Download 1 - Darden Faculty - University of Virginia

Demand Complementarities and Cross-Country
Price Differences∗
Daniel Murphy
Darden School of Business, University of Virginia
April 15, 2016
Abstract: Empirical studies document a relationship between markups and income across
countries. This paper proposes a novel mechanism to explain the relationship between markups
and income: Consumers’ utility from final goods and services depends on their consumption of
complementary goods and services. I develop a two-country model to demonstrate the relevance
of the demand complementarities mechanism for understanding real exchange rates. In countries
with more complementary goods and services consumer demand is less elastic, enabling
monopolistically competitive firms to charge higher prices. The paper provides empirical
evidence documenting a dependence of prices on demand complementarities.
JEL:E31, F12, L11
Keywords: Markups, real exchange rates, demand complementarity
∗
Thanks to George Alessandria, Raphael Auer, Alan Deardorff, Peter Debaere, Jonathan Eaton, Yuriy
Gorodnichenko, Gordon Hanson, Andrei Levchenko, Lutz Kilian, Pravin Krishna, Bill Lincoln, Andrew McCallum,
Brent Neiman, Philip Sauré, Ina Simonovska, Martin Strieborny, Carlos Vegh, Frank Warnock, Jing Zhang, and
seminar participants at Michigan, Dartmouth, Virginia, Federal Reserve Board, Miami, UCSD, UBC, SAIS, and
Penn State for helpful comments and discussions.
Contact: Darden School of Business, Charlottesville, VA 22903. E-mail: [email protected].
1. Introduction
Price determination is a central focus of international economics and macroeconomics. In
international economics, understanding the nature of real exchange rates is important for
understanding causes of cross-country and sectoral differences in productivity and investment
rates, for measuring country-level welfare, and for predicting changes in wealth. In
macroeconomics, the predictions of models used for policy analysis depend crucially on how
prices respond to aggregate shocks.
Traditional theories of price determination focus on costs. For example, standard
explanations of cross-country price differences are based on cost differences under the
assumption that the law of one price holds (e.g., Balassa 1964; Samuelson 1964; Crucini,
Telmer, and Zacharides 2005), and the standard New Keynesian model predicts that prices
depend on costs and the ability of producers to adjust to cost changes. Recent evidence points to
the importance of markups, rather than only costs, in determining prices. Simonovska (2015)
documents that an online apparel retailer charges higher markups to consumers in rich countries
than to consumers in poor countries, which suggests that real exchange rates depend on low
demand elasticities in rich countries. Simonovska’s evidence is consistent with other recent
empirical work documenting a strong role for markups of tradable goods that differ by
characteristics specific to the destination countries (e.g., Engel 1999; Gopinath, Gourinchas,
Hsieh, and Li 2011; Fitzgerald and Haller 2012; Cavallo, Neiman, and Rogobon 2014).
An open question is what determines these markups and demand elasticities. I propose a
new explanation for high markups based on high (and inelastic) demand arising from high
consumption of goods and services that complement demand for consumer goods.
That demand for one good depends on the availability of another is quite natural. Home
entertainment systems can provide substantial utility in a country with reliable access to
electricity, but would provide much less utility in a land without reliable electricity. A brand-new
sedan provides more utility in a country with well-paved roads than in a country with dirt roads.
Consumers without electricity (or well-paved roads) get less utility from entertainment systems
(or new sedans) and thus have lower, more elastic demand for such products.
Many types of goods and services may complement demand for differentiated consumer
goods (and differentiated consumer goods could complement demand for each other). To
distinguish the complementary goods from the consumer goods in the analysis below, I refer to
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these complementary goods and services as catalyst goods. Often catalyst goods will be
durables, such as housing or public infrastructure, but they may also be services or intangibles,
such as public safety, other consumer goods, or advertising. The concept of a catalyst captures
the notion that some goods and services facilitate consumers’ derivation of utility from other
final goods and services. The notion of catalysts is similar to the notion of consumer demand
proposed by Lancaster (1966), who suggests that goods and services are not direct objects of
utility themselves, but rather contain properties and characteristics that consumers combine to
generate utility.
Demand complementarity may affect price patterns in a number of contexts. Here I focus
on its role in understanding the well-documented price–income relationship across countries.
Below I embed demand complementarity and pricing-to-market in a two-country general
equilibrium model to demonstrate the relevance of the mechanism for the real exchange rate. The
model features demand complementarity between catalyst goods and differentiated final
consumption goods. Specifically, the intercept of the demand curve for a differentiated final
good depends on the level of consumption of catalyst goods. In equilibrium, the rich country
consumes more catalyst goods and pays more for tradable goods. The theoretical dependence of
prices on catalysts is robust to a wide class of models that deviate from the common CES utility
function.
A number of recent papers propose alternative multicountry models to explain the
positive relationship between markups and country-level income per capita (e.g., Simonovska
2015; Alessandria and Kaboski 2011). This work, while informative, has been unable to isolate
the proposed mechanism in the data from other competing mechanisms that may be responsible
for the markup–income correlation. Rather, it uses model-based inference to determine the
potential validity of the proposed mechanism. Here I provide evidence that isolates the demandcomplementarities mechanism from other mechanisms associated with income per capita.
A test of my theory requires data on catalysts that are imperfectly correlated with income
per capita across countries. If the catalysts were perfectly correlated with income across
countries, then it would be impossible to isolate the demand-complementarities channel from
other potential mechanisms. The analysis also requires isolating catalysts that are strong demand
complements for subsets of tradable goods. Differential demand complementarity permits a test
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of a differential dependence of prices on catalysts between strongly complemented goods and
other goods.
A plausible catalyst that is relevant for a large subset of tradable goods is electricity
access, which is an important determinant of demand for electric appliances. I use data on
electricity production, which is a proxy for access that is measured across a range of countries
over time, to show that electric goods are sold at higher prices to countries with higher electricity
production, conditional on destination-country income per capita and conditional on the average
dependence of consumer goods prices on country-level determinants.
Although electric goods account for a substantial share of traded consumer goods and
accurate data on electricity production is available for a wide range of countries, the empirical
test faces a number of limitations. First, electricity is highly correlated with income per capita,
which poses the challenge of distinguishing demand complementarities from other pricing-tomarket mechanisms associated with high income. Second, electricity may complement demand
for retail goods generally (if, for example, reliable electricity supply allows retail stores to keep
the lights on and stay open). Despite these challenges that bias the results against detection of the
demand-complementarities mechanism, the results nonetheless demonstrate a strong dependence
of prices on electricity. Placebo tests demonstrate that other subsets of consumer goods, such as
battery-powered electronics and luxury items, exhibit a below-average dependence on electricity
and an above-average dependence on income per capita.
Another catalyst for which I can obtain data across a range of countries is snowfall,
which complements demand for skis. To corroborate the evidence on electricity as a catalyst, I
show that prices of skies demonstrate the exact same pattern of an above-average dependence on
snowfall and a below-average dependence on GDP. An advantage of the ski-based test is that
snowfall is less correlated with income per capita, permitting a stronger test of whether prices
depend on independent variation of catalysis. However the relevant catalyst, snowfall, is
endowed rather than produced, and therefore is less relevant for understanding why prices of
tradables increase with income per capita across countries. Therefore the test based on skis
should be viewed as supplementary to the test based on electricity, and as additional support for
the hypothesis that cross-country prices depend on demand complementarities.
In addition to predicting that prices of tradables are higher in rich countries, the
theoretical model also predicts that prices of catalyst services are lower in rich countries. The
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prediction that some services are cheaper in rich countries may seem contrary to the welldocumented fact that prices of services are higher in rich countries (see Harrod [1933], Balassa
[1964], Samuelson [1964], and a long subsequent literature). Therefore, for my theory to provide
an accurate account of the drivers of cross-country price differences, it is important that it can be
reconciled with evidence on prices of nontradables.
I show, first, that my theory is consistent with the evidence from the International
Comparison Program (ICP) that prices of some services are higher in rich countries. The
intuition is based on a straightforward extension of the model that incorporates differentiated
nontradable services. My theory also predicts that some services (catalysts) must be less
expensive in rich countries. How is this prediction consistent with the conventional wisdom that
service prices broadly are more expensive in rich countries? The ICP data are based on a subset
of services that excludes many catalysts. For example, road quality, infrastructure, and
advertising are potential catalysts that are not included in country-level price indices. I provide
suggestive evidence that a number of potential catalysts are indeed more efficient or less costly
in rich countries, consistent with the model’s predictions. One implication is that aggregate price
indices in rich countries are lower than estimates based on ICP data suggest.
2. A Model of Catalyst-Dependent Pricing
Here I formalize how prices and markups depend on consumption of complementary goods and
services. I first show that the dependence of prices on catalysts holds for a wide class of demand
functions that deviate from the assumption of constant price elasticities of demand. I then embed
demand complementarities and pricing-to-market in a two-country model to demonstrate that the
mechanism can account for the evidence of higher prices of tradable goods in rich countries than
in poor countries.
