Global COE Hi-Stat Discussion Paper Series 245

Research Unit for Statisticaland Empirical Analysis in Social Sciences (Hi-Stat)

Exaggerated Death of Distance:
Revisiting Distance Effects on
Regional Price Dispersions

Hi-Stat Discussion Paper

Kazuko Kano
Takashi Kano
Kazutaka Takechi

October 2012

Hi-Stat
Institute of Economic Research
Hitotsubashi University
2-1 Naka, Kunitatchi Tokyo, 186-8601 Japan
http://gcoe.ier.hit-u.ac.jp

Exaggerated Death of Distance:
Revisiting Distance Effects on Regional Price Dispersions

Kazuko Kano

Takashi Kano†

Kazutaka Takechi

Graduate School of Economics
The University of Tokyo
Hongo 7-3-1, Bunkyo-ku
Tokyo, 113-0033, Japan
Tel: +81-3-5841-1746
Fax: +81-3-5841-1747
Email: kkano@e.u-tokyo.ac.jp

Graduate School of Economics
Hitotsubashi University
2-1 Naka, Kunitachi
Tokyo, 186-8601, Japan
Tel: +81-42-580-8283
Fax: +81-42-580-8283
Email: tkano@econ.hit-u.ac.jp

Faculty of Economics
Hosei University
4342 Aihara-machi, Machida-shi
Tokyo, 194-0298, Japan
Tel: +81-42-783-2566
Fax: +81-42-783-2611
Email: ktakechi@hosei.ac.jp

Current Draft: September 26, 2012
Abstract
This paper empirically establishes the significant roles of transport costs in price dispersions acrossregions. We identify and estimate the iceberg-type distance-elastic transport costs as a parameter ofa structural model of cross-regional price differentials featuring product delivery decisions. Utilizing
a data set of wholesale prices and product delivery patterns of agricultural products in Japan, ourstructural estimation approach finds large distance elasticities of the transport costs. The result
confirms that geographical barriers are an economically significant contributor to the failures of thelaw of one price.
Key Words : Law of one price; Regional price dispersion; Transport cost; Geographical distance;
Agricultural wholesale price; Sample-selection bias
JEL Classification Number : F11, F14, F41†

Corresponding author.

1.

Introduction

Recent years have witnessed the increased roles of trade costs in international macroeconomics. Highlighting the microfoundations of international trade patterns and geographical market segmentations with trade costs, careful calibration studies deepen our understanding of puzzling data characteristics in international macroeconomics.1
This paper empirically establishes the significant roles of transport costs, which are
the major component of trade costs, in price dispersions across regions. Utilizing a data set ofprice differentials and product delivery patterns across regions, we identify and estimate thedistance-elastic transport costs as a parameter of a structural model. The previous reducedform regression studies treat the data associations between price differential and distanceas a proxy of transport costs liberally, as in Rogers and Jenkins (1995), Engel and Rogers(1996), Engel and Rogers (2001), and Crucini et al.(2010). To the contrary, our structural
estimation approach econometrically extracts the unobservable size of the transport costs
from the reduced-form data associations in our data set.2 The resulting structural estimateof the distance elasticity of transport costs evaluates an implicit price of the geographicalbarrier between the segmented markets. Our estimation of a “price of distance,” indeed,is the first attempt to parse out structurally different potential contributors to the crossregional price dispersions.
According to Anderson and van Wincoop (2004), trade costs in general consist of two
categories: costs imposed by policies (e.g., tariffs, quotas, and the like) and costs imposedby the environment (e.g., transportation, insurance against various hazards, and time costs).
Except for the extensive work by Hummels (1999), the direct measures of both categories
are scarce and inaccurate. The empirical task of probing trade costs, therefore, largely relies
on indirect econometric inferences from the measurements of equilibrium prices and quantities. Particularly in the field of international macroeconomics, the most common method
1

Obstfeld and Rogoff (2001) point out trade costs as a central factor to explain six major puzzles inopen-economy macroeconomics. Utilizing trade costs to motivate entry and exit behavior of heterogenous
firms in export markets, Ghironi and Melitz (2005) provide a microfounded explanation for the HarrodBalassa-Samuelson effect. Allowing for the distribution of trade costs over goods, Bergin and Glick (2009)
endogenously determine the tradedness of goods in a small open-economy model. The resulting endogenous
share of non-traded goods in the consumer price index accounts for the empirically observed low volatility
in the relative price of non-traded goods. Atkeson and Burstein (2008) show that trade costs are essential to pricing-to-market behaviors of firms with variable markups in an open-economy model of imperfectcompetitive markets.
2
Our structural estimate is a cousin of those identified in recent works by Crozet and Koenig (2010) andBalistreri et al.(2011) who use structural gravity models of international trade. Our approach, however, isquite different from theirs.

1

of inferring trade costs exploits the hypothesis of the law of one price (LOP) because trade
costs are recognized to be the main obstacles to the perfect arbitrage of goods across regions. To approach the hypothesis, previous studies scrutinize disaggregate consumer prices,which are surveyed internationally as well as domestically across retail stores. In addition
to the well-known violations of the LOP, one of the most robust findings across the previous reduced-form regression exercises is the statistically significant effects of geographicaldistance on the absolute levels or the times-series variances of the cross-regional price differentials.3 Because distance is used as a liberal proxy for the transport costs, the empiricallysignificant distance effects in the price differentials are suggestive, but still indecisive, evidence for transport costs as a major contributor to the LOP violations. There are at least
three concerns.
The first concern relates to the measurement of transport costs. As argued by Engeland Rogers (1996) and Engel et al.(2005), the dependence of consumer price differentials
on the distance observed in the reduced-form regressions is a mixture of several mutually
exclusive effects: it reflects not only the transport costs but also other factors such as thegeographical differences in the local distributional costs and the heterogeneous markups due
to a home bias in preferences. The second concern regards the economic significance ofthe transport costs in the price differentials. Many of the past studies estimate that theelasticity of the price differential with respect to distance is less than 3%.4 This small
estimate for the distance elasticity of the price differential requires an unrealistically large
degree of geographical scattering of sampling points (i.e., retail stores in cities) to explain
the observed degree of price dispersions alone.5 This observation naturally casts doubt on
3

A not-exhaustive list of studies that conduct gravity-type regressions contains Engel and Rogers (1996),
Parsley and Wei (1995), Broda and Weinstein (2008), Engel et al. (2005), Ceglowski (2003), Crucini at al.
(2010), and Baba (2007).
4
Among a series of past studies, for example, Broda and Weinstein (2008) observe the 1.2% distanceelasticity of the absolute log price differentials within the barcode-level scanner data of retail prices acrossCanadian and U.S. cities. Engel et al. (2005) find the distance elasticity of 0.32% with pooled annual
panel data distributed by the Economic Intelligence Unit (EIU) that covers retail prices of 100 consumer
goods surveyed in 17 Canadian and U.S. cities. Ceglowski (2003) reports 1.6-2.0% estimates for the distanceelasticities of 45 different products across 25 Canadian cities. Baba (2007) scrutinizes Japanese and Koreanretail price survey data and estimates less than approximately 3% of the distance elasticity after taking into
account a border dummy between the two countries.
5
Because the standard deviation of the absolute value of the log price differential is typically reported at
approximately 20% in this literature, we need a standard deviation of the log of distance of 6.66 to explain theobserved degree of regional price dispersions only by geographical distance. The required standard deviationof the log of distance, however, is too large to be consistent with the actual degree for the geographicalscattering of cities. For instance, the standard deviation of the log of distance between two prefectural
capital cities in Japan is 0.803 over all of the 1081 city-pairs from 47 prefectures.

2

defining the transport costs as a main economic source for the cross-regional price dispersions:distance is empirically “dead” as a prime suspect for the commonly observed violations of
the LOP.
Lastly, this economically subtle distance effect on the price differentials appears tobe sharply inconsistent with the indirect econometric inferences from equilibrium trade volumes. Past empirical studies in international trade unambiguously recognize that distanceplays an economically crucial role in determining bilateral trade volumes. Anderson andvan Wincoop (2003) estimate a gravity model of bilateral trade volumes and infer that the
distance elasticity of transport costs is approximately 20% conditional on a conventional
calibration of the elasticity of substitution. Helpman et al.(2008) find that the distance elasticity of bilateral export volumes is approximately 80%, taking account of firms’ selections
into bilateral export markets with firm heterogeneity in productivity.6 Importantly, theirestimate suggests a 20% distance elasticity of transport costs under the same calibrationof the elasticity of substitution as that used in Anderson and van Wincoop (2003). Why
is our inference of the distance elasticity of transport costs widely diverse, at between approximately 3% and 20% when using data of equilibrium prices and quantities, respectively?
This question is a serious challenge for the students of international economics who admit
the importance of trade costs.
We incorporate the above concerns into our inferences on the effects of transport
costs on price dispersions. In so doing, we investigate a unique daily data set of wholesale
prices of agricultural products in Japan.7 Following the spirit of Parsley and Wei (1996), we
use disaggregate price data within a country to avoid any potential effects of cross-country
differences in tax, tariff, quota, and currency on our inference on transport costs. Scrutinizing
the information of wholesale prices helps us overcome the first concern: we make our estimateof transport costs immune to the influences of local distributional costs as well as to the local
retailers’ pricing strategies.8
More importantly, there are two outstanding characteristics of our data set. First,
6

Indeed, this size for the distance effects on export volumes is common in the literature of empirical
trade. For example, in their meta analysis based on 1,051 past estimates of distance effects, Disdier andHead (2008) report the average of 0.893.
7This is not the first paper that intensively scrutinizes price data of agricultural products in the literatureof the LOP and PPP. Midrigan (2007) employs the prices of agricultural products sold in open-air markets
in European countries to test the theoretical implications of his state-dependent pricing model with trade
costs.
8
As pointed out by the editor Charles Engel, our inferences from the wholesale prices are still not immune
to the influence of the cross-regional heterogeneity of markups. We empirically control for these effects byregional fixed effects in our estimation exercise.

