Global COE Hi-Stat Discussion Paper Series 246

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

The Price of Distance: Producer Heterogeneity,
Pricing to Market, and Geographic Barriers

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

The Price of Distance:
Producer Heterogeneity, Pricing to Market, and Geographic Barriers

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: October 1, 2012
Abstract
This study investigates the effect of distance on price differentials across regions. To identify the
distance effect, we need to incorporate producer heterogeneity and pricing-to-market behavior.
Because geographic barriers alter the threshold levels of productivity to set a positive price acrossmarkets, the effect of distance on price differentials can be underestimated if heterogeneity andpricing to market are not accounted for. By incorporating these factors, empirical analysis using
micro-level data reveals that the distance effect is significantly large, suggesting that the price ofgeographic barriers is still high for regional transportation.
Key Words : law of one price; Transportation costs; Geographic barriers; Producer heterogeneity;
Pricing to market
JEL Classification Number : F11, F14, F41

We would like to thank Andrew Bernard for useful discussions and the suggested title. We are also grateful to
Alexandre Skiba for helpful discussions and to Russell Hillberry, Kiyoyasu Tanaka, Dao-Zhi Zeng and seminar participants at Hosei University, the APTS meeting at Singapore Management University, and the JSIE Meeting at Nanzan
University for insightful comments. Financial support for this research was provided by a Grant-in-Aid for Scientific
Research (No. 24530270) and the Seimeikai Foundation.
†
Corresponding author.

1.

Introduction

The effect of distance on price differentials across regions is a key factor in understanding the significance of geographic barriers. Geographic separation creates price differentials
across regions even in the absence of institutional differences (such as tariffs, taxes, and national borders). Law of one price (LOP) studies report a small distance effect (the distanceelasticity parameter is normally less than 0.01), and the distance effect is assumed to include
trade costs other than transportation costs (Engel and Rogers, 1996; Parsley and Wei, 1996;
Parsley and Wei, 2001; Crucini, Shintani, and Tsuruga, 2010). Hence, it is not clear why
the distance effect is so small and to what extent geographic barriers (transportation costs)
explain price differentials. Because the distance elasticity of transportation costs is a key
parameter when assessing the impact of geographic barriers, the trade literature, such as
Hummels (2007), Helpman, Melitz, and Rubinstein (2008), Crozet and Koenig (2010), andBalistreri, Hillberry, and Rutherford (2011), has tried to identify and estimate this parameter. Their empirical findings indicate that the distance elasticity in the trade literature tends
to be larger than that in the international finance literature, which exceeds 0.15. However,
the identification problem for the price differential effect of geographic barriers (distance)
has not been examined extensively.
This study sets out to measure the impact of transportation costs by using pricedifferential data. To measure transportation costs correctly using price data, as Anderson
and van Wincoop (2004) point out, the difference between market prices and prices at the
point of production must be used, not just two market prices. In addition, because anincrease in distance causes not only increases in price differentials, but also decreases in
product delivery propensity, distance causes selection biases. Thus, delivery choice to otherregions (export decision) should be accounted for to control for sample selection biases, as
in Helpman, Meliz, and Rubinstein (2008). Recent studies, in particular Donaldson (2010)
and Kano, Kano, and Takechi (2010) (hereafter KKT (2010)), follow Anderson and van
Wincoop’s (2004) suggestion of using the price in the source region of production. Donaldson(2010) identifies the source region of salt production in India and employs this information
to measure transportation costs using market prices. KKT (2010) use agricultural wholesale
price data in Japan, where the source and market prices are available. They also propose
an estimation procedure to take into account selection bias following Helpman et al. (2008).
Because high transportation costs are likely to deter firms from shipping their products toa more distant market, shipment data will be truncated for more distant markets. This
causes underbiases in the distance elasticity. KKT (2010) demonstrate that, if this bias is
not controlled for, the distance effect is quite weak. However, if these aspects are controlled
1for, distance has a significant impact on price differentials.
Although these studies identify the biases in the estimation of the distance effect,
the possible causes of the biases, that is, producer heterogeneity and pricing to market,
have not been examined in detail. Because producer heterogeneity and pricing-to-market
behavior cause different pricing across markets, price differentials may reflect more than justtransportation costs. In KKT (2010), in which markets are monopolistically competitive,
producers set invariant markups and there is no producer heterogeneity. By contrast, Donaldson (2010) uses the Eaton and Kortum (2002) model in which producer productivity isdispersed and the market is perfectly competitive. In both these studies, therefore, pricedifferentials are characterized by transportation costs only and different pricing behavior
across markets is not taken into account.
In this paper, we show that the estimates of the distance effect are underbiased if producer heterogeneity and pricing to market are ignored. We incorporate producer heterogeneity and nonhomothetic preferences in a monopolistic competition model. KKT (2010) use a
CES utility function and monopolistic competition, and the price differential is a function oftransportation cost only. By contrast, in a nonhomothetic preference framework, because anindividual firm’s pricing depends on local market characteristics (as shown by, for example,
Melitz and Ottaviano, 2008), price differentials do not simply reflect transportation costs,
but also include market structure (the number of products) and the productivity thresholdvalue. Because transportation costs reduce profitability in a remote market, the productivity threshold level to set a positive price depends on transportation costs. In particular, as
the productivity threshold increases, only highly productive and thus low-price-setting firms
produce. Hence, ignoring producer heterogeneity creates omitted variable bias, which causes
underestimation of the distance effect. Thus, we contribute to the literature by estimating
the distance effect while controlling for heterogeneity and pricing to market.
By estimating the price differential equation with sample selection, producer heterogeneity, and pricing-to-market behavior taken into account, we find a large distance effect on
price differentials. In the previous literature, using information on source regions, Donaldson(2010) and KKT (2010) both find a significant and moderate distance effect coefficient: 0.24
and 0.21 to 0.325, respectively. In this study, the coefficients of the distance effect range from
0.46 to 0.768. Although these estimates seem large, they are consistent with results in theeconomic geography literature. In particular, large distance effects are found when investigating truck transportation. Because truck transportation is a major type of transportationin our analysis, our results are close to those of Combes and Lafourcade (2005), who use
data on trade shipped by truck and estimate the distance elasticity to be 0.8. Therefore, we
conclude that there is a substantially large bias when producer heterogeneity and pricing2

