Substitution elasticity of Japan’s meat imports:
estimation with and without instruments
Jiyoung Kima, Kazuhiko Nishimurab

Abstract
This paper is concerned with the measurement of the elasticity of substitution between goods from different
countries. The commodities of our interest are bovine, swine, and poultry meat imports by Japan. To
remedy potential endogeneity problems in regression estimations, we use the instrumental variables (IV)approach, and the Feenstra method that does not require the use of instruments. We find that the two
approaches yield very similar results. Further, upon extracting the implicit IVs of the Feenstra method, we
find them as useful as the external IVs for measuring the aggregate of foreign commodities with a fixed effects
regression and for estimating the foreign-domestic substitution elasticity, possibly for each commodity. The
elasticities are then utilized for examining the effect of tariff elimination.
Keywords: Two-stage CES aggregator, Instrumental variables approach, Feenstra method, Implicit
instrumental variable

1. Introduction
Japan has been the world’s largest meat importer (see, Figure 1). According to the 2015 input-output
tables, Japan’s household sector yearly consumed 635 BJPY (Billion Japanese Yens) of bovine meat, 528
BJPY of swine meat, and 273 BJPY of poultry meat. As known, these commodities are subject to tradenegotiations such as the TPP, the RCEP, and numerous bilateral FTAs. To study the welfare implicationsof the trade liberalization regimes, general equilibrium models have been the standard device. For thesemodels, the import demand module is typically comprised of constant elasticity of substitution (CES)
aggregator functions, where the elasticity of substitution between products from different countries, called theArmington elasticity, plays an essential role. Our main purpose is thus to carefully estimate the Armington
elasticities of the aforementioned commodities for Japan.
Previous empirical studies on the measurement of Armington elasticities include Corado and De Melo(1986); Reinert and Roland-Holst (1992); Gallaway et al. (2003). These studies, nevertheless, do not take
into account the potential endogeneity of the explanatory variable (which typically is the international price)arising from reverse causality vis-a-vis the response variable (which typically is the demanded quantity inthe home country). In contrast, the method developed by Feenstra (1994) and its extensions by Broda andWeinstein (2006), Soderbery (2015) and Feenstra et al. (2018) enable us to account for potential reverse
causality without having to find instrumental variables. As we verify in the following section, the Feenstra
method has the potential to provide consistent estimates in a panel setting under mild assumptions.
Our recourse to the Feenstra method stems from the difficulty of finding valid instruments. Above all,panel data analysis techniques, such as fixed effects, do not allow lagged explanatory variables as instruments.
Alternatively, we could consider other indicators, such as the average prices of other exporters, as explanatory
variables (as in Kee et al., 2008) under the assumption that the demand shocks for different items are
independent. However, these variables have to be ruled out when the expenditure share is our response
variable. We hence explore potentially relevant instruments for the components of the explanatory variable
a Graduate School of Humanities and Social Science, Okayama University, Okayama Japan, 700-8530. (Email: jiyoung@okayama-u.ac.jp)
b School of Global Studies, Chukyo University, Aichi Japan, 466-8666.

1
30
2

World share rankings

World share [%]

3

20

4

5

6
10
7

8
1995

2000

2005

2010

2015

1995

Year

2000

2005

2010

2015

Year

Figure 1: Japan’s world share of imports (left) and their rankings (right) from 1995 to 2018. The solid line indicates bovine
meat, the dashed line indicates swine meat (as pig meat), and the dotted line indicates poultry meat. Source: oec.world(i.e., the international price). Nevertheless, the main component, i.e., the transportation cost measured by
the difference between cost, insurance and freight (CIF) and free on board (FOB) prices, can depend on thequantity demanded.
On the other hand, components such as bilateral distances, tariff rates, and exchange rates may beconsidered exogenous. 1 Naturally, distances cannot be affected by demand; tariff rates may affect demand,
but not the other way around; and exchange rates may not be affected by demand for the commodity as
long as we assume that the underlying market is small. While distances that are temporally constant cannot
be effective in a panel setting, tariff rates, as employed in Fajgelbaum et al. (2019), may be useful as long as
they vary in time series. In a panel setting, exchange rates, as employed in Erkel-Rousse and Mirza (2002),
seem particularly useful in the sense that they affect the international price directly. The difficulty of using
the instrumental variables (IV) approach is, however, that even after one finds an exogenous instrument, it
has to be approved by tests for relevancy.
Because of its versatility and ease of implementation, we may prefer to apply the Feenstra method if
the Armington elasticities estimated by this method and the IV approach are not so different. In the end,
the estimators for both approaches are biased but consistent. Thus, one of our purposes in this study is tocompare and assess the two standing approaches under the same framework. In accordance with Feenstra
et al. (2018), we focus on the CES Armington aggregator that is comprised of two stages. The first (lower)stage aggregates goods from different countries into a foreign good, and the second (upper) stage aggregatesdomestic and foreign goods into the partial utility of the home country. The first-stage aggregation isgoverned by the microelasticity, and the second-stage aggregation is governed by the macroelasticity.2
Previous studies that are concerned with the measurement of the Armington elasticity (Erkel-Rousse
and Mirza, 2002; Saito, 2004; Feenstra et al., 2018) apply between estimation for multi-input elasticity,a typical strategy for the two-input case. Between estimation nevertheless eliminates time-specific effects
such as the first stage aggregates. Previous studies deploying two-stage models hence use auxiliary indices
1 Japan levies various non-ad valorem tariffs (e.g., tariff quotas and gate price system) on meat imports, in addition to thebaseline ad valorem tariffs. Since CIF prices affect non-ad valorem tariffs, the overall tariff rates may be endogenous. To secure
exogeneity of the instruments we confine our focus to Armington aggregators based on pre-fixed ad valorem tariff rates.
2 While Saito (2004) uses the terms intragroup and intergroup, we use micro and macro as employed in Feenstra et al. (2018).

2such as the Laspeyres or Sato-Vartia index for estimating the second-stage macroelasticities.3 In contrast,
we apply within (fixed effects) estimation for the first-stage regression that allows us to retrieve the firststage aggregates as a time-varying index, together with the microelasticity estimation, while eliminating
the individual specific share parameters. The indexed first-stage aggregates can be readily utilized for thesecond-stage macroelasticity estimation.
In this study, we find that the Feenstra method is capable of finding first-stage microelasticities very
similar to those obtained by fixed effects IV regression with valid external instruments. On the other hand,
while fixed effects IV regression is capable of identifying the first-stage aggregates that can be utilized forthe second-stage macroelasticity estimation, the Feenstra method (Feenstra et al., 2018), with removed
first-stage panel variations, evaluates the macroelasticity in a reduced manner, such that a macroelasticity
common to several kinds of commodities is measured. In this regard, we take a step forward and discovera way to estimate individual macroelasticities without external instruments. Particularly, we find that the
implicit IV of the Feenstra method is just as useful as the external IV in estimating microelasticities andmacroelasticities.
We organize the paper as follows. In the next section, we specify the two-stage Armington aggregator.
In section 3, we show how the Feenstra method works in a panel setting to maintain consistency in theestimation of microelasticity and further find a way to extract the implicit IV. In section 4, based on thesame dataset, we empirically estimate microelasticities by four different means, namely, 1) IV regression
using external IV, 2) the Feenstra method, 3) the Feenstra method with extended moment conditions, and
4) IV regression using the implicit IV of the Feenstra method. Then, macroelasticities are estimated by wayof 1) and 4), where the first-stage aggregates are derivable. In section 5, tariff elimination is examined byfurther estimating the tariff elasticity of demand quantity. Finally, section 6 concludes.
2. Two-stage Armington aggregator
2.1. Two-stage CES specification
Consider, for each kind of commodity g (index omitted), a two-stage Armington aggregator of thefollowing type:1ρ

u= β zρ−1ρ1ρ+ (1 − β) y

ρ−1
ρ

ρ
 ρ−1

y=

N
X

1
σ

(αi ) (xi )