2.1. Markups and Catalysts
Consider a generic demand curve 𝑞𝑞 = 𝑞𝑞(𝐶𝐶, 𝑝𝑝), where 𝐶𝐶 is the complementary catalyst and 𝑝𝑝 is
the price of the good. By assumption, 𝑞𝑞1 > 0 and 𝑞𝑞2 < 0. The price elasticity of demand is
𝜕𝜕𝜕𝜕
𝜕𝜕𝜕𝜕 𝑝𝑝
𝜕𝜕𝜕𝜕
decreasing in 𝐶𝐶 if and only if 𝜕𝜕𝜕𝜕 < 0, where 𝜖𝜖 ≡ �𝜕𝜕𝜕𝜕 𝑞𝑞 �. We can write 𝜕𝜕𝜕𝜕 = −𝑞𝑞21
𝑝𝑝
𝑞𝑞2 𝑞𝑞(𝐷𝐷,𝑝𝑝)2 𝑞𝑞1 , in which case the necessary and sufficient condition simplifies to
5
𝑝𝑝
𝑞𝑞(𝐷𝐷,𝑝𝑝)
+
𝑞𝑞𝑞𝑞21 > 𝑞𝑞2 𝑞𝑞1 .
(1)
Condition (1) states that any slope-increasing effects of an increase in 𝐶𝐶 on the demand curve
must be more than compensated by a shift out of the demand curve. In the commonly used case
of a constant elasticity demand curve, 𝑞𝑞 = 𝐶𝐶𝑝𝑝−𝜖𝜖 , these two effects exactly cancel out so that
𝑞𝑞𝑞𝑞21 = 𝑞𝑞2 𝑞𝑞1 . As discussed in Nakamura and Zerom (2010), constant demand elasticities are
difficult to reconcile with the data. Their estimates on coffee demand suggest that the price
elasticity of demand is increasing in the price, consistent with a linear demand curve. 1 Foster,
Haltiwanger, and Syverson (2008) find that utility functions yielding linear demand curves fit the
data well for a range of industries. Linear demand curves satisfy condition (1), as demonstrated
in the model below.
Incorporating catalysts into two of the most commonly used forms of nonhomothetic
preferences yields demand curves that satisfy condition (1) and exhibit a price elasticity of
demand that is increasing in the price. The model below examines a modified quadratic utility
function (which gives rise to a linear demand curve). The results also hold under modified
versions of Stone-Geary preferences, such as 𝑈𝑈 = 𝐶𝐶 log(𝑞𝑞 − 𝑞𝑞�).
2.2. A Two-Country Model of Demand Complementarities and Pricing to Market
Here I demonstrate that incorporating catalysts into a two-country model can account for the
well-documented relationship between prices and income per capita across countries. Although
the theoretical application is to tradable goods, the mechanism applies to markups for
nontradable services as well. For simplicity, the theory presents catalysts as a homogenous
product that is directly purchased by consumers. However, the notion of catalysts applies broadly
to both private and public goods and services. It also applies to firm-specific products for which
there is no explicit market price, as discussed in Section 3. For example, customers do not
directly pay for enjoying a restaurant’s atmosphere (furniture, artwork, etc.), but these catalysts
increase their willingness to pay for food at a restaurant.
Consider a two-country model in which the countries, 𝑁𝑁 (North) and 𝑆𝑆 (South), are each
endowed with a numeraire good, and inelastically supply labor to produce catalyst goods and
differentiated final goods. Catalyst goods are not traded across countries. This assumption is for
𝜕𝜕𝜕𝜕
Price-dependent elasticities are not necessary for < 0. Consider, for example, 𝑞𝑞 = 𝑝𝑝 −𝑓𝑓(𝐶𝐶)𝜖𝜖 , where 𝑓𝑓 is some
𝜕𝜕𝜕𝜕
function that is independent of 𝑝𝑝.
1
6
simplicity (the qualitative results are robust to permitting the catalyst to be traded), and because
some catalyst goods represent housing and public infrastructure, which are fixed immobile
assets. The endowed numeraire is traded and enters the utility function linearly. 2 Following
Krugman (1980), each country specializes in a unique set of differentiated final goods. Final
goods are produced by monopolistically competitive firms. Firms can move final goods
costlessly across international borders and charge country-specific prices, but consumers do not
arbitrage because they face large costs of moving goods across international borders; these costs
can be the time required to travel across international borders or other transportation costs and
information rigidities. 3
Model Setup. Each country 𝑗𝑗 ∈ {𝑁𝑁, 𝑆𝑆} produces a mass Ω𝑗𝑗 of final goods that are
consumed at home and abroad. Goods produced in country 𝑗𝑗 are indexed by 𝜔𝜔𝑗𝑗 ∈ Ω𝑗𝑗 . The utility
function of the representative consumer in country 𝑗𝑗 is
2
𝛾𝛾
�𝐶𝐶𝑗𝑗 𝑓𝑓𝑗𝑗 (𝜔𝜔𝑖𝑖 ) − �𝑓𝑓𝑗𝑗 (𝜔𝜔𝑖𝑖 )� � 𝑑𝑑𝜔𝜔𝑖𝑖 ,
2
𝜔𝜔𝑖𝑖 ∈Ω𝑖𝑖
𝑈𝑈𝑗𝑗 = 𝑦𝑦𝑗𝑗 + � �
𝑖𝑖=𝑁𝑁,𝑆𝑆
(2)
where 𝑦𝑦𝑗𝑗 and 𝐶𝐶𝑗𝑗 are consumption of the numeraire and catalyst by country 𝑗𝑗 and 𝑓𝑓𝑗𝑗 (𝜔𝜔𝑖𝑖 ) is
consumption in country 𝑗𝑗 of variety 𝜔𝜔𝑖𝑖 from country 𝑖𝑖 ∈ {𝑁𝑁, 𝑆𝑆}. Equation (2) is a simplified
version of the utility functions used in Ottaviano et al. (2002); Melitz and Ottaviano (2008); and
Foster, Haltiwanger, and Syverson (2008); but differs in two ways. First, the marginal utility
from consuming any variety 𝜔𝜔 is independent of consumption of any other variety 𝜔𝜔′ ≠ 𝜔𝜔.
Second, equation (2) features a catalyst good 𝐶𝐶 that acts as a demand shifter for the consumption
goods.
The budget constraint of the representative agent in country 𝑗𝑗 is
𝑦𝑦𝑗𝑗0 + 𝑤𝑤𝑗𝑗 𝐿𝐿𝑗𝑗 + � �
𝑖𝑖=𝑁𝑁,𝑆𝑆 𝜔𝜔𝑗𝑗 ∈Ω𝑗𝑗
Π𝑖𝑖 �𝜔𝜔𝑗𝑗 � = 𝑦𝑦𝑗𝑗 + 𝑝𝑝𝐶𝐶𝐶𝐶 𝐶𝐶𝑗𝑗 + � �
𝑖𝑖=𝑁𝑁,𝑆𝑆 𝜔𝜔𝑖𝑖 ∈Ω𝑖𝑖
2
𝑝𝑝𝑗𝑗 (𝜔𝜔𝑖𝑖 )𝑓𝑓𝑗𝑗 (𝜔𝜔𝑖𝑖 ), (3)
The setup is based on a variant of the linear demand system developed by Ottaviano, Tabuchi, and Thisse (2002),
which is analytically convenient, in part because the marginal utility of income is unity for all levels of income.
Murphy (2013) demonstrates that the results of this section are robust to alternative specifications for which the
marginal utility of income varies with income and the numeraire is produced with labor.
3
The assumption that producing firms can freely move goods across borders is for simplicity only. Price differences
will emerge whenever arbitraging price differences is costly, such as in the presence of transportation costs.
7
where 𝑦𝑦𝑗𝑗0 is the endowment of the numeraire in country 𝑗𝑗, Π𝑖𝑖 �𝜔𝜔𝑗𝑗 � is the profit from sales of
variety 𝜔𝜔𝑗𝑗 to country 𝑖𝑖, 𝑦𝑦𝑗𝑗 is the amount of the numeraire consumed in country 𝑗𝑗, 𝑝𝑝𝐶𝐶𝐶𝐶 is the price
of the catalyst in 𝑗𝑗, and 𝑝𝑝𝑗𝑗 (𝜔𝜔𝑖𝑖 ) is the price of variety 𝜔𝜔𝑖𝑖 in 𝑗𝑗.
Consumer optimization with respect to 𝑓𝑓𝑗𝑗 (𝜔𝜔𝑖𝑖 ) yields demand for variety 𝜔𝜔𝑖𝑖 in country 𝑗𝑗:
1
𝑓𝑓𝑗𝑗𝑑𝑑 (𝜔𝜔𝑖𝑖 ) = �𝐶𝐶𝑗𝑗 − 𝑝𝑝𝑗𝑗 (𝜔𝜔𝑖𝑖 )�.
𝛾𝛾
Similarly, the first order condition with respect to 𝐶𝐶𝑗𝑗 yields
𝐹𝐹𝑗𝑗 = 𝑝𝑝𝐶𝐶 ,
(4)
(5)
where 𝐹𝐹𝑗𝑗 ≡ ∑𝑖𝑖=𝑁𝑁,𝑆𝑆 ∫𝜔𝜔 ∈Ω 𝑓𝑓𝑗𝑗 (𝜔𝜔𝑖𝑖 ) is the total quantity of final goods consumed in country 𝑗𝑗.
