. Gravity and Comparative Advantage: Estimation of Trade ...Gravity and Comparative Advantage:...
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.Gravity and Comparative Advantage:
Estimation of Trade Elasticities for theAgricultural Sector
Kari E.R. Heerman, Economic Research Service, USDAIan Sheldon, Ohio State University
2018 IATRC Annual Meeting
Whistler, BC CanadaJuly 25-27, 2018
The analysis and views expressed are the authors’ and do not represent theviews of the Economic Research Service or USDA.
Heerman and Sheldon July 25-27, 2018
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
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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...
Heerman and Sheldon July 25-27, 2018
Example: U.S. raises tariffs on Costa Rican agriculture
Other 9.1%
Beef 2.8% Fruit, nes
3.2%
Melons 7.5%
Coffee 10.7%
Pineapples 16.8%
Bananas 40.8%
US Ag Imports: Costa Rica
Standard gravity predicts equal increases in trade flows for any two
exporters with the same share of the US ag market
Heerman and Sheldon July 25-27, 2018
Example: U.S. raises tariffs on Costa Rican agriculture
Other 9.1%
Beef 2.8% Fruit, nes
3.2%
Melons 7.5%
Coffee 10.7%
Pineapples 16.8%
Bananas 40.8%
US Ag Imports: Costa Rica
Other 5.0% Coffee 2.6%
Mangoes 2.8%
Fruit, Nes 3.7%
Cocoa 4.7%
Plantains 5%
Bananas 71.4%
Ecuador US Ag Market Share = .001%
Other 4.2%
Eggplants 2.4%
Green Chiles
& Peppers 44.1%
Tomatoes 45.8%
The Netherlands: US Ag Market Share = .001%
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Roadmap
• Structural model overview
• Specification of econometric model
• Estimation
• Selected results
• Conclusion
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Structural Model Overview
Heerman and Sheldon July 25-27, 2018
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 productshave the highest productivity
• All markets are perfectly competitive
• Trade occurs as buyers look for the lowest price
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Model Overview
Production Technology Country i , product j technology
qi (j) = zi (j)× (Niβi (ai (j)Li )
1−βi )αi Qi1−αi
• Input bundle: labor (Ni ), land (Li ), intermediates Qi
• zi (j) Technological productivity-enhancing Frechet r.v.
Fi (z) = exp{−Tiz−θ}
– Ti drives average technological productivity in country i
– θ drives dispersion of technological productivity
– Independently distributed across products
• E.g., coffee
• ai (j) is deterministic variable representing land productivity
Heerman and Sheldon July 25-27, 2018
Model Overview
Production Technology Country i , product j technology
qi (j) = zi (j)× (Niβi (ai (j)Li )
1−βi )αi Qi1−αi
• ai (j) is deterministic variable representing land productivity
– Value reflects the coincidence of product requirements andcountry ecological characteristics
• E.g., coffee
– Country-specific parametric density, independent of zi (j)
Heerman and Sheldon July 25-27, 2018
Trade
Heerman and Sheldon July 25-27, 2018
Model Overview
Comparative Advantage Probability country i has comparativeadvantage in product j in market n
πni (j) =Ti (ai (j)ciτni (j))−θ
N∑l=1
Tl(al(j)clτnl(j))−θ
• Probability country i price offer is lowest in market n
– ci is the cost of an input bundle
• τni (j) ≥ 1 is exporter i ’s cost to export products to market n
– Deterministic variable with parametric density
– Independent of zi (j) and ai (j)
Heerman and Sheldon July 25-27, 2018
Model Overview
Market Share Exporter i share in country n agriculture expenditure
πni =
∫Ti (aiciτni )
−θ
N∑l=1
Tl(alclτnl)−θdFan(a)dFτ n(τ )