σ−1
σ

σ
! σ−1

i=1

where xi denotes the quantity (of commodity g) imported from country i, y denotes the utility of aggregated imports, z denotes the quantity produced and consumed in the home country, and u denotes therepresentative utility in the home country. For the parameters, σ denotes the elasticity of substitution
among imports from different countries (or microelasticity), ρ denotes the elasticity of substitution between
domestic and aggregate imports (or macroelasticity), and αi ≥ 0 and β ≥ 0 are the preference parameters
PN
with i=1 αi = 1 and β ≤ 1. The first function (on the right) is called the first-stage aggregator, and thesecond (on the left) is called the second-stage aggregator.
The dual function of this two-stage Armington aggregator is as follows:v = βr1−ρ + (1 − β)q 1
1−ρ 1−ρ

q=

N
X

1
! 1−σ

αi (pi )

1−σ

(1)

i=1

where pi denotes the import commodity price from country i in the home country. Note that the price ofthe commodity from the ith country pi (LCU/kg) in terms of the home country’s LCU (local currency unit),
domestic price r (LCU/kg), import physical quantity xi (kg), and domestic physical quantity z (kg) are all
3 Note that the Sato-Vartia index is an exact index for a two-input CES aggregator but is not for multi-input versions of
CES like the ones that we are considering for a micro-aggregator function (see Lau, 1979).

3

observable, but the aggregated values, namely, y (utility), q (LCU/utility), u (utility) and v (LCU/utility),
are not. As per duality, however, we know that the following identities must hold.
vu = rz + qy

qy =

N
X

pi xi

(2)

i=1

Applying Shephard’s lemma for the first-stage aggregator gives the following:∂q pi
p i xi
=
= αi
si =
qy
∂pi q



pi
q

1−σ

Here, si denotes the value share of imports of the commodity from the ith country. As we label observations
by t = 1, · · · , T , we have the following regression equation:
pit xitln sit = ln PN= −(1 − σ) ln qt + (1 − σ) ln pit + ln αi + it
i=1 pit xit(3)

where the error terms it are assumed to be iid normally distributed with mean zero. The regression
equation (3) can be estimated (for σ and qt from pit and sit ) by fixed effects (FE) panel regression.4 Morespecifically, we measure qt by the coefficients on time dummy variables (see section 4) through FE panel
regression. Alternatively, we could instead measure αi by the coefficients on item (country) dummy variables
through between panel regression. In this case, the first-stage aggregates qt must be evaluated by the proxies,
as done in previous studies, or by applying the estimates α̂i and σ̂ to (1). In the latter case, however, thePNcriteria thati=1 α̂i = 1 can hardly be met. We shall hence remain with FE panel regression for the
first-stage microelasticity estimation.
Below are the first-order conditions (Shephard’s lemma) for the second-stage aggregator: r 1−ρ
r ∂v
rz
=
=β
v ∂r
vu
v

 q 1−ρqyq ∂v== (1 − β)
v ∂q
vu
v

In this case, we shall fully utilize the time series variation since the cross-sectional variation is minimal. By
combining the above two identities, we obtain the following simple regression equation:
ln

rt zt
rt zt
rt
β
= ln PN+ (1 − ρ) ln + νt= ln
q t yt1−βqt
i=1 pit xit(4)

where the error terms νt are assumed to be iid normally distributed with mean zero. Regression equation(4) can be estimated (for ρ and β from zt , yt , rt , and qt ) by time series analysis, where we can use thefirst-stage aggregates (q̂t ) obtainable from (3) for the explanatory variable in (4).
2.2. External instruments
Regression equation (3) for the first-stage suffers from an endogeneity problem because the demand shockit enters the explanatory variable ln pit through the reverse causality between ln sit and ln pit so that theerror term it and the explanatory variable ln pit become correlated with each other. To obtain a consistentestimation, we must apply instrumental variables onto the endogenous explanatory variable. As we assume
independence of the error terms, we may consider lagged explanatory variables such as ln pit−1 and it to
be uncorrelated even when ln pit−1 and it−1 are correlated and ln pit and it are correlated. However, alagged explanatory variable cannot be used if we estimate (3) by FE or first-difference (FD) regression. This
4 In contrast, Saito (2004) estimate σ via between regression, which eliminates q . The Feenstra method (as well as Romalist(2007)) uses double differences (within-between) estimation, eliminating both αi and qt . The first-stage aggregates qt arehence proxied by auxiliary indices such as the Laspeyres (Saito, 2004), Stone (Blonigen and Wilson, 1999; Huchet-Bourdon
and Pishbahar, 2009), and Sato-Vartia (Feenstra et al., 2018) indices.

4

is because ∆ ln pit−1 = ln pit−1 − ln pit−2 and ∆it = it − it−1 are correlated when ln pit−1 and it−1 arecorrelated. From another point of view, one might consider using ln pkt , where k =6 i, to instrument forln pit . This idea fails, however, because ln pkt affects the response variable ln sit directly.
We shall thus search for external IVs. The usual practice in this case is to look at the components ofthe explanatory variable, since the relevancy of the instrument is imperative. The price of a commodity
imported from country i faced by consumers in the home country can be decomposed as follows:
pit = e01t (1 + rit )cit

cit = (1 + mit )fit /ei1t

where fit (LCU/kg) denotes the FOB price in terms of country i’s LCU at time t, cit (USD/kg) denotes the
CIF price of i’s product in terms of US dollars (USD) at t, rit > 0 denotes the tariff rate on i’s commodities
at t, mit > 0 denotes the transportation cost (including freight and insurance) for the commodity shippedfrom i at t, and e01t (LCU/USD) and ei1t (LCU/USD) denote the home currency exchange rate against
USD and i’s local currency exchange rate against USD, respectively.
Here, we note that fit and mit (and thus cit ) depend on the quantity demanded and therefore must be
endogenous with respect to taste shocks it in the home country. On the other hand, tariff rates rit andexchange rates e1it can be considered exogenous.5 Hence, we prepare them for further examination withrespect to their relevance. A similar strategy (to utilize an exogenous component of the explanatory variable)
can be sought for the second-stage regression (4). Note that the first-stage aggregate qt in (3) is uncorrelatedwith it because it does not enter qt , even if there were reverse causation between sit and pit . That given,
the error term νt in (4), which represents the difference between domestic and (aggregated) foreign taste
shocks, where both are uncorrelated with qt , must also be uncorrelated with qt . We can therefore use qt to
instrument the explanatory variable in (4).
3. Feenstra method and extensions
3.1. Microelasticity
Below, we briefly review the framework of the Feenstra method. By timely differencing (3), we have thefollowing:∆ ln sit = −(1 − σ)∆ ln qt + (1 − σ)∆ ln pit + ∆it
By subtracting the item average values, such that ∆ln st =