to-market behavior are not incorporated. The price of geographic barriers (distance) is stillhigh for regional transportation, even in a country with highly developed transportation
infrastructure such as Japan.
The introduction of nonhomothetic preferences is essential for investigating the distance effect on price differentials with producer heterogeneity. If a CES utility function isused and thus monopolistically competitive firms set constant markup prices, the heterogeneity term will be cancelled out in the price differential equation and the price differential
depends on transportation costs only. If the focus is not on individual price differentials, thenimportant implications are obtained for aggregate price levels under firm heterogeneity using CES, because, as Ghironi and Melitz (2005) and Bergin, Glick, and Taylor (2006) show,
Balassa–Samuelson effects emerge. Here, because we study individual price differentials,
there is no room for producer heterogeneity in a standard CES framework. Nonhomothetic
preferences lead firms to set different prices across markets, and these prices depend on aheterogeneous threshold; therefore, heterogeneity plays an important role in this analysis.
Even in a CES utility framework, pricing-to-market behavior may be taken into account. If the utility function parameter is different across markets, price differentials are afunction of not only transportation costs, but also the elasticity parameter in each market.
Thus, the price in each market is different. However, these elasticity parameters are not directly related to transportation costs, and can therefore be controlled for by market-specificeffects. In a nonhomothetic preference model, the thresholds are related to transportation
costs; hence, the distance effect will be biased unless it is controlled for. We estimate bothnonhomothetic and CES models to capture the magnitude of the bias.
This paper is organized as follows. In Section 2, we develop our nonhomothetic
preference model with producer heterogeneity. For comparison, we also develop a CES
model. Then, in Section 3, the empirical framework is derived and Section 4 reports theestimation results. The final section concludes.

2.

Model

In this section, we develop a model of pricing and delivery patterns. Consumers purchase avariety of products delivered from their own and other regions. Each product is produced bya single producer. These producers are heterogeneous in terms of productivity and engage inmonopolistic competition. Because one of the main purposes of this paper is to demonstrate
the differences between cases of nonhomothetic and CES preferences, we first introduce anonhomothetic model. Then, we consider a CES utility model for comparison.
2.1. Consumers
3Consumer preferences are expressed by a nonhomothetic utility function. Nonhomothetic preferences have been introduced to account for pricing to market (Melitz andOttaviano, 2008; Simonovska, 2010). We employ the Simonovska (2010) framework, which
is suitable for our analysis because it enables us to make comparisons with the CES model
easily. Our derivations rely on Simonovska (2010), although she focuses on trade volumes
and price levels, whereas the focus here is on individual pricing across markets.1
Consumer nonhomothetic preferences in region i are expressed by:Zui =ln(qi (ω) + q̄)dω,(1)ω∈Ω

where ω is a variety index, Ω is the set of products available in market i, and qi (ω) is
consumption of variety ω. The presence of q̄ makes these preferences nonhomothetic. This
represents the minimum consumption requirement for consumers. If q̄ = 0, the utility
function is a typical homothetic function. The size of q̄ can be changed, so this can benormalized to 1 as in Young (1991). Each consumer is assumed to supply one unit of labor.
Thus, income is equal to wages, wi . The budget constraint is:Zwi =pi (ω)qi (ω)dω.
(2)ω∈ΩThen, from utility maximization, the demand function is obtained by:
wi + q̄Pi− q̄,(3)
Ni pi (ω)
R
R
where Pi = ω∈Ω pi (ω) is the price index and Ni = ω∈Ω dω is the number of products inmarket i. This demand function has regular characteristics such that demand is decreasing
in prices and increasing in income (wages). If the number of products supplied to thismarket rises, the demand for each product will fall. This will in turn affect producers’
pricing behavior.
qi (ω) =2.2. Producers
Consider a producer located in region j. The number of potential producers is assumed to be fixed, so firms decide whether to produce or shut down. This is similar tothe short-run equilibrium case in Melitz and Ottaviano (2008). The timing of the delivery
decision is made as follows. Producer productivity, φ, is assumed to follow a random distribution, G(φ). Producers incur a fixed cost before their productivity level is realized and,1

Simonovska (2010) demonstrates how the nonhomothetic model works in general equilibrium and compares it with the CES model.

4based on realized productivity, they decide whether to deliver and set their optimal prices.
This enables us to establish a similar delivery choice decision problem as in the CES case.
The producer profit maximization problem is to maximize profits, πij :max πij = pij qij −pij

τij wjqij − fij ,φ(4)where pij is the price in region i for products from region j, qij is the quantity of products
from region j sold in region i, and τij is the iceberg-type transportation cost, τij > 1 fori 6= j and τij = 1 for i = j. Because labor is assumed to be the only input, the wage rate,
wj , indicates the unit cost and φ is a measure of productivity. This productivity parameter
differs among producers (firm heterogeneity). Because each product is produced by a single
producer, the number of varieties is equal to the number of producers. The optimal priceset by a producer with productivity φ is:pij (φ) = (τij wj (wi + q̄Pi ) 1/2) .
φNi q̄

(5)

