. Gravity and Comparative Advantage: Estimation of Trade ...Gravity and Comparative Advantage:...

.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


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...


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


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%


Roadmap

• Structural model overview

• Specification of econometric model

• Estimation

• Selected results

• Conclusion


Structural Model Overview


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


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


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)


Trade


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)


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


Specification


Random Coefficients Logit Specification

• Average productivity and input bundle cost as in EK

lnTi − θlnci ≡ Si

– Country fixed effect



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



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



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


Estimation


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


Results


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


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 )′


Does it matter?


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


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


Conclusion


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


Elasticities


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


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 .


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


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

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