(5)

PN

6
i=1 ∆ ln sit /N , from (5), we have the following:(∆ ln sit − ∆ln st ) = (1 − σ) (∆ ln pit − ∆ln pt ) + (∆it − ∆t )Below, we rewrite this demand function (left) along with the supply function (right), which is supposed togive rise to the endogeneity problem:
Sit = γPit + εit

Pit = κSit + δit(6)where γ = 1 − σ, Pit = ∆ ln pit − ∆ ln pt , Sit = ∆ ln sit − ∆ ln st , and εit = ∆it − t . Note that taste shocks
εit and innovations δit are not observable to the econometrician, and we assert that they are independent.
While it is obvious that Pit is endogenous in the demand (left) equation of (6), consistent estimationis possible by instrumenting Pit with δit . In the Feenstra method, the corresponding moment condition isconsidered by means of the following linear regression equation:
Yit = θ1 X1it + θ2 X2it + uit
5 Although exogenous, e(7)01t has no cross-sectional variation; thus, we exclude it from the candidates.
6 To this end, Feenstra (1994) uses a reference source k that supplies in every year, whereas Feenstra et al. (2018) use theSato-Vartia aggregate of N sources. Here, we use the arithmetic mean for simplicity.

5where Yit = (Pit )2 , X1it = (Sit )2 , X2it = Pit Sit , θ1 = −κ/γ, θ2 = (1 + γκ)/γ, and uit = −εit δit /γ. Since weknow by (6) that
X1it =(εit )2 + 2γεit δit + γ 2 (δit )2(1 + γκ)2X2it =

κ(εit )2 + (1 + γ)εit δit + γ(δit )2(1 + γκ)2

it is obvious that uit and both X1it and X2it in (7) are correlated.
In the Feenstra method, we take the temporal average of (7), i.e.,
Yi = θ1 X1i + θ2 X2i + ui
where, for example, ui =

(8)

PT

t=1 uit /Ti , and assume thatplim ui = plimTX

i = 1, · · · , N

uit /Ti = 0(9)T →∞ t=1

Notice that, in this case, the following must be true:i = 1, · · · , N

plim Xi ui = (plim Xi )(plim ui ) = 0(10)

Then, by (9) and (10), we can assert that the least squares estimator of (8) is consistent with the following
exposition:
PN
plim dcov (X, u) = plim

i=1 Xi ui − X̄

N −1

PN

i=1 ui=0

In the Feenstra method, equation (8) is estimated by weighted least squares (WLS) regression, with theweights being the number of years Ti that country i appears as a source during the observation period T .
Moreover, (8) is weighted further to improve efficiency. That is, the variance of the residuals from (7) isutilized to weight regression equation (8). This procedure, which is equivalent to the optimal weighting
in generalized method of moments (GMM) estimation, can be iterated to obtain more efficient estimates.
Below, we note σ (the microelasticity) and κ in terms of the parameters estimated by the Feenstra method:pp−θ2 ± (θ2 )2 + 4θ1
θ2 ∓ (θ2 )2 + 4θ1
1−σ =γ =
(11)
κ=
2θ1
2
For later convenience, we label these solutions as (γ1 , γ2 ) and (κ1 , κ2 ), respectively.
3.2. Empirical strategy
For the sake of convenience, instead of manually performing WLS regression of (8) using Ti and Ti /Vi as(i)weights, we take an alternative approach. Let akt for k = 1, · · · N denote N dummy variables (of dimension
N × T ) that indicate source country i = k at period t of the panel data. More specifically,
1 (if i = k and Yit =
6 0)
(i)
akt =
0 (otherwise)
If we use all N dummy variables to instrument the two explanatory variables for (7), the N moment
conditions for i = 1, . . . , N is reduced as follows:
N X
T
X

(i)

(Ykt − θ1 X1kt − θ2 X2kt )akt = (Yi − θ1 X1i − θ2 X2i )Ti = 0

k=1 t=1

6

PT PN
PT
PT PN
(i)
(i)
where t=1 k=1 Ykt akt = t=1 Yit = Yi Ti , Ti = t=1 k=1 akt and so on. That is, a pooled two-stage
least squares (2SLS) regression for (7) using all N dummy variables as instruments would yield the same
result as that derived from performing WLS regression for (8) using Ti as weights. Moreover, a pooled GMM
using all these instruments would yield the same result as that derived from performing WLS regression
using Ti /Vi as weights. Thus, by means of the Feenstra method, we use the latter scheme (by way of GMM)
to estimate the parameters θ1 and θ2 .
Furthermore, we might be tempted to consider an alternative version of the Feenstra method that takes
the cross-section average of (7), i.e.,
Yt = θ1 X1t + θ2 X2t + ut
where, for example, ut =

(12)

PN

i=1 uit /Nt , and assume thatplim ut = plimNX

t = 1, · · · , T

uit /Nt = 0(13)

N →∞ i=1

The same logic as that behind the the original time-averaged version can be applied to show the consistencyof the least squares estimate of (12). Moreover, by using the following T dummy variables of dimension
N × T , WLS regression is possible given the panel structure of the data.

1 (if k = t and Yit 6= 0)
(t)
bik =
0 (otherwise)
If we use all these variables to instrument the two regressors in pooled regression (7), we obtain the following
T moment conditions for t = 1, . . . , T :
T X
N
X

(t)

(Yik − θ1 X1ik − θ2 X2ik )bik = (Yt − θ1 X1t − θ2 X2t )Nt = 0

k=1 i=1PN
PT PN (t)(t)
where k=1 i=1 Yik bik = i=1 Yit = Yt Nt , Nt = k=1 i=1 bik and so on. In the following sections, inaddition to our scheme to perform the Feenstra method by way of N dummy variables a(1) , a(2) , · · · , a(N ) , weexamine the two-way Feenstra method by way of N +T dummy variables a(1) , a(2) , · · · , a(N ) , b(1) , b(2) , · · · , b(T )to impose the two moment conditions (9) and (13) at the same time.
PT

PN

3.3. Implicit IV and macroelasticity
As we assert that εit and δit of (6) are independent (and thus uncorrelated), and since δit is correlatedwith Pit through the supply function, δit must be a valid IV for the explanatory variable (Pit ) of the demand
function Sit = γPit + εit . We therefore call δit the implicit IV of the Feenstra method. Empirically, an∗
implicit IV (δit, defined below) can be extracted from the supply function parallel to (3) as follows:∗
ln pit = πt + κ ln sit + ωi + ξit = κ̂ ln sit + δit(14)∗
Since it does not enter πt or ωi while it directly enters ln sit through (3), δitmust be uncorrelated with it .
The implicit IV approach is beneficial when we consider the measurement of macroelasticity. The Feenstra
method heavily depends on the panel structure of the data, so estimation of the second-stage macroelasticity
when the cross-sectional dimension is two may be ineffective. Consequently, Feenstra et al. (2018) consider
a common macroelasticity over several commodities and not for each commodity.7 In contrast, just like thestandard IV approach, the IV approach using the implicit IV is capable of estimating the macroelasticity
for each commodity, and external instruments are not needed.

7 For the macroelasticity estimation, Feenstra et al. (2018) make use of the macro version of (7) with the variation of gt
instead of that of it simultaneously with the micro-macro combined moment conditions.

