across sectors Independence implies random within-sector specialization

4 Introduction Does this matter? Allows for more flexible system of bilateral trade elasticities Elasticities drive predicted trade flow responses Standard gravity models impose restrictive elasticities Arkolakis, Costinot and Rodriguez-Clare (2012), Adao, Costinot and Donaldson (2017) Independence of Irrelevant Exporters (IIE) property Relative demand is unaffected by third-country costs An illustration...

5 Example: U.S. raises tariffs on Costa Rican agriculture US Ag Imports: Costa Rica Bananas 40.8% Coffee 10.7% Beef 2.8% Melons 7.5% Other 9.1% Pineapples 16.8% Fruit, nes 3.2% Standard gravity predicts equal increases in trade flows for any two exporters with the same share of the US ag market

6 Example: U.S. raises tariffs on Costa Rican agriculture US Ag Imports: Costa Rica Bananas 40.8% Coffee 10.7% Beef 2.8% Melons 7.5% Other 9.1% Pineapples 16.8% Fruit, nes 3.2% Ecuador US Ag Market Share =.001% The Netherlands: US Ag Market Share =.001% Bananas 71.4% Tomatoes 45.8% Cocoa 4.7% Coffee 2.6% Fruit, Nes 3.7% Plantains 5% Mangoes Other 5.0% 2.8% Eggplants 2.4% Green Chiles & Peppers 44.1% Other 4.2%

7 Introduction SH model loosens IIE in a single equation model Requires little additional data beyond gravity requirements Multiple subsector approach Define subsectors such that IIE holds Practical disadvantages Production and trade data may not be available Subsector-level data may be very thin Particular disadvantage for GE gravity

8 Motivation Contribute to improving applied general equlibrium (AGE) models for trade analysis Most common source of quantitative analysis for decision-makers (Kehoe, Pujolàs and Rossbach (2017)) Martin (2018) and Kehoe et al call for more research into key parameters that drive results Gravity-based AGEs: key parameters estimated from data on which the model is simulated SH Model goal: Set of parameters that allow for nuanced interpretation of agricultural markets

9 Roadmap Structural model overview Specification of econometric model Data, testing and estimation Selected results Conclusion

10 Structural Model Overview

11 About the Model The SH Gravity Model In Brief Extension of Eaton and Kortum (2002) probabilistic Ricardian gravity model Parametric distribution of productivity and trade costs linked to country and product characteristics Parameters estimated from product-country interactions in random coefficients logit model Berry, Levinsohn and Pakes (1995)

12 About the Model Environment I countries engaged in bilateral agricultural trade Exporter indexed by i Importer index by n A continuum of products indexed by j Production technology is heterogeneous across products Climate and land characteristics influence which products have the highest productivity All markets are perfectly competitive Trade occurs as buyers look for the lowest price

13 Model Overview Production Technology Country i, product j technology q i (j) = z i (j) (N i β i (a i (j)l i ) 1 β i ) α i Q i 1 α i Input bundle is the same for all ag products N i is labor L i is land Q i is intermediate inputs

14 Model Overview Production Technology Country i, product j technology q i (j) = z i (j) (N i β i (a i (j)l i ) 1 β i ) α i Q i 1 α i z i (j) Technological productivity-enhancing Frechet r.v. F i (z) = exp{ T i z θ } T i drives average technological productivity in country i θ drives dispersion of technological productivity Independently distributed across products E.g., coffee

15 Model Overview Production Technology Country i, product j technology β q i (j) = z i (j) (N i i (a i (j)l i ) 1 β i ) α i 1 α Q i i a i (j) is deterministic variable representing land productivity Value reflects the coincidence of product requirements and country ecological characteristics E.g., coffee Country-specific parametric density, independent of z i (j)

16 Trade

17 Model Overview Comparative Advantage Probability country i has comparative advantage in product j in market n π ni (j) = T i(ã i (j)c i τ ni (j)) θ N T l (ã l (j)c l τ nl (j)) θ l=1 Probability country i price offer is lowest in market n c i is the cost of an input bundle