The optimal price depends on not only transportation costs, but also local market characteristics. If income in markets (wi ) is high, producers can charge high prices. The existenceof a large number of competitors means large N i, which induces low prices because of toughcompetition.
In contrast to the CES preference case, if the price is sufficiently high, demand will
be zero. Then, the profit for the firm in region j derived from supplying this product toregion i will also be zero. We denote the productivity of this firm φ∗ij . Then, this thresholdvalue is expressed by:φ∗ij =

τij wj Ni q̄
.
wi + q̄Pi(6)

The threshold value, φ∗ij , is increasing in transportation costs, τij : only high- productivity
firms can overcome trade barriers. This property also holds in the CES preference case.
On the other hand, market structure measured by the number of firms, Ni , influences thethreshold value, whereas it has no effect in the CES case. This is because of variable markups
in the nonhomothetic model.
Furthermore, in the CES model, firms charge a constant markup over the marginalcost. The optimal price in the nonhomothetic case depends on market structure throughφ∗ij , which means that the productivity threshold matters for each producer’s price. In
other words, aggregate producer characteristics affect individual pricing behavior. Thisrequires us to account for heterogeneity and pricing to market to identify transportation
costs using regional price differential data. Because of the assumption of monopolistic
5

competition, the product index can be expressed by the producer’s productivity measure:
P R
P
P R
Pi =
p
(φ)µ(φ)dφ
and
N
=
N
=
∗
iν
i
iν
ν φiν
ν
ν φ∗iν µ(φ)dφ, where µ is a conditional
density function of φ conditional on delivery.
The relationship between the optimal price and the threshold value in this case issimilar to that in the Melitz and Ottaviano (2008) case. Melitz and Ottaviano (2008) use
a quadratic utility function and show how market size affects the key features in a modelwith firm heterogeneity. The optimal price is increasing in the threshold level of productivity
and the number of firms is related to the threshold value negatively. Thus, many properties
derived here are common to nonhomothetic models.
Assuming that productivity follows a Pareto distribution (G(φ) = 1 − bθ /φθ , θ > 0),
the expected profit will be:Z∗
Eπij = (1 − G(φij )) πij µdφ,(7)where µ = g/(1 − G(φ∗ )) = φ∗ θ /φθ+1 . This is the conditional density where the productivity
exceeds φ∗ij . Then, expected profit is calculated as follows:(1 − G(φ∗ij ))Z

πij µdφ =bθ τij wj q̄
.
(2θ + 1)(θ + 1)φ∗ θ+1(8)

Firms decide whether to deliver their product to region i depending on the above profit
measure and fixed entry costs. This captures the self-selection problem in delivery patterns.
The productivity threshold, φ∗ , affects pricing behavior and delivery choice. In our setting,even though productivity is higher than the threshold level, such firms may still choose
not to deliver their products because of negative expected profits. Thus, this thresholdparameter does not directly separate producers that deliver and those that do not. Rather,
the threshold directly influences prices across markets.
2.3. CES caseWe intend to compare our results with those for the CES utility function case. As wewill see, the same implications for price differentials are derived with or without producer
heterogeneity. Thus, we consider the CES model without heterogeneity for comparison withthe results in KKT (2010).
We briefly specify a consumer’s preferences using a simple CES model as follows:Zui = [xi (ω)α dω]1/α .
ω∈Ω6Then, maximizing utility subject to the budget constraint (wi =following demand function:xi =Rpi (ω)qi (ω)dω) yields thepi (ω)−
wi ,
Pi1−

R
where  is the elasticity of substitution,  = 1/(1 − α), and Pi = [ ω∈Ω pi (ω)1− dω]1/(1−) .
We consider a homogeneous firm in a monopolistically competitive market. The firm’s
profits are:πij = pj (ω)xj (ω) −τij wj xj (ω)− fij .
φThen, by profit maximization, the optimal price is obtained using constant markup pricing
as follows:pij (φ) =τij wj.
φαSubstituting this into the profit function yields:
πij (φ) = (1 − α)(τij wj 1−) wi .
αPi φ

Because firms are assumed to be homogeneous, their decision to deliver does not depend on
a randomly selected level of productivity. Rather, the choice is based on the comparisonof profits and fixed cost of delivery. If πij /fij > 1, then firms in region j will deliver theirproducts to region i. Thus, similarly to the heterogeneous firm case, delivery data aretruncated because of self-selection by the producers.
This break-even productivity level depends on transportation costs. If transportation
costs, τij , are high, firms that are productive enough are able to make positive profits: φij isincreasing in τij . However, as mentioned, market structure does not affect φij directly, but
only through the price index, Pi .
2.4. Price differentials
Our approach of taking the difference between the price in markets and that in source
regions allows us to measure transportation costs accurately. Because retail prices do notconsider information about the source, taking the difference between two market prices does
not necessarily enable the measurement of transportation costs. However, if the source priceand the market price with information about the source are available, the difference between
these prices captures the costs of transportation.
7

Using the optimal prices set by firms, the price differential between market and sourceis:pij /pjj = τij φ∗jj 1/2 /φ∗ij 1/2 .