3

we can identify the wholesale prices of an identical product at both the producing and theconsuming regions. The first characteristic is essential for identifying the transport costs
because, as discussed by Anderson and van Wincoop (2004), only when the source region ofa product is identified, can the correct information for the transport costs be extracted fromthe relative prices at the consuming regions to the corresponding source region. The maindifficulty that past studies face is the fact that a retail price survey at retail stores rarely
provides information on the source regions of a product and the market prices prevailed
in these regions. Our data set, on the other hand, shows us not only in which regions inJapan a variety of fruits and vegetables are produced but also at what wholesale prices theseproducts are sold in their originated regions.9
The second outstanding characteristic of our data set is the provision of informationon the daily delivery patterns of an identical product from the source region to the final
consuming regions. This data aspect empirically shows us how far a product is deliveredfrom the source region. In this paper, we build a structural model to explain the observed
patterns of product delivery, and we claim theoretically that ignoring the underlying choiceof delivery might result in a serious bias toward our inference on the role of distance in crossregional price differentials. Because the price of the product at a consuming region is observed
only when a product delivery occurs, an inference drawn only from the information of pricedifferentials could be subject to a sample-selection bias due to an incidental truncation.
In particular, the direction of the potential bias should be downward because a rise in
the unobservable component of transport costs in general increases a price differential but
simultaneously deteriorates the probability of delivery.
Following Melitz (2003) and Helpman et al.(2008), we build a simple structural modelof cross-regional product-delivery in which cross-regional price differentials and delivery patterns are jointly determined by the same structure of transport costs.10 We then show that9

In a recent paper, Inanc and Zachariadis (2010) identify the source regions of products reported in theEurostat survey in several indirect ways and find approximately 10% distance elasticity of price differentials
in the 1990 survey. This finding could be indirect evidence that the identification of the origin of a productis essential for the inference of transportation costs. A more direct identification of source regions is taken
by Donaldson (2010) who scrutinizes the cross-regional data for prices of salt in North India during the
British colonial period. In his paper, the source regions of salt are identified because salt was produced
only in several licensed districts in India. He observes approximately 24% distance elasticity of the pricedifferentials of salts.
10
Closely related to this paper, Johnson (2010) investigates the implications of the model of Helpman etal. (2008) on the aggregate sectoral export prices. He exploits the model’s implications on f.o.b. export
prices to improve the statistical inferences on the role of firms’ heterogeneity in the intensive and extensive
margins of international trades. Using f.o.b. export prices, however, means that his econometrics exercise issilent about the distance effects on price differentials across countries or regions.

4the degree of the sample-selection bias depends critically on two structural parameters ofthe model: the elasticity of transport costs to distance and that of substitution. Our theoretical analysis implies that drawing a correct inference on transport costs requires us toestimate these two elasticities jointly. To do so, we propose a structural sample-selection
model, which consists of the price differential and the sample-selection equations, imposing
nonlinear theoretical restrictions on the joint probability distribution of data. We develop a
full information maximum likelihood (FIML) estimator incorporating instrumental variables
for the empirical model.
We estimate our sample-selection model by FIML using the data for wholesale pricesof several selected vegetables. The estimated sample-selection model passes two diagnostic
criteria in that it does a fairly good job in replicating the actual delivery patterns of thesevegetables and the actual data association of the price differentials with distances. More
importantly, the resulting estimates resolve the second and third concerns. We find large
estimates for the distance elasticity of transport costs across all of the vegetables relative tothe existing estimates in the LOP literature: all of them are over 20% and their average isapproximately 24%. The estimate of this paper, therefore, implies an economically significant
role of transport costs in cross-regional price differentials. Moreover, this size of the estimateof the distance elasticity of transport costs is fairly consistent with those identified by theinternational trade models that explain equilibrium trade volumes.
The organization of the rest of this paper is as follows. In the next section, we
introduce our model and derive our FIML estimator based on the corresponding sampleselection model. Section 3 describes our data set. After reporting the empirical results in
section 4, we conclude in section 5.

2.

Model and empirical framework

2.1. A model of cross-regional product delivery
The empirical analysis of this paper relies on a model of monopolistic competitive
firms as observed in Melitz (2003) and Helpman et al. (2008). In our model, a country
consists of distinct consuming regions indexed by i = 1, 2, · · · , I. Each region i is endowedwith a representative household who consumes a continuum of agricultural products (such as
cabbages, carrots, potatoes, and so on) by purchasing them at the regional wholesale market.
Agricultural products are indexed by l ∈ [0, 1]. Each product l is produced in distinct source
regions indexed by j = 1, 2, · · · , J. Source region j delivers its product to the wholesale
5markets in the same region j and in consuming regions i 6= j when the product delivery is
expected to be profitable.
The representative household in consuming region i differentiates product l over the
distinct source regions with an imperfect degree of substitution. Let xijl denote the demandof region i for product l that is produced in and delivered from region j. The representative
household in region i then earns its utility from consuming product l with the following
constant elastic utility function
xil =

Z

αl

(δijl xijl ) dj
j∈Bil

1/αl

,

0 < αl < 1,

where Bil is the set of source regions that deliver product l to consuming region i. Thisutility function specific to product l shows that the representative household in region irecognizes product l, if it is produced in different source regions, as different products:
the substitution of product l across distinct source regions is imperfect with the constantelasticity l ≡ 1/(1 − αl ) > 1. Term δijl reflects the household’s biased preference fordifferent producing regions: the greater the term δijl , the more the household in region iprefers product l from source region j relative to those from other source regions, ceterisparibus. The above utility function then derives region i’s demand function for product ldelivered from source region j under the price pijl
xijl =



pijl
pil

−l

l −1
δijl
xil ,

(1)

R
where pil ≡ [ j∈Bil (δijl pijl )1−l dj]1/(1−l ) is the average (i.e., aggregate) price level of productl in consuming region i.
A producer in region j is a monopolistically competitive producer at the wholesalemarkets in its own region as well as in the other regions to deliver. As specified by Helpman
et al. (2008), a producer in region j yields a unit of an agricultural product paying costs thatminimize a bundle of factor inputs. The marginal cost of producing product l is denotedby cj al , where al measures the number of bundles of factor inputs used per unit output of
product l, and cj measures the unit cost of this bundle of factor inputs. Notice that alis product-specific while cj is region-specific. This means that the efficient combination of
inputs for producing a product is common across regions, while factor costs are different
across regions.
We assume that a producer in a region does not need to bear any transport costs
when selling its product at the wholesale market in the same region. Hence, at the wholesalemarket in region j, the producer of product l, who faces the demand function (1), maximizes
6profits by charging a markup price. However, if the same producer seeks to sell its product at
the wholesale market in distinct consuming region i 6= j, two types of delivery costs should
be borne by the producer: a fixed cost of serving the market in region i, denoted by cj fij ,and an iceberg-type transport cost, denoted by τijl . As in Helpman et al. (2008), no fixedor transport costs are required for a delivery to the local wholesale market: f jjl = 0 andτjjl = 1 for any j. However, a producer in source region j needs to bear positive fixed andtransport costs: fijl > 0 and τijl > 1 for i 6= j. The optimal markup price, then, ispijl = τijl

cj a l.
αl(2)

In this case, the operating profits of delivering product l to region i is1−l
τijl cj
1−lπijl = (1 − αl )
θijl
pil xil − cj fijl ,αl pilwhere θijl ≡ al /δijl is the ratio of the productivity level to the producing regional bias. If
the producer in region j sells its product l at the local wholesale market, the corresponding
monopolistic profit πjjl is always positive. However, delivering the same product to anotherconsuming region i is profitable only if θijl is smaller than a threshold θ̄ijl , where θ̄ijl isdefined by the zero profit condition,1−lτijl cj1−l(1 − αl )θ̄ijlpil xil = cj fijl .
(3)
αl pilLet Tijl denote an indicator function that takes either the value of one if there is a deliveryof product l from source region j to consuming region i or the value of zero if there is nodelivery. The above determination of threshold (3) then implies1 if θ < θ̄ ,ijl
ijl
Tijl =(4)
0 otherwise.

Therefore, equations (3) and (4) describe the decision mechanism for a profitable delivery.
Optimal price (2) implies that a price differential of an identical product between
the source and the consuming regions provides a precise identification of transport cost τ ijl .
Let qijl denote the log of the price differential of product l between the producing and theconsuming regions j and i: qijl ≡ ln pijl − ln pjjl . Then, optimal price (2) and delivery
decision mechanism (4) together yield the price differential equation
qijl = ln τijl ,only if Tijl = 1.
7

(5)

Price differential equation (5) has two important empirical implications. First, transport
cost τijl can be measured from the corresponding price differential only when we can identify
the prices in the source and the consuming regions. This is the argument made by Anderson
and van Wincoop (2004) against the conventional approach to measuring trade costs in theliterature on regional and cross-country price dispersions. The second implication, however,says that identifying the source and the consuming regions is not enough for a precise estimation of the transport costs. Equation (5) shows that there is an incidental truncation or
sample section: we can observe the price differential of product l between the source and theconsuming regions only when the product is indeed delivered from the former region to thelatter. Hence, the sample is non-randomly selected by the selection mechanism of (4). This
selection mechanism depends on transport cost τijl through the threshold characterized byequation (3). Therefore, transport cost τijl in equation (5) could be inconsistently estimatedunless we take sample-selection mechanism (4) explicitly into account.
An important caveat of the above identification of transport costs stems from productarbitrage among distinct wholesale markets. With cross-market product arbitrage, a pricedifferential (5) might not be a sufficient statistic for the underlying transport cost because
the observed equilibrium price in a consuming region can deviate from the optimal price (2).
In this paper, we do not impose a no-arbitrage condition on our data as a restriction of ourmodel a priori. However, as we discuss in more detail in the next section, the amount of
product transfers across the wholesale markets of agricultural products is quite small relative
to the total amount of wholesale transactions in Japan. We interpret this fact as meaningthat there is almost no opportunity for product arbitrage in the equilibrium wholesale prices
in our data set. We simply control for any possible effects of product arbitrage on the pricedifferentials by adding an i.i.d. zero-mean random error to the price differential equation(5).112.2. The empirical framework
Given the structural model, we now discuss our empirical framework. Following
Helpman et al.(2008), we parametrically specify transport cost τijl byγlτijl = Dij
exp(µl + uijl ),2uijl ∼ N (0, σu,l),where Dij represents the symmetric distance between regions i and j, γl exhibits the distanceelasticity of the transport cost, and uijl is an i.i.d. unobserved region-pair specific part of the11

Atkeson and Burstein (2008) also discuss the possibility of international product arbitrage in their twocountry general equilibrium model with imperfect competition and trade costs. They report that productarbitrage plays almost no role in their quantitative simulation results. Therefore, our data set shares thesame characteristic of product arbitrage as in their simulation exercise.

8

transport cost. The positive constant µl > 0 confirms that the transport cost always takes
a value greater than 1 for all (i, j) pairs. We further assume that the fixed cost of delivery,
fijl , is stochastic due to an i.i.d. unobserved regional-pair specific element vijl . Just as in
Helpman et al. (2008), we exploit a parametric specification of fijl :fijl = exp(λjl + λil − vijl ),2vijl ∼ N (0, σv,l),where λil and λjl are consuming and producing regional specific constants. vijl is assumed
to be uncorrelated with uijl .
The product delivery choice is characterized as follows. Define a latent variable Z ijl
h
i1−l
τ c
1−l
(1 − αl ) αijll piljθijl
pil xil
Zijl =.
cj fijl
According to zero profit condition (3), product l is delivered from region j to region i only
if Zijl is greater than 1. The logarithm of Zijl , denoted by zijl ≡ log Zijl , then iszijl = βl − (l − 1)γl dij + l ln pil + ln xil + ξjl + λil − %ijl + ηijl ,2
ηijl ∼ N (0, ση,l),(6)where βl ≡ ln(1 − αl ) + (l − 1) ln αl + (1 − l )µl + (1 − l ) ln al , ξjl ≡ −l ln cj − λjl , and%ijl ≡ (1 − l ) ln δijl . In particular, disturbance ηijl is given as a linear combination of theunobserved components of the transport and the fixed costs, ηijl = (1 − l )uijl + vijl , with the222variance ση,l= (1 − l )2 σu,l
+ σv,l. Notice that the delivery of product l occurs from source
region j to consuming region i and the corresponding price differential is selected into thesample only when zijl > 0. We thus call equation (6) the selection equation below. Pricedifferential (5), in turn, is rewritten as
qijl = µl + γl dij + uijl ,only if zijl > 0.