18 Model Overview Comparative Advantage Probability country i has comparative advantage in product j in market n π ni (j) = T i(ã i (j)c i τ ni (j)) θ N T l (ã l (j)c l τ nl (j)) θ l=1 Systematic Sources of Comparative Advantage ã i (j) product j land suitability τ ni (j) 1 is exporter i s cost to export products to market n Deterministic variable with parametric density Independent of z i (j) and ã i (j)

19 Model Overview Market Share Exporter i share in country n agriculture expenditure π ni = T i (ã i c i τ ni ) θ dfãn (ã)df τ N n (τ ) T l (ã l c l τ nl ) θ l=1 Fãn (ã) is the distribution of ã n = [ã 1,..., ã I ] across all products consumed in market n F τ n (τ ) is the distribution of τ = [τ n1,..., τ ni ] across all products consumed in market n

20 Model Overview Market Share Exporter i share in country n agriculture expenditure π ni = T i (ã i c i τ ni ) θ dfãn (ã)df τ N n (τ ) T l (ã l c l τ nl ) θ l=1 This is the structural equation from which the SH gravity model is derived In a standard EK gravity model, heterogeneity integrates out

21 Elasticities

22 Trade Elasticities SH Elasticity Elasticity of market share with respect to competitor trade costs π ni τ nl τ nl π ni = θ π ni (cov (π ni (j), π nl (j)) + π ni π nl ) l i EK Elasticity Constant elasticity across exporters π ni τ nl τ nl π ni = θ π nl l i

23 Specification

24 Random Coefficients Logit Specification Average productivity and input bundle cost as in EK lnt i θlnc i S i Country fixed effect

25 Random Coefficients Logit Specification Land Productivity ln(a i (j)) X i δ(j) Exporter Characteristics X i = [ al i elv i trop i temp i bor i ] al i - (log) arable land per capita elv i share of rural land at high altitude trop i - share of land in tropical climate zone

26 Random Coefficients Logit Specification Land Productivity ln(a i (j)) X i δ(j) Product characteristics δ(j) = δ + (E(j)Λ) + (ν E (j)σ E ) Observable production requirements E(j) = [ alw(j) elv(j) trop(j) temp(j) bor(j) ] Ex., trop(j) - tropical climate intensity of cultivation Unobservable product-specific requirements ν E (j) - vector of normal r.v. s

27 Random Coefficients Logit Specification Land Productivity ln(a i (j)) X i δ(j) δ(j) = δ + (E(j)Λ) + (ν E (j)σ E ) δ, Λ, Σ E - coefficients to estimate

28 Random Coefficients Logit Specification Trade Costs ln(τ ni (j)) t ni β(j) + ex i + ξ ni β(j) = β + (ν tn (j)σ t ) Country-pair characteristics t ni, ex i - border, language, distance, RTA & exporter effects Unobservable product-specific trade costs ν tn (j) - vector of normal r.v. s

29 Estimation and Data

30 Estimation Random coefficients logit model π ni = 1 ns ns j=1 exp{s i + X i δ(j) θ(t ni β(j) + ξ ni )} I exp{s l + X l δ(j) θ(t nl β(j) + ξ nl )} l=1 Estimates obtained using simulated method of moments Smooth simulator (Nevo (2000)) ns draws from each country s empirical distribution of expenditure d ˆF En (E)d ˆF νn (ν)

31 Data Dependent variable π ni calculated from FAO production and trade data Exporter i share of market n agricultural expenditure Country Characteristics al i, arable land - World Development Indicators trop i, temp i, bor i, - GTAP land use database Trade Costs t ni obtained from CEPII Gravity database

32 Data Observable Product Characteristics Land and elevation intensity - export-weighted average of country characteristic ˆ elv(coffee) = I w i (coffee) elv i i=1 w i (coffee) - country i share of global coffee exports

33 Data Observable Product Characteristics Climate intensity Crops: Export-weighted average of land rent distribution across climate zones - GTAP Land Use Database ˆ trop(wheat) = I w i (wheat) trop i (wheat) i=1 trop i (wheat) - share of country i wheat land rent in tropical zone w i (wheat) - country i share of global wheat exports

34 Data Observable Product Characteristics Climate intensity Crops: Export-weighted average of land rent distribution across climate zones - GTAP Land Use Database Animal products: Export-weighted average of country characteristics