𝑖𝑖
𝑖𝑖
Final Good Sector. Output in the final-goods sector is produced using the technology
𝑓𝑓�𝜔𝜔𝑗𝑗 � = 𝐴𝐴𝑗𝑗 𝐿𝐿𝜔𝜔𝑗𝑗 ,
(6)
where 𝑓𝑓�𝜔𝜔𝑗𝑗 � ≡ 𝑓𝑓𝑁𝑁 �𝜔𝜔𝑗𝑗 � + 𝑓𝑓𝑆𝑆 �𝜔𝜔𝑗𝑗 �. Each firm 𝜔𝜔𝑗𝑗 charges a country-specific price to maximize the
profits Π𝑖𝑖 �𝜔𝜔𝑗𝑗 � from selling variety 𝜔𝜔𝑗𝑗 in country 𝑖𝑖 ∈ {𝑁𝑁, 𝑆𝑆}.
Profits from sales of 𝜔𝜔𝑗𝑗 in 𝑖𝑖 can be written
Π𝑖𝑖 �𝜔𝜔𝑗𝑗 � = 𝑝𝑝𝑖𝑖 �𝜔𝜔𝑗𝑗 �𝑓𝑓𝑖𝑖 �𝜔𝜔𝑗𝑗 � −
The profit-maximizing price charged in country 𝑖𝑖 is
𝑤𝑤𝑗𝑗
𝑓𝑓 �𝜔𝜔 �.
𝐴𝐴𝑗𝑗 𝑖𝑖 𝑗𝑗
𝑤𝑤𝑗𝑗
1
𝑝𝑝𝑖𝑖 �𝜔𝜔𝑗𝑗 � = �𝐶𝐶𝑖𝑖 + �.
2
𝐴𝐴𝑗𝑗
(7)
(8)
Equation (8) can help explain why rich countries pay higher prices for tradable goods: The
optimal price of an identical good varies across countries based on the stock of catalyst goods in
each country.
It remains to be seen that in equilibrium, the rich country will produce more of the
catalyst good and therefore pay higher prices for final goods. Given the price defined by (8),
consumer demand in country 𝑖𝑖 for 𝜔𝜔𝑗𝑗 is
𝑓𝑓𝑖𝑖𝑑𝑑 �𝜔𝜔𝑗𝑗 � =
𝑤𝑤𝑗𝑗
1
�𝐶𝐶𝑖𝑖 − �,
2𝛾𝛾
𝐴𝐴𝑗𝑗
The resulting revenues of firm 𝜔𝜔𝑗𝑗 from sales to country 𝑖𝑖 are
𝑤𝑤𝑗𝑗2
1
2
𝑝𝑝𝑖𝑖 �𝜔𝜔𝑗𝑗 �𝑓𝑓𝑖𝑖 �𝜔𝜔𝑗𝑗 � =
�𝐶𝐶 − 2 �,
4𝛾𝛾 𝑖𝑖
𝐴𝐴𝑗𝑗
8
(9)
(10)
and profits are
2
𝑤𝑤𝑗𝑗
1
Π𝑖𝑖 �𝜔𝜔𝑗𝑗 � =
�𝐶𝐶𝑖𝑖 − � .
4𝛾𝛾
𝐴𝐴𝑗𝑗
(11)
Catalyst Sector. The catalyst in country 𝑗𝑗 is produced competitively according to 𝐶𝐶𝑗𝑗 =
𝐴𝐴𝑗𝑗 𝐿𝐿𝐶𝐶𝐶𝐶 , where 𝐴𝐴𝑗𝑗 is productivity in country 𝑗𝑗 and 𝐿𝐿𝐶𝐶𝐶𝐶 is labor employed in 𝑗𝑗’s catalyst sector. I
assume that productivity in country 𝑗𝑗 is equal across sectors. This is for simplicity and to isolate
the role of demand complementarities, rather than within-country productivity differentials, in
driving cross-country price differences. The price of the catalyst is 𝑝𝑝𝐶𝐶𝐶𝐶 = 𝑤𝑤𝑗𝑗 /𝐴𝐴𝑗𝑗 , which is
derived from cost minimization by the representative catalyst firm. Since the catalyst is not
traded across countries, there is no role for comparative advantage, and each country will
produce some of the catalyst in equilibrium.
Equilibrium. Since 𝑝𝑝𝑖𝑖 �𝜔𝜔𝑗𝑗 � and 𝑓𝑓𝑖𝑖 �𝜔𝜔𝑗𝑗 � are identical for any variety 𝜔𝜔𝑗𝑗 from country 𝑗𝑗, it
will be helpful to omit variety indices by writing 𝑝𝑝𝑖𝑖𝑖𝑖 = 𝑝𝑝𝑖𝑖 �𝜔𝜔𝑗𝑗 �, 𝑓𝑓𝑖𝑖𝑖𝑖 = 𝑓𝑓𝑖𝑖 �𝜔𝜔𝑗𝑗 �, and Π𝑖𝑖𝑖𝑖 =
Π𝑖𝑖 �𝜔𝜔𝑗𝑗 � ∀ 𝜔𝜔𝑗𝑗 ∈ Ω𝑗𝑗 . Then 𝐹𝐹𝑗𝑗 becomes 𝐹𝐹𝑗𝑗 = Ω𝑗𝑗 𝑓𝑓𝑗𝑗𝑗𝑗 + Ω𝑖𝑖 𝑓𝑓𝑗𝑗𝑗𝑗 . The budget constraint in country 𝑗𝑗
simplifies to
𝑦𝑦𝑗𝑗0 + 𝑤𝑤𝑗𝑗 𝐿𝐿𝑗𝑗 + Ω𝑗𝑗 �Π𝑗𝑗𝑗𝑗 + Π𝑖𝑖𝑖𝑖 � = 𝑦𝑦𝑗𝑗 + 𝑝𝑝𝐶𝐶𝐶𝐶 𝐶𝐶𝑗𝑗 + Ω𝑗𝑗 𝑝𝑝𝑗𝑗𝑗𝑗 𝑓𝑓𝑗𝑗𝑗𝑗 + Ω𝑖𝑖 𝑝𝑝𝑗𝑗𝑗𝑗 𝑓𝑓𝑗𝑗𝑗𝑗
Labor market clearing in 𝑗𝑗 is 𝐿𝐿 = 𝐿𝐿𝑄𝑄𝑄𝑄 + 𝐿𝐿𝐶𝐶𝐶𝐶 , where 𝐿𝐿𝑄𝑄𝑄𝑄 ≡ ∫𝜔𝜔
𝑗𝑗 ∈Ω𝑗𝑗
(12)
𝐿𝐿𝜔𝜔𝑗𝑗 𝑑𝑑𝜔𝜔𝑗𝑗 is total labor used in
the final goods sector and total labor 𝐿𝐿 is the same in each country. By substituting in the
production functions for final goods and the catalyst, labor market clearing in country 𝑗𝑗 can be
written
𝐿𝐿 =
Market clearing for the numeraire is
1
�Ω �𝑓𝑓 + 𝑓𝑓𝑖𝑖𝑖𝑖 � + 𝐶𝐶𝑗𝑗 �.
𝐴𝐴𝑗𝑗 𝑗𝑗 𝑗𝑗𝑗𝑗
𝑦𝑦𝑁𝑁0 + 𝑦𝑦𝑆𝑆0 = 𝑦𝑦𝑁𝑁 + 𝑦𝑦𝑆𝑆 .
(13)
(14)
Equilibrium is characterized by the first order conditions for catalyst consumption (5),
demand for final goods (9), labor market clearing in each country (13), market clearing for the
numeraire (14), and the budget constraints (12). By Walras’ Law, one of these equations is
redundant. For clarity, the equilibrium conditions are written explicitly as:
𝑤𝑤𝑁𝑁
𝑤𝑤𝑆𝑆
𝐹𝐹𝑁𝑁 =
,
𝐹𝐹𝑆𝑆 = ,
𝐴𝐴𝑁𝑁
𝐴𝐴𝑆𝑆
9
𝑓𝑓𝑁𝑁𝑁𝑁 =
𝑓𝑓𝑆𝑆𝑆𝑆 =
𝐿𝐿 =
1
𝑤𝑤𝑁𝑁
�𝐶𝐶𝑁𝑁 −
�,
2𝛾𝛾
𝐴𝐴𝑁𝑁
1
𝑤𝑤𝑆𝑆
�𝐶𝐶𝑆𝑆 − �,
2𝛾𝛾
𝐴𝐴𝑆𝑆
1
[Ω (𝑓𝑓 + 𝑓𝑓𝑆𝑆𝑆𝑆 ) + 𝐶𝐶𝑁𝑁 ],
𝐴𝐴𝑁𝑁 𝑁𝑁 𝑁𝑁𝑁𝑁
𝑓𝑓𝑁𝑁𝑁𝑁 =
𝑓𝑓𝑆𝑆𝑆𝑆 =
𝐿𝐿 =
1
𝑤𝑤𝑆𝑆
�𝐶𝐶𝑁𝑁 − �,
2𝛾𝛾
𝐴𝐴𝑆𝑆
1
𝑤𝑤𝑁𝑁
�𝐶𝐶𝑆𝑆 −
�,
2𝛾𝛾
𝐴𝐴𝑁𝑁
1
[Ω (𝑓𝑓 + 𝑓𝑓𝑁𝑁𝑁𝑁 ) + 𝐶𝐶𝑆𝑆 ],
𝐴𝐴𝑆𝑆 𝑆𝑆 𝑆𝑆𝑆𝑆
𝑦𝑦𝑁𝑁0 + 𝑦𝑦𝑆𝑆0 = 𝑦𝑦𝑁𝑁 + 𝑦𝑦𝑆𝑆 ,
𝑦𝑦𝑁𝑁0 − 𝑦𝑦𝑁𝑁 + Ω𝑁𝑁 𝑝𝑝𝑆𝑆𝑆𝑆 𝑓𝑓𝑆𝑆𝑆𝑆 = Ω𝑆𝑆 𝑝𝑝𝑁𝑁𝑁𝑁 𝑓𝑓𝑁𝑁𝑁𝑁 ,
where the last equilibrium equation is a simplified version of the budget constraint for country 𝑁𝑁.