(7)

Disturbances ηijl and uijl of the selection and price differential equations (6) and (7) are(1−l )σu,l< 0 because l > 1.
correlated negatively with the correlation coefficient ρl ≡ √2
2 2(1−l ) σu,l +σv,lSelection and price differential equations (6) and (7) jointly reveal two critical aspects when identifying the distance elasticity of the transport cost, γl . First, estimating
γl respecting only price differential equation (7) might lead to an under-biased inference.
Our model explains the joint distribution of the price differential and the distance by two
economic mechanisms. The first one, which is captured by price differential equation (7), is
an intensive margin effect of distance: the longer the delivery distance is, the wider the pricedifferential between the source and the consuming regions due to the greater transport cost.
The second one is an extensive margin effect of distance. A negative correlation between
9the disturbances of the two equations, ηijl and uijl , implies that, given the delivery distance
between the source and the consuming regions, a product having a higher price at the finaldestination due to a greater unobservable factor of the transport cost tends not to be delivered to the consuming region. The intensive and the extensive margin effects then meanthat only data points with relatively smaller price differentials, which correspond to shorter
delivery distances and/or smaller unobservable factors of the transport costs, are likely to be
selected into the sample. If we estimate price differential equation (7) with such a truncatedsample, we obtain an under-biased estimate of distance elasticity γl .12
Second, the severity of the under-biasedness depends crucially on the elasticity of substitution, l . As shown by the correlation coefficient ρl , the degree of the negative correlation
between two disturbances uijl and ηijl relies on the size of the elasticity of substitution, which
the model restricts to being less than 1. In particular, notice that there is no correlation
under the unit elasticity of substitution. Only in this special case, can we obtain an unbiased
estimate of the distance elasticity estimating the price differential equation alone. This isbecause the distribution of the price differentials becomes independent with the underlying
product delivery decision. Moreover, the distance effect on the delivery choice depends on
both the distance elasticity and the elasticity of substitution in a nonlinear way. Selection
equation (6) shows that the sensitivity of the delivery choice with respect to distance isnonlinearly associated with the two elasticities: if l is small, the marginal effect of γl on thesensitivity of the delivery choice against distance, i.e., (l − 1)dij , is small, and vice versa.
The above empirical implications of our model require that to identify the distanceelasticity correctly, we jointly estimate the distance elasticity of transport costs and theelasticity of substitution within a sample-selection model that consists of equations (6) and(7). For this purpose, we conduct a FIML estimation of a sample-selection model on which we
impose nonlinear constraints. A concern when implementing the FIML estimation, however,is that the disturbance of the selection equation, ηijl , might be correlated with the endogenous
variables pil and xil in the RHS of the selection equation. If this is the case, our point
estimates of the structural parameters will be biased due to endogeneity.13 To take into
account the potential endogeneity bias, we further incorporate instrumental variables (IVs)into the FIML estimation as follows.14 Let yi denote a bivariate vector that contains ln pil
and ln xil as its elements: yi ≡ [ln pil ln xil ]0 . We assume that vector yi is linearly related to
12

In Appendix A, we analytically describe the possibility of an under-biased estimate of distance elasticity
γl due to a sample selection.
13
We greatly appreciate the suggestion of Mike Keane on the case of endogeneity.
14
Maximum likelihood methods of limited dependent variable models with endogenous explanatory variables are proposed by, for example, Newey (1987), Rivers and Vuong (1988), and Vella and Verbeek (1999)
among past studies.

10

a vector of exogenous IVs, si , up to i.i.d. 2 × 1 mean zero random vector ei :yi = Γsi + ei .

(8)Endogeneity bias occurs if the error of the selection equation (6), ηijl , is correlated withthe errors in equation (8), ei . More specifically, we assume that the 4 × 1 random vector
of disturbances, [e0i uijl ηijl ]0 , is stochastically governed by a joint normal density with themean of zero and the 4 × 4 symmetric positive-definite variance-covariance matrix ΩΩ11 ϕ0u,l ϕ0η,l2Ω = ϕu,l σu,l(9)
σuη,l  ,2
ϕη,l σuη,l ση,lwhere Ω11 is a 2 × 2 matrix, ϕu,l , and ϕη,l are 1 × 2 row vectors. The non-zero vector
ϕη,l characterizes the covariances between the disturbances of selection equation (6) andinstrument equation (8) that would lead to potential endogeneity bias. Through our analysis,
we presume that there is no correlation between the disturbances of price differential equation(7) and instrument equation (8): ϕu,l = [0 0].
The accompaning technical appendix shows in detail how our structural sampleselection model consisting of equations (7), (6), (8), and (9) provides the log likelihood
functionX
X(1 − Tijl ) ln [Φ (λijl )] +Tijl ln [Φ (κijl )]
i,j

i,j

+

X
i,j

Tijl ln [φ (ωijl )] −X

Tijl ln σu,l +

i,j

X
i,j

ln [f (yi |si )] , (10)where
κijl =p−1
βl − (l − 1)γl dij + [l 1]yi + bsijl + ϕη,l Ω−1
11 (yi − Γsi ) + ρl σu,l [qijl − µl − γl dij − bijl ]10
2 2(1 − ϕη,l Ω−1
11 ϕη,l − ρl ),qijl − µl − γl dij − bpijl$ijl =,σu,lβl − (l − 1)γl dij + [l 1]yi + bsijl + ϕη,l Ω−1
11 (yi − Γsi )
λijl =,
10
2(1 − ϕη,l Ω−1ϕ)
11 η,l


1
−1
−1/2
0 −1
f (yi |si ) = (2π) |Ω11 |exp − (yi − Γsi ) Ω11 (yi − Γsi ) ,2Here, constant bpijl and bsijl control for the regional fixed effects in price differential andselection equations (7) and (6), respectively.15 We also normalize the selection equation (6)15We also include monthly dummies in the price differential and selection equations to control for seasonality.

11

by setting the standard deviation of its error term, ση,l , equal to 1.16 To maximize the log
likelihood function (10) conditional on the observations of the delivery index {Tijl }, the pricedifferential {qijl }Tijl =1 , the log of distance {dij }, the average price and aggregate transactionof product l in consuming regions {pil } and {xil }, and instruments {si }, we take a twostep approach to make our computation tractable. In the first step, we regress endogenous
variable vector yi on IV vector si by OLS and keep the estimates of Γ and Ω11 . In the second
step, we then insert the OLS estimates of Γ and Ω11 into the log likelihood function (10) andmaximize the resulting log likelihood function with respect to the rest of the parameters.17

3. Data and descriptive statistics
In this paper, we investigate a daily data set of the wholesale prices of agricultural
products in Japan — the Daily Wholesale Market Information of Fresh Vegetables andFruits. The details of our data set are provided in Appendix B. This daily market survey
covers the wholesale prices of 120 different fruits and vegetables. Each agricultural productis further categorized by different varieties, sizes, grades, and producing prefectures. Hence,for example, the data set reports the wholesale prices at 6 different wholesale markets of
the “Dansyaku (Irish Cobbler equivalent)” variety of potato of size “L” with grade “Syu(excellent)” that was produced in “Hokkaido” prefecture on September 7, 2007. This highdegree of categorization is ideal for our purpose of approaching the absolute LOP rigorously
and inferring transport costs precisely because the LOP requires the identification of identicalgoods as its theoretical premise.18 This daily market survey has been recorded since 1976.
In this paper, we scrutinize the 2007 survey that reports the market transactions on 274
market opening days.
Price differential qijl is constructed by subtracting the wholesale price in producing
16

This standard normalization in a sample-selection model makes ρl equal to (1−l )σu,l . During estimation,
we further impose a restriction that the correlation coefficient is always less than or equal to 1 in the absolutevalue.
17
Although reported in the accompaning technical appendix, our Monte Carlo experiments based on themodel show us that, given the elasticity of substitution, the degree of sample selection depends positively on
the distance elasticity of transport costs. The experiments also uncover two crucial facts: (i) the standard
exercise of regressing price differentials on the corresponding distances provides a heavily downwards-biased
estimate of the true distance elasticity of transport costs and (ii) our FIML estimator successfully identifies
the distance elasticity.
18
The hypothesis of the LOP maintains an identical product with respect to the date of production.
Without exact information of the production date, working with daily data is likely to provide a close
identification of an identical product in terms of the production date.

12

prefecture j, pjjl , from that in consuming prefecture i, pijl .19 We set Tijl = 1 for pair (i, j)
if the sample of qijl is available.20 The geographical distance between prefectural pair (i, j)
is approximated by that between the prefectural governments’ head offices placed in theprefectural capital cities. Taking the logarithm of the geographical distance yields variable
dij . Our data set provides the daily aggregate transaction quantity of product l in consuming
region i, xil .21 We are unable to obtain daily data of the aggregate price of product l in the
consuming region i, pil . Hence, we use as a proxy of pil the monthly data of the retail price of
product l. Moreover, to control for the daily variations in the producing and the consuming
prefectures, we include into selection equation (6) the daily temperature data in both of thetwo prefectures as other explanatory variables. This inclusion of the regional temperatures
as determinants of delivery choice comes from our prior belief that the temperatures in the
producing and the consuming regions are important factors for the production of and thedemand for agricultural products. Finally, as valid IVs, we use the monthly numbers of
regular employees and the scheduled cash earnings in each prefecture in addition to themonthly and consuming-region dummies.
We focus our exercise on 8 selected vegetables: cabbages, carrots, Chinese cabbages (ccabbage, hereafter), lettuce, shiitake-mushrooms (s-mushroom, hereafter), spinach, potatoes,
and welsh onions. Table 1 summarizes several descriptive statistics for these products. Panel(a) of the table shows that each product is highly categorized by product varieties, sizes, andgrades. The number of distinct product entries is quite large; 1,207 for cabbages; 1,186 forcarrots; 1,001 for c-cabbages; 903 for lettuce; 1,423 for potatoes; 909 for s-mushrooms; 551
for spinach; and 1,115 for welsh onions.
For each product entry l, we count the number of the delivery Tijl = 1 and thenon-delivery Tijl = 0 only for the dates on which the product entry is indeed traded at thewholesale market in producing prefecture j. We identify the product delivery Tijl = 1 if thedata reports that the source prefecture of the product entry l sold in consuming region i isregion j.22 The first row of panel (b) of the table reports that the total number of both the19

