On estimating Armington elasticities for Japans meat imports

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arXiv:2210.05358v2 [econ.EM] 18 Oct 2022

On estimating Armington elasticities for Japan’s meat imports

Satoshi Nakano and Kazuhiko Nishimura

Abstract

By fully accounting for the distinct tariﬀ regimes levied on imported meat, we estimate substitution elas-

ticities of Japan’s two-stage import aggregation functions for beef, chicken and pork. While the regression

analysis crucially depends on the price that consumers face, the post-tariﬀ price of imported meat depends

not only on ad valorem duties but also on tariﬀ rate quotas and gate price system regimes. The eﬀective

tariﬀ rate is consequently evaluated by utilizing monthly transaction data. To address potential endogeneity

problems, we apply exchange rates that we believe to be independent of the demand shocks for imported

meat. The panel nature of the data allows us to retrieve the ﬁrst-stage aggregates via time dummy vari-

ables, free of demand shocks, to be used as part of the explanatory variable and as an instrument in the

second-stage regression.

Keywords: Two-stage CES aggregation, Armington elasticity, Instrumental variables, Exchange rates,

Tariﬀ rate quotas, Gate price system

1. Introduction

This study focuses on estimating Japan’s elasticity of substitution among commodities from diﬀerent

countries (or Armington elasticity) for three diﬀerent kinds of meat, i.e., beef, chicken and pork. Our

interest is driven by the fact that Japan has been the world’s largest meat importer. The importance

of Armington elasticities in the quantitative analysis of various trade policies has been well documented

(Hillberry and Hummels, 2013; Bajzik et al., 2020). We are aware that the welfare implications of any

trade policy cannot be properly evaluated without a ﬁnely tuned model with reliable elasticity parameters.

Conversely, reliable estimates of elasticity parameters cannot be obtained unless we are able to properly

incorporate the myriad trade regimes that exist. In Japan, meat imports are subject to a TRQ (tariﬀ rate

quota) regime that allows a lower rate for under-quota imports. Pork imports are speciﬁcally subject to a

GPS (gate price system) regime that discourages imports with prices lower than the gate price.

The main concern of previous related studies has been the diﬃculty of identifying demand and supply

parameters. The potential simultaneity of demand and supply equations creates endogeneity problems in

any attempt to estimate the elasticity of substitution of imports (i.e., the demand side) by way of a single

demand-side equation. A method established by Feenstra (1994) and its extensions by Broda and Weinstein

(2006); Soderbery (2015); Feenstra et al. (2018) focus on the combined quadratic equation that delivers

consistent estimators under the orthogonality assumption between the demand and supply shocks in a panel

data setting. Feenstra’s method is a convenient workaround when one cannot ﬁnd a relevant instrument

for the endogenous variable (i.e., the post-tariﬀ price). An orthodox approach to remediate such bias is

to ﬁnd and apply an instrument that is expected to be independent of the demand shocks. In this regard

Fajgelbaum et al. (2019) use tariﬀ rates, while Erkel-Rousse and Mirza (2002) use exchange rates.

For the purposes of this study, we seek to evaluate the applied tariﬀ rates as accurately as possible by

fully accounting for the modiﬁcations of TRQ regimes and schedule changes of the thresholds governing the

GPS. The tariﬀ duty under a TRQ depends on in- and out-quota duty rates and on the cumulative volume

∗Replication data for this study are available at Nakano and Nishimura (2022).

of registered imports that determines which of the two rates applies to each import incident. To determine

the timing of the cumulative volume exceeding the annually scheduled quotas, we utilize monthly data on

import incidents in all cases. Under a GPS, tariﬀs are levied to hold the post-tariﬀ price at a constant level

for all import incidents with pretax prices lower than the gate price. From another perspective, the applied

tariﬀ duties under TRQ and GPS depend on volumes and pretax prices of import incidents, and hence, they

must be correlated with import demand and hence with import demand shocks. We must therefore rule

tariﬀs out as a potential instrument.

Consequently, we utilize exchange rates to instrument for the endogenous explanatory variable, i.e., the

post-tariﬀ price, in the ﬁrst-stage regression under the assumption that exchange rates and meat import

demand shocks are independent. Our instrument is suﬃciently relevant in all cases. The ﬁrst-stage regression

is based on a multi-input CES function where the elasticity of substitution (microelasticity) can be estimated

via ﬁxed eﬀects (FE) estimation based on our country-level import observations in time series. Additionally,

by using time dummy variables, we are able to retrieve the ﬁrst-stage aggregates from the dummy coeﬃcients

and the microelasticity. Since the estimates of the ﬁrst-stage aggregates do not contain (the estimates of) the

demand shocks, we are able to apply them as an instrument to address the endogeneity in the second-stage

regression, where the error term may contain the ﬁrst-stage demand shocks. In this way, the second-stage

elasticity of substitution (macroelasticity) is estimated.