The 10 equations above yield a unique solution for the endogenous variables
𝑤𝑤𝑁𝑁 , 𝑤𝑤𝑆𝑆 , 𝑦𝑦𝑁𝑁 , 𝑦𝑦𝑆𝑆 , 𝐶𝐶𝑁𝑁 , 𝐶𝐶𝑆𝑆 , 𝑓𝑓𝑁𝑁𝑁𝑁 , 𝑓𝑓𝑁𝑁𝑁𝑁 , 𝑓𝑓𝑆𝑆𝑆𝑆 , and 𝑓𝑓𝑆𝑆𝑆𝑆 . To see this, note that we can reduce the system to
four linear equations in four unknowns by substituting demand for final goods into the first order
conditions for catalyst consumption and the labor market clearing conditions:
Catalyst First Order Condition:
Ω
1
𝑤𝑤𝑁𝑁 𝑤𝑤𝑆𝑆
𝑤𝑤𝑆𝑆
�2𝐶𝐶𝑆𝑆 −
− �=
,
2𝛾𝛾
𝐴𝐴𝑁𝑁 𝐴𝐴𝑆𝑆
𝐴𝐴𝑆𝑆
Ω
1
𝑤𝑤𝑁𝑁 𝑤𝑤𝑆𝑆
𝑤𝑤𝑁𝑁
�2𝐶𝐶𝑁𝑁 −
− �=
2𝛾𝛾
𝐴𝐴𝑁𝑁 𝐴𝐴𝑆𝑆
𝐴𝐴𝑁𝑁
(15)
Labor Market Clearing:
𝐿𝐿 =
Ω 1
𝑤𝑤𝑁𝑁
𝐶𝐶𝑁𝑁
�𝐶𝐶𝑆𝑆 + 𝐶𝐶𝑁𝑁 − 2 � +
,
2𝛾𝛾 𝐴𝐴𝑁𝑁
𝐴𝐴𝑁𝑁
𝐴𝐴𝑁𝑁
𝐿𝐿 =
Ω 1
𝑤𝑤𝑆𝑆
𝐶𝐶𝑆𝑆
�𝐶𝐶𝑆𝑆 + 𝐶𝐶𝑁𝑁 − 2 � + .
2𝛾𝛾 𝐴𝐴𝑆𝑆
𝐴𝐴𝑆𝑆
𝐴𝐴𝑆𝑆
(16)
Uniqueness of the equilibrium follows from a nonzero determinant of this system. Given
𝐶𝐶𝑁𝑁 , 𝐶𝐶𝑆𝑆 , 𝑤𝑤𝑁𝑁 , and 𝑤𝑤𝑆𝑆 , one can solve for 𝑦𝑦𝑁𝑁 and 𝑦𝑦𝑆𝑆 from numeraire market clearing and the trade
balance condition.
Prices and Income. The price of a final good in the North relative to the South is
𝑝𝑝𝑁𝑁𝑁𝑁 𝐶𝐶𝑁𝑁 + 𝑤𝑤𝑗𝑗 /𝐴𝐴𝑗𝑗
=
,
𝑝𝑝𝑆𝑆𝑆𝑆
𝐶𝐶𝑆𝑆 + 𝑤𝑤𝑗𝑗 /𝐴𝐴𝑗𝑗
(17)
where 𝑤𝑤𝑗𝑗 /𝐴𝐴𝑗𝑗 is the cost of production in origin country 𝑗𝑗. The North is characterized by its
higher productivity, 𝐴𝐴𝑁𝑁 > 𝐴𝐴𝑆𝑆 . According to equation (17), a sufficient condition for higher prices
10
in the North is that 𝐶𝐶𝑁𝑁 > 𝐶𝐶𝑆𝑆 . Intuitively, this result follows from the fact that 𝑁𝑁 has more
effective labor and thus can produce more catalyst goods. To derive the conditions under which
this intuition prevails in the model, we can subtract the catalyst first order condition in 𝑆𝑆 from
that in 𝑁𝑁 and collect terms to yield
Ω
𝑤𝑤𝑁𝑁 𝑤𝑤𝑆𝑆
(18)
(𝐶𝐶𝑁𝑁 − 𝐶𝐶𝑆𝑆 ) = �
− �.
𝛾𝛾
𝐴𝐴𝑁𝑁 𝐴𝐴𝑆𝑆
Likewise, the labor market clearing conditions can be combined and simplified to yield
Ω 𝑤𝑤𝑁𝑁 𝑤𝑤𝑆𝑆
�
− �.
2𝛾𝛾 𝐴𝐴𝑁𝑁 𝐴𝐴𝑆𝑆
Solving equation (18) for the cost difference and substituting into (19) yields
𝐶𝐶𝑁𝑁 − 𝐶𝐶𝑆𝑆 = 𝐿𝐿(𝐴𝐴𝑁𝑁 − 𝐴𝐴𝑆𝑆 ) +
Ω
(19)
2
(20)
(𝐶𝐶𝑁𝑁 − 𝐶𝐶𝑆𝑆 ) �1 − �
� � = 𝐿𝐿(𝐴𝐴𝑁𝑁 − 𝐴𝐴𝑆𝑆 ).
√2𝛾𝛾
Equation (20) implies that the necessary and sufficient condition for higher prices in 𝑁𝑁 is
√2𝛾𝛾 > Ω. The intuition behind this result is that a large mass of firms causes sufficiently high
demand for final goods that equilibrium catalyst consumption falls with wealth. High marginal
utility from final goods consumption (low 𝛾𝛾) has a similar effect. Under the assumption of
sufficiently declining marginal utility of final goods consumption, the higher-income country
produces more of the catalyst good and therefore pays higher prices for final goods. As discussed
in the empirical section, the relevant case is when rich countries produce more catalysts,
consistent with the assumption in the model that 𝛾𝛾 is high.
3. Cross-Country Evidence
Here I provide evidence that prices and markups of subsets of tradables depend on countries’
stock of relevant catalysts. I use disaggregated export data from the U.S. Exports Harmonized
System data. These data are available on Robert Feenstra’s webpage and contains unit values and
quantities of bilateral exports leaving U.S. docks for each Harmonized System (HS)-10 product
category for years prior to 2006. As discussed by Alessandria and Kaboski (2011), there are two
advantages of using these data to study the extent of pricing-to-market for tradable goods. First,
the unit values are free-alongside-ship values, which exclude transportation costs, tariffs, and
additional costs incurred in the importing country. Thus the unit values capture the actual price
11
of the good, rather than the price of taking the good to retail. Second, the disaggregated nature of
the data mitigates potential concerns that different unit values may reflect differences in quality. 4
3.1 Testing Demand Complementarities and Pricing-to-Market
There are a number of challenges in testing the model’s prediction that prices of tradable goods
depend on countries’ consumption of relevant catalyst goods. First, it is necessary to isolate the
effect of catalyst-based demand from other factors that are associated with income per capita.
Indeed, income and catalyst consumption are perfectly correlated in my theoretical model, and if
the same were true of reality, it would be impossible to distinguish between demand
complementarities and other potential explanations for the price–income relationship. In reality,
however, catalyst consumption is imperfectly correlated with income per capita, which permits
me to test the dependence of prices on the component of catalyst consumption that is not
correlated with income. 5 Different catalysts are likely to have different degrees of correlation
with income, and the challenge is to identify a catalyst with (a) reliable cross-country data, and
(b) sufficient variation in the component that is orthogonal to income per capita.
A second challenge is to identify a catalyst that is a strong demand complement for a
subset of identifiable consumer goods relative to other goods. This differential demand
complementarity is necessary to test the dependence of prices of relevant catalyzed goods on
catalyst consumption while conditioning on the average dependence of prices on factors related
to income and catalyst consumption.
One such catalyst that should exhibit differential demand complementarity is access to
electricity, which complements demand for electric goods. McRae (2010), for example, shows
that access to reliable electricity in developing countries is associated with a higher likelihood of
purchasing electronic appliances.
Data on access to electricity are available from World Development Indicators for only a
limited subset of countries, and only starting in 2009, a year past the dates for which I have
4
Despite the disaggregated nature of the data, there is still room for quality variation within a product category. To
help condition on quality, I examine the extent to which catalyst-driven prices are differ between goods with high
and low quality ladders.
5
There are many potential reasons for the imperfect correlation between catalyst consumption and income. I do not
suggest any particular reason, but assume that these reasons are exogenous to prices of consumer imports. In the
closed-economy and two-country models, it is straightforward to introduce imperfect correlation between catalyst
consumption and income by assuming that productivity in the catalyst sector has a random component.