• This is the structural equation from which the SH gravitymodel is derived
– Fan(a) is the distribution of an = [a1, ..., aI ] across allproducts consumed in market n
– Fτ n(τ ) is the distribution of τ = [τn1, ..., τnI ] across allproducts consumed in market n
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Specification
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Random Coefficients Logit Specification
• Average productivity and input bundle cost as in EK
lnTi − θlnci ≡ Si
– Country fixed effect
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Random Coefficients Logit Specification
Land Productivityln(ai (j)) ≡ Xiδ(j)
• Exporter Characteristics
– Xi =[aLi elvi tropi tempi bori
]• ali - (log) arable land per capita, World Bank• elvi share of rural land at high altitude, CIESIN• tropi - share of land in tropical climate zone, GTAP
Heerman and Sheldon July 25-27, 2018
Random Coefficients Logit Specification
Land Productivityln(ai (j)) ≡ Xiδ(j)
δ(j) = δ + (E(j)Λ)′ + (νE (j)ΣE )′
• Product characteristics
– “Observable” production requirements
• E(j) =[alw(j) elv(j) trop(j) temp(j) bor(j)
]– Ex., trop(j) - tropical climate intensity of cultivation
– Trade-weighted averages of country characteristics
– “Unobservable” product-specific requirements
• νE (j) - vector of normal r.v.’s
Heerman and Sheldon July 25-27, 2018
Random Coefficients Logit Specification
Trade Costsln(τni (j)) ≡ tniβ(j) + exi + ξni
β(j) = β + (νtn(j)Σt)′
• Country-pair characteristics
– tni , exi - border, language, distance, RTA & exporter effects
• “Unobservable” product-specific trade costs
– νtn(j) - vector of normal r.v.’s
Heerman and Sheldon July 25-27, 2018
Estimation
Heerman and Sheldon July 25-27, 2018
Estimation
Random coefficients logit model
πni =1
ns
ns∑j=1
exp{Si + Xiδ(j)− θ(tniβ(j) + ξni )}I∑
l=1
exp{Sl + Xlδ(j)− θ(tnlβ(j) + ξnl)}
• Estimates obtained using simulated method of moments
– Smooth simulator (Nevo (2000))– ns draws from each country’s empirical distribution of
expenditure dFEn(E)dFνn(ν) More .
• Dependent variable πni calculated from FAO production andtrade data
Heerman and Sheldon July 25-27, 2018
Results
Heerman and Sheldon July 25-27, 2018
Parameter Estimates
Land Productivity Distribution
ln Arable Land per Ag Worker 0.17*** -0.01 -4.51*** 0.42*** 1.81*** 0.33***
High Elevation 1.14*** -0.21 47.96*** 0.44*** 1.31*** -12.32***
Tropical Climate Share 0.7*** -0.16** -3.96*** 0.73*** 6.86*** 0.19
Temp. Climate Share 0.19*** -0.03 1.46*** -0.53*** -2.8*** 0.7***
Boreal Climate Share -0.88*** 0.19** 2.5*** -0.2*** -4.06*** -0.89***
Exporter Characteristics
Mean Effects
Unobserved Reqs
Agro-Ecological Requirements
𝑿𝑿𝒊𝒊 (𝜹𝜹) (𝚺𝚺𝐄𝐄) 𝒆𝒆𝒆𝒆𝒆𝒆(𝒋𝒋) 𝒂𝒂𝒆𝒆𝒂𝒂 𝒋𝒋 𝒕𝒕𝒕𝒕𝒕𝒕(𝒋𝒋) 𝒕𝒕𝒕𝒕𝒕𝒕(𝒋𝒋)
(𝚲𝚲)
• Effect of country characteristics varies significantly with productrequirements → Reject standard gravity model of agricultural sector
Heerman and Sheldon July 25-27, 2018
Parameter Estimates
Land Productivity Distribution
ln Arable Land per Ag Worker 0.17*** -0.01 -4.51*** 0.42*** 1.81*** 0.33***
High Elevation 1.14*** -0.21 47.96*** 0.44*** 1.31*** -12.32***
Tropical Climate Share 0.7*** -0.16** -3.96*** 0.73*** 6.86*** 0.19
Temp. Climate Share 0.19*** -0.03 1.46*** -0.53*** -2.8*** 0.7***
Boreal Climate Share -0.88*** 0.19** 2.5*** -0.2*** -4.06*** -0.89***
Exporter Characteristics
Mean Effects
Unobserved Reqs
Agro-Ecological Requirements
𝑿𝑿𝒊𝒊 (𝜹𝜹) (𝚺𝚺𝐄𝐄) 𝒆𝒆𝒆𝒆𝒆𝒆(𝒋𝒋) 𝒂𝒂𝒆𝒆𝒂𝒂 𝒋𝒋 𝒕𝒕𝒕𝒕𝒕𝒕(𝒋𝒋) 𝒕𝒕𝒕𝒕𝒕𝒕(𝒋𝒋)
(𝚲𝚲)
• Total effect of high elevation for product j
δ(j) = δ + (E(j)Λ)′ + (νE (j)ΣE )′
Heerman and Sheldon July 25-27, 2018
Does it matter?