For some products, we cannot find the wholesale prices in the producing prefectures, although we canobserve those prices in the consuming prefectures. In this case, because we cannot construct the pricedifferentials between the producing and the consuming prefectures, we drop the data of these product entries
from our investigation.
20
We also set Tjjl = 1 whenever we can observe pjjl . We consider such observations as the case that
product l is delivered from the producer to the wholesale market in the producing prefecture. We attach theminimum distance of 10.00km to the samples with Tjjl = 1 to avoid taking the log of zero distance.
21
Whenever the data set reports that xil = 0, we interpolate xil by a very small number of 0.00001 to
avoid taking the logarithm of zero.
22
A problem with this identification would be that we cannot eliminate the possibility of product transfer:a product yielded in a source region is delivered to a consuming region and then transferred to another13

delivery and the non-delivery cases over all of the product entries is almost over 190,000 foreach vegetable. This is the number of observations for our FIML estimation. Out of the total
number of delivery and non-delivery cases, the number of delivery cases is relatively small, as
exhibited in the second row of panel (b): it is approximately 10,000 for each vegetable. Ourdata set, hence, indicates that the product delivery is quite limited.23 The third row of panel(b) shows that the mean distance from the producing to the consuming prefectures over all
delivery and non-delivery cases is about 6.00 in the logarithmic term (or 403.428 km) andalmost identical across the vegetables. The fourth row of panel (b), however, conveys thatthe mean distance over the delivery cases only is much shorter depending on the vegetable,with the minimum number of 2.691 (14.746 km) for s-mushrooms and the maximum of 4.339(76.630 km) for potatoes. Product delivery, therefore, is localized and concentrated on thelocal areas neighboring the producing prefectures.
Figure 1 also confirms the locality of the product delivery graphically. Each windowof the figure depicts as a contour plot the data frequencies of the product delivery from theproducing to the consuming prefectures, which are calculated over all product entries on all
traded dates. The horizontal axis represents the producing prefectures and the vertical axis
represents the consuming prefectures. The order of the prefectures reflects the geographicalpositions of the prefectures from the northern most prefecture, Hokkaido, to the southern
most, Okinawa. Therefore, two prefectures that are indexed by close integers are indeed
geographically close to each other. The brighter the contour line is, the higher the probabilityof product delivery. The figure then uncovers three facts. First, each vegetable has several
dominant producing prefectures that are characterized by vertical contour lines. These main
producing prefectures deliver their products to not only the nearby prefectures but also to
the other remote prefectures. Second, the data frequencies of product delivery of the main
producing prefectures are decreasing in distance. Therefore, even the dominant producers do
not deliver their products to the consuming prefectures that are farthest away.24 Third, thecontour lines for the other minor producing prefectures are concentrated on the 45 degree
consuming region. If this case is dominant in our data set, our inference on the distance effects might bebiased. However, according to the Ministry of Agriculture, Forestry, and Fishery, the amount of producttransfers across the wholesale markets is very small relative to the total amount of wholesale transactions inJapan. For example, in 2007, the ratio of product transfers to the total wholesale transactions is 4.8% forcabbages; 6.5% for carrots; 4.9% for c-cabbages; 6.3% for lettuce; 6.0% for potatoes; 3.3% for s-mushrooms;
4.1% for spinach; and 3.9% for welsh onions. These ratios mean that almost all products in our data are
directly delivered from the source regions to the consuming regions as their final destinations.
23
This observation echoes the findings of recent research on the extent of firms’ participation in export.
For instance, Bernard and Jensen (2004) report that only a small portion of the U.S. manufacturing plants
export their products.
24
An exception is observed in the first producing prefecture, Hokkaido, in the cases of carrots and potatoes.

14

line. The product delivery of these relatively minor producing prefectures, thus, is highly
localized.
The locality of product delivery that Table 1 and Figure 1 together unmask brings
us two important implications. First, as observed by Broda and Weinstein (2008) in theirbarcode data of retail products, the agricultural products in our data set are segmented
and clustered geographically. Even in the same vegetable category, products that are soldin two distinct prefectures far away from one another come from different sources and thecorresponding wholesale prices might be affected by regional factors that are idiosyncratic to
the product origins. The price differentials across the consuming regions that are generated
by these idiosyncratic factors cannot be attributed to transport costs. Hence, given theobserved high degree of the regional product clustering, it is crucial to scrutinize the pricedifferentials of a product that shares a source region to correctly infer the role that transport
costs play in absolute LOP violations. Second, drawing an inference on the transport costs
only from observed price differentials might be subject to a serious sample-selection bias, as
we repeatedly claim in this paper.
The mean of the observed log price differential is reported on the first row of panel(c) of Table 1. The positive numbers reported in the first row imply that the wholesale
prices in the consuming prefectures are higher on average by between 0.3% and 8.1% thanthose of the producing prefectures. This observation is suggestive for the important roleof transport costs in price differentials, as predicted by equation (7). The corresponding
standard deviation of the observed log price differential, which is displayed on the second
row of panel (c), is approximately 20 %. Our data set, thus, shows the almost same degreeof absolute LOP violations as observed in the previous studies (e.g., Crucini et al 2005,
and Broda and Weinstein 2008), even after identifying the source regions of products. We
also conduct an OLS regression of the observed price differential on the corresponding log
distance and the constant for each vegetable. The resulting OLS estimates of the coefficienton the log distance, γ̂l OLS , are shown in the third row of panel (c), which are accompaniedby the standard errors. All of the point estimates are positive, with values between theminimum of 0.007 and the maximum of 0.051 at any conventional statistical significancelevels. This range of the estimated distance elasticity of the price differential is consistent
with the estimates that past studies commonly found using different data sets such as inEngel et al. (2005), Broda and Weinstein (2008), and Inanc and Zachariadis (2009).

4. Results
4.1. Results of the FIML estimation
15

Table 2 summarizes the results of the FIML estimation based on the log likelihood(10). The first and second rows of panel(a) of the table show that the distance elasticityof transport costs, γ̂l FIML , is estimated to be positive and statistically significant for eachvegetable. The outstanding fact that this row tells us is the large size of the FIML estimates: the mean (over the 8 vegetables) of the estimated distance elasticity is 0.238 withthe minimum of 0.210 for cabbages and the maximum of 0.325 for lettuce. According toequation (7), the price differential of a product between the consuming and the producing
regions increases by approximately 24% in response to the 100 % stretch in delivery distancewhen ignoring selection mechanism (6). Compared with the small size of the OLS estimateof the distance elasticity, which is reported to be between 0.008 and 0.051 in the last row
of Table 1, this large size of the FIML estimate implies that the OLS estimate is seriously
biased downwards due to the underlying data truncation.
As discussed in section 2, the strength of the observed under bias tightly connectswith the elasticity of substitution, l . As reported in the third and fourth rows of panel (a)of Table 2, l is estimated sensibly and significantly: the mean of the point estimate of lis 3.132 over the 8 vegetables. Combined with the large estimate of the distance elasticityof transport costs, the estimated elasticity of substitution implies that the probability of
product delivery from the producing to the consuming prefectures depends negatively aswell as sensitively on the delivery distance. The point estimate of the correlation coefficient
between the unobserved disturbances of price differential equation (7) and selection equation(6), ρl , then provides empirical evidence that sample-selection bias does matter. As displayedin the fifth and sixth rows of panel(a) of Table 2, ρl is estimated to be negative with a highstatistical significance: the mean of the estimates of ρl over the 8 vegetables is -0.536 withthe minimum of -0.684 for welsh onions and the maximum of -0.278 for potatoes. Thishighly negative correlation between the unobserved disturbances in the two equations is thefundamental source for the under bias in the OLS estimate of the distance elasticity in theprice differential equation, as shown in equation (A.1).
In summary, our FIML estimates of the sample-selection model reveal the dual roles
that geographical distance plays in the regional price differentials. Distance creates a large
price gap between the consuming and the producing regions. At the same time, distancesignificantly affects the choice of product delivery from the latter to the former regions. As aresult, the price differentials are not randomly sampled and, especially, their observations areconcentrated on the local areas that neighbor the producing regions. This concentration of
the observations within a relatively short distance conceals the actual size of the underlying
distance elasticity of transport costs and makes the OLS estimates biased downwards.

16

4.2. Model validation through diagnostic checks
The above FIML estimates of the three structural parameters depend on the identification provided by our structural sample-selection model. Therefore, the relevance of theestimates relies on the empirical validity of our model. As a model validation, we conduct
diagnostic checks of our model with respect to two important aspects of the actual data: thepattern of product delivery and the association of price differentials with delivery distances.
If our sample-selection model is reliable, it should explain the pattern of productdelivery, Tijl , that is actually observed in our data. To check the ability of our model tomimic the product delivery pattern in the data, we calculate the percents correctly predicted(PCPs) measures for Tijl = 0 or 1.25 To construct the PCPs, we calculate the predictedconditional probabilities of Tijl = 0 and Tijl = 1 on the observables, P̂ (Tijl = 0|.) andP̂ (Tijl = 1|.), respectively. Then, if P̂ (Tijl = 0|.) > 0.5, we recognize that our model predicts
Tijl = 0, while if P̂ (Tijl = 1|.) > 0.5, it predicts Tijl = 1. The PCP for Tijl = 0 (or 1) is
calculated as the percentage of the total number of the observations of Tijl = 0 (or 1) thatare accompanied by P̂ (Tijl = 0|.) > 0.5 (or P̂ (Tijl = 1|.) > 0.5). The PCP for either Tijl = 0
or 1 is simply derived as a weighted average of the PCPs for Tijl = 0 and 1.
The results of the PCPs are summarized in the first, second, and third rows of panel(b) of Table 2. As shown in the first row, our sample-selection model yields high PCPs ofapproximately 0.990 for either Tijl = 0 or 1 for all of the vegetables. These results mean thatthe model is fairly successful in replicating the observed pattern of product delivery overall.
In particular, as implied by the PCPs reported in the second and third rows of panel (b), themodel’s ability to replicate no delivery choice Tijl = 0 is better than its ability to replicatedelivery choice Tijl = 1. On the one hand, the high PCPs for Tijl = 0 of approximately 0.990
suggest the model’s outstanding predictive ability of no delivery choice. On the other hand,
the PCPs for Tijl = 1 are lower than those of no delivery choice with the mean of 0.820. The
model does a good job in predicting the delivery choice especially for some vegetables suchas s-mushrooms, spinach, and welsh onions.26 We confirm through this diagnosis criterion
that the model’s predictive ability for the pattern of product delivery is remarkable.
The second diagnosis criterion is the data association of the price differentials withthe delivery distances. As observed in the last row of Table 1, the OLS regression of theformer on the latter in actual data yields the estimate of the distance elasticity, γ̂OLS , at25

Wooldridge (2002) discusses the PCP for the model validation of probit models.
The main reason for the model’s slightly lower predictive performance for carrots and potatoes is understandable. As observed in Figure 1, the main producing prefecture of these two vegetables, Hokkaido,delivers its products to all other prefectures regardless of the delivery distance. This data aspect is hard to
explain with our simple structural model.
26

17

approximately 3% on average. The question we ask here is if our sample-selection model
predicts this size of the OLS estimate or not.
To perform this diagnosis check, we derive the prediction of the model on price differentials following equation (A.1). Each window of Figure 2 plots the resulting predicted
price differentials (blue dots) as well as the data counterparts (gray crosses) against the corresponding log distances for each vegetable. The blue dots are distributed inside the cloudmade of the gray crosses in all of the windows except in the case of carrots. Hence our model
successfully predicts the data association of the price differentials with the distances overall,although the actual data show us a much sparser joint distribution between the two variables.
The fourth row of panel (b) of Table 2 reports the OLS estimate of regressing the predicted
price differentials on the corresponding distances. For comparison, we also display in the lastrow of the panel the OLS estimate with the actual data that has already been reported inTable 1. The model’s prediction on the OLS estimate is close to, but slightly larger than, its
actual data counterpart: the cross-vegetable average of the predicted OLS estimate is 0.063
whereas that with the actual data is 0.033. It is important, however, to remember that the
distance elasticity of the transport cost of our model is estimated at 0.238 by FIML. Whatis striking is that the sample-selection model with such a large distance elasticity indeed
mimics such a small size of the OLS estimate. In this sense, we conclude that our model
successfully passes the second diagnostic check, although we fully understand that there is
still an unexplained gap between the model’s prediction and the actual data with respect tothe observed joint distribution of the price differentials and the distances.