12
export price data. As a proxy for electricity access, I use a measure that is both available and
consistently measured in multiple years for a broad range of countries: International Energy
Agency (IEA) data on electricity consumption, defined as total electricity production less any
power used by power plants or lost in transmission and distribution. 6
The IEA proxy is most appropriate for countries with low levels of electricity access and
low incomes. There is a mass of countries for which access is nearly 100% of the population and
electricity consumption is unrelated to access because everyone has access (Figure 1). But for
low values of electricity consumption and low-income areas, access is strongly correlated with
electricity consumption. Above incomes per capita of $15,000 (in 2005 USD), incomes and
access are nearly independent and access is nearly 100%. Therefore I limit the sample of
countries to those with income per capita of less than $15,000. The results presented below are
slightly stronger for lower thresholds, consistent with the notion that electricity consumption is a
stronger proxy for access among countries with low levels of access. 7
Despite a number of features of electricity production that are amenable to an empirical
test, there are other features that present challenges. First, electricity is highly correlated with
income per capita (correlation coefficient of 0.81 among countries in the sample), which poses
the challenge of distinguishing demand complementarities from other pricing-to-market
mechanisms associated with high income. Second, electricity may complement demand for retail
goods generally (if, for example, a reliable electricity supply allows retail stores to keep the
lights on and stay open). Therefore much of the dependence of prices on electricity production
may be captured by country-level fixed effects. If so, the estimates presented below are a lower
bound on the extent to which prices depend on catalysts.
The test of electricity production as a catalyst is based on panel data from 1998 through
2006. Table 1 shows summary statistics for the 116 countries in the sample. Data on electricity
consumption and income per capita exhibit substantial variation across countries and over time.
6
I also test a number of other catalysts that are less suitable for testing due to lack of accurate data across a range of
countries (or a lack of exports of relevant tradables), including paved roads as a catalyst for new cars and housing as
a catalyst for household goods. The dependence of prices on catalysts in these tests is consistent with the results
presented below.
7
It may seem that an alternative to using data on electricity production is to use data on electricity prices. As
discussed below, price data are available for only approximately 50 countries. For many of these countries, access to
electricity is unreliable for many consumers, so the listed price of electricity does not accurately capture the true cost
to consumers of obtaining reliable electricity. As discussed in McRae (2010) and McRae (2013), consumers’ desire
to own durables depends on whether reliable electricity is available. Therefore production of accessible electricity is
the relevant catalyst and a more accurate proxy for the true cost of obtaining reliable electricity.
13
As mentioned above, electricity consumption is highly correlated with income, so the test of
demand complementarities will be based on the limited variation in electricity consumption that
is independent of variation in income.
The trade data are limited to consumer goods as identified by their end-use codes. To
prevent nonrepresentative products from driving the results, the samples are limited to products
that are exported to at least 10 countries and to country–product pairs with more than 100 units
sold and more than $1,000 in value. 8 Electric goods are identified in the trade data based on the
product description associated with each harmonized system code. I explore two different
approaches to classifying electric goods. Under the first approach, I classify any good that is
clearly electric and not battery powered as electric, along with associated parts. This approach
results in a number of high-unit-value appliances being classified as electric—such as air
conditioning units and washing machines—that may be affordable by only limited subsets of the
population. It also includes parts of electric goods that may not be sold directly to consumers.
Therefore, under an alternative approach, I identify only smaller routine household appliances
(but not their parts) as electric. Table 2 lists examples of goods classified as electric, along with
the goods that are classified as routine electric appliances.
3.1.1. Electricity and Prices of Electric Goods
To test whether prices of electric goods depend on electricity, I employ the following empirical
specification:
𝑝𝑝𝑐𝑐ℎ𝑡𝑡 = 𝛼𝛼𝑐𝑐𝑐𝑐 + 𝛾𝛾ℎ𝑡𝑡 + 𝛽𝛽1 ln 𝑀𝑀𝑀𝑀𝐻𝐻𝑐𝑐𝑐𝑐 × 𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝑑𝑑ℎ 𝑡𝑡 + 𝛽𝛽2 ln 𝑦𝑦𝑐𝑐𝑐𝑐 × 𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝑑𝑑ℎ + 𝜖𝜖𝑐𝑐ℎ𝑡𝑡 ,
(21)
where 𝑝𝑝𝑐𝑐ℎ is the log of the unit value of good ℎ exported to country 𝑐𝑐 in year 𝑡𝑡. The coefficient
𝛼𝛼𝑐𝑐𝑐𝑐 represents country-year fixed effects, 𝛾𝛾ℎ𝑡𝑡 represents fixed effects for each good category in
each year, and 𝑀𝑀𝑀𝑀𝐻𝐻𝑐𝑐𝑐𝑐 is the per capita electricity consumption in country 𝑐𝑐 in year 𝑡𝑡. 𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝑑𝑑ℎ
indicates whether good ℎ is electric, and 𝜖𝜖𝑐𝑐ℎ𝑡𝑡 denotes the regression error.
The coefficient 𝛽𝛽1 captures the extent to which prices of electric goods depend on
electricity access, conditional on the average dependence of prices on country-level determinants
including electricity consumption (captured by product-time fixed effects) and conditional on the
8
The quantity restriction excludes high-priced products that are clearly unrepresentative (e.g., 17 fans sold to Macau
for $66,000, etc.). The results are robust to different quantity and value thresholds.
14
dependence of prices of electric goods on income per capita (captured by 𝛽𝛽2). The difference
between 𝛽𝛽1 and 𝛽𝛽2 captures the extent to which the dependence of electric goods prices on
electricity relative to income per capita exceeds the average dependence of consumer goods
prices on electricity relative to income per capita. Since electricity consumption and income are
highly correlated, interacting both with a dummy for electric goods isolates the effect of
electricity on prices of electric goods from the effect of other mechanisms associated with
income.
𝛽𝛽1 can be interpreted as representing a causal relationship if electricity consumption is
exogenous to the product price. Electricity consumption is indeed likely to be exogenous with
respect to the price of a single imported product. If there is any endogenous response to electric
prices, demand complementarity implies that electricity consumption should respond negatively
to high import prices. In this case, high electricity consumption is associated with low prices of
electric goods, and 𝛽𝛽1 will underestimate the causal effect of electricity consumption on electric
goods prices. In other words, the estimate of 𝛽𝛽1 is biased downward in the presence of
endogenous electricity consumption.
Table 3 shows results from estimating (21), along with variations that replace the
country-time fixed effects with country-level covariates. Column (1) reproduces the finding in
Alessandria and Kaboski (2011) that unit values of U.S. exports are increasing in destination
country income per capita. One potential concern with GDP measures is that they do not
accurately capture economic activity for low-income countries. For this reason, Henderson,
Storeygard, and Weil (2012) propose energy-related estimates of country-level growth.
Consistent with their intuition, column (2) shows that prices are more strongly related to
electricity consumption than to GDP. The stronger dependence of prices on electricity could be
due either to mismeasurement of GDP or to electricity as a catalyst for consumer goods broadly.
To isolate the catalyst effect in the data, columns (3) through (6) interact GDP and electricity
with a dummy for electric goods. Consistent with the demand-complementarities hypothesis,
electric goods exhibit a statistically significant above-average dependence on electricity
consumption and a below-average dependence on income per capita (column (3)). Column (4)
shows that the differential effect remains when including country-time fixed effects. Specifically,
a 100 percent increase in electricity consumption is associated with a 7.0 percent increase in the
price of electric goods. Columns 5 and 6 show that values and quantities of electric goods also
15
exhibit an above-average differential dependence on electricity consumption, consistent with the
theory’s prediction that high catalyst consumption is associated with outward shifts in the
demand curves for tradable consumer goods that increase quantities and reduce the price
elasticity of demand.
Alternative Classifications, Quality Controls, and Placebo Tests. Table 4 shows the
results from a similar empirical specification using a narrower definition of electric goods. This
narrower definition excludes parts of electric goods as well as high-unit-cost appliances such as
air conditioning units and dishwashers that may be considered luxury items in low-income
countries. It also limits the classification of electric goods to those that are representative of
electronics exported from the U.S. to the countries in the sample. Of U.S. exports of
dishwashers, for example, only 4% are destined for the low-income countries for which there is
variation in electricity access, while 44% of U.S. exports of small kitchen appliances are destined
for low-income countries. Column 1 shows that a 100 percent increase in electricity production
is associated with a 20 percent increase in the price of routine electric appliances, conditional on
the average dependence of consumer goods prices on electricity and conditional on the
dependence of prices of routine electric appliances on income per capita.
The strong dependence of prices of electric appliances on electricity may reflect both
markups and quality variation. To control for quality variation, I separate appliances into those
with high levels of within-product quality variation (long quality ladders) and low levels of
within-product quality variation (short quality ladders) based on the quality ladder estimates in
Khandelwal (2010). The estimate of the dependence of electric-appliance prices on electricity is
above 0.20 for appliances with long and short quality ladders, suggesting that markups, rather
than solely differences in quality, are contributing to price variation. 9
One may wonder whether other nonelectric consumer-good categories display a similar
dependence on electricity consumption, implying that the estimated dependence is due to some
other artifact of the data rather than to demand complementarity. In other words, would placebo
goods generate the same result as electric goods? One way to address this question is to estimate
9
For a model predicting a relationship between quality of imports and income, see Hallak (2006). To the extent that
the evidence here captures some quality variation, it suggests that catalysts, and not only income, contribute to
import demand for quality, consistent with the assumption in new theoretical trade models that explain patterns of
trade and income across countries. Fajgelbaum, Grossman, and Helpman (2011) develop a model featuring
complementarity between a homogenous good and quality of vertically differentiated goods.