35 Data Empirical distribution of expenditure: d ˆF En (E)d ˆF νn (ν) List of 1000 products purchased in market n Each product is represented in proportion to import share If j=wheat is 50% of country n imports, 500 entries are E(wheat) Each draw from d ˆF En (E) associated with vector of random normal draws Data set of ns products for each market: d ˆF En (E)d ˆF νn (ν)

36 Results

37 Parameter Estimates Land Productivity Distribution Exporter Characteristics ln Arable Land per Ag Worker 0.17*** *** 0.42*** 1.81*** 0.33*** High Elevation 1.14*** *** 0.44*** 1.31*** *** Tropical Climate Share Temp. Climate Share Boreal Climate Share Mean Effects Unobserved Reqs Agro-Ecological Requirements XX ii (δδ) (ΣΣ EE ) eeeeee(jj) aaaaaa jj tttttt(jj) tttttt(jj) 0.7*** -0.16** -3.96*** 0.73*** 6.86*** *** *** -0.53*** -2.8*** 0.7*** -0.88*** 0.19** 2.5*** -0.2*** -4.06*** -0.89*** (ΛΛ) Effect of country characteristics varies significantly with product requirements Reject standard gravity model of agricultural sector

38 Parameter Estimates Land Productivity Distribution Exporter Characteristics ln Arable Land per Ag Worker 0.17*** *** 0.42*** 1.81*** 0.33*** High Elevation 1.14*** *** 0.44*** 1.31*** *** Tropical Climate Share Temp. Climate Share Boreal Climate Share Mean Effects Unobserved Reqs Agro-Ecological Requirements XX ii (δδ) (ΣΣ EE ) eeeeee(jj) aaaaaa jj tttttt(jj) tttttt(jj) 0.7*** -0.16** -3.96*** 0.73*** 6.86*** *** *** -0.53*** -2.8*** 0.7*** -0.88*** 0.19** 2.5*** -0.2*** -4.06*** -0.89*** (ΛΛ) Total effect of high elevation for product j δ(j) = δ + (E(j)Λ) + (ν E (j)σ E )

39 Does it matter?

40 Elasticities SH Model Overcomes Restrictive Elasticities Source country Elasticity Mex. Market Share Costa Rica Honduras Venezuela Australia 3.35 USA 2.22 ππ nnnn ττ nnnn ττ nnnn ππ nnnn /ππ nnnn Ex.,1% increase in Mexican trade costs in Canada Standard Prediction: Elasticity Mex.MarketShare = θ SH Prediction: Disproportionately larger response for close competitors

41 Elasticities Implication: Change in policy can alter relative demand Source Country ππ nnnn / ππ nnnn ππ nnnn ππ nnnn Costa Rica Honduras Venezuela Australia USA Median Ex., Canada raises tariffs on Mexican products Standard Prediction: Relative demand is constant SH Prediction: Relative demand for Costa Rican products increases, and more than others

42 Conclusion

43 Conclusion Standard gravity models will be misleading if IIE does not hold Systematic forces influence comparative advantage within agriculture SH gravity generates variation in bilateral elasticities These models and AGE models built on them capture how intra-sector comparative advantage drives the response to policy change SH gravity permits analysis of policy at the product level Changes in the distribution of trade costs within the sector can be analyzed from a single equation

44 Objectives for improvement Introduce observable sources of trade cost heterogeneity Tariffs, perishability Improve methodology for product, sub-sector analysis Improve characterization of distribution of consumption Model evaluation

45 Parameter Estimates Variation in effect of high elevation land 25 Frequency plot: High elevation effect Number of traded products, Thousands Product-specific effect

46 Parameter Estimates: Trade Costs Country Pair Characteristics tt nnnn Mean Effect β Unobserved Heterogeneity ΣΣ tt Common Border -1.76*** 3.13*** Common Language 1.24*** 0.95*** Common RTA 0.19** ΣΣ Distance *** 2.36*** Distance *** 2.33*** Distance *** Distance *** 1.37*** Distance *** Distance *** 0.64*** Large ˆσ t implies signifcant unexplained variation