The Determinants of Quality Specialization∗
Jonathan I. Dingel†
Chicago Booth and NBER
September 2016

Abstract
A growing literature suggests that high-income countries export high-quality goods.
Two hypotheses may explain such specialization, with different implications for welfare, inequality, and trade policy. Fajgelbaum, Grossman, and Helpman (2011) formalize the Linder hypothesis that home demand determines the pattern of specializationand therefore predict that high-income locations export high-quality products. The
factor-proportions model also predicts that skill-abundant, high-income locations export skill-intensive, high-quality products. Prior empirical evidence does not separate
these explanations. I develop a model that nests both hypotheses and employ microdata on US manufacturing plants’ shipments and factor inputs to quantify the two
mechanisms’ roles in quality specialization across US cities. Home-market demand explains as much of the relationship between income and quality as differences in factor
usage.
JEL codes: F12, F14, R12
Keywords: quality specialization, product quality, market access, home-market effect∗I am grateful to Donald Davis, Amit Khandelwal, Eric Verhoogen, Jonathan Vogel, and David Weinstein
for invaluable discussions, guidance, and support. Thanks to the editor, three anonymous referees, Michael
Best, Brianna Cardiff, Arnaud Costinot, Dave Donaldson, Ben Faber, Pablo Fajgelbaum, Gene Grossman,
Juan Carlos Hallak, Jessie Handbury, Corinne Low, Kyle Meng, Joan Monras, Eduardo Morales, David
Munroe, Paul Piveteau, Bernard Salanie, Daniel Sturm, Allie Tepper, Felix Tintelnot, Sebastien Turban,
Reed Walker, Columbia colloquia participants, and numerous seminar audiences for very helpful comments
and suggestions. I am grateful to Rob Feenstra and John Romalis for sharing their parameter estimates.
Support from the Institute for Humane Studies and the Kathryn and Grant Swick Faculty Research Fund at
the University of Chicago Booth School of Business is gratefully acknowledged. This research was conducted
while I was a special sworn status researcher of the US Census Bureau. Any opinions and conclusions
expressed herein are those of the author and do not necessarily represent the views of the US Census
Bureau. All results have been reviewed to ensure that no confidential information is disclosed.
†
jdingel@chicagobooth.edu

1Introduction

The Linder hypothesis is the oldest theory of quality specialization in international trade.
Staffan Burenstam Linder (1961) posited that profitably exporting a product requires robust
demand for that product in the exporter’s home market. Since higher-income consumers
tend to purchase higher-quality products, he conjectured that local demand causes highincome countries to produce and export high-quality products. This “home-market effect”
explanation of quality specialization was recently formalized by Fajgelbaum, Grossman, andHelpman (2011) in a general-equilibrium model. In contrast, the canonical factor-abundancetheory of comparative advantage identifies high-income countries’ greater supplies of capitaland skills as the reason they produce and export high-quality products.1 These competingtheories have distinct implications for welfare, inequality, and trade policy. Empirical work
to date has not identified the importance of each mechanism in quality specialization.
The empirical challenge is that the two theories make the same predictions about countrylevel trade flows. Each predicts that high-income locations export high-quality products,
consistent with the finding that higher-income countries export products at higher prices
within narrowly defined product categories (Schott, 2004; Hummels and Klenow, 2005).2
Similarly, each predicts that non-homothetic preferences cause high-income locations to import high-quality products, consistent with the finding that higher-income countries import
more from higher-price exporters (Hallak, 2006; Choi, Hummels, and Xiang, 2009). Combining these export and import patterns, each predicts that countries with more similar incomes
trade more intensely with each other, as found by Hallak (2010) and Bernasconi (2013).3
In this paper, I use theory and data to quantify the roles of the home-market effectand the factor-abundance mechanism in quality specialization across US cities. I develop amodel that yields an empirical approach to separate the two mechanisms. It exploits plantlevel data on shipments and inputs and location-level data on populations and incomes. I
implement the empirical strategy using data on US cities and manufacturing plants and findthat the home-market effect influences quality specialization across cities of different income
levels as much as factor abundance.
To guide my empirical investigation, I introduce a theoretical framework that nests the1