5. Conclusion
As claimed by Anderson and van Wincoop (2004), this paper provides evidence thatthe “death of distance” is exaggerated, even in the literature of regional price dispersions.
Exploiting data on the wholesale price differentials and the delivery patterns of agricultural
products in Japan, our structural estimation approach featuring product delivery choice
uncovers the high implicit prices of the geographical barriers across regions. The size of the
distance elasticity of transport costs that our FIML procedure estimates is fairly consistent
with those found in the past empirical studies using gravity-type models of equilibrium
trade volumes. The transport costs we infer as distance effects do indeed play economicallysignificant roles in regional price dispersions. The empirical exercise that this paper conducts
is the first rigid step to an ambitious goal of international finance — parsing out structurally
different potential contributors to the widely documented reduced-form observations of LOP
failures in retail prices.
18

Although this paper intensively scrutinizes the data aspects of agricultural products,
the main arguments in this paper are also applicable to other products. For instance, identifying in which plant products are manufactured and taking into account the underlying
location choice of plants could be crucial for correct inferences on the role of transport costs
in regional price dispersions for manufactured non-perishable products. If the transport costs
are expensive, the firms might decide to locate their plants close to the consuming markets
to economize on transport costs.27 In this case, because product delivery becomes limited
around the local areas that neighbor the plants, the observations of the price of a productsharing an identical plant will be truncated. The resulting sample selectivity then leads to abiased inference on the role of transport costs in regional price dispersions, as in our exercise.
This conjecture suggests that there should be a more intensive use of plant level data in the
LOP literature.
Finally, it is worth noting a caveat regarding our inferences that depend on theimplications of the highly stylized structural model. An obvious limitation of our structuralinferences stems from the model’s assumption of monopolistically competitive firms facing
regional demand functions with a constant elasticity. To figure out the historical movementsof the relative PPP of the United States, a recent paper by Atkeson and Burstein (2008)
emphasizes the importance of richer market structures that make the price elasticity ofdemand and markup variable in the market shares. If this is the case, the delivery choiceof a source region to its wholesale market should have a non-negligible impact on the priceelasticities of demand for the products from other source regions because the market sharesof the other source regions change. Given the transport costs, this change in the sensitivityof demand then might affect the product delivery choices of the other source regions. Thismechanism potentially makes our inferences on the distance effects biased. We leave thisextension to future research.

Appendix A.

Analytical description of under-biasedness due to sample selectivity

Taking the expectation of price differential equation (7) conditional on Tijl = 1 and other observables yields E[qijl |., Tijl = 1] = µl + γl dij + E[uijl |., Tijl = 1] where . represents the otherobservables. Notice that the term E[u ijl |. , Tijl = 1] is related to the conditional expectationση̄ijl . A consistent estimate of η̄ijl is obtainedη̄ijl ≡ E[ηijl |. , Tijl = 1] by E[uijl |. , Tijl = 1] = ρl σu,lη,lˆ
by the inverse Mills ratio η̄ijl = φ[ẑijl ]/Φ[ẑijl ], where φ(.) and Φ(.) are the standard normal density
27

A recent paper by Evans and Hariggan (2005) emphasizes the importance of transport time proxied bydistance on the producers’ choices of plant location, and it provides empirical evidence that the products
where timely delivery is crucial are produced near the final demand markets.

19and cumulative distribution functions, respectively. Therefore, we can rewrite price differential
equation (7) as
qijl = µl + γl dij + βuη η̄ˆijl + eijl ,(A.1)
σ

where βuη = ρl σu,l, and eijl is an i.i.d. error term that satisfies E[e ijl |., Tijl = 1] = 0. Our model
η,limplies that ρl < 0. Moreover, the inverse Mills ratio η̄ˆijl is increasing in distance because η̄ˆijl isa decreasing function of the predicted latent variable ẑ ijl , which then depends negatively on the
distance through selection equation (6). Hence, if we ignore the third term of the RHS of equation(A.1) when estimating the distance elasticity γ l only through the price differential equation, theresulting estimate could be biased downwards.
Appendix B.

Data sources

Wholesale prices:
The data source for wholesale prices is the Daily Wholesale Market Information of Fresh
Vegetables and Fruits (“Seikabutsu Hinmokubetsu Shikyo Joho” in Japanese). The data set is
distributed by the Center of Fresh Food Market Information Service (“Zenkoku Seisen Syokuryohin
Ryutsu Joho Senta” with the following URL: http://www2s.biglobe.ne.jp/ fains/index.html). Allof the contents in the data set are surveyed by the Ministry of Agriculture, Forestry, and Fishery(MAFF) for almost all transactions at 55 wholesale markets that are officially opened and operated
in the 47 prefectures in Japan on a daily basis.
The data file contains information on the name of the product, the market prices, the nameof the production site, the name of the market-place, and the product characteristics. The pricereported has three forms: the highest price, the mode price, and the lowest price. Most of themarkets record all three prices, but several markets report only the highest and the lowest prices or
only the mode price. Thus, we construct our price variable by averaging these price variables. We
use the mode price when only the mode price is available. The transaction unit of each product isalso reported. To obtain the same unit for each product, we divide the price by the number of thetransaction unit.
We need to control for product characteristics to examine the prices between the production
site and the market place. Thus, we construct the same category products by using the productcharacteristics and the production site. The product characteristics are: brand name, size of
products, and grade of products. The size is coded by categorical variables, such as large, medium,and small. The grade is also measured by the categorical variables, such as A, B or superior. 28
Because prices depend on detailed characteristics, we use each combination of characteristics torepresent the same product.
The coverage of the vegetables traded through the central wholesale markets is substantial in
Japan. While currently, the large supermarket and restaurant chains can not only directly purchaseagricultural products from producers but can also directly import from foreign producers, the shareof agricultural products covered by these markets in the entire set of vegetable transactions is stillover 75% in Japan in 2006, according to MAFF. Thus, our data set enables us to approach the
population characteristics of transport costs.
28

For example, according to the guideline document of Yamanashi prefecture, spinach is classified as grade
A under the following conditions: it is of one type and no mixture of types affects the appearance, and it isclean, trimmed, and free from decay and damage by insects. Otherwise, it is ranked as B.

20

Geographical distance:
The data of distance is provided by the Geographical Survey Institute (GSI) of the Government of Japan. The data are publicly available at the GSI website (http://www.gsi.go.jp/kokujyoho/kenchokan.html).
Retail prices :The monthly data of the retail price of product l is reported in the Retail Price Survey(“Kouri Bukka Tokei Chosa” with the following URL: http://www.stat.go.jp/data/kouri/index.htm)
from the Ministry of Internal Affairs and Communication conducts.
Daily temperatures:
The daily temperature data are reported by the Japan Meteorological Agency. We download
the data from the website: http://www.data.jma.go.jp/obd/stats/etrn/index.php.
Regular employees and scheduled cash earnings:
The monthly data for the number of regular employees and scheduled cash earnings are reported in the Monthly Labor Survey (“Maitsuki Kinrou Tokei Chosa”) conducted by the Ministry of
Health, Labour, and Welfare. The data are available from the website: http://www.mhlw.go.jp/toukei/list/301.html.

21

Acknowledgements
We would like to thank the editor Charles Engel, two anonymous referees, Naohito Abe,
Kazumi Asako, Martin Berka, Andrew Bernard, Toni Braun, Dave Cook, Mario Crucini, Alexandre
Dmitriev, Wei Dong, Shin-ichi Fukuda, Naoto Jinji, Daiji Kawaguchi, Michael Keane, Junko Koeda,
Chul-In Lee, Shiko Maruyama, Yoshiro Miwa, Hideyuki Mizobuchi, Toshi Mukoyama, Jim Nason,
Makoto Nirei, Hiroshi Ohashi, Glenn Otto, Ke Pang, John Rogers, Makoto Saito, Yasuyuki Sawada,
Shigenori Shiratsuka, Alexandre Skiba, Gregor Smith, Yi-Chan Tsai, Takayuki Tsuruga, Tsutomu
Watanabe, Jenny Xu, and the seminar participants in Hitotsubashi, Hong Kong University of
Science and Technology, Hosei, Keio, Kyoto, Shanghai University of Finance and Economics, Seoul
National, New South Wales, the Institute of Developing Economies of the Japan External Trade
Organization, the National Graduate Institute for Policy Study Japan, the Policy Research Instituteof the Ministry of Finance of the Government of Japan, the Research Institute of Capital Formationof the Development Bank of Japan, the 2010 Asia Pacific Trade Seminar, the fifth conferenceof Empirical Investigations in Trade and Investment, the 2011 Canadian Economic Association
Meetings, the 2011 North American Summer Meetings of the Econometric Society, the 2011 Spring
Meetings of the Japanese Economics Association, the 2010 Summer Workshop on Economic Theory,and the 2010 Tokyo Macro Workshop for their helpful and valuable comments, discussions andsuggestions. The first and second authors wish to thank the Kikawada foundation and the Japan
Center for Economic Research for financial support. The second and third authors would like tothank the Japan Society for the Promotion of Science for financial support from grants-in-aid forscientific research (numbers 20730205 and 24530270). We are solely responsible for any errors andmisinterpretations of this paper.