74. Data and estimation
4.1. Main variables
Our empirical analysis is aimed at measuring the micro- and macroelasticities for three kinds of commodities, namely, bovine (g = 1), swine (g = 2), and poultry (g = 3) meat exported to Japan. For thesecases, we were able to find valid external instruments to estimate the microelasticities. We set the period of
our analysis from 1994 to 2018 (i.e., t = 1, · · · , 25). As illustrated in Figure 1, Japan was long the world’s
largest meat importer: during this period, it imported all three kinds of meat from as many as N = 88
countries.We draw our main data from UN Comtrade (2020). The HS product codes for bovine meat correspond to HS0201, HS0202, HS020610, and HS020629; swine meat corresponds to HS0203, HS020630, andHS020649; and poultry meat corresponds to HS0207. We draw the yearly import transactions in terms of
the CIF trade value (USD) and net weight (kg) of the home country (Japan) from all partner countries
by setting Japan as the reporter, All as partners, and Import as trade flows. For each commodity g, theCIF price cit (USD/kg) is evaluated by means of the corresponding total CIF trade values divided by thecorresponding total net weight xit of the HS products from all partner countries for all periods concerned.
To obtain the foreign commodity price in the home country pit (JPY/kg), we need the exchange rateset (JPY/USD) against the home currency and tariff rates rit applied to all partner countries for all periods concerned. The exchange rates against all currencies eit were drawn from the historical rates tab
at fxtop.com. The tariff rates rit levied in the home country against any HS products from any partnercountries from 1996 to 2018 were obtained from the tariff download facility of WTO (2020). For the 1994
and 1995 tariff rates, however, we use the rate for 1996. The home country’s yearly expenditure on country
i’s commodity thus amounts to pit xit (JPY), and this is used to evaluate the expenditure share sit for the
regression analyses.
For domestic production pertaining to bovine and swine meat, the data were drawn from the Survey ofLivestock Distribution (Chikusanbutsu Ryutsu Tokei), available at e-Stat (2020). For yearly domestic meatproduction zt (kg), we use the survey on carcass (Edaniku) production of adult beef cattle (Seigyu) and pigs
(Buta). For domestic poultry meat, we use the yearly production (in metric tons) available in the surveyof broiler slaughterhouses (Shokucho Shorijo Chosa). For unavailable years, the amount of meat produced
is estimated by the ratio (60%) against the processed broilers measured in metric tons. 8 For domestic
prices rt (JPY/kg) of bovine and swine meat, we use the survey of central wholesale meat market prices(Shokuniku Chuo Oroshiuri Shijo Kakaku). For poultry meat prices, we use the 2015-based corporate goods
price index (CGPI) provided by BOJ (2020) for chicken (Tori).9
4.2. First-stage aggregator
Let us rewrite the regression equation (3) using time dummy variables as follows:
Yit = µ1 + (µ2 − µ1 ) D2 + · · · + (µ25 − µ1 ) D25 + µXit + ln αi + it(15)

where Yit = ln sit , Xit = ln pit and Dk , for k = 2, · · · , 25, denotes a dummy variable that equals 1 if k = t
and 0 otherwise. The coefficients therefore denote thatµt = −(1 − σ) ln qt

µ=1−σ

(16)

As we normalize the microaggregated prices at 1994 (i.e., q1 = 1 and thus µ1 = 0), the parameters µ andµt for t = 2, . . . , 25 can all be estimated by FE regression of (15), and hence, qt for t = 2, · · · , 25 can be
resolved by the following calculation:
qt = eµt /µt = 2, · · · , 25

8 The data for years in which figures for both processed broilers and poultry meat produced are available suggest that theratio is 60%.
9 The price index for poultry meat is identified as item PR01’PRCG15_2202050011. The 2015-based index is converted into
JPY using the 2015 representative wholesale price of poultry meat, which we estimated as 395 (JPY/kg).

8

Table 1: Microelasticity estimation for bovine meat.

FE (LS)FE (IV)

Delta Method
estim.

s.e.

σ
q25
q24
q23
q22
q21
q20
q19
q18
q17
q16
q15
q14
q13
q12
q11
q10
q9
q8
q7
q6
q5
q4
q3
q2
q1

2.710
1.304
1.315
1.303
1.358
0.986
1.247
1.166
0.999
0.894
0.618
1.444
1.493
1.649
1.349
1.049
0.351
0.595
0.468
0.534
0.650
0.807
0.860
0.693
0.775
1.000

0.272
0.364
0.374
0.375
0.413
0.294
0.399
0.405
0.347
0.322
0.212
0.473
0.492
0.533
0.434
0.351
0.141
0.200
0.155
0.151
0.202
0.231
0.246
0.202
0.220
.

obs.
347
330
F stat.
3.2 (0.000)
1.61 (0.036)— Tests for 2SLS estimation — tr20629, trall
Underidentification
Anderson LM statistic
Weak identification
Cragg-Donald Wald F statistic
Overidentifying restriction
Sargan statistic
Endogeneity
Davidson-MacKinnon F statistic

21.25510.4460.303
0.701(0.000)

X
D25
D24
D23
D22
D21
D20
D19
D18
D17
D16
D15
D14
D13
D12
D11
D10
D9
D8
D7
D6
D5
D4
D3
D2

coef.

s.e.

coef.

s.e.

−1.710
0.454
0.469
0.452
0.523
−0.0240.377
0.263−0.002−0.192−0.823
0.628
0.685
0.856
0.512
0.081
−1.791−0.888−1.300−1.072−0.736−0.367−0.258−0.628−0.436

0.272
0.477
0.480
0.488
0.513
0.510
0.544
0.589
0.594
0.619
0.596
0.549
0.549
0.537
0.551
0.572
0.615
0.560
0.545
0.491
0.532
0.486
0.490
0.495
0.477

−0.921
0.345
0.482
0.429
0.518
−0.182
0.390
0.421
0.276
0.043
−0.508
0.660
0.735
0.827
0.380
0.028
−1.853−0.859−1.168−0.769−0.556−0.365−0.186−0.523−0.487

0.993
0.482
0.467
0.476
0.499
0.531
0.529
0.604
0.669
0.666
0.694
0.535
0.537
0.523
0.558
0.560
0.602
0.545
0.553
0.603
0.561
0.473
0.484
0.498
0.468

(0.582)(0.402)

Notes: The numbers in parentheses are the p-values for rejecting the null hypotheses. Excluded instruments are thesum of all rates of tariffs on bovine meat, and tariff rate for HS20629. Based on the endogeneity test results, FE (LS) is
selected for delta method estimation.

The estimation results are summarized in Tables 1, 2, and 3 for bovine, swine, and poultry meat,
respectively. Below, let us briefly review the diagnostics regarding the 2SLS regression. The first two
tests are concerned with whether the instruments are relevant—that is, whether the instruments (e.g., Z)
are relevant predictors of the endogenous regressors (e.g., X). The corresponding statistic (the LM from
Anderson’s canonical correlation test) is used to assess the null hypothesis that the minimal canonicalcorrelations between X and Z are zero. The relevance of instruments is further examined by the weakidentification test. The rule of thumb for rejection of the null hypothesis that X are only weakly correlatedwith Z is for the first-stage (Cragg-Donald Wald) F statistic to exceed 10. The third test is concerned with
9

Table 2: Microelasticity estimation for swine meat.

FE (LS)FE (IV)

Delta Method
estim.

s.e.