(9)

Because the threshold value, φ∗ij , depends on transportation costs, ignoring producer heterogeneity causes biases in identifying the relationship between the price differential andtransportation costs. If τij increases, φ∗ij will increase. Because φ∗jj does not depend on τij ,a larger φ∗ij induces a smaller price differential. Thus, heterogeneity reduces the price differential. This omitted variable bias may cause underestimation of the effect of transportation
costs.
In addition, φ∗ij depends on the number of firms, Ni . This is a function of the thresholdvalue itself and thus is affected by transportation costs. Hence, the changes in τij areassociated with the changes in market structure. This implies that market prices are set
depending on market structure and, therefore, the number of firms across markets is adeterminant of price differentials. If this type of pricing-to-market behavior is not controlled
for, the estimates of transportation costs will be biased.
In a CES utility framework, the price differential is:pij /pjj = τij .
As we mentioned, one of our objectives in this paper is to highlight the changes by incorporating firm heterogeneity. As a matter of fact, this equation holds with and without producer
heterogeneity. This is because even if firms’ productivity is heterogeneous, optimal pricing
does not depend on the threshold value of productivity, which is a key factor of heterogeneity. Besides, each firm’s productivity is cancelled out when considering price differentials.
Hence, producer heterogeneity does not play an important role in the link between price differentials and transportation costs in a CES model. Producer heterogeneity matters for thelink between price differentials and distance not when preferences are CES, but when they
are nonhomothetic. If we introduce nonhomothetic preferences, firms set variable markups
across markets in the setting of optimal prices and thus we deal with pricing-to-market behavior. Therefore, the bias caused by producer heterogeneity is indispensable for pricing tomarket.
In contrast to the nonhomothetic case, price differentials in the CES case are independent of market characteristics. This is because in the CES case, again, the productivity
threshold level does not affect individual pricing. The thresholds are derived from the zeroprofit conditions and determine the selection of producers that deliver, rather than determining prices. As a result, when obtaining price differentials, market characteristic variables are8cancelled out. Hence, market characteristics such as income and the number of competitors
can be taken into account in the nonhomothetic case only.
As mentioned in the Introduction, even in a CES model, pricing-to-market behavior
can be taken into account by introducing demand parameter heterogeneity across markets.
That is, if the elasticity of substitution parameter differs across markets, the price differential
will be:pij /pjj = τij (αj /αi ),where αi and αj are demand parameters in the CES utility function. However, these can becontrolled for by using region-specific effects and have nothing to do with the transportation
cost, τij . Hence, this does not cause any biases in the estimation of the distance effect.
By using the formula for the threshold value in the nonhomothetic model, φ∗ij , we areable to express the price differential as follows:
1/2 (wi + q̄Pi )pij /pjj = τij

1/2(wj + q̄Pj )1/2(

Nj 1/2
) .
Ni

(10)
1/2

The heterogeneity effect reduces the direct impact of transportation costs from τij to τij
in our nonhomothetic specification. In general, the effect of transportation costs will also
be weakened in a nonhomothetic specification because the effect of a transportation cost
increase on price differentials is mitigated by the producer selection. In the presence of hightransportation costs, only high-productivity firms are able to ship their products. Such firms
set their prices at a low level. Thus, the greater the distance between markets, the lower isthe magnitude of the increase in prices. This mechanism creates underbias in the distanceelasticity using the price differential data only.
This selection mechanism operates at the individual pricing level. This mechanism
also influences average price changes associated with general productivity shocks, as Ghironi
and Melitz (2005) and Atkeson and Burstein (2008) show. If only high-productivity firms canexport because of negative shocks, then, because they set the price at a low level, the average
price will be low. If free entry is assumed, firm exit because of negative shocks will cause
labor demand to decrease and thus labor costs to decrease. This enables low-productivity
firms to export, implying an increase in the average export price. Thus, depending on theentry condition assumptions, the average price either increases or decreases. In our study,
because we do not consider free entry, negative shocks will decrease individual prices set in
the market.
Other factors that affect the price differentials are source, market characteristics, andmarket structure. If these factors are correlated with transportation costs, omitted variable9biases occur. Taking the log of the above equation yields:
ln pij − ln pjj = (1/2) ln τij + (1/2) ln Nj − (1/2) ln Ni+ (1/2) ln(wi + q̄Pi ) − (1/2) ln(wj + q̄Pj ). (11)The price differential depends on not only transportation costs, but also market characteristics, such as the number of products and price indices. This property reflects the pricingto-market behavior. Because the optimal price depends on local market characteristics,
the price differentials reflect market structure. The ability to capture this element is anadvantage of the nonhomothetic model over the CES framework.
So far, we have not imposed any functional form on transportation costs. We adopt
the following conventional specification:
γ µ+uijτij = Dije,where Dij is the distance between two regions. That is, if γ > 0, then as distance increases,transportation costs increase. The constant term µ corresponds to the uniform transportation costs component and uij denotes unobservable transportation costs, uij ∼ N (0, σu ).
The log form is:ln τij = γ ln Dij + µ + uij .
The distance elasticity, γ, is our main parameter. Identifying this parameter is important if
delivery choice, producer heterogeneity, and pricing to market are to be accounted for.
Regarding the threshold value (φ∗ij ), even if φ∗ij < φ, the producer with productivity φ
may not deliver its product because demand is too low to cover fixed costs. Thus, producer
heterogeneity (threshold value φ∗ ) matters mainly for the individual pricing decision, andnot for the delivery decision. We take the delivery decision into account by considering thesample selection problem caused by the positive profit condition.
2.5. Delivery choice
The price differential is observed only when there is an actual delivery. Thus, there
will be a data truncation problem. As the delivery choice is made based on profitability, we
consider the producer’s delivery decision. Because producers pay fij , the delivery decision
is summarized by the variable Zij :Zij =bθ τij wj q̄
(2θ+1)(θ+1)φ∗ij θ+1

fij
10

.

Thus, if Zij is greater than 1, firms in region j choose to deliver the product to region i. By
taking logs, we have the following delivery choice equation:ln Zij = θ ln b + ln τij + ln wj + ln q̄ − ln(2θ + 1)(θ + 1) − (θ + 1) ln φ∗ ij − ln fij= θ ln b − θ ln τij − θ ln wj − θ ln q̄ − ln(2θ + 1)(θ + 1)
− (θ + 1) ln Ni + (θ + 1) ln(wi + q̄Pi ) − ln fij .
If ln Zij > 0, then delivery from j to i will take place. Because the price differential isobserved only when ln Zij > 0, we take into account this selection bias to estimate the pricedifferential equation. We estimate the price differential and delivery choice equations jointly.
Similarly, in the CES framework, the delivery choice is expressed by Zij :
τ w

Zij =

ij j 1−
(1 − α)[ αP
] wi
iφ

fij

.