16
the dependence of placebo-goods prices on electricity, and then see whether the dependence of
electric goods exceeds the average dependence of placebos on electricity consumption. The
estimates based on equation (21) do exactly this by capturing the average dependence of prices
of electric goods on electricity in the country-time fixed effects.
While the results based on averages over placebos are informative, it is nonetheless
useful to see whether the dependence on electricity differs for subsets of consumer goods that we
would most expect to exhibit a different relationship with electricity and income. In particular,
battery-powered goods should be in higher demand in countries with less electricity, all else
equal. Similarly, prices of nonelectric luxury sports goods are expected to exhibit a weaker
dependence on electricity (and stronger dependence on income) than the dependence for prices
of electric goods. I identify battery-powered electronics as those for which the description
identifies the product as exclusively battery powered. The classification consists primarily of
battery-powered lamps and radios. Luxury goods include equipment for water sports, skiing,
golf, tennis, and adventure sports.
Consistent with this intuition, column (4) shows that prices of battery-powered goods
exhibit a strong below-average dependence on electricity and a positive (but statistically
insignificant) positive dependence on income. Luxury items similarly exhibit a strong belowaverage conditional dependence on electricity. The dependence on income per capita is positive
and significant, consistent with the notion that demand for luxury goods depends more on
income (and other associated mechanisms) than on electricity.
Evidence from Electricity Prices. The evidence from Tables 3 and 4 based on electricity
production is consistent with the theory’s prediction that higher catalyst consumption causes
higher prices. A corresponding prediction is that lower catalyst prices (which are associated with
higher catalyst quantities) should lead to higher prices of tradable goods. As discussed above,
cross-country price data are limited to a small subset of high-income countries and is less
amenable to an empirical test. Despite these limitations, the price data for this subset of countries
can nonetheless help identify differential demand for electric products that exhibit different
degrees of energy intensity. Data on electricity prices faced by households in 36 countries is
from the Energy Information Association and is available from 2001. To correspond with the
trade data, the sample spans 2001 through 2006. Table 5 shows summary statistics for the sample
based on electricity prices.
17
A number of electronic goods in the sample exhibit varying energy intensity that can be
identified based on their product descriptions. These appliances are refrigerators and air
conditioning units. Electricity prices determine which level of energy intensity consumers choose
to purchase. In particular, energy-intensive appliances should be in lower demand (and have
lower prices) in countries with high electricity prices, all else equal. Table 6 shows that prices of
high-energy appliances exhibit a relatively lower dependence on electricity prices than do prices
of their low-energy counterparts. The differential dependence on electricity prices between highintensity and low-intensity units holds across specifications, consistent with the notion that prices
of appliances depend on prices of relevant catalysts.
3.1.2. An Additional Test of the Demand-Complementarities Hypothesis
Here I test whether prices of skis depend on ski resorts and snowfall over mountainous terrain.
Although skis are a small share of trade, they are very suitable for a test of the demandcomplementarities hypothesis because the catalysts (ski resorts and snowfall) exhibit a relatively
low correlation with income per capita, and because the catalysts exhibit strong differential
demand complementarity (demand for skis depends on snowfall far more than does demand for
other consumer goods).
Of the two catalysts for skis, one is an endowment (snowfall) which may indeed be
complementary to demand for the other catalyst (ski resorts). Therefore any dependence of prices
of skis on the catalysts may reflect preferences related to endowment differences rather than
differences related to catalysts that are driven by income per capita. If so, the test based on skis is
useful for identifying the dependence of prices on country-level demand complements, but is less
useful for identifying how prices depend on catalysts that increase specifically with an
economy’s productive capacity. In this sense, the evidence from skis should be viewed as
supplementary to the evidence on electricity.
Country-level data on ski resorts are provided by Snow-forecast.com (http://www.snowforecast.com/countries). These data were collected in 2013. 85 countries have nonmissing data
on ski resorts. The correlations of ski resorts with income per capita is 0.70. Since the data exist
only for a snapshot in time, the empirical test below will be based on cross-section variation only
18
based on the most recent U.S. trade data. Specifically, I use average trade value and quantities
sold over 2004 to 2006 to obtain unit values of product-level exports to each country.
I construct data on snowfall over mountainous terrain based on information on rainfall,
temperature, and elevation across countries. The Climate Change Knowledge Portal at the World
Bank provides country-level data on monthly precipitation and temperature, averaged over the
years 1961 through 1999. I compute country-level measures of snowfall by summing a country’s
precipitation over months when average temperatures are less than 5 degrees Celsius. I consider
this snowfall to be conducive to skiing if a country’s highest point of elevation is greater than
5,000 feet; otherwise I set the country’s measure of skiable snowfall to slightly above zero. 10
The test for demand complementarity and pricing to market for skis is based on the
following specification,
𝑝𝑝𝑐𝑐ℎ = 𝛾𝛾ℎ + 𝛽𝛽1 ln 𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑐𝑐 × 𝑆𝑆𝑆𝑆𝑖𝑖ℎ + 𝛽𝛽2 ln 𝑦𝑦𝑐𝑐 × 𝑆𝑆𝑆𝑆𝑖𝑖ℎ + 𝜖𝜖𝑐𝑐ℎ ,
(22)
Where 𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑠𝑠𝑐𝑐 is the number of ski resorts per capita in country 𝑐𝑐 and other variable
definitions are analogous to those in equation (21). The tests include variations of (22) that
instrument for ski resorts with measures of snowfall in mountains and that directly test the
dependence of ski prices on snowfall. Since the number of ski resorts is positively correlated
with income, and since skis may have an above-average dependence on income per capita,
𝛽𝛽2 ln 𝑦𝑦𝑐𝑐 × 𝑆𝑆𝑆𝑆𝑖𝑖ℎ is included to isolate the dependence of prices of skis on ski resorts from their
dependence on income per capita.
Table 5 shows the results based on the 33 countries in with data on ski resorts. This
sample of countries is much richer than the sample based on the electricity test, with a median
GDP per capita in 2005 of $22,858. Column (1) shows that ski prices exhibit an economically
and statistically significant above-average dependence on ski resorts and below-average
dependence on income per capita. The estimates are nearly identical when replacing the countrylevel covariates with country-level fixed effects (column (2)). The magnitude of the elasticity of
ski prices with respect to ski resorts nearly doubles to 0.26 when instrumenting ski resorts with
10
Data on country-level elevation is from the CIA World Factbook. The results are robust to using different
temperature and elevation thresholds when computing skiable snowfall. The elevation threshold limits the measure
of skiable snowfall in countries, such as Ireland, which are wet and often cold, but which do not have and mountains
conducive to skiing.
19
snowfall (column (3)). The direct effect of snowfall in ski prices is also strong and significant
(column (4)).
According to the estimates, catalysts are a strong determinant of prices, conditional on
the dependence of prices on other mechanisms associated with income per capita. The estimated
price elasticities with respect to catalysts are much larger than the typical estimates of pricing-tomarket (e.g., Simonovska 2015). The high estimates may reflect quality variation since the data
do not distinguish between skis of different quality levels. Despite this caveat, the results
document a strong dependence of unit values on catalysts, and a below-average dependence of
unit values on income per capita. The below-average dependence of prices of skis on income per
capita is especially striking considering that skis are luxury goods for which expenditure shares
rise sharply with income. The large negative coefficients on income per capita suggest that
demand complementarities, rather than other nonhomotheticities, are responsible for variation in
prices of skis.
4. Additional Implications of Demand Complementarities and Pricing-to-Market
Evidence in the previous section supports the notion that demand complementarities can help
explain high prices of tradable goods in rich countries. Conventional wisdom is that prices of
nontradables are also higher in rich countries. Here I demonstrate that the theory of demand
complementarities is consistent with the conventional wisdom. I also provide examples of a
number of potential catalysts that are less expensive (or more accessible) in rich countries.
4.1 Demand Complementarities and Prices of Nontradables
A prominent explanation for the observed correlation between country income per capita and
nontradable prices is that the law of one price (LOP) holds in tradables but rich-country
productivity is higher in the tradable sector than in the nontradable sector (Harrod [1933],
Balassa [1964], and Samuelson [1964]). High productivity in the tradable sector drives up wages
in rich countries, which causes higher prices in the sector with lower productivity (nontradables).
A difficulty for the HBS explanation, as recently noted by Alessandria and Kaboski (2011), is
that the rise in relative productivity of tradables within rich countries appears too small to
account for the strong relationship between prices and incomes across countries: Differences in
20
prices of services across countries cannot be solely attributed to differences in costs; and
markups for nontradables are higher in countries with high per capita income.