σ
q25
q24
q23
q22
q21
q20
q19
q18
q17
q16
q15
q14
q13
q12
q11
q10
q9
q8
q7
q6
q5
q4
q3
q2
q1

7.657
1.005
1.009
0.981
1.011
0.968
0.922
0.981
0.890
0.967
0.881
0.921
1.041
0.965
0.953
1.083
1.091
1.129
0.974
0.974
0.922
0.906
1.097
1.085
0.976
1.000

1.401
0.075
0.076
0.074
0.077
0.072
0.071
0.076
0.070
0.076
0.072
0.072
0.081
0.074
0.075
0.083
0.088
0.095
0.083
0.073
0.072
0.072
0.085
0.089
0.083
.

obs.
492
464
F stat.
1.3 (0.157)
1.55 (0.045)— Tests for 2SLS estimation — lnxrall, L.xrall
Underidentification
Anderson LM statistic
Weak identification
Cragg-Donald Wald F statistic
Overidentifying restriction
Sargan statistic
Endogeneity
Davidson-MacKinnon F statistic

52.68528.191
0.005
11.528(0.000)

X
D25
D24
D23
D22
D21
D20
D19
D18
D17
D16
D15
D14
D13
D12
D11
D10
D9
D8
D7
D6
D5
D4
D3
D2

coef.

s.e.

coef.

s.e.

−1.656
0.754
0.733
0.578
0.739
0.537
0.228
0.603
0.030
0.511
−0.126
0.161
0.446
0.473
0.282
0.720
0.376
0.520
−0.117
0.518
0.223
0.181
0.694
0.296
0.050

0.433
0.428
0.428
0.428
0.436
0.422
0.429
0.445
0.429
0.446
0.429
0.429
0.439
0.437
0.436
0.438
0.447
0.484
0.441
0.412
0.431
0.428
0.432
0.432
0.440

−6.6570.032
0.059−0.1260.073−0.215−0.539−0.130−0.776−0.224−0.842−0.5500.269−0.239−0.318
0.531
0.579
0.806
−0.178−0.173−0.541−0.6540.614
0.541−0.160

1.401
0.498
0.499
0.498
0.506
0.495
0.500
0.516
0.502
0.517
0.504
0.502
0.536
0.509
0.511
0.535
0.582
0.621
0.550
0.494
0.506
0.508
0.550
0.595
0.551

(0.943)(0.001)

Notes: Excluded instruments are the log and first lag of exchange rates. Based on the endogeneity test results, FE (IV)is selected for delta method estimation.

the exogeneity of the instruments—that is, whether Z are uncorrelated with the error term (e.g., u). The
corresponding statistic (Sargan) examines the null hypothesis that Z are uncorrelated with the residuals ûgiven that at least one of the instruments is exogenous. The fourth test (endogeneity) is concerned with theendogeneity of the regressor—that is, whether X are correlated with u. The corresponding statistic (theDavidson-MacKinnon F) tests the endogeneity of the regressor in the fixed effects setting. A rejection of
the null hypothesis indicates that the instrumental variables fixed effects estimator should be employed.
According to the results obtained, the fixed effects instrumental variables (FE (IV)) estimation for allcases (bovine, swine, and poultry meat) are satisfactory with regard to the relevance and exogeneity of the
instruments used. Regarding the endogeneity test, the null hypothesis is rejected for swine and poultry meat,10

Table 3: Microelasticity estimation for poultry meat.

FE (LS)FE (IV)

Delta Method
estim.

s.e.

σ
q25
q24
q23
q22
q21
q20
q19
q18
q17
q16
q15
q14
q13
q12
q11
q10
q9
q8
q7
q6
q5
q4
q3
q2
q1

4.155
1.310
1.415
1.344
1.463
1.617
1.288
1.114
1.015
1.152
1.483
1.450
1.169
1.294
1.238
1.106
0.933
1.090
0.923
0.616
0.919
1.083
1.019
1.029
0.856
1.000

0.982
0.307
0.334
0.330
0.358
0.421
0.331
0.285
0.249
0.289
0.386
0.373
0.287
0.316
0.297
0.259
0.213
0.258
0.211
0.145
0.216
0.262
0.238
0.242
0.188
.

obs.
480
445
F stat.
0.68 (0.875)
0.71 (0.851)— Tests for 2SLS estimation — L.key, tr207
Underidentification
Anderson LM statistic
Weak identification
Cragg-Donald Wald F statistic
Overidentifying restriction
Sargan statistic
Endogeneity
Davidson-MacKinnon F statistic

21.22610.4811.078
14.266(0.000)

X
D25
D24
D23
D22
D21
D20
D19
D18
D17
D16
D15
D14
D13
D12
D11
D10
D9
D8
D7
D6
D5
D4
D3
D2

coef.

s.e.

coef.

s.e.

−0.321
0.386
0.406
0.762
0.487
0.599
0.328
0.595
−0.234
0.107
0.450
0.180
−0.057
0.486
0.642
0.577
0.152
0.387
−0.197−0.427−0.014
0.144
0.061
0.078
−0.333

0.166
0.502
0.503
0.501
0.524
0.568
0.566
0.541
0.536
0.550
0.572
0.572
0.536
0.515
0.488
0.464
0.474
0.491
0.477
0.494
0.495
0.512
0.490
0.493
0.441

−3.155
0.852
1.096
0.932
1.201
1.516
0.800
0.339
0.046
0.447
1.244
1.173
0.492
0.813
0.673
0.318
−0.2200.272−0.252−1.529−0.267
0.250
0.060
0.091
−0.492

0.982
0.745
0.769
0.737
0.790
0.854
0.814
0.786
0.776
0.797
0.847
0.870
0.791
0.758
0.727
0.717
0.731
0.734
0.719
0.838
0.748
0.760
0.736
0.740
0.695

(0.299)(0.000)Notes: Excluded instruments are the first lag of the variable ‘key’ (which is a concatenation of the year followed by the
ISO numeric country code) and tariff rate for HS207. Based on the endogeneity test results, FE (IV) is selected for delta
method estimation. However, overall the model is nonsignificant, according to the F statistic.

whereas it is not rejected for bovine meat. Correspondingly, the noninstrumented (FE (LS)) estimator is used
for the final assessment of σ̂ and q̂t via the delta method subject to (16) for bovine meat, while the FE (IV)estimator is employed for swine and poultry meat cases. Tariff rates turn out to be relevant instruments forbovine meat, and for swine meat, exchange rates are found to be relevant. These instruments, however, are
not relevant for poultry meat. The instrument (named ‘key’) that we use for poultry meat is a concatenationof year t and ISO numeric country code i, which we accidentally discovered to be relevant in this case.
Regarding the Feenstra method estimation, the result is summarized in Table 4. The parameters θ1
and θ2 of equation (8) are estimated by WLS using N dummy variables (a(i) , i = 1, · · · , N ) as described11

Table 4: Summary of Feenstra method estimation.

Bovine
γ1
κ1
γ2
κ2

Swine

Poultry

estim.

s.e.

estim.

s.e.

estim.

s.e.

−2.3730.030
32.922−0.421

0.137
0.004
3.822
0.024

−5.1850.067
14.876−0.193

1.069
0.019
4.217
0.040

−2.7950.160
6.262−0.358

0.663
0.030
1.167
0.085

Notes: The standard errors are obtained through the delta method via (11). In all cases, the relevant solution is γ1 sinceconcavity requires that σ = 1 − γ > 0. The slope of the supply function must therefore be κ1 .