Thus, taking logs yields a similar expression for delivery choice:ln Zij = zij = ln(1 − α) + (1 − ) ln τij + (1 − ) ln wj− (1 − ) ln α − (1 − ) ln Pi − (1 − ) ln φ + ln wi − ln fij .
Our focus is on the individual firm’s choice of prices, rather than on trade volume as in
Helpman et al. (2008). Thus, it is not necessary to control for the effect of heterogeneity
on aggregate variables. Rather, we need to account for the impact of heterogeneity on theindividual firm’s pricing across markets and its delivery choice according to this selection
mechanism.
Similarly to the nonhomothetic preference case, we estimate the price differential
equation taking this selection bias into account. Whereas the KKT (2010) model is estimatedusing an instrumental variable approach, controlling for selection bias is based on this delivery
choice equation. Thus, in this paper, we simply estimate the price differential and delivery
choice equations by maximum likelihood. We use regional dummies to control for marketspecific effects such as price indices (Anderson and van Wincoop, 2003; Helpman et al.,2008).
2.6. Empirical specification
For the estimation, we need to parameterize the price differential and delivery choice
equations. As in Helpman et al. (2008), fixed costs have the following specification: f ij =11

exp(λi + λj − νij ). The estimating equations are expressed as follows:
zij = − ln fij + θ(ln b − q̄) − θµ − θuij − ln(2θ + 1)(θ + 1)
− θγ ln Dij − θ ln wj − (θ + 1) ln Ni + (θ + 1) ln(wi + q̄Pi )=c0 + c1 − θγ ln Dij − θ ln wj − (θ + 1) ln Ni + (θ + 1 + c2 )dumi + c3 dumj + ηij ,(12)

where c0 = −θµ − ln(2θ + 1)(θ + 1), c1 = θ(ln b − q̄), ln(wi + q̄Pi ) − λi is captured by region i’s
specific effect; therefore, (θ + 1) ln(wi + q̄Pi ) − λi = (θ + 1 + c2 )dumi , and dumi is region i’s
specific effect. We consider that the number of product may be noisy variable or the way of
introducing the number of product may be misspecified, thus we use χ ln Ni instead of ln Ni inestimations, where χ is a free parameter. The error term is ηij = −θuij +νij ∼ N (0, θ 2 σu2 +σν2 ).
Similarly, the price differential equation is:
qij = ln pij − ln pjj= (1/2)µ + (1/2)γ ln Dij + (1/2) ln Nj − (1/2) ln Ni + c4 dumj − c5 dumi + (1/2)uij , (13)where dumj controls for region-specific effects including wages and price indices, as in thedelivery choice equation. Because of pricing to market, the disturbance term is modified touij /2. Thus, not only the covariates, but also the shape of price differential distribution isdifferent from the CES case.
As in KKT (2010), with regard to the identification of the distance elasticity, γ, theprice differential and product delivery equations reveal an important result. Simply estimating the price differential equation only may lead to underestimation of γ. This is because theerrors in these equations are correlated: because ηij = −θuij + νij , the error terms ηij anduij are correlated. As shown by Helpman et al. (2008), taking the conditional expectation of
qij yields: E[qij |X] = (1/2)µ + (1/2)γ ln Dij + (1/2) ln(1 + Ni ) − (1/2) ln(1 + Nj ) + c4 dumj −c5 dumi +(1/2)E[uij |X], where X is a vector of observables. Because E[uij |X] = ρ σσuη E[ηij |X],
if we ignore this correlation, there will be bias in the estimate of the distance effect.2 Thisbias term is expressed as an inverse Mills ratio: E[ηij |X] = φ(ẑij )/Φ(ẑij ). Hence, to obtainconsistent estimates, we need to account for the correlation between the price differential
and delivery choice equations; the significance of sample selection relies on this correlation
parameter, ρ.
To take into consideration this selection effect, we employ a full information maximum
likelihood (FIML) approach. We assume that the distribution of the errors is joint normal.
2

Because u and ν are orthogonal, E[ηu] = E[(−θu + ν)u] = −θσu2 . The correlation ρ is defined byρ = σηu /σu . Thus, σηu = ρσu = −θσu2 . Then, σu = −ρ/θ.

12The log-likelihood function is: 
W1ij + 2ρσu−1 (W2ij )L=(1 − Tij ) ln[Φ(−W1ij )] +Tij ln Φ(1 − ρ2 )1/2
i,j
i,j
 X

X
W2ij
+
Tij ln φ−
Tij ln(σu /2),(σu /2)
i,j
i,j
X

X

where W1ij = c0 + c1 + θγ ln Dij + θ ln wj + (θ + 1)χ1 ln Ni + (θ + 1 + c2 )dumi + c3 dumj andW2ij = qij − (1/2)µ − (1/2)γ ln Dij − (1/2)χ2 ln Nj + (1/2)χ3 ln Ni − c4 dumj − c5 dumi . Using
FIML has several advantages: it is efficient, it allows us to examine delivery choice, and it
can detect unobservable factors driving self-selection bias in an explicit way. However, ourapproach has the disadvantage of possible misspecification; we address this misspecification
issue by doing diagnosis checks.
In the case of CES utility without producer heterogeneity, the estimating equation is:zij = β − ( − 1)γdji + ( − 1) ln Pi + (1 − ) ln wj + ln wi + ξj + ωl + λi + ηij ,where β = − ln  − (1 − ) ln( − 1) + (1 − )µ, ωl = (1 − )φ, and ηij = (1 − )uij + νij . The
price differential equation is:
qij = µ + γdij + c6 dumi + c7 dumj + uij .
Then, the log-likelihood function is as follows: 
W3ij + ρσu−1 (W4ij )L=(1 − Tij ) ln[Φ(−W3ij )] +Tij ln Φ(1 − ρ2 )1/2
i,j
i,j