References
Anderson, J.E., van Wincoop, E., 2003, “Gravity with gravitas: a solution to the border
puzzles,” American Economic Review 93, 170 − 192.
Anderson, J.E., van Wincoop, E., 2004, “Trade costs,” Journal of Economic Literature 42,691 − 751.
Atkeson, A. and Burstein, A., 2008, “Pricing-to-market, trade costs, and international relative prices,” American Economic Review 98, 1998 − 2031.
Baba, C., 2007, “Price dispersion across and within countries: the case of Japan and Korea,”
Journal of the Japanese and International Economies 21, 237 − 259.
Balistreri, E.J., Hillberry, R.H., Rutherford, T.F., 2011, “Structural estimation and solution of international trade models with heterogeneous firms,” Journal of International
Economics 83, 95 − 108.
22

Bergin, P.R., Glick, R., 2009, “Endogenous tradability and some macroeconomic implications,” Journal of Monetary Economics 56, 1086 − 1095.
Bernard, A.B., Eaton, J., Jensen, J.B., Kortum, S., 2003, “Plants and productivity in international trade,” American Economic Review 93, 1268 − 1290.
Bernard, A.B., Jensen, J.B., 2004, “Entry, expansion, and intensity in the US export boom
1987-1992,” Review of International Economics 12, 662 − 675.
Broda, C., Weinstein, D.E., 2008, “Understanding international price differences using barcode data,” NBER working paper 14017.
Crozet, M., Koenig, P., 2010, “Structural gravity equations with intensive and extensive
margins,” Canadian Journal of Economics 43, 41-62.
Crucini, M. J., Shintani, M., Tsuruga, T., 2010, “The law of one price without the border:
the role of distance versus sticky prices,” The Economic Journal 120, 462 − 480.
Ceglowski, J., 2003, “The law of one price: intranational evidence for Canada,” Canadian
Journal of Economics 36, 373 − 400.
Disdier, A.-C., Head, K., 2008, “The puzzling persistence of the distance effect on bilateral
trade,” Review of Economics and Statistics 90, 37 − 48.
Donaldson, D., 2010, “Railloads of the Raj: estimating the impact of transportation infrastructure,” NBER working paper 16487.
Engel, C., Rogers, J.H., 2001, “Deviations from purchasing power parity: causes and welfare
costs,” Journal of International Economics 55, 29 − 57.
Engel, C., Rogers, J.H., 1996, “How wide is the border?” American Economic Review 86,1112 − 1125.
Engel, C., Rogers, J.H., Wang, S.-Y., 2005, “Revisiting the boarder: an assessment of thelaw of one price using very disaggregate consumer price data,” in Driver, R., Sinclair,P., Thoenissen, C., eds., Exchange Rates, Capital Flows and Policy, Routledge, NY.
Evans, C.L., Harrigan, J., 2005, “Distance, time, and specialization: lean retailing in generalequilibrium,” American Economic Review 95, 292 − 313.
Ghironi, F., Melitz, M.J., 2005, “International trade and macroeconomic dynamics withheterogeneous firms,” Quarterly Journal of Economics 120, 865 − 915.
23

Helpman, E., Meitz, M., Rubinstein, Y., 2008, “Estimating trade flows: trading partners
and trading volumes,” Quarterly Journal of Economics 123, 441 − 487.
Hummels, D., 1999, “Towards a geography of trade costs,” GTAP working paper No.17.
Inanc, O., Zachariadis, M., 2010, “The importance of trade costs in deviations from the lawof one price: estimates based on the direction of trade,” Economic Inquiry, forthcoming.
Johnson, R., 2012, “Trade and prices with heterogeneous firms,” Journal of International
Economics 86, 43-56.
Melitz, M., 2003, “The impact of trade on intra-industry reallocations and aggregate industry
productivity,” Econometrica 71, 1695 − 1725.
Midrigan, V., 2007, “International price dispersion in state-dependent pricing models,” Journal of Monetary Economics 54, 2231 − 2250.
Newey, W.K., 1987, “Efficient estimation of limited dependent variable models with endogenous explanatory variables,” Journal of Econometrics 36, 231 − 250.
Obstfeld, M., Rogoff, K., 2001, “”The six major puzzles in international macroeconomics:
Is there a common cause?” in Bernanke, B.S., Rogoff, K. eds. NBER Macroeconomics
Annual 2000 vol 15, 339 − 412.
Parsley, D. C., Wei, S.-J., 1996, “Convergence to the law of one price without trade barriers
or currency fluctuations,” Quarterly Journal of Economics 114, 1211 − 1236.
Rivers, D., Vuong, Q.H., 1988, “Limited information estimators and exogeneity tests for
simultaneous probit models,” Journal of Econometrics 39, 347 − 366.
Rogers, J.H., Jenkins, M., 1995, “Haircuts or hysteresis? Sources of movements in realexchange rates” Journal of International Economics 38, 339 − 360.
Vella, F., Verbeek, M., 1999, “Two-step estimation of panel data models with censoredendogenous variables and selection bias,” Journal of Econometrics 90, 239 − 263.
Wooldridge, J.M., 2002, Econometric Analysis of Cross Section and Panel Data MIT Press,
Cambridge.

24

Table 1:

Descriptive Statistics of Data

CabbageNo. of varieties
No. of size categories
No. of grade categories
No. of producing prefectures
No. of wholesale markets
No. of distinct product entries

3
63
34
47
47
1,207

No. of Tijl = 0 or 1
No. of Tijl = 1
Mean log distance over Tijl = 0 or 1
Mean log distance of Tijl = 1

369,343
15,841
5.939
3.705

Mean log price differential qijl
SD. log price differential qijlγ̂l OLS(s.e.)

0.039
0.167
0.033
(0.001)

Carrot C-Cabbage Lettuce Potato S-Mushroom(a) Product entry
10
4
7
10
1
62
50
71
50
74
66
50
46
93
55
46
46
43
47
44
47
47
47
47
47
1,186
1,001
903
1,423
909
(b) Data truncation
198,129
241,871239,703 264,280
476,919
8,395
10,803
11,565 10,921
11,845
6.027
5.938
5.984
6.219
5.930
3.990
4.009
3.950
4.339
2.691
(c) Price differential
0.075
0.065
0.026
0.081
0.003
0.285
0.227
0.267
0.265
0.127
0.051
0.042
0.022
0.037
0.008
(0.001)(0.001)(0.001) (0.001)(0.001)

SpinachWelsh Onion

4
17
85
47
47
551

11
103
58
46
47
1,115

466,337
15,9775.922
3.255

547,272
14,874
5.944
2.943

0.029
0.216
0.044
(0.001)

0.016
0.178
0.033
(0.001)

Note 1: γ̂l OLS represents the OLS estimate of the coefficient γl in the regression specification qijl = µl + γl dij + uijl where µl is constat and uijl isan OLS disturbance. Note that qijl is the price differential between consuming and producing regions i and j. “(s.e.)” reports the corresponding
standard error.

Table 2:γ̂l FIML(s.e.)
ˆl(s.e.)
ρ̂l(s.e.)
log likelihood
No. of observations
PCP for Tijl = 0 or 1
PCP for Tijl = 0
PCP for Tijl = 1γ̂l OLS with predicted qijlγ̂l OLS

Results of FIML-IVs estimation

Cabbage

Carrot0.210(0.001)3.907(0.012)-0.629(0.003)0.312(0.003)1.819(0.010)-0.313(0.004)-36434.658 -192952.779
369,343
198,129
0.989
0.995
0.856
0.059
0.033

0.962
0.976
0.642
0.113
0.051

C-Cabbage
Lettuce
Potato(a) Point estimates and s.e.
0.304
0.325
0.256
(0.003)(0.003)(0.002)
3.435
2.876
1.919
(0.016)(0.013)(0.012)-0.646-0.691-0.278(0.002)(0.002)(0.003)

S-Mushroom

SpinachWelsh onion

0.303(0.002)3.576(0.041)-0.395(0.006)0.302(0.002)3.521(0.013)-0.656(0.003)0.256(0.002)4.004(0.014)-0.684(0.002)-11670.878 -53524.355 -144737.779
241,871239,703
264,280(b) Diagnosis check
0.990
0.990
0.981
0.995
0.996
0.997
0.874
0.865
0.612
0.062
0.068
0.040
0.042
0.022
0.037

-448473.896
476,919-29364.250
466,337

99351.534
547,272

0.994
0.997
0.903
0.018
0.008

0.994
0.998
0.902
0.085
0.044

0.996
0.999
0.911
0.063
0.033

Note 1: The log likelihood of the FIML estimation is given by equation (11). Each estimation includes monthly dummies, consuming prefectural
dummies, and producing prefectural dummies both in selection and price differential equations (6) and (7).
Note 2: “Pcp” represents the “percent correctly predicted.”corresponding vegetable from producing to consuming prefectures as contour lines. In each window, the horizontal line
represents producing prefectures and the vertical line consuming prefectures. The lighter the blue contour line is, the higher
the probability of product delivery is. If product delivery is perfectly local, contour lines are concentrated along the 45
degree line.

Figure 1: Data Frequencies of Product Delivery. Note. Each window plots data frequencies of product delivery of theon the logarithm of distance for the corresponding vegetable. In each window, the blue dots represent the predicted pricediﬀerentials, while the gray crosses the actual price diﬀerentials.

Figure 2: Predicted and Actual Price Diﬀerentials. Note. Each window plots the predicted and the actual price diﬀerentials

Appendix:
Exaggerated Death of Distance:
Revisiting Distance Effects on Regional Price Dispersions

Kazuko Kano

Takashi Kano

Kazutaka Takechi

Gruduate School of Economics
The University of Tokyo
Hongo 7-3-1, Bunkyo-ku
Tokyo, 113-0033, Japan
Tel: +81-3-5841-1746
Fax: +81-3-5841-1747
Email: kkano@e.u-tokyo.ac.jp

Graduate School of Economics
Hitotsubashi University
Naka 2-1, Kunitachi
Tokyo, 186-8601, Japan
Tel: +81-42-580-8283
Fax: +81-42-580-8283
Email: tkano@econ.hit-u.ac.jp

Faculty of Economics
Hosei University
4342 Aihara-machi, Machida-shi
Tokyo, 194-0298, Japan
Tel: +81-42-783-2566
Fax: +81-42-783-2611
Email: ktakechi@hosei.ac.jp

May 6, 2012

This appendix is not intended for publication.

Appendix A. A structural sample-selection model withendogenous explanatory variables in selection

A.1. Derivation of the conditional likelihood function
Consider the structural sample-selection model in the main text
qij = µ + γdij + bpij + uij , if Tij = 1,

(A.1)

Tij = 1[β − ( − 1)γdij + [ 1]yi + bsij + ηij > 0]

(A.2)

yi = Γsi + ei .