Table 5: Summary of estimated microelasticities (σ).

BovineExternal IV
FeenstraTwo-way
Implicit IV

Swine

Poultry

estim.

s.e.

estim.

s.e.

estim.

s.e.

2.710
3.373
3.725
3.297

0.272
0.137
0.206
0.265

7.657
6.185
5.344
7.481

1.401
1.069
0.406
0.544

4.155
3.795
3.072
3.020

0.982
0.663
0.029
0.203

Notes: All external IV estimates are based on FE (IV) except for the bovine estimates, which are based on FE (LS). All
implicit IV estimates are based on FE (IV).

in section 3.2, and then the estimates for γ and κ by (11) are obtained by the delta method. Since γ1turns out to be a legitimate solution in all cases, where σ = 1 − γ > 0 must hold for concavity of theaggregator, the corresponding κ1 is used to extract the implicit IV in all cases. In Table 5, we summarize
the microelasticities estimated by way of all approaches considered in this study. Here, ‘External IV’ refers
to IV estimation by the external IV (such as tariffs and exchange rates), the results of which are shownin Tables 1, 2 and 3; ‘Feenstra’ refers to the Feenstra method based on the estimate of γ1 , the results ofwhich are shown in Table 4; ‘Two-way’ refers to the two-way Feenstra method as described in section 3.2;
and ‘Implicit IV’ refers to IV estimation by the implicit IV extracted from (14), using κ̂ = κ1 , in all cases.
Furthermore, the implicit IVs are relevant; thus, FE(IV) estimators are selected in all cases.10 Figures 2, 3,
and 4 show how the first-stage aggregates q̂t (the foreign meat price index) are estimated with the implicit
IVs and compared with those estimated by the external IVs.11
4.3. Second-stage aggregator
Let us rewrite the regression equation (4) for the macroelasticity estimation as follows:
Yt = µ0 + µXt + νt

(17)

where the parameters are denoted as µ0 = ln β − ln(1 − β) and µ = 1 − ρ. The response variable is the log
PN
ratio of cost shares for which we can use the observable data, i.e., Yt = ln rt zt − ln i=1 pit xit . On the other
hand, the explanatory variable in (4) includes the first-stage aggregate (or foreign price) qt , which in thiscase can be evaluated by the predicted value q̂t obtained from the first-stage regression.12 The explanatory
variable is therefore Xt = ln rt − ln q̂t . As noted in the previous section, we examine two sets of estimates
10 Tables not shown for brevity. In this case, the explanatory variable X is instrumented solely by δ ∗ .
itit
11 Note that the foreign meat price indices q̂ obtained by the external IV in Figures 2, 3 and 4 are taken from Tables 1, 2,
t

and 3.
12 We treat q̂ as stochastic like any other stochastic variable such as r , even when we know the variances.
t
t

12

1.50

Foreign bovine meat price index (Implicit IV)

Foreign bovine meat price index (Implicit IV)

1.50

1.25

1.00

0.75

0.50

1.25

1.00

0.75

0.50
1995

2000

2005

2010

2015

0.4

Year

0.8

1.2

1.6

Foreign bovine meat price index (External IV)

Figure 2: The foreign price index qt estimated by means of the implicit IV (left) and its comparison with the estimate basedon the external IV (right) for Japan’s bovine meat imports.

1.25

Foreign swine meat price index (Implicit IV)

Foreign swine meat price index (Implicit IV)

1.25

1.20

1.15

1.10

1.05

1.00

1.20

1.15

1.10

1.05

1.00

1995

2000

2005

2010

2015

0.90

Year

0.95

1.00

1.05

1.10

Foreign swine meat price index (External IV)

Figure 3: The foreign price index qt estimated by means of the implicit IV (left) and its comparison with the estimate basedon the external IV (right) for Japan’s swine meat imports.

of first-stage aggregators (q̂t , t = 1, · · · , T ), where one is obtained by the external IV and the other by the
implicit IV of the Feenstra method.
In regard to the time-series nature of regression equation (17), we first examine the stationarity of all
variables. We perform a unit root test on all variables in levels (Xt and Yt ) and first differences (∆Xtand ∆Yt ) based on augmented Dickey-Fuller statistics. The results (not shown for brevity) suggest that thevariables are nonstationary in levels but stationary in first differences in all cases. We therefore estimate (17)with first differences. Regarding the endogeneity problem, we use q̂t to instrument for Xt , as we describe
13Foreign poultry meat price index (Implicit IV)

Foreign poultry meat price index (Implicit IV)

1.6

1.5

1.0

1.4

1.2

1.0

0.8
1995

2000

2005

2010

2015

0.6

Year

0.8

1.0

1.2

1.4

1.6

Foreign poultry meat price index (External IV)

Figure 4: The foreign price index qt estimated by means of the implicit IV (left) and its comparison with the estimate basedon the external IV (right) for Japan’s poultry meat imports.
Table 6: Macroelasticity estimation for bovine meat (first-stage instrument: external IV).

OLS
∆X
const.

2SLS

Delta Method

coef.

s.e.

coef.

s.e.

estim.

s.e.

−0.225−0.006

0.129
0.030

−0.223−0.006

0.132
0.029

1.225

0.129

5.688
165.798
0.031
0.003

(0.058)

DW stat.
2.460
2.462
— Tests for 2SLS estimation — D.lnqib, L.lnqip
Underidentification
Anderson LM statistic
Weak identification
Cragg-Donald Wald F statistic
Overidentifying restriction
Sargan statistic
Endogeneity
Davidson-MacKinnon F statistic(0.861)(0.956)

Notes: Excluded instruments are the difference of the log of the first-stage aggregate and the first lag of the first-stage
aggregate for poultry meat. Based on the endogeneity test results, OLS is selected for delta method estimation.

earlier (in section 2.2). Tables 6, 7, and 8 show the estimation results using the first-stage aggregates
estimated by the external IV for bovine, swine, and poultry meat, respectively. Similarly, Tables 9, 10,
and 11 show the estimation results using the first-stage aggregates estimated by the implicit IV for bovine,
swine, and poultry meat, respectively. As we coordinate the estimates (in Table 12) with the first-stage
instruments used, we find that the two approaches yield similar results.
Our macroelasticity estimates are significantly smaller (less elastic) than those employed in the GTAP
database, which we also display in Table 12. The micro- and macroelasticity estimates for bovine meat(where the noninstrumented estimates are selected) indicate that the ‘rule of two,’ i.e., an assumption (madefollowing Corado and De Melo (1986)) that the macroelasticity should be roughly half the microelasticity,
may be in effect. However, this rule does not seem to be operative for the other cases (swine and poultrymeat), for which the instrumented estimates are selected. Finally, we find that for swine meat (of which
Japan was the world’s largest importer in the sample period), the microelasticity is large (with the most14

Table 7: Macroelasticity estimation for swine meat (first-stage instrument: external IV).

OLS
∆X
const.

2SLS

Delta Method

coef.

s.e.

coef.

s.e.

estim.

s.e.