 X
X
W4ij
−
Tij ln σu ,+Tij ln φ
σ
u
i,j
i,j
X

X

where W3ij = β − ( − 1)γdji + ( − 1) ln Pi + (1 − ) ln wj + ln wi + ξj + ωl + λi andW4ij = qij − µ − γdij . We use the consumer price index as the price index, and the use ofregion-specific effects controls for other region-specific factors.
These two empirical models, namely the nonhomothetic model and the CES model,
account for the data truncation problem caused by the self-selection of producers. The maindifference between these approaches is in the price differential equation. In the CES case, it
is simply a function of distance. In the nonhomothetic case, the effect of distance is different,
and there are local market characteristics, which reflect producer heterogeneity and pricingto-market behavior. We apply our model to the price and delivery data to find the distanceelasticity.

133. Data
We apply our approach to data on wholesale prices of individual goods and delivery
patterns across regions. Using wholesale prices enables us to focus on transportation costs
because retail prices include local distribution costs. The individual goods are agricultural
products in Japan. As the wholesale prices of agricultural products in source regions andmarkets are available, the price differential between market and source prices can be used tomeasure transportation costs properly.
The data source for wholesale prices is the Daily Wholesale Market Information on
Fresh Fruit and Vegetables (“Seikabutsu Hinmokubetsu Shikyo Joho” in Japanese). The data
set is collected by the Center for Fresh Food Market Information Services (“Zenkoku Seisen
Syokuryohin Ryutsu Joho Senta”; URL: www2s.biglobe.ne.jp/fains/index.html), which provides data for almost all transactions at 55 wholesale markets operating daily in the 47
prefectures of Japan. Each prefecture has at least one wholesale market, so the data variation is nationwide. This daily market survey covers the wholesale prices of 120 different
fruits and vegetables.
Each agricultural product is further categorized by different varieties, sizes, andgrades, as well as producing prefectures. Hence, for example, the data set reports thewholesale prices of potatoes at six different wholesale markets of the “Dansyaku (Irish Cobbler equivalent)” variety, size “L”, with grade “Syu (excellent)” produced in “Hokkaido”
Prefecture on September 7, 2007. Because prices depend on characteristics, each combination of characteristics is identified as the same product. This high degree of categorization
is important because the LOP requires a comparison of the prices of identical goods toinfer transportation costs precisely. We focus on eight vegetables: cabbages, carrots, Chinese cabbages (c-cabbages, hereafter), lettuce, shiitake mushrooms (s-mushrooms, hereafter),spinach, potatoes, and Welsh onions. In this paper, we examine the 2007 survey that reports
the market transactions for a period of 274 days. Thus, the unit of measurement for the
sample is source-market price differentials of the same product on a given trading day.
The price reported in each market has three forms: the highest price, the mode price,and the lowest price. Most markets record all three prices, but several markets report only thehighest and the lowest prices or only the mode price. Thus, we construct our price variable byaveraging these price variables. We use the mode price when this is the only price available.
The transaction unit of measurement for each product is also reported. To obtain the same
unit of measurement for each product, we divide the price by the number of transaction
units (kilogram). Table 1 summarizes several descriptive statistics for these products. The
first row reports the average price per kilogram (1 kilogram = approximately 2.2 pounds).
14

S-mushrooms are the most expensive, at 1113.627 yen (approximately 13 US dollars), andthe cheapest are c-cabbages, which are 61.628 yen (approximately 0.9 US dollars).
Table 1 also shows that each product is highly categorized by product variety, size, andgrade. The number of distinct products is large: 1,207 for cabbages; 1,186 for carrots; 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 deliveries
as Tij (l) = 1 and nondeliveries as Tij (l) = 0 only for the dates on which the product istraded at the wholesale market in producing prefecture j. We identify product delivery
Tij (l) = 1 if the data report that the source prefecture of product entry l sold in consuming
region i is region j. The price differential is constructed by subtracting the wholesale pricein producing prefecture j, pj (ω), from that in consuming prefecture i, pi (ω). If the sampleof qij (ω) is available, this means that Tij (ω) = 1 for pair (i, j).
The bottom part of Table 1 reports that the total number of both delivery and nondelivery observations across all products is greater than 190,000 for each vegetable. We use
this as the number of observations in our FIML estimation. Out of the total number ofdelivery and nondelivery cases, the number of delivery cases is relatively small, at approximately 10,000 for each vegetable. Our data set, therefore, indicates that product delivery isquite limited. Many products are delivered only locally; for example, carrots are producedin every prefecture and shipped to own-prefecture markets. Only agriculture-intensive prefectures such as Hokkaido ship to remote markets. Thus, the data truncation issue is quite
important in this sample.
The other data we use in this paper are obtained as follows. The geographic distance between prefectural pair (i, j) is approximated by the distance between the prefectural
head offices located in the prefectural capital cities. The distance data are provided by the
Geospatial Information Authority of Japan (GSI). The data are publicly available on the
GSI website.3 We use daily temperature to control for supply and demand shocks. The
daily temperature data are reported by the Japan Meteorological Agency, which we download from their website.4 Finally, we use the monthly data of the scheduled cash earnings forwages, which are reported in the Monthly Labour Survey (“Maitsuki Kinrou Tokei Chosa”)
conducted by the Ministry of Health, Labour, and Welfare.5
One verification strategy of introducing a nonhomothetic preference is to check whether
high quality (therefore high price) goods are sold in high income markets. We use the data on
wholesale market prices and the scheduled cash earnings to see a positive correlation between
3

www.gsi.go.jp/kokujyoho/kenchokan.html
www.data.jma.go.jp/obd/stats/etrn/index.php
5The data are available at www.mhlw.go.jp/toukei/list/30-1.html.