(A.3)

To economize notation, we ignore product index l in this appendix. Eqs. (A.1) and (A.2) are theprice differential equation and the selection equation, respectively. In this paper, we allow for a
possibility that the explanatory variables in the selection equation, y i = [ln pi ln xi ]0 , are correlatedwith the error term of the selection equation, η ij . As shown in eq. (A.3), we assume that yi islinearly related to a vector of exogenous variables (i.e., instruments), s i , up to i.i.d. mean zerorandom vector ei . An endogeneity problem then is the case when η ij is correlated with ei . Morespecifically, we assume that random vector  ij = [e0i uij ηij ]0 is stochastically governed by a joint
normal density with the mean of zero and the 4 × 4 symmetric positive-definite variance-covariancematrix ΩΩ11 ϕ0u ϕ0ηΩ =  ϕu σu2 σuη  , ,(A.4)
2ϕη σuη σηwhere Ω11 is an 2 × 2 matrix, ϕu and ϕη are 1 × 2 row vectors, respectively. The endogeneity
problem then occurs when ϕη 6= 0.
Given the above sample-selection model, we characterize the corresponding conditional
likelihood f (qij , Tij , yi |dij , si ) ≡ f (qij , Tij = 1, yi |dij , si )Tij f (qij , Tij = 0, yi |dij , si )1−Tij . Since qij isobserved only when Tij = 1, we can factorize the density f (q ij , Tij = 1, yi |dij , si ) as follows:f (qij , Tij = 1, yi |dij , si ) = f (qij |Tij = 1, yi , dij , si )f (Tij = 1, yi |dij , si ),=P(Tij = 1|qij , yi , dij , si )f (qij |yi , dij , si )f (Tij = 1, yi |dij , si ),P(Tij = 1|yi , dij , si )= P(Tij = 1|qij , yi , dij , si )f (qij |yi , dij , si )f (yi |dij , si ),where the second line results from the Bayes’ rule and the third line comes from the fact thatf (yi |Tij = 1, dij , si ) = f (yi |dij , si ). When Tij = 0, we cannot observe qij . In this case, we factorize
the conditional density f (qij , Tij = 0, yi |dij , si ) asf (qij , Tij = 0, yi |dij , si ) = f (Tij = 0, yi |dij , si ),= P(Tij = 0|yi , dij , si )f (yi |dij , si ).
1Our task then is to characterize conditional densities, P(T ij = 0|yi , dij , si ), P(Tij = 1|qij , yi , dij , si ),f (qij |yi , dij , si ), and f (yi |dij , si ), respectively.
To accomplish this task, we first figure out the conditional densities of the error terms,f (ηij |ei ), f (ηij |ei , uij ), and f (uij |ei ) by conducting the triangular factorization of the variancecovariance matrix Ω (A.4). We then obtain Ω = ADA0 in whichΩ11 02,1
In
0
0
02,1




A = ϕu Ω−1
10 and D = 01,2 H22
0
,
11
−1
−1
ϕη Ω−1
H
H
1
0
0
H
−
H
H
H
32 22
1,2
33
32 22
23
11
−1 0
−1 0
0
2
for H22 = σu2 − ϕu Ω−1
11 ϕu , H23 = H32 = σuη − ϕu Ω11 ϕη , and H33 = ση − ϕη Ω11 ϕη . Let a new
random vector ˜ij ≡ [e˜i 0 ũij η̃ij ]0 denote A−1 ij . The above triangular factorization implies that ˜ij
is normally distributed with the mean of zero and the diagonal variance-covariance matrix of D.
Then, by construction, we can obtain the following system of equations:ei = ẽi ,(A.5)

uij = ϕu Ω−1
11 ẽi + ũij ,−1−1
ηij = ϕη Ω11 ẽi + H32 H22ũij + η̃ij .

(A.6)
(A.7)

−1
To derive the conditional density f (η ij |ei ), let ãij denote H32 H22ũij + η̃ij . Notice that ãij isnormally distributed with the mean of zero and the variance of H 33 .1 Using this fact, we canrewrite equation (A.7) as
ηij = ϕη Ω−1
11 ei + ãij

Since ãij is orthogonal to ei = ẽi , the above equation implies that the conditional distribution of
ηij on ei is normal with the mean of ϕη Ω−1
11 ei and the variance of H33 .
ηij |ei ∼ N (ϕη Ω−1
11 ei , H33 ).
Following the similar process, we can characterize the conditional densities f (η ij |ei , uij ) and f (uij |ei )from the corresponding conditional distributions−1−1−1
ηij |ei , uij ∼ N (ϕη Ω−1
11 ei + H32 H22 (uij − ϕu Ω11 ei ), H33 − H32 H22 H23 ),anduij |ei ∼ N (ϕu Ω−1
11 ei , H22 ).
Now we can characterize conditional probability P(T ij = 0|yi , dij , si ) asP(Tij = 0|yi , dij , si )= P(β − ( − 1)γdij + [ 1]yi + bsij + ηij ≤ 0|yi , dij , si ),= P(ηij ≤ −β + ( − 1)γdij − [ 1]yi − bsij |yi , dij , si ),= P(ãij ≤ −β + ( − 1)γdij − [ 1]yi − bsij − ϕη Ω−1
11 ei |yi , dij , si ),= 1 − Φ(λij )1−1 2 2−1 2−1
The variance of ãij is (H32 H22) σũ + ση̃2 = (H32 H22) H22 + H33 − H32 H22
H23 = H33 .

2where Φ(.) is the standard normal cumulative distribution andλij =β − ( − 1)γdij + [ 1]yi + bsij + ϕη Ω−1
11 (yi − Γsi )1

0 2(ση2 − ϕη Ω−1
11 ϕη ).

We can show conditional probability P(T ij = 1|qij , yi , dij , si ) asP(Tij = 1|qij , yi , dij , si )= P(β − ( − 1)γdij + [ 1]yi + bsij + ηij > 0|qij , yi , dij , si ),= P(ηij > −β + ( − 1)γdij − [ 1]yi − bsij |qij , yi , dij , si ),−1−1= P(η̃ij > −β + ( − 1)γdij − [ 1]yi − bsij − ϕη Ω−1
11 ei − H32 H22 (uij − ϕu Ω11 ei )|qij , yi , dij , si ),= Φ(κij ),

where
κij =

p
−1
−1
β − ( − 1)γdij + [ 1]yi + bsij + (ϕη − H32 H22
ϕu )Ω−1
11 (yi − Γsi ) + H32 H22 (qij − µ − γdij − bij )1−1(H33 − H32 H22
H23 ) 2

To find out conditional density f (qij |yi , dij , si ), consider conditional distribution
Fqij |yi ,dij ,si (q ∗ ) = P(qij < q ∗ |yi , dij , si ),= P(µ + γdij + bpij + uij < q ∗ |yi , dij , si ),= P(uij < q ∗ − µ − γdij − bpij |yi , dij , si ),= P(ũij < q ∗ − µ − γdij − bpij − ϕu Ω−1
11 ei |yi , dij , si ),= Φ($ij )
where
$ij =

q ∗ − µ − γdij − bpij − ϕu Ω−1
11 (yi − Γsi )
1

.

2
H22

We then can construct conditional density f (q ij |yi , dij , si ) taking a derivative of Fqij |yi ,dij ,si (q ∗ )with respect to q ∗ and evaluating the result at qij :−1

f (qij |yi , dij , si ) = H222 φ($ij )where φ(.) is the standard normal kernel. Finally, it is straight-forward for us to characterize conditional density f (yi |dij , si ). Since the vector of the endogenous explanatory variables, y i , is always
observable regardless of the value of T ij , conditional density f (yi |dij , si ) is simply characterized byeq. (A.3) as a Gaussian joint density with the mean of Γs i and the variance-covariance matrix of
Ω11 :


1
−1
−1/2
0 −1
f (yi |dij , si ) = f (yi |si ) = (2π) |Ω11 |exp − (yi − Γsi ) Ω11 (yi − Γsi ) .
23.

Summarizing the above characterization of the conditional densities, we can derive theconditional likelihood f (qij , Tij , yi |dij , si ) as−1

f (qij , Tij , yi |dij , si ) = [Φ(κij )H222 φ($ij )]Tij [1 − Φ(λij )]1−Tij f (yi |dij , si ).
Following the conventional identification exercise with a sample selection model, we normalize thestandard deviation of the error term of the selection equation to one: σ η = 1. We also assume thatuij is uncorrelated with ei : ϕu = 0. The likelihood function then turns out to be much simpler:f (qij , Tij , yi |dij , si ) = [Φ(κij )σu−1 φ($ij )]Tij [1 − Φ(λij )]1−Tij f (yi |dij , si ),

(A.8)

where
κij =

p
−1
β − ( − 1)dij + [ 1]yi + bsij + ϕη Ω−1
11 (yi − Γsi ) + ρσu (qij − µ − γdij − bij )$ij =qij − µ − γdij − bpij

λij =

1

0
2 2
(1 − ϕη Ω−1
11 ϕη − ρ ),σuβ − ( − 1)γdij + bsij + [ 1]yi + ϕη Ω−1
11 (yi − Γsi )1

0 2(1 − ϕη Ω−1
11 ϕη ),,

for the correlation coefficient between u i and ηi , ρ.
A.2. The inverse-Mills ratio
The sample selection model predicts the price differential by the conditional expectation
E[qij |., Tij = 1] = µ + γdij + E[uij |., Tij = 1].
To understand the conditional expectation of the error term, E[u ij |., Tij = 1], consider a random
vector ωij = [e0i ηij uij ]0 that is stochastically governed by a joint normal density with the mean ofzero and the 4 × 4 symmetric positive-definite variance-covariance matrix ΣΩ11 ϕ0η ϕ0uΣ =  ϕη ση2 σuη  .
ϕu σuη σu2
Covariance matrix Σ has a triangular factorization Σ = BQB 0 such that




In
0
0
Ω11 02,1
02,1




B = ϕη Ω−1
10 , and Q = 01,2 J22
0
,
11
−1
−1
−1
ϕu Ω11 J32 J22 101,2
0 J33 − J32 J22 J23
−1 0
−1 0
0
2
where J22 = ση2 − ϕη Ω−1
11 ϕη , J23 = J32 = σuη − ϕη Ω11 ϕu , and J33 = σu − ϕu Ω11 ϕu . Define a0
new random vector ω̃ij = [ẽi η̃ij ũij ]0 = B −1 ωij . The above triangular factorization implies that4

new vector ω̃ij is normally distributed with the mean of zero and the diagonal variance-covariancematrix of Q. Then, by construction, we can obtain the following system of equations:ei = ẽi ,ηij = ϕη Ω−1
11 ẽi + η̃ij ,−1
uij = ϕu Ω−1
11 ẽi + J32 J22 η̃ij + ũij .

Under the assumption of ϕu = 0 and the normalization of ση = 1, the above equations imply that−1
0 −1
uij = σuη (1 − ϕη Ω−1
11 ϕη ) (ηij − ϕη Ω11 ei ) + ũij ,and conditional expectation E[uij |., Tij = 1] is−1
0 −1
E[uij |., Tij = 1] = σuη (1 − ϕη Ω−1
11 ϕη ) E[ηij − ϕη Ω11 ei |., Tij = 1],0 −1= σuη (1 − ϕη Ω−1
11 ϕη ) E[η̃ij |., Tij = 1].

(A.9)

Conditional expectation E[η̃ij |., Tij = 1] is then given asE[η̃ij |., Tij = 1] = E[η̃ij |ηij > −β + ( − 1)γdij − [ 1]yi − bij ],= E[η̃ij |ϕη Ω−1
11 ẽi + η̃ij > −β + ( − 1)γdij − [ 1]yi − bij ],= E[η̃ij |η̃ij > −β + ( − 1)γdij − [ 1]yi − bij − ϕη Ω−1
11 ẽi ],= E[η̃ij |η̃ij > −ẑij ],∗∗)/Φ(ẑij).
= φ(ẑij(A.10)∗ = β − ( − 1)γd + [ 1]y + b + ϕ Ω−1 (y − Γs ). Equation (A.10) is the corresponding
where ẑij
ij
ij
η 11
i
i
i
inverse-Mills ratio.