0.402−0.024

0.131
0.024

0.656
−0.025

0.165
0.023

0.344

0.165

9.111
11.9
0.897
4.056

(0.011)

DW stat.
1.821
2.077
— Tests for 2SLS estimation — D.lnqis, D.lnqib
Underidentification
Anderson LM statistic
Weak identification
Cragg-Donald Wald F statistic
Overidentifying restriction
Sargan statistic
Endogeneity
Davidson-MacKinnon F statistic(0.344)(0.044)

Notes: Excluded instruments are the difference of the log of the first-stage aggregate and the difference of the log of thefirst-stage aggregate for bovine meat. Based on the endogeneity test results, 2SLS is selected for delta method estimation.

Table 8: Macroelasticity estimation for poultry meat (first-stage instrument: external IV).

OLS
∆X
const.

2SLS

Delta Method

coef.

s.e.

coef.

s.e.

estim.

s.e.

−0.118
0.014

0.217
0.035

0.190
0.015

0.194
0.036

0.810

0.194

6.827
38.4770.028
5.9(0.033)

DW stat.
2.559
2.770
— Tests for 2SLS estimation — D.lnqip, D.lnxrjpy
Underidentification
Anderson LM statistic
Weak identification
Cragg-Donald Wald F statistic
Overidentifying restriction
Sargan statistic
Endogeneity
Davidson-MacKinnon F statistic(0.867)(0.015)

Notes: Excluded instruments are the difference of the log of the first-stage aggregate and the difference of the log of theexchange rate (JPY/USD). Based on the endogeneity test results, 2SLS is selected for delta method estimation.

Table 9: Macroelasticity estimation for bovine meat (first-stage instrument: implicit IV).

OLS
∆X
const.

2SLS

Delta Method

coef.

s.e.

coef.

s.e.

estim.

s.e.

−0.263−0.006

0.180
0.031

−0.267−0.006

0.190
0.030

1.263

0.180

5.058
97.0750.006
0.008(0.080)

DW stat.
2.499
2.493
— Tests for 2SLS estimation — D.lnqib, D.lnqip
Underidentification
Anderson LM statistic
Weak identification
Cragg-Donald Wald F statistic
Overidentifying restriction
Sargan statistic
Endogeneity
Davidson-MacKinnon F statistic(0.938)(0.928)Notes: Excluded instruments are the difference of the log of the first-stage aggregate and the difference of the log of
the first-stage aggregate for poultry meat. Based on the endogeneity test results, OLS is selected for delta method
estimation.

15

Table 10: Macroelasticity estimation for swine meat (first-stage instrument: implicit IV).

OLS
∆X
const.

2SLS

Delta Method

coef.

s.e.

coef.

s.e.

estim.

s.e.

0.451−0.023

0.135
0.023

0.717
−0.022

0.185
0.023

0.283

0.185

9.718
12.9360.272
4.79(0.008)

DW stat.
1.971
2.293
— Tests for 2SLS estimation — D.lnqis, D.lnqib
Underidentification
Anderson LM statistic
Weak identification
Cragg-Donald Wald F statistic
Overidentifying restriction
Sargan statistic
Endogeneity
Davidson-MacKinnon F statistic(0.602)(0.029)Notes: Excluded instruments are the difference of the log of the first-stage aggregate and the difference of the log of thefirst-stage aggregate for bovine meat. Based on the endogeneity test results, 2SLS is selected for delta method estimation.

Table 11: Macroelasticity estimation for poultry meat (first-stage instrument: implicit IV).

OLS
∆X
const.

2SLS

Delta Method

coef.

s.e.

coef.

s.e.

estim.

s.e.

−0.107
0.014

0.171
0.035

0.072
0.015

0.152
0.035

0.928

0.152

8.444
68.0330.112
5.838(0.015)obs.
24
24
DW stat.
2.694
2.779
— Tests for 2SLS estimation — D.lnqip0, D.lnxrjpy
Underidentification
Anderson LM statistic
Weak identification
Cragg-Donald Wald F statistic
Overidentifying restriction
Sargan statistic
Endogeneity
Davidson-MacKinnon F statistic(0.738)(0.016)

Notes: Excluded instruments are the difference of the log of the first-stage aggregate and the difference of the log of theexchange rate (JPY/USD). Based on the endogeneity test results, 2SLS is selected for delta method estimation.

Table 12: Summary of estimated macroelasticities (ρ).

BovineExternal IV
Implicit IV
GTAP
macro
micro

Swine

Poultry

estim.

s.e.

estim.

s.e.

estim.

s.e.

1.225
1.263

0.129
0.180

0.344
0.283

0.165
0.185

0.810
0.928

0.194
0.152

Bovine meat products

Meat products nec.

3.85
7.70

4.40
8.80

Notes: For both external IV and implicit IV cases, bovine estimates are based on OLS. All other cases are based on
2SLS. The GTAP elasticities are taken from Hertel et al. (2007), where the microelasticities are evaluated by doubling
the estimates of the macroelasticities, following the ‘rule of two.’elastic response among the three kinds of meat), whereas the macroelasticity is small (with the least elastic
16

response among the three kinds of meat).
5. Application
5.1. Tariff elimination
Below, let us consider tariff elimination as a counterfactual scenario. Our purpose here is to evaluate
the potential shifts in foreign and domestic expenditures to assess the shifts in total expenditures for eachcommodity over the course of the counterfactual scenario. Tariff elimination reduces prices by the rate of
the tariff levied, i.e.,
ln p0it = ln pit − ln (1 + rit )All counterfactual variables are hereafter indicated by a prime. We then can evaluate the counterfactual
foreign aggregate price q̂t0 as follows:!
PN
0
i=1 pit xit
ln q̂t = ln q̂t − ln (1 + r̄t ) = ln q̂t − ln PN0
i=1 pit xit
where we call r̄t the effective tariff rate.13
Now, let us consider foreign utility shifts concerning foreign commodities. To do so, however, we need
the price elasticity of demand η so that we can evaluate the counterfactual shifts in foreign commodity
demand (y) by means of the shifts in the foreign commodity price (q). The elasticity can be estimated by
the following simple regression equation, with λt (the demand shock for the foreign commodity) being theerror term, which must be uncorrelated with the explanatory variable; we treat q̂t as exogenous with respect
to the demand shock.
ln ŷt = η0 + η ln q̂t + λt

(18)Here, the response variable is obtained with the following identity, in regard to (2):ln q̂t + ln ŷt = lnNX

pit xiti=1

We can use the estimates of parameters (i.e., η̂0 and η̂) to evaluate ŷt0 from q̂t0 . However, since (18) is likely
to be estimated by the differences of variables, in which event η0 is dropped from the estimation, we measure
yt0 relatively by means of the following identity:−1ln ŷt0 − ln ŷt = η̂ (ln q̂t0 − ln q̂t ) = η̂ ln (1 + r̄t )(19)

Next, let us consider the shifts in domestic commodity consumption zt . We know that the domestic/foreign expenditure ratios (ln rt zt − ln qt yt ) can be evaluated with the corresponding price ratios (ln rt − ln qt )by using the estimated parameters of regression (17). Counterfactual variables can also be evaluated withthe same function.
ln

rt ẑtrt= µ̂0 + µ̂ ln
q̂t ŷtq̂tln

rt ẑt0rt= µ̂0 + µ̂ ln 0q̂t0 ŷt0
q̂t

(20)

Note that the price of domestic commodity rt is assumed to be unaffected in the course of the counterfactual
scenario. We may then use the parameters (i.e., µ̂0 and µ̂) to evaluate ẑt0 from q̂t0 and ŷt0 . However, since (17)13 Since the share parameters α are dropped from the fixed effects regression, we opt to evaluate q̂ 0 with the total recordeditamount of the tariff levied.