415

these. Figure 1 depicts each prefecture’s salary on the vertical line and vegetable prices on
the horizontal axis. All data variations reveal a positive relationship between incomes andprices as shown by the solid line with positive slope. This indicates that high income regions
tend to consume high quality (price) goods, suggesting that our nonhomothetic preference
specification is consistent with a certain characteristic in our data.

4. Estimation results
Table 2 reports the estimation results. The top half of Table 2 reports our main
results. For comparison, the results using the CES utility function and the simple regression
results are reported in the bottom half of Table 2. The distance elasticity in the nonhomothetic framework ranges from 0.46 (cabbages) to 0.768 (s-mushrooms). This indicatesthat when the shipment distance from origin to destination increases by 1 percent, the pricedifferential increases by about 0.5 percent. These values for the distance elasticity are larger
than those in previous studies, which implies the presence of an underbias of the distanceelasticity in previous studies. As in previous studies, if we use two market prices to construct price differentials and regress these on distance, then the distance effect coefficient is
at most 0.05. That is, even if the distance is doubled, the price differential increases by only
5 percent. Thus, even using our data, regressing only the price differential (not identifying
the source region) on distance, which is the conventional method in the literature, yields
similar results. The results of the CES utility function are similar to those in KKT (2010).
As in KKT (2010), and following Anderson and van Wincoop (2004), the price differential
measure is the difference between the market price and the price in the producing prefecture. Delivery choice is modeled explicitly to control for sample selection. One differencein estimations between this study and KKT (2010) is that they propose an instrumental
variable approach for the structural estimation. Although the results of the CES framework
indicate significantly large distance effects of 0.287 to 0.49, these are smaller than those of
the nonhomothetic model.
When incorporating producer heterogeneity and pricing to market, the results under
nonhomothetic preferences indicate a much larger distance effect compared with both asimple regression and the CES framework; the CES results, in turn, are larger than theconventional OLS results. The results under nonhomothetic preferences are found to be evenlarger than the CES case. This is consistent with our argument that producer heterogeneity
affects the pricing decision in each market and thus causes underbias in the distance elasticity
estimates. This is because transportation costs induce only productive firms to deliverproducts, and these firms can charge a low price. Large distance elasticity estimates also
16

imply that geographic barriers influence delivery choice. The probability of delivery will be
reduced by an increase in transportation costs. Thus, the presence of large distance effects
after accounting for producer heterogeneity suggests that the price of geographic barriers isstill high for regional transportation.
Another important parameter in our estimations is the heterogeneity parameter, θ.
Our estimates range from 1.169 to 2.329. A small θ means that there is a large dispersion
in productivity. These estimates can be considered to be small (producer heterogeneity ishighly dispersed). This may be because farmers in Japan are quite heterogeneous. Small
farms operated by elderly people in suburban areas produce agricultural products, whereas
agriculture-intensive prefectures such as Hokkaido are home to large-scale farms. In 2009,
the average area under cultivation for each farm in Hokkaido Prefecture was 20.50 hectares(approximately 50.66 acres), compared with an average area of 1.41 hectares (approximately
3.48 acres) in other prefectures.6 These farms may deliver their products to the same markets.
In our framework, all prefectures have the same productivity distribution, so the low valueof θ may reflect this dispersion among farms. In fact, in Table 2, the estimates obtainedusing carrots and potatoes have small values of θ. Because Hokkaido is known to be a highproductivity region for these products, the presence of heterogeneous suppliers gives us large
dispersion results.
The heterogeneity parameter, θ, has been investigated extensively in the trade literature. In the Eaton and Kortum (2002) framework, this is the elasticity of the trade
parameter, which is a crucial parameter for welfare gain analysis from trade (Arkolakis,
Costinot, and Rodriguez-Clare, 2011). Eaton and Kortum (2002) estimate this parameterto be 8.28, Bernard, Eaton, Jensen, and Kortum (2003) estimate it to be 3.6, Crozet andKoenig (2010) estimate it to be from 1.65 to 7.31, Simonovska and Waugh (2010) use thesimulated method of moments to obtain estimates from 3.57 to 4.46, and Balistreri et al.
(2011) estimate it to be from 3.924 to 5.171. Donaldson (2010) uses the Eaton and Kortum(2002) model to estimate the productivity variability parameter, and estimates an averagevalue of 3.8. As in Donaldson (2010), we use price data to estimate two crucial parameters in the producer heterogeneity model. Our estimates are lower than these other studies,possibly because the more disaggregated the product level is, the higher the dispersion ofheterogeneity. Our sample contains disaggregated product-level data and has a quite finecategorization; as such, our estimates report a small θ.
The correlation parameter ρ is also important for the significance of sample selection.
These estimates range from −0.624 to −0.868. All results are negative and statistically significant. Hence, to identify the true parameter, controlling for selectivity bias is crucial. A
6

www.maff.go.jp/j/tokei/sihyo/index.html.