A theory based on demand complementarities helps explain how markups of
nontradables increase with income per capita. The model that formally demonstrates the
dependence of prices of nontradables on catalyst consumption is a straightforward extension of
the theoretical model in Section 2 and is presented formally in Murphy (2013). The results of
such a model are very similar to those from Section 2: As productivity in 𝑁𝑁 increases, 𝑁𝑁’s
production and consumption of catalyst and final goods increases, as does the price of tradables
in 𝑁𝑁. In addition, the relative price of services is higher in 𝑁𝑁 because the increase in 𝐶𝐶𝑁𝑁 lowers
the price elasticity of demand for services, causing service-sector firms in 𝑁𝑁 to charge a higher
markup than service-sector firms in 𝑆𝑆.
Complementarities between catalysts and nontradables are likely to be relevant in a
number of situations. For example, the value of services such as window washing, carpet
cleaning, and lawn mowing all depend on whether consumers have homes that can accommodate
windows, carpets, and lawns. In Quito, Ecuador, these services are of little value because few
homes there are suitable for windows and nice carpets, and few households own lawns.
Likewise, the utility from a haircut may depend on the prevalence of other goods and services for
which one might need a haircut to fully enjoy. Salon services are more valuable, for example,
when consumers attend formal events in which a certain style of appearance is required.
4.2. Examples of Catalyst Goods
The theory predicts that catalysts are less expensive in rich countries, which may seem contrary
to the conventional wisdom that nontradables are more expensive in rich countries. The evidence
that nontradables are more expensive in rich countries is based on the Interational Comparison
Program’s survey of prices across countries. However, the ICP analysis excludes a range of
goods that may be considered catalysts, or fails to adjust for quality due to the lack of appropriate
data. Here I present further examples of the types of goods and services that can be identified as
catalysts due to complementarity with other consumer goods, and due to their cost advantages in
rich countries.
One of the primary examples of catalyst goods is infrastructure such as roads, which
complement demand for a range of goods and services by permitting consumers to travel to
21
service establishments and retail outlets. Infrastructure and government services are types of
services that the ICP considers to be comparison-resistant areas due to the lack of comparable
data across countries (Rao 2013). Therefore it is not possible to identify potential catalysts by
examining price dispersion across countries. Instead, I identify a list of potential candidates for
catalysts that broadly complement demand for consumer goods and services. Table 8 shows that
each of these goods or services are either of higher quality, more available (less costly to obtain),
or more efficient in rich countries, consistent with the theory’s predictions.
Public Infrastructure. Roads complement demand for goods by facilitating consumers’
access to retail services. Lagakos (2014) suggests that transportation complements demand for
retail services, which helps rationalize why retail sectors in poor countries are slow to adopt new
technologies. Transportation quality may also cause pricing to market if it shifts consumers’
demand curves. The measure of a country’s road quality is the percentage of roads that are
paved, provided by the World Development Indicators. Another form of public infrastructure
that acts as a catalyst is public safety, which increases the ability of consumers to travel to retail
outlets to obtain goods and services. Table 8 includes two measures of public safety, “Political
Stability and the Absence of Violence,” and “Rule of Law,” which captures the public’s faith in
the police. Each measure is provided through the World Databank by the Worldwide Governance
Indicators at Brookings.
Housing. Housing complements demand for a range of consumer goods, including home
entertainment systems and furniture. In the U.S., for example, consumers have relatively
inelastic demand for home entertainment systems because they also have spacious TV rooms in
their homes and a reliable supply of energy. In Ecuador, by contrast, the average consumer has
less space in his home and an unreliable power supply, and thus lower demand for home
entertainment systems. As discussed above, housing also complements demand for housing
services. Comparable measures of the housing stock are not available across countries. Therefore
the housing data are based on the ICP’s measure of the housing stock for European countries in
2005.
Advertising and Marketing. One can consider marketing/advertising (either informative
or persuasive) to be a catalyst good. Arkolakis (2010) demonstrates that marketing and
advertising, which account for as much 7.7% of GDP in the U.S., costs less in larger markets.
Arkolakis’s evidence is based on a small subset of countries, and primarily reflects the price of
22
placing an ad with television, radio, or newspaper outlets in European and Caribbean markets.
However, the cost of reaching consumers depends not only on the cost of an ad, but also the
efficiency of the ad in reaching consumers. Table 8 shows that consumers in rich countries have
greater access to the media through which ads are delivered, including television, radio,
telephone, Internet, and computers; thus generating greater efficiency in the delivery of ads to
consumers. The data are provided by the United Nation’s International Telecommunication
Union.
Urbanization. Cities are associated with high consumer demand due to proximity
between consumers and retail and service establishments (e.g., Glaeser, Kolko, and Saiz 2001;
Gollin, Jedwab, and Vollrath 2015; Murphy 2014). Living near malls and shopping centers
increases demand for tradable goods sold there, and living near service establishments increases
demand for services. The data on urbanization rates are provided by the World Development
Indicators at the World Bank.
5. Conclusion
Recent evidence documents that markups are correlated with income per capita, both across
countries and over time at business cycle frequencies. Understanding the nature of this
relationship is important for understanding the determinants of income, investment rates,
aggregate price indices, and sectoral productivity. This paper proposes a new explanation—the
utility consumers derive from consumer goods depends on their consumption of complementary
goods—to account for the relationship between income and prices. A range of empirical tests
demonstrates an important role of demand complementarities for price determination.
The theoretical conditions under which prices depend on demand complements are quite
general. The sufficient condition is likely satisfied for a range of goods and services beyond
those examined in this study, which implies that the demand-complementarities mechanism may
shed light on price determination in a number of settings.
The dependence of prices on country-level catalysts suggests a number of avenues for
future research. Catalysts such as infrastructure and marketing may be more efficient in rich
countries, which implies that rich-country price indices may be overstated. The dependence of
demand for consumer goods on country-level catalysts may have additional implications for
trade flows, patterns of competitive advantage, and cross-country differences in income. For
23
example, Krugman (1980) illustrates how preferences determine the location of production, and
Krugman and Venables (1995) demonstrate how local demand generates production externalities
and income.
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26
Table 1-Summary Statistics.
N
Mean
StDev
p25
p50
p75
Real GDP per capita 1998 (2005
USD)
115
2798.8
2841.0
718.6
1878.5
4030.0
Real GDP per capita 2006 (2005
USD)
116
3648.2
3571.7
887.2
2402.0
5061.7
Electricity Consumption per
capita 1998 (MwH)
117
1467.5
1404.6
348.8
1043.5
2107.9
Electricity Consumption per
capita 2006 (MwH)
117
1846.4
1682.5
516.3
1497.9
2513.6
Electricity Access (percent of
population)
69
68.7%
30.6%
41.0%
77.5%
98.0%
Growth in Electricity
Consumption, 1998-2006
117
42.6%
82.9%
14.9%
28.6%
44.5%
Growth in Real GDP per capita,
1998-2006
117
32.3%
30.8%
12.3%
27.7%
43.9%
Note: Data on is available through the World Development Indicators. The sample is limited to
countries with GDP per capita (in 2005 USD) less than $15,000
27
Table 2: Examples of Electric Goods
harmonizd system code
description
8414510010
FANS FOR PERMANENT INSTALLATION,ELEC MOTOR LE 125W
8414510090
FANS, NOT PERM INST,SLF-CONT ELEC MTR N/E 125 W
8414599080
FANS, NESOI
8414901040
PTS OF FANS INC BLOWERS (OF SUBHEADING 8414.51.00)
8415100040
AIR-CONDITIONERS,WIND/WALL,SELF-CONTAIN <2.93KW/HR
8415100060
AIR-COND,WIND/WALL,SELF-CONTAIN,2.93KW/HR><4.98KW
8415100080
AIR-COND,WIND/WALL,SELF-CONTAIN GE 4.98 KW/HR
8415103040
AIR-CONDTNRS,WIND/WALL, SELF-CONTAIN LT 2.93 KW/HR
8415103060
AIR-COND,WIND/WALL,SELF-CONTAIN (2.93-4.98 KW/HR)
8418210010
REFRIGERATORS, HOUSEHOLD, COMP TYP, VOL <184 LITER
8418210020
REFRIG,HOUSEHOLD,COMP TYP,VOL 184 < 269 LITERS
8418210030
REFRIG,HOUSEHOLD,COMP TYP,VOL 269 < 382 LITERS
8418210090
REFRIG,HOUSEHOLD, COMP TYP, VOL 382 LITERS & OVER
8418220000
REFRIGERATORS, HOUSEHOLD, ABSORPTION, ELECTRICAL
8418290000
REFRIGERATORS, HOUSEHOLD TYPE, NESOI
8422110000
DISHWASHING MACHINES, HOUSEHOLD TYPE
8422900540
PARTS OF HOUSEHOLD TYPE DISHWASHING MACHINES
8450110090
WASH MACH,EXC COIN OPERATE, AUTO,CAP NOT EXC 10 KG
8450120000
WASH MAC WITH BLT-IN CENT DRY,CAP NOT EXC 10 KG
8450190000
WASH MACH, CAPACITY NOT EXC 10 KG, HOUSEHOLD,NESOI
8450200090
WASH MACH,CAP EXC 10KG, HOUSEHOLD,LANDRY-TYP,NESOI
8450900000
PTS OF HOUSEHOLD OR LNDRY-TYP WASH MAC INC WSH/DRY
8509100020
ELECTRIC DOMESTIC VACUUM CLEANERS, PORTABLE, HAND
8509100040
ELECTRIC VACUUM CLEANERS, NESOI
8509200000
ELECTRIC DOMESTIC FLOOR POLISHERS
8509300000
ELECTRIC DOMESTIC KITCHEN WASTE DISPOSALS
8509400020
ELECTRIC DOMESTIC FOOD MIXERS
8509400030
ELECTRIC DOMESTIC JUICE EXTRACTORS
8509400040
ELECTRIC DOMESTIC FOOD GRINDERS AND PROCESSORS
8509800040
ELECTRIC DOMESTIC CAN OPENERS INCL COMBINATION UNI
8509800060
ELECTROMECHANICAL DOMESTIC APPLIANCES,HUMIDFIERS
8509800091
ELECTROMECHANICAL DOMESTIC APPLIANCES, NESOI
8509902000
ELECTRIC DOMESTIC VACUUM CLEANER PARTS
8509903000
ELECTRIC DOMESTIC FLOOR POLISHER PARTS
8509904050
ELECTRIC DOMESTIC APPLIANCE PARTS, NESOI
8510100000
ELECTRIC SHAVERS
8510200000
ELECTRIC HAIR CLIPPERS
8510300000
HAIR REMOVING APPLIANCES
8516210000
ELECTRIC STORAGE HEATING RADIATORS
8516290000
ELECTRIC SPACE HEATING APPARATUS,NESOI
8516310000
ELECTRIC HAIR DRYERS
8516400000
ELECTRIC FLATIRONS
8516500000
MICROWAVE OVENS
8516604000
ELECTRIC COOKING STOVES, RANGES AND OVENS
8516606000
COOKING PLATES, BOILING RINGS, GRILLERS,& ROASTERS
8516710000
ELECTRIC COFFEE OR TEA MAKERS
8516720000
ELECTRIC TOASTERS
8539224000
CHRISTMAS-TREE LAMPS > 100 V BUT NOT > 200 W
Note: X indicates goods that are classified as a small electric appliance.