17

Table 13: Tariff elasticity of expenditure for domestic and foreign commodities.

BovineSwine

Poultry

coef.

s.e.

coef.

s.e.

coef.

s.e.

∆ ln q̂const.

−1.116
0.011

0.131
0.031

−0.474
0.022

0.180
0.024

−0.644
0.005

0.210
0.047

ρ̂
ρ̂ + η̂
1 + η̂
1 + ρ̂ + 2η̂

1.225
0.109
−0.116−0.0070.344−0.131
0.526
0.395

0.810
0.166
0.356
0.522

Notes: The first row (i.e., as coefficients for ∆ ln q̂) shows the estimates of the tariff elasticity of demand for a foreigncommodity η. The estimates of the macroelasticity (foreign-domestic substitution elasticity ρ̂) based on the external IV
are statistically significant in all cases, and they are repeated from Table 12.

is likely to be estimated by the differences of variables, in which event µ0 is dropped from the estimation,
we measure ẑt0 relatively by means of the following identity based on (20):ln ẑt0 − ln ẑt = (1 − µ̂) (ln q̂t0 − ln q̂t ) + (ln ŷt0 − ln ŷt )(21)

In regard to (19, 21) and taking the fact that ρ̂ = 1 − µ̂ into account, we have:ln ẑt0 − ln ẑt = (η̂ + ρ̂) (ln q̂t0 − ln q̂t ) = (η̂ + ρ̂) ln (1 + r̄t )

−1

(22)

We may then evaluate the counterfactual expenditure change by using (19, 22) as follows:0ln (vt ut ) − ln (vt ut ) = ln (rt ẑt0 ) − ln (rt ẑt ) + ln (q̂t0 ŷt0 ) − ln (q̂t ŷt )= (η̂ + ρ̂) ln (1 + r̄t )−1−1+ (1 + η̂) ln (1 + r̄t )Correspondingly, (η̂ + ρ̂) denotes the tariff elasticity of expenditure for a domestic commodity, whereas(η̂ + 1) denotes the tariff elasticity of expenditure for a foreign commodity.
5.2. Tariff elasticity and tariff elimination
In regard to the time series nature of regression equation (18), we first examine the stationarity of all
variables. We perform a unit root test on all variables in levels (ln q̂t and ln ŷt ) and first differences (∆ ln q̂tand ∆ ln ŷt ) based on augmented Dickey-Fuller statistics. The results (not shown for brevity) suggest thatthe variables are nonstationary in levels but stationary in first differences in all cases. We therefore estimate
the parameters of the regression equation (18) with the first differences. The results are provided in Table
13. As expected, the estimates of the tariff elasticity of demand for a foreign commodity η̂ are all negative
and are statistically significant. Additionally, as expected, the corresponding standard errors indicate thatthe intercepts are essentially zero in all cases.
Table 13 summarizes the various tariff elasticities of expenditure in the home country. 14 For bovine
meat, a positive tariff elasticity of domestic commodity expenditure (ρ̂ + η̂ > 0) and negative tariff elasticity
of foreign commodity expenditure (1 + η̂ < 0) indicate that tariff elimination would decrease domestic
and increase foreign commodity expenditure, and this is indeed reflected in Figure 5. For swine meat, anegative tariff elasticity of domestic commodity expenditure (ρ̂ + η̂ < 0) and positive tariff elasticity of
14 To clarify, we note that if 1+ η̂ > 0, then a tariff increases (tariff elimination decreases) expenditure for a foreign commodity
more; and if 1 + η̂ < 0, then a tariff decreases (tariff elimination increases) expenditure for a foreign commodity more. Similarly,
if η̂ + ρ̂ > 0, then tariff increases (tariff elimination decreases) expenditure for a domestic commodity more; and if η̂ + ρ̂ < 0,then a tariff decreases (tariff elimination increases) expenditure for a domestic commodity more.

18

Foreign bovine meat expenditure (BJPY)

Domestic bovine meat expenditure (BJPY)

600

900

800

700

500

400

600
300

1995

2000

2005

2010

2015

1995

2000

Year

2005

2010

2015

Year

Figure 5: Factual and counterfactual expenditures for domestic (left) and foreign (right) bovine meat. Dotted lines indicate
counterfactual expenditures under tariff elimination.

500

Foreign swine meat expenditure (BJPY)

Domestic swine meat expenditure (BJPY)

650

600

550

500

450

400

350

300
450
1995

2000

2005

2010

2015

1995

Year

2000

2005

2010

2015

Year

Figure 6: Factual and counterfactual expenditures on domestic (left) and foreign (right) swine meat. Dotted lines indicate
counterfactual expenditures under tariff elimination.

foreign commodity expenditure (1 + η̂ > 0) indicate that tariff elimination would increase domestic anddecrease foreign commodity expenditure, and this is reflected in Figure 6. For swine meat, a positive tariffelasticity of domestic commodity expenditure (ρ̂ + η̂ > 0) and positive tariff elasticity of foreign commodity
expenditure (1 + η̂ > 0) indicate that tariff elimination would decrease domestic and foreign commodity
expenditure, and this is reflected in Figure 7. Finally, by looking at the tariff elasticity of overall expenditure(1 + ρ̂ + 2η̂), we see that tariff elimination would increase expenditure for bovine meat, whereas for swine
and poultry meat, expenditure would decrease.
19Foreign poultry meat expenditure (BJPY)

Domestic poultry meat expenditure (BJPY)

700

600

500

150

125

100

400
1995

2000

2005

2010

2015

1995

Year

2000

2005

2010

2015

Year

Figure 7: Factual and counterfactual expenditures for domestic (left) and foreign (right) poultry meat. Dotted lines indicate
counterfactual expenditures under tariff elimination.

6. Concluding Remarks
Finding relevant instruments is generally an exacting task. As a matter of fact, it was only by luckthat we were able to discover an external instrument that was sufficiently relevant to conduct the firststage microelasticity estimation for poultry meat. Thus, if an alternative method exists that does not
involve finding i nstruments a nd i s s till c apable o f y ielding s imilar r esults t o t he p rimary o nes, w e would
choose the alternative. The problem is that we cannot judge whether the alternative method is credible
unless we find r elevant i nstruments f or u se a s t he p rimary m ethod. F or i ts p art, t he F eenstra method
employs an assumption so that the estimator maintains consistency. Fortunately, we were able to findrelevant instruments for the three cases (the bovine, swine and poultry meat imports of Japan), and thetwo methods converged to similar results for the first-stage m icroelasticity estimation.
The similarity of the results led us to investigate the potential compatibility of the implicit IV that was
effectively at work within the Feenstra method estimation with the external IV that we found sufficiently
relevant. To extract the implicit IV of the Feenstra method from the data, we utilized the slope parameterof the reverse (supply) function obtainable from the Feenstra method estimation. The advantage of applying
IVs (regardless of whether they are external or implicit) for the first-stage fi xed eff ects re gression is thatthe first-stage a ggregate i s n ot o nly f ed i nto b ut a lso u tilized t o i nstrument t he e xplanatory v ariable ofthe second-stage regression. In this sense, implicit IV extraction and utilization complement the Feenstra
method’s capability of evaluating macroelasticities and still help us avoid the need to find relevant external
instruments.

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