17

positive shock that increases the price differentials caused by transportation costs (for example, a fuel price increase) will also decrease the probability of delivery. Without controlling
for this negative correlation caused by unobservable shocks, as we have seen, the distanceeffects are found to be small. We detect the existence of such a negative effect.
The relevance of the estimates depends on the empirical validity of our model. For
model validation purposes, we conduct diagnostic checks of our model with respect to two
important aspects of the actual data: the pattern of product delivery and the associationof price differentials with delivery distances. First, we calculate the percentage correctlypredicted (PCPs) measures for Tij (l) = 0 or 1. To construct the PCPs, we calculate thepredicted conditional probabilities and the predicted delivery index where the predictedprobabilities are greater than 0.5. The results are reported in the bottom row of Table 2.
The PCPs are all greater than 0.96, which suggests that our model successfully predicts
actual delivery patterns.
The second diagnosis concerns price differentials with respect to delivery distances.
The question is whether our sample-selection model predicts the actual price differentials. To
conduct this diagnosis check, we derive the prediction of the model for price differentials withthe selection bias controlled for. Each panel in Figure 2 plots the resulting predicted pricedifferentials (dots), as well as the data counterparts (crosses), against the corresponding log
distances for each vegetable. The dots are distributed inside the cloud formed by the crosses
in all panels. This means that our model successfully predicts the relationship between theprice differentials and distances overall.
One issue remaining when comparing the results of the nonhomothetic and CES
models is the elasticity of the substitution parameter, . In the nonhomothetic preference
model, the utility function is in log form to obtain an explicit solution for the optimal price.
Because the coefficient of distance in the selection equation is θγ in the nonhomothetic caseand ( − 1)γ in the CES model, ignoring the elasticity of substitution may cause small
estimates of θ and large estimates of γ. If this composite remains constant, a small elasticity
of substitution may imply a large distance effect. The identification of these parameters
separately requires a model incorporating both the dispersion and elasticity of substitution
components. This is a limitation of our study and an importatnt issue for future research.

5. Concluding remarks
We have investigated the impact of producer heterogeneity and pricing-to-market
behavior on the distance elasticity in regional price differentials. Because producer heterogeneity is not treated as crucial in the identification of the distance effect in a conventional
18

CES utility framework, we developed a nonhomothetic preference model, thus incorporating
pricing-to-market behavior.
Our empirical analysis showed that ignoring these factors causes underestimation in
the CES utility framework. The distance effect is significantly large for regional price differentials. These results suggest that the price of geographic barriers is still high for regionaltransportation. Even though Japan is considered to have well-established infrastructure anda sophisticated logistics system, the geographic barriers are large enough to create substantial price differentials. Thus, in a country with poor transportation facilities and services,
regional differences may be large and markets geographically segmented.
Although incorporating producer heterogeneity and pricing to market corrects thebiases in the distance elasticity, there are other concerns regarding pricing behavior. As
Hummels and Skiba (2004) have shown, there may be specific transportation costs, thepresence of which leads firms to ship high-quality goods to a remote market (Alchian–Allen
effect). Although our study extends the previous studies to account for variable markups,
iceberg-type transportation costs are assumed and the Alchian-Allen effect is not taken into
account. Investigating these effects is a topic for further research.

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prices, American Economic Review 98, 1998-2031.
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[21] Simonovska, I., 2010 Income differences and prices of tradables, NBER Working Paper
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21

Average price (yen per kg)
Product entry
No. of varieties
No. of size categories
No. of grade categories
No. of producing prefectures
No. of wholesale markets
No. of distinct product entries
Data truncation
No. of Tij (ω) = 0 or 1
No. of Tij (ω) = 1
3
63
34
47
47
1,207

Cabbages
77.833

198,129
8,395

10
62
66
46
47
1,186

Carrots
101.25

241,871
10,803

4
50
50
46
47
1,001

C-cabbages
61.628

239,703
11,565

7
71
46
43
47
903

Lettuce183.909264,280
10,921

10
50
93
47
47
1,423

Potatoes
79.565476,919
11,845

1
74
55
44
47
909

S-mushrooms
1113.627

466,337
15,977

4
17
85
47
47
551

Spinach496.372

547,272
14,874

11
103
58
46
47
1,115

Welsh onions
382.099

Table 1: Summary Statistics

369,343
15,841

Nonhomotheticγθρ
log-likelihood
CES
γ

ρ
log-likelihood
OLSγN
PCP for Tij

0.687
0.613
(0.006)(0.006)1.203
1.272(0.008)(0.008)-0.854-0.775(0.137)(0.089)-21025.084 -24321.708

0.49(0.004)3.688(0.028)-0.546(0.24)-4383.126

0.768(0.008)2.329(0.008)-0.624(0.034)-1779.114

S-mushrooms

0.402(0.002)2.83(0.013)-0.848(0.106)-22797.953

0.666(0.005)1.667(0.009)-0.845(0.105)-18609.021

Spinach0.033
547,272
0.988

0.354
(0.002)3.292(0.018)-0.848(0.109)-18319.21

0.566(0.006)1.98(0.008)-0.831(0.103)-14368.145

Welsh onions

Table 2: Estimation Results
C-cabbages

0.335(0.002)2.381(0.012)-0.793(0.07)-26013.89

0.044
466,337
0.979

Potatoes

Cabbages
0.655(0.005)1.585(0.01)-0.809(0.096)-13569.56
0.402(0.003)2.126(0.014)-0.874(0.161)-23317.952

0.007
476,919
0.994

Lettuce

0.46
0.627(0.003)(0.006)2.013
1.169(0.011)(0.009)-0.83-0.868(0.086)(0.194)-19646.143 -17034.691
0.382(0.003)2.78(0.017)-0.83(0.127)-15956.433

0.037
264,280
0.966

Carrots

0.287
0.345
(0.002)(0.003)3.326
2.123(0.019)(0.014)-0.86-0.884(0.132)(0.214)-24137.852 -18563.794

0.022
239,703
0.961

0.051
198,129
0.964

0.042
241,871
0.961

0.033
369,3430.966

Note: The numbers in parentheses are standard errors. All estimations include origin and destination dummies, origin and destination daily
temperatures, the number of products in both equations, and wages for the selection equation.

Figure 1: Log of price and log of per capita income relationshipFigure 2: Actual (+) and predicted (.) values