The remainder of this paper proceeds as follows. In the following section, we introduce the two-stage

CES aggregation model, deriving two (ﬁrst- and second-stage) regression equations for estimating the mi-

croelasticity and the macroelasticity. While the microelasticity and ﬁrst-stage aggregates are estimated by

the ﬁrst-stage regression, the second-stage regression utilizes the ﬁrst-stage aggregates and estimates the

macroelasticity. In Section 3, we present how we prepare the data for the abovementioned regression analy-

ses. All applied tariﬀ rates are calculated according to the tariﬀ scheme applied for meat imports to Japan,

which we summarize in the Appendix. Our main results are presented in Section 4, where we show the

ﬁnal estimates of microelasticities and macroelasticities for beef, chicken, and pork. Section 5 concludes the

paper.

2. Model

2.1. Two-stage CES aggregation

Consider, for some commodity m(index suppressed), a two-stage Armington aggregator as follows:

u=β1

ρzρ−1

ρ+ (1 −β)1

ρyρ−1

ρρ

ρ−1y=



i=1

(αi)

σ(xi)σ−1

σ



σ−1

where xidenotes the quantity (of commodity m) imported from country i,ydenotes the utility of ag-

gregated imports, zdenotes the quantity produced and consumed in the home country, and udenotes the

representative utility in the home country. Regarding the parameters, σdenotes the elasticity of substitution

among imports from diﬀerent countries (or microelasticity), ρdenotes the elasticity of substitution between

domestic and aggregate imports (or macroelasticity), and αi≥0and β≥0are the preference parameters

with PN

i=1 αi= 1 and β≤1. The ﬁrst function (on the right) is called the ﬁrst-stage aggregator, and the

second (on the left) is called the second-stage aggregator.

The dual function of this two-stage Armington aggregator can be written as follows:

v=βr1−ρ+ (1 −β)q1−ρ

1−ρq=



i=1

αi(pi)1−σ



1−σ

(1)

where pidenotes the (tariﬀ-inclusive) import commodity price from country iin the home country. Note that

the price of the commodity from the ith country pi(JPY/kg) in terms of Japan’s currency unit, domestic

price r(JPY/kg), import physical quantity xi(kg), and domestic physical quantity z(kg) are all observable,

but the aggregated values, namely, y(utility), q(JPY/utility), u(utility) and v(JPY/utility), are not. As

per duality, however, we know that the following identities must hold.

vu =rz +qy qy =

i=1

pixi

2.2. First-stage estimation

Applying Shephard’s lemma for the ﬁrst-stage aggregator (1) yields the following:

si=pitxit

i=1 pitxit

=pixi

qy =∂q

∂pi

q=αipi

q1−σ

Here, sidenotes the value share of imports of the commodity from the ith country. As we label observations

by t= 1,··· , J, we have the following regression equation:

ln sit =−(1 −σ) ln qt+ (1 −σ) ln pit + ln αi+ǫit (2)

where the error terms ǫit are assumed to be iid normally distributed with mean zero. The regression equation

(2) can be estimated (for σand qtfrom pit and sit) by FE panel regression. That is, the ﬁrst-stage aggregates

qt, in terms of indices, are indirectly measured by the coeﬃcients on the time dummy variables through the

FE panel regression. Let us rewrite regression equation (2) using time dummy variables (Dℓ= 1 if t=ℓ

and Dℓ= 0 otherwise), as follows:

Sit =

ℓ=1

(µℓ−µJ)Dℓ+µJ+γPit + ln αi+ǫit (3)

where Sit = ln sit,Pit = ln pit, and the coeﬃcients therefore denote that

µt=−γln qtγ= 1 −σ

The ﬁrst-stage aggregates qtcan be resolved, in terms of an index standardized at t=J, as follows:

qt=e−(µt−µJ)/γ t= 1,··· , J (4)

The ﬁrst-stage regression (3) suﬀers from endogeneity problems because the demand shock ǫit enters the

explanatory variable Pit via the potential supply function connecting Sit (the demand for meat from country

i) to Fit (the FOB (free on board) price of meat from country i), where Fit is a component of Pit, such that

Pit =Cit +Tit = (Fit +Eit + ∆it) + Tit (5)

where Cdenotes the CIF (cost, insurance and freight) price in JPY (Japanese yen), Tdenotes the tariﬀ rate,

and Edenotes the exchange rate, all in log terms, and ∆ = C−(F+E)denotes the CIF/FOB discrepancy.1

To obtain a consistent estimation for (3), we apply exchange rate Eit as an instrumental variable for the

endogenous explanatory variable Pit. Because we believe that demand shocks ǫit for meat from country i

and the exchange rate Eit against the currency of country iare independent, our instrument Eit must be

exogenous. Moreover, because Eit is a component of Pit, our instrument Eit must be relevant, i.e., strongly

correlated with our explanatory variable Pit.2

1Note that C,T, and Eare observable, while Fand ∆are not.