Appendix B. A Monte Carlo experiment with a linear economy
In this section, we conduct Monte Carlo experiments based on our model in section 2 tounderstand the following two questions: (i) what bias does the conventional regression exercise
without identifying producing regions and ignoring the sample-selection mechanism introduce into
our inference on the distance elasticity γ, and (ii) how much can our FIML estimator correct thebias successfully. To implement the experiments, we assign hypothetical values to the structuralparameters of our model as follows.
Consider an economy that is geographically separated into 47 regions. Each region is indexedby an integer between 1 and 47, respectively. 2 The distance between regions i and j, D ij , isequal to 100|i − j| with the minimum distance of 100 and the maximum of 4600. Each region
yields an identical product under productivity level a l that is set equal to 1.00. The parameter
2

This assumption of the linear economy might be the most relevant for an island country with a long-narrow arc
shape like Japan that consists of 47 prefectures.

5

of demand function (1), α, is common across the regions and equal to 0.75. This number of
α means that the price elasticity of demand is 4.00 and the wholesale price is 33.33 % marked
up over the corresponding marginal cost. All the producing regions share the same factor cost
cj of 0.55. Each region is also characterized by the aggregate price and transaction, p i and xi ,respectively, both of which we set to 20.00. For simplicity, we ignore the cross-regional variationsin the productivity-regional bias ratio θ ij by setting δij = 1.00 for all pairs of regions i and j. The
fixed cost fij = exp(λi + λj − vij ) is specified as follows. We calibrate the sum of the producing
and consuming regional fixed effects, λ i + λj , so that, when γ = 0.00, the probability of productdelivery from source to consuming regions is always equal to 0.50. The resulting fixed effect term
λi + λj then is (1 − α)α−1 c−j pi xi for all (i, j) pairs. The Gaussian random component in the fixed
cost, vij , has the standard deviation of σv = 0.30. We set the constant term of the transportation
cost µ to 1.50 and allow for idiosyncratic random variations in the transportation cost setting thestandard deviations of the random component of the transportation cost, σ u , to 0.30. Finally, in
our experiments, we admit no possibility of endogeneity bias simply setting ϕ η = [0 0].
In our Monte Carlo experiments, we first draw 1000 sets of Gaussian random variables u ij
and vij independently from their distributions. We then calculate price differential q ij and latentvariable zij following equations (6) and (7) under one of the three hypothetical values of γ, 0.00,
0.15, and 0.50. In each Monte Carlo draw with each true value of γ, we then implement four
different estimations of γ. The first one is the simple OLS regression of price differential q ij on thelog of the distance dij using the whole synthetic samples regardless of T ij = 0 or 1. By construction,
this OLS estimator, denoted by γ̂whole , is consistent and, hence, should be distributed around the
hypothetical true value. The second one is the OLS regression of the price differential q ij on thelog of the distance dij using only the samples that are selected with T ij = 1. This second OLS
estimator, denoted by γ̂OLS , suffers from sample-selection bias. Therefore, we expect to observethat the distribution of γ̂OLS is biased against the true value. The third estimation is with the FIML
estimator we introduce in section 3. This estimator, denoted by γ̂ FIML , should correct potential
bias due to sample selection. Finally, to explain the fourth estimator, consider the price differential
between two consuming regions without identifying producing regions, i.e., ln p̃ i − ln p̃k for any two
consuming regions i and k, where p̃i denotes the price of product l in consuming region i. The
OLS estimator conventional in the literature of the absolute LOP, which is denoted by γ̂ conv , thenis constructed by regressing the absolute value of the price differential between consuming regions
i and k, | ln p̃i − ln p̃k |, on the log of the corresponding distance d ik .3 Comparing the distribution ofγ̂conv with that of γ̂whole , we can understand the degree of bias the conventional regression exercise
suffers from on the inference of γ.
We first observe how the size of γ affects delivery choice. The left, middle, and rightwindows of Figure B.1 depict the contour plots of the probabilities of delivery from producing
3

For each Monte Carlo draw, the price of product l that is sampled in consuming region i, p̃i , is constructed asfollows. For each consuming region i, we obtain the set of the truncated prices that are delivered from producing
regions Si = {pij |j ∈ Bi }. This set Si includes the prices of the product that can be sampled as the representative
price in consuming region i, p̃i . We uniformly draw 100 prices from this set Si and take the average over them toconstruct p̃i .

6

regions to consumption regions for the cases of γ = 0.50, 0.15, and 0.00, respectively. In eachwindow, the contour lines represent the combinations of the producing and consuming regionsthat have an identical delivery probability. The left window shows that with the large distanceelasticity of γ = 0.50, the product delivery is profitable only locally. This is obvious from the factthat all contour lines are parallel to the 45 degree line and the equiprobability bands, which areconstructed by two contour lines with the same probability, are very narrow and always include
the 45 degree line. This shape of the contour plot implies that the product delivery occurs only
to consuming regions neighboring source regions closely. The middle window then exhibits thatthe equiprobability bands become much wider with the smaller distance elasticity of γ = 0.15.
Hence, in this model, a larger distance elasticity creates geographical clustering of products basedon different source regions. This is clearer if we set γ = 0.00. As displayed in the right window,
the equiprobability lines with the delivery probability of 0.50 are almost randomly placed over thewhole window: the product delivery occurs with the 50 % chance even between the producing andconsuming regions that are farthest apart each other.
Figure B.2 depicts simulated price differentials against the corresponding logs of distances.
The first, second, and third rows of the figure are for the cases with γ = 0.50, 0.15, and 0.00,
respectively. In each row, the first column reports the simulated samples conditional on the choiceof delivery Tij = 1, while the second column plots the whole samples regardless of delivery choice
Tij = 0, or 1. The two windows in the first row reveal severe data truncation under γ = 0.50.
Although the whole samples of the simulated price differentials have a clear positive association
with the logs of distances, the underlying selection mechanism is so strong that the observed
samples are concentrated only on local areas surrounding source regions with short range delivery.
The association of the observed price differentials with the logs of distances then becomes quitevague. The second and third rows prove that the sample selection turns out to be weaker when γ
becomes smaller to 0.15 and 0.00.
Figure B.3 reports the densities of the four different estimators of γ that are nonparametrically smoothed with the Epanechnikov kernel. The first row corresponds to the case with γ = 0.50;
the second the case with γ = 0.15; and the third the case with γ = 0.00. The first column plots
the smoothed densities of γ̂whole ; the second γ̂OLS ; the third γ̂FIML ; and the fourth γ̂conv . The threewindows in the first column show that γ̂ whole is consistent and distributed around the underlying
true value. The three windows in the second column, however, uncover that γ̂ OLS is subject tosevere downward bias. On the one hand, as displayed in the first and second rows in the second
column, γ̂OLS is distributed far left from the corresponding true value when γ is set to either 0.50
or 0.15. On the other hand, as shown in the third row of the second column, γ̂ OLS is consistent anddistributed around the true value if γ = 0.00. Therefore, a positive distance elasticity generates
the data truncation that causes the OLS estimates to be biased downwards. The three windows in
the third column clearly reveal that γ̂ FIML is consistent and distributed around the underlying true
value. The most striking fact from the three windows in the fourth column is that γ̂ conv performs
the worst among the other estimators. In the first and second rows for the cases of γ = 0.50 and
0.15, γ̂conv is distributed with the means of 0.019 and 0.003, respectively, and even far left fromthe corresponding density of γ̂OLS . This is the evidence that the conventional regression exercise
7without identifying producing regions suffers from the worst under-bias toward an inference on γ
among all the other estimators.
The Monte Carlo experiments of this section, therefore, confirm the necessity of identifying
producing regions and taking into account the sample-selection mechanism to draw a correct inference on the distance elasticity of transportation costs. The proposed FIML estimator can correctly
identify the true values of the distance elasticity with synthetic data generated from our structuralmodel.

8

Consuming region
5

10

15

20

25

30

35

40

45

10

0 .250.1
0.
5
0.75
0.10.25 0.5

γ = 0.50

40

0.5 0.250.1

5

10

15

20

25

30

35

40

45

0.1

10
20
30
Producing region

γ = 0.15

0 .1

40

0.5

5

10

15

20

25

30

35
0.5

0.25

0.5

10

0.
5

0.5
0 .5

0.
5

0.5

0.5

0.5

40

0.5

0.5

0.75

5
0.

0.5

20
30
Producing region

0.5

0.75 0.5

0.5

0.5

0.5

.
5
0.75 0.5

40

0

0.5

0.5

0.5

γ = 0.00

0.5

0.5

0.5

0.5

0.5

0.5
0.5

0 .5

0.5

0.5

0.75

0.5

0.5

5
0.

0.5

0.5

0.5
0.5

45 0.5

0.5
0.5
0.5

0.5
0.5
0.5

0.5

0.5

0.5

0.5
0.5

0.5

0.5

0.5

Figure B.1: Simulated probabilities of product delivery

20
30
Producing region

0.75
0.75 0.5 0.2 0.1
50.75
0.10.25 0.5

0.75
0.1 0.25 0.5

0 .2 5
0.5
0.75
0.5

0.25

0.75
0.1

0.25
0.75 0.5
0.75
0.5

0.25

0.1
0.75

0.25

0.1

0.5
0.5
0.5 0.75

0.5
0.50.5

0.5

0.5

0.5
0.5

0.5
0.5

0.5

0.5

0.5

0 .5

5
0.

0.5
0.5

0 .5

0.5

0.5

5
0.

0.5

Figure B.2: Simulated price diﬀerentials

H0: γ = 0.50

H0: γ = 0.15

H0: γ = 0.00

0.16

0

0.08

-0.02

0

0.02

0
-0.1

5

10

15

20

25

-0.05

0.4

0

0.15

0.6

FIML, γFIML

0.05

0.8

0.1

0.2

1

0
-0.04

5

10

15

20

25

0
-0.02

10

20

30

40

0
-0.1

1

2

3

4

0

-0.02

0

0.1

0

0.02

0.2

Conventional, γconv

Figure B.3: Kernel-smoothed densities of distance elasticity estimators

0
-0.04

0
-0.04
0.04

5

5

0.02

10

10

-0.02

15

20

20

15

25

25

0
0.1

0.06

4

6

8

10

12

0
0.2

0
0.02
0.04

0.6

0
0.12
0.18

0.4

2

0.2

0.5

1

1.5

2

2.5

5

0

OLS: truncated sample, γOLS

5

10

10

15

20

15

20

25

0
-0.2

0.14

0.55

0
0.45

0.5

1

5

10

2

3

20

15

4

OLS: whole sample, γwhole

25

0.02

0.04

0.3