Heerman and Sheldon July 25-27, 2018
Elasticities
SH Model Overcomes Restrictive Elasticities
Source country
Elasticity Mex. Market
Share
Costa Rica 19.41Honduras 18.63Venezuela 18.33Australia 3.35USA 2.22
𝝏𝝏𝝅𝝅𝒏𝒏𝒏𝒏𝝏𝝏𝝉𝝉𝒏𝒏𝒏𝒏
𝝉𝝉𝒏𝒏𝒏𝒏𝝅𝝅𝒏𝒏𝒏𝒏
/𝝅𝝅𝒏𝒏𝒏𝒏
• Ex.,1% increase in Mexican trade costs in Canada
Standard Prediction: ElasticityMex .MarketShare = θ
SH Prediction: Disproportionately larger response for closecompetitors
Heerman and Sheldon July 25-27, 2018
Elasticities
Implication: Change in policy can alter relative demand
Source Country
Costa Rica 1.0043Honduras 1.0041Venezuela 1.0041Australia 1.0000USA 0.9997Median 1.0000
𝝅𝝅𝒏𝒏𝒏𝒏′
𝝅𝝅𝒏𝒏𝒏𝒏′/𝝅𝝅𝒏𝒏𝒏𝒏𝝅𝝅𝒏𝒏𝒏𝒏
• Ex., Canada raises tariffs on Mexican products
Standard Prediction: Relative demand is constant
SH Prediction: Relative demand for Costa Rican productsincreases, and more than others
Heerman and Sheldon July 25-27, 2018
Conclusion
Heerman and Sheldon July 25-27, 2018
Conclusion
• Standard gravity models will be misleading if IIE does not hold
– Systematic forces influence comparative advantage withinagriculture
• SH gravity generates variation in bilateral elasticities
– These models and AGE models built on them capture howintra-sector comparative advantage drives the response topolicy change
• SH gravity permits analysis of policy at the product level
– Changes in the distribution of trade costs within the sectorcan be analyzed from a single equation
Heerman and Sheldon July 25-27, 2018
Elasticities
Heerman and Sheldon July 25-27, 2018
Trade Elasticities
SH Elasticity Elasticity of market share with respect to competitortrade costs
∂πni∂τnl
τnlπni
=θ
πni(cov (πni (j), πnl(j)) + πni × πnl) l 6= i
EK Elasticity Constant elasticity across exporters
∂πni∂τnl
τnlπni
= θ × πnl l 6= i
Heerman and Sheldon July 25-27, 2018
Estimation
Empirical distribution of expenditure: dFEn(E)dFνn(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 areE (wheat)
• Each draw from dFEn(E) associated with vector of randomnormal draws
– “Data set” of ns products for each market: dFEn(E)dFνn(ν)
Go Back .
Heerman and Sheldon July 25-27, 2018
Parameter Estimates
Variation in effect of high elevation land
0
5
10
15
20
25
-15 -12 -9 -6 -3 0 3 6 9 12 15
Num
ber o
f tra
ded
prod
ucts
, Tho
usan
ds
Product-specific effect
Frequency plot: High elevation effect
Heerman and Sheldon July 25-27, 2018
Parameter Estimates: Trade Costs
Common Border -1.76*** 3.13***
Common Language 1.24*** 0.95***
Common RTA 0.19** -0.11
Distance 1 -5.28*** 2.36***
Distance 2 -7.67*** 2.33***
Distance 3 -7.43*** -0.16
Distance 4 -9.95*** 1.37***
Distance 5 -11.56*** -0.04
Distance 6 -12.94*** 0.64***
Country Pair Characteristics
Mean Effect
Unobserved Heterogeneity
𝒕𝒕𝑛𝑛𝑛𝑛 β
𝚺𝚺
𝚺𝚺𝒕𝒕
• Large σt implies signifcant unexplained variation