2On the other hand, the eﬀective tariﬀ rate Tit will not be exogenous because Tit will depend on quantity demanded xit

(which will inevitably be correlated with the demand shock ǫit ) under the tariﬀ regime of import quotas and GPSs.

2.3. Second-stage estimation

Application of Shephard’s lemma for the second-stage aggregator of (1) yields the following:

∂v

∂r =rz

vu =βr

v1−ρq

∂v

∂q =qy

vu = (1 −β)q

v1−ρ

By combining the above two identities and labelling observations by t= 1,··· , J, we have the following

simple regression equation:

ln rtzt

i=1 pitxit != ln β

1−β+ (1 −ρ) ln rt

qt+νt(6)

where νtdenotes the demand shocks that include the demand shocks for foreign meat (ǫit) and those for

domestic meat (δt). The explanatory variable ln(rt/qt), however, must be correlated with νtbecause of the

reverse causality of the response variable on the explanatory variable via the possible supply function.

Thus, the second-stage regression (6) also suﬀers from an endogeneity problem. To obtain consistent

estimates, we apply Qt= ln ˆqtto the endogenous explanatory variable (Rt−Qt)in regression (6) which can

be rewritten as follows:

Ht=φ+η(Rt−Qt) + νt(7)

where η= 1 −ρ,Rt= ln rt, and so forth. We suppose that Qt= ln ˆqtis exogenous because ˆqtdoes not

contain the (estimate of) demand shocks ˆǫit and δt, both of which constitute νt. Moreover, because Qtis

a component of the explanatory variable, our instrument Qtmust be relevant for our explanatory variable

(Rt−Qt).

3. Data compilation

3.1. First-stage estimation

We draw our main data, i.e., monthly import values and quantities from January 1996 to December

2020 for all 78 items whose HS codes are speciﬁed in Table 8, from the Commodity by Country link of

Trade Statistics (2022). Let vg

it and xg

it denote the JPY value and kg quantity of item g= 1,··· , G

imported from country i= 1,··· , N at time t= 1,··· , J, respectively, where N= 86,G= 78, and J= 300.

Additionally, let Gmdenote the set of item IDs of meat type mwhere m= 1 denotes beef, m= 2 denotes

pork, and m= 3 denotes chicken. Speciﬁcally, G1={1,··· ,16},G2={28,··· ,48}, and G3={68,··· ,74}

as regards to Table 8. We ﬁrst prepare the data as follows:

vit =X

g∈Gm

it xit =X

g∈Gm

it cit =vit

xit

(8)

for three kinds of meat (m= 1,2,3). Here, cit denotes the CIF price (for one kind of meat) where ln cit =Cit

as mentioned in (5). Furthermore, note that sit =eSit is calculated by using pit =ePit from (5) and xit

given above, according to its deﬁnition.

Eﬀective tariﬀ rates Tit are evaluated according to Japan’s tariﬀ scheme summarized in Appendix. We

obtain the tariﬀ schedules applied to each item (g) with respect to each regime classiﬁcation from Chapter 2

(Meat and edible meat oﬀal) and Chapter 16 (Preparation of meat etc.) links of Tariﬀ Schedule (2022). The

above source however only provides tariﬀ schedules from April 2007 onward, and so we refer to the version

in Japanese that covers schedules from January 2003 onward. For earlier schedules prior to 2002, we refer to

the hardcopy version of the Customs Tariﬀ Schedules of Japan (published by the Japan Tariﬀ Association).

We assign the proper tariﬀ schedule to each partner country iin each period taccording to the tariﬀ regime

classiﬁcations available from WTO (2020) (by selecting Japan in the Reporter window and 02 and 16 in the

Products window). The tariﬀ quota schemes (i.e., quota eligible items and annual in-quota quantities) for

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arXiv:2210.05358v2[econ.EM]18Oct2022OnestimatingArmingtonelasticitiesforJapan’smeatimportsSatoshiNakanoandKazuhikoNishimuraAbstractByfullyaccountingforthedistincttariﬀregimesleviedonimportedmeat,weestimatesubstitutionelas-ticitiesofJapan’stwo-stageimportaggregationfunctionsforbeef,chickenandpork.Whi...

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