28
Small Appliance
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
Table 3-Prices of Electric Goods and Per Capita Electricity Consumption
Dependent Variable:
Regressors
log(GDP per capita)
Log(price)
Log(price)
Log(price)
Log(price)
Log(value)
Log(quantity)
(1)
(2)
(3)
(4)
(5)
(6)
0.082**
0.070**
0.198***
0.128**
(0.035)
(0.035)
(0.047)
(0.058)
-0.063
-0.055
-0.046
0.009
(0.043)
(0.043)
(0.052)
(0.069)
YES
0.038***
-0.084***
(0.005)
(0.009)
log(MwH per capita)
0.058***
0.118***
(0.004)
(0.008)
log(MWh per capita) X Electric good
log(GDP per capita) X Electric good
Country-Year FEs
NO
NO
NO
YES
YES
Product-Year FEs
YES
YES
YES
YES
YES
YES
R-squared
0.76
0.76
0.76
0.77
0.48
0.54
175128
175159
174726
174721
174721
174721
1,748
1,748
1,748
1,748
1,748
1,748
# observations
# products
Notes: Data source: World Bank Development Indicators and U.S. Exports by HS-10 classification. Robust standard errors clustered at the product level in
parentheses. ***, **, and * indicate significance at the 1%, 5%, and 10% level, respectively.
29
Table 4-The Dependence of Prices of Subsets of Consumer Goods on Electricity and Income Per Capita
Dependent Variable: Log(price)
Regressors
log(MWh per capita) X Routine electric appliance
log(GDP per capita) X Routine electric appliance
(1)
(2)
(3)
(4)
(5)
0.209***
0.208***
(0.056)
(0.056)
-0.229***
-0.228***
(0.061)
(0.061)
0.242*
log(MWh per capita) X Short ladder routine electric appliance
(0.143)
log(MWh per capita) X Long ladder routine electric appliance
0.226***
(0.085)
log(GDP per capita) X Short ladder routine electric appliance
-0.316**
(0.137)
log(GDP per capita) X Long ladder routine electric appliance
-0.211**
(0.085)
log(MWh per capita) X battery-powered appliance
-0.137***
(0.053)
-0.134**
(0.053)
log(GDP per capita) X battery-powered appliance
0.092
(0.080)
0.087
(0.080)
log(MWh per capita) X luxury good
-0.108***
(0.033)
log(GDP per capita) X luxury good
-0.104***
(0.037)
0.093***
0.089**
(0.033)
(0.041)
YES
Country-Year FEs
YES
YES
YES
YES
Product-Year FEs
YES
YES
YES
YES
YES
R-squared
0.77
0.77
0.76
0.76
0.77
174721
174721
175123
175123
174721
# observations
Notes: Data source: World Bank Development Indicators and U.S. Exports by HS-10 classification. Robust standard errors clustered at the product level in
parentheses. ***, **, and * indicate significance at the 1%, 5%, and 10% level, respectively.
30
Table 5-Summary Statistics for Electricity Price Sample
N
Mean
StDev
p25
p50
p75
Real GDP per capita 1998 (2005
USD)
35
24776.0
18705.2
7615.7
24996.1
36412.4
Real GDP per capita 2006 (2005
USD)
35
27487.9
20157.2
8475.4
27154.4
40394.1
Electricity Price 2001 ($/KwH)
36
0.087
0.040
0.062
0.077
0.105
Electricity Price 2006 ($/KwH)
32
0.142
0.061
0.099
0.133
0.181
Growth in Electricity Price, 20012006
32
45.7%
24.7%
28.8%
46.4%
61.8%
Growth in Real GDP per capita,
2001-2006
35
16.6%
12.1%
7.2%
11.5%
Note: Data on electricity prices faced by households is from the Energy Information
Administration.
31
24.8%
Table 6-Dependence of Prices of Appliances with Varying Energy Intensity on Electricity Prices
Dependent Variable: Log(price)
Regressors
(1)
(2)
(3)
0.254***
-0.078***
0.061**
(0.004)
(0.021)
(0.024)
-0.350***
-0.404***
-0.513***
(0.011)
(0.017)
(0.020)
0.374***
0.169***
0.336***
(0.006)
(0.021)
(0.026)
-0.378***
-0.577***
-0.350***
(0.008)
(0.020)
(0.023)
Country-Year FEs
NO
YES
YES
Product-Year FEs
YES
YES
YES
log(GDP per capita)
0.091***
(0.006)
log(Electricity Price) X SMALL Refrigerator
log(Electricity price) X LARGE Refrigerator
log(Electricity Price) X SMALL Window AC Unit
log(Electricity Price) X LARGE Window AC Unit
Controls for interactions with log(GDP per capita)
NO
NO
YES
R-squared
0.79
0.80
0.80
94641
94641
94641
# observations
Notes: Small refrigerators are less than 184 Liters in size. Large Refrigerators are greater than 382 Liters. Small AC units use
less than 2.93 KW/hour of energy. Large units use greater than 4.98 KW/hour. Electricity price data is from the Energy
Information Administration. The sample is limited to countries with data on electricity prices faced by households. Robust
standard errors clustered at the product level are in parentheses. ***, **, and * indicate significance at the 1%, 5%, and 10%
level, respectively.
32
Table 7-Dependence of Prices of Skis on Ski Resorts and Snowfall
Dependent Variable: Log(price)
IV specification
Regressors
log(GDP per capita)
(1)
(2)
(3)
0.137***
0.139***
0.262***
(0.005)
(0.006)
(0.007)
-0.502***
(0.011)
-0.549***
(0.015)
-0.777***
(0.016)
(4)
0.055***
(0.011)
log(ski resorts per capita)
0.013**
(0.005)
log(ski resorts per capita) X ski
log(GDP per capita) X ski
log(snowfall) X ski
-0.288***
(0.010)
0.112***
(0.003)
Country Fes
NO
YES
YES
YES
Product FEs
YES
YES
YES
YES
R-squared
0.80
0.81
0.81
0.81
20473
20473
20473
20473
# observations
Notes: Robust standard errors clustered at the product level in parentheses. In column 3, log(snowfall) X ski is an instrument
for log(ski resorts per capita) X ski. Estimates are based on countries with data on ski resorts. ***, **, and * indicate
significance at the 1%, 5%, and 10% level, respectively.
33
Table 8 - Catalysts and Income Per Capita
Public Infrastructure
Advertising and
Marketing
Catalyst
Catalyst Data Source
Correlation
between catalyst
and log (GDP per
capita)
Percent of Paved Roads
WDI
0.58
209
Absence of Violence
WGI
0.67
208
Rule of Law
WGI
0.79
210
Housing Volume
ICP
0.86
31
Radio Access (percent of population)
ITU
0.21
64
TV Access (percent of population)
ITU
0.72
104
Telephone Access (percent of population)
ITU
0.71
83
Internet Access (percent of population)
ITU
0.88
158
Computer Access (percent of population)
ITU
0.90
160
Urbanization Rate
WDI
0.70
210
34
Number of
Countries
with nonmissing Data
Figure 1: Electricity Access and GDP Per Capita across Countries.
Note: The vertical line is drawn at GDP per capita equal to $15,000.
Figure 2: Electricity Consumption and GDP Per Capita, Low-Income Countries.
35