For example, Schott (2004, p. 676) suggests that “high-wage countries use their endowment advantage
to add features or quality to their varieties that are not present among the varieties emanating from low-wagecountries.” Linking quality specialization to relative factor supplies dates to at least Falvey (1981).
2
Throughout this paper, observed “prices” refer to unit values, which are shipments’ value-to-quantity
ratios. Like international trade data, the data used in this paper describe transactions’ values and quantities.
3
Hallak (2010, p. 459) notes that “several theories can explain a systematic relationship between percapita income and quality production... The prediction of the Linder hypothesis about the direction of trade
can be founded on any of these theories.”1

two mechanisms, each of which has been studied separately. Individuals have non-homothetic
preferences over a homogeneous and a differentiated good; higher-income individuals consume higher-quality varieties of the differentiated good. This demand assumption makes
high-income locations import high-quality products and generates the home-market effectwhen trade is costly. Individuals have heterogeneous skills, and goods can be ranked bytheir skill intensities. This production assumption allows skill-abundant locations to have acomparative advantage in higher qualities when quality is skill-intensive. The model serves
two purposes. First, it confirms that each mechanism alone can generate trade flows consistent with the empirical findings described above. Second, the theory identifies a way toseparate the two mechanisms using plant-level data. Factor abundance affects specialization
exclusively through plants’ factor usage. Conditional on plant-level factor intensity, demandalone determines quality specialization. Thus, plant-level data on shipments and inputs canbe combined with data on locations’ incomes to identify the home-market effect.
To implement this empirical strategy, I use microdata on US manufacturing plants’ shipments and inputs from the Commodity Flow Survey and the Census of Manufactures. Thesesources provide microdata on plants in many cities with different income levels in a single
dataset. In contrast, I am not aware of a source containing plant-level shipment and input
data from many countries.4 I document that US cities exhibit the key patterns found in international data. Both outgoing and incoming shipments exhibit higher prices in higher-income
cities, and cities with more similar incomes trade more intensely with each other. I therefore proceed to use these data to distinguish between the two hypotheses by constructing
empirical measures of factor inputs and market access.
Guided by the model, my empirical investigation yields two main results. First, observed
differences in plants’ inputs, which may be induced by either mechanism, explain only amodest share of within-product specialization across cities of different incomes. Most of thevariation is within-factor-intensity variation. Second, a market-access measure that describes
the income composition of proximate potential customers is strongly related to the patternof within-intensity specialization. Quantitatively, I find that the home-market effect plays atleast as large a role as the factor-abundance mechanism in quality specialization by income.
More specifically, in my empirical work I infer quality specialization from two empiricalmeasures commonly used in the literature: unit values and demand shifters. The firstmeasure is based on the idea that higher-quality products sell at higher prices and has been
widely used in the international trade literature (Hummels and Skiba, 2004; Schott, 2004;
4
My empirical approach thus follows the counsel of Krugman (1991, p.3): “if we want to understandinternational specialization, a good place to start is with local specialization. The data will be better andpose fewer problems of compatibility, and the underlying economic forces will be less distorted by government
policies.”

2

Hallak, 2006; Baldwin and Harrigan, 2011). The second measure follows Sutton (1991, 2012),
Berry (1994), Hummels and Klenow (2005), Khandelwal (2010), and others in identifying
a product as higher-quality when, conditional on price, it has higher market share. Whenboth measures are available in my data, they yield comparable results.
The first empirical finding is that observed factor-usage differences explain a modest
share of within-product specialization. Guided by the model, I construct factor-intensity
measures using data on plants’ employees, equipment, and wages. Between-intensity variation explains about one quarter of the covariance between locations’ per capita incomes
and outgoing shipment prices. It explains a larger share of the covariance between incomes and demand shifters, but observed factor-usage differences never explain more thanhalf of the specialization by income per capita in any regression specification. Since thefactor-abundance mechanism operates only through between-intensity variation, this finding
bounds its explanatory power, at least in terms of observed factor usage.5
The second empirical finding is that the home-market effect plays a quantitatively significant role in quality specialization, at least as large as differences in observed factor usage.
Using data on cities’ incomes and geographic locations, I construct two market-access measures describing the income composition of proximate potential customers. The first omits
the residents of the city in which the plant is located, so that it does not reflect any unobserved local supply-side mechanisms. I find that this measure of demand is strongly positively
correlated with manufacturing plants’ outgoing shipment prices. In fact, this measure explains a larger share of the covariance between income per capita and outgoing shipment
prices, 36%, than plant-level factor usage. The second market-access measure follows themodel by including residents in the city of production. This demand measure consistently
explains a larger share of the observed specialization across cities of different incomes thanplants’ factor inputs. Within-intensity variation in market access explains 58% of the covariance between product prices and incomes per capita, twice that attributable to factor-usage
differences.6 It explains a similar share, 48%, of the covariance between demand shifters
and incomes per capita.7 Market access is orthogonal to incoming shipment characteristics,
so proximity to higher-income consumers is associated with net exporting of higher-quality
varieties. I conclude that the home-market effect for quality plays a substantial role in theeconomic geography of US manufacturing.
5

Section 5 discusses the particular properties unobserved inputs would need to exhibit in order to accountfor my findings.
6
Using only within-intensity variation is conservative. Unconditionally, variation in market access accounts for 77% of the price-income covariance.
7
Factor-usage differences explain 46% of the covariance between demand shifters and incomes per capita,
so there is considerably smaller residual variation in the decomposition of this measure.

3

These findings are important because the two theories have distinct implications. In
predicting the quality of a location’s exports, one emphasizes its relative factor supplies
while the other stresses its relative proximity to high-income customers. These yield different
predictions, for instance, for poor countries that have rich neighbors.8 To the extent thatspecializing in producing high-quality goods improves growth prospects, the home-market
effect found here suggests an advantage of proximity to high-income countries.9 And sincetrade policy governs market access, governments may influence quality specialization.10
My empirical strategy of using plant-level data from US cities of different income levels
links my results to a number of findings in urban and regional economics. I provide the firstcharacterization of production specialization within product categories across cities. Previous
empirical work describing variation in manufacturing across US cities has focused on interindustry specialization (Henderson, 1991; Holmes and Stevens, 2004; Davis and Dingel, 2014)or described the products available to retail consumers without tracking production locations(Handbury and Weinstein, 2015). The finding that the geography of demand plays a majorrole in specialization complements a nascent literature describing the consumption benefitsof living in cities with high-income populations (Glaeser, Kolko, and Saiz, 2001; Handbury,
2012; Diamond, 2016).
The paper is organized as follows. Section 2 describes the two competing hypotheses.
Section 3 introduces a model nesting both and shows how to separate them using plant-level
data. Section 4 describes the US microdata and pattern of specialization and exchange.
Section 5 reports the empirical results. Section 6 concludes.

2

BackgroundBurenstam Linder (1961) posited that demand differences can determine production specialization.11 Krugman (1980) formalized how economies of scale and trade costs can cause acountry with a larger home market for a product to be a net exporter of that good. First,
economies of scale cause each product to be produced in a single location and sold to manymarkets. Second, producing in the larger market minimizes transportation costs. Krugman (1980) obtains this result by assuming exogenous differences in countries’ demand for8

For example, Mexico and Turkey are developing economies that are proximate to high-income customers
in the US and EU, respectively. Verhoogen (2008) shows that increased incentive to export caused quality
upgrading by Mexican firms.
9
See Redding (1996) and Lederman and Maloney (2012) on quality and growth.
10Helpman and Krugman (1989, p.2): “It is clear that changing one’s view of why trade happens, andhow international markets work, ought to change one’s view of what kind of trade policy is appropriate.”
11
His informal narrative focused on the role of entrepreneurial discovery (p.89-90). He emphasized informational costs of distance more than transport costs and did not explicitly address economics of scale.

4different industries’ products. Fajgelbaum, Grossman, and Helpman (2011) show how income differences can determine quality specialization within products when preferences are
non-homothetic. In their model, the composition of income determines the composition ofdemand, since higher-income households purchase higher-quality varieties. Plants produce
higher qualities in higher-income locations because it is more profitable to produce in thelarger home market. In equilibrium, greater demand elicits a more-than-proportionate production response, such that high-income locations are net exporters of high-quality products.
The canonical factor-abundance theory of comparative advantage can yield the same setof predictions when preferences are non-homothetic. An early example is Markusen (1986),
in which the income elasticity of demand for capital-intensive manufactures is greater thanone, so that high-income, capital-abundant countries specialize in manufactures that areexported to other high-income countries.12 Many other models make analogous assumptions
about the alignment of comparative advantage and relative demand, so that “tastes andcapabilities are correlated” but not causally linked (Murphy and Shleifer, 1997, p. 6).13 In
these theories, higher-income countries are net exporters of higher-quality products if thecomparative-advantage mechanism exceeds differences in demand.
Thus, both theories are consistent with the growing body of empirical evidence suggesting that higher-income countries export and import higher-quality products. Schott (2004)shows that unit values in product-level US import data are higher for higher-income, more
capital- and skill-abundant exporting countries; Hummels and Klenow (2005) find a positive
relationship between unit values and exporter incomes using data from 59 importing countries. Khandelwal (2010) estimates demand shifters using US import data and finds thatthey are positively related to exporting countries’ GDP per capita and capital abundance.
Feenstra and Romalis (2014) and Hallak and Schott (2011), using other methods, also reportthat higher-income countries export products inferred to be higher quality.
These common predictions for country-level trade flows motivate this paper’s use of plantlevel data to separate the two mechanisms. In short, the challenge prior work has faced isthat customers and workers are the same people in country-level data.14 As my model12

See also Bergstrand (1990). Strictly speaking, these are general-equilibrium models of intersectoral
specialization. Falvey (1981) introduced a partial-equilibrium model of within-industry specialization acrossqualities by capital intensity consonant with the within-product interpretation of factor-abundance theory
suggested by Schott (2004).
13
Two recent papers study specialization across sectors using models with non-homothetic preferences.
Using aggregate trade flows, Fieler (2011) estimates a two-sector version of the Eaton and Kortum (2002)
Ricardian model. She infers that the more income-elastic industry has greater dispersion in idiosyncratic
productivities, causing higher-TFP countries to have comparative advantage in these luxuries. Examining
variation across 56 sectors, Caron, Fally, and Markusen (2014) find a positive correlation between industries’
income elasticities of demand and skill intensities. These perfect-competition models do not feature homemarket effects.
14
In addition to looking at country-level capital abundance, Schott (2004) shows that the unit values

5demonstrates, assessing the factor-abundance hypothesis requires looking at the factors of
production employed by exporting plants. A series of studies using firm-level data have shownthat exporters and firms producing higher-quality products use more capital-intensive andskill-intensive production (Verhoogen, 2008; Hallak and Sivadasan, 2013). These firm-level
findings are consistent with the factor-abundance explanation of quality specialization. But
they do not provide evidence that differences in factor abundance relate to differences in
output across locations, since they describe establishments in a single location.
As a result, there is no prior empirical evidence distinguishing the home-market effectfor quality from factor-abundance-determined quality specialization. There is an empirical literature on the Helpman and Krugman (1985) home-market effect, in which a larger
home market causes specialization in the industry with greater economies of scale (Davisand Weinstein, 1999, 2003; Hanson and Xiang, 2004). This work has relied upon using
observable sectoral characteristics, such as transport costs and demand elasticities. Suchcross-industry variation is unavailable when considering quality specialization within products. Moreover, since the distributions of income and human capital are closely related, bothacross countries and cities, it is empirically difficult to distinguish the home-market effectfrom factor-abundance theories of comparative advantage using aggregate data.
I proceed to introduce a theoretical framework that incorporates both mechanisms andtheir interaction in equilibrium. This allows me to derive an empirical strategy that relies
on observing plants’ inputs and outputs.

3

TheoryI introduce a theoretical framework in which both market access and factor abundance may
influence the pattern of production and exchange. I use a high-dimensional model withmany locations, qualities, and skills.15 It nests a version of the Fajgelbaum, Grossman, andHelpman (2011, henceforth FGH) model and a factor-abundance model as special cases.
Nesting the two mechanisms in one framework allows me to analyze each in isolation andtheir interaction. For brevity, details and derivations appear in appendix A.
The theory delivers two results key to the empirical investigation. First, it confirms thatof exported products are positively correlated with the capital-labor ratio of the relevant three-digit ISIC
industry in the exporting country. However, much of the variation reflects cross-country differences in capitalabundance, a fact noted by Dollar, Wolff, and Baumol (1988, p. 33). The mean pairwise correlation between
the 28 industries’ capital-labor ratios across the 34 countries in the Schott (2003) data is 0.5. Moreover,industry data necessarily aggregate heterogeneous plants and may not represent exporters’ factor intensities.
15
Matching the facts that both outgoing and incoming shipment prices are increasing in average income
necessitates a many-location model. Making comparisons across and within qualities of different factor
intensities, which is at the heart of my empirical strategy, necessitates many quality levels.

6

quality specialization is overdetermined. Each mechanism alone can cause higher-income
locations to produce, export, and import higher-quality varieties in equilibrium. Second,
the theory identifies an important distinction between the two mechanisms. Conditional onplant-level skill intensity, any correlation between local income and plants’ output quality
is due to the home-market effect. This result is the basis of my empirical approach. The
model also informs my construction of empirical measures of the relevant objects.
In the model, there are K locations indexed by k. Location k has a population of size Nkmade up of heterogeneous individuals whose skills, indexed by ω, are distributed according to
the density f (ω, k). These skill distributions are exogenous, a standard assumption in trade
theory that is innocuous for the purpose of distinguishing the roles of the two mechanisms.16
I assume that locations can be ranked by their skill abundance in the likelihood-ratio sense.
The density f (ω, k) is strictly log-supermodular, so high-k locations are skill-abundant.17

3.1

Preferences

Consumer preferences are non-homothetic, so demand varies with income. As in FGH,
individuals consume a homogeneous good and one unit of a differentiated good. Varieties ofthe latter are indexed by j, with price pj and quality qj ∈ Q. For individual h, the utility of
consuming z units of the homogeneous good and a unit of variety j is
uhj = zqj + hj ,(1)with idiosyncratic valuation hj drawn from a generalized extreme value (GEV) distribution.
A consumer chooses quantity z and variety j to maximize utility. The homogeneous goodis the numeraire. A consumer with income yh therefore chooses j to maximize (yh −pj )qj +hj ,where z = yh −pj . As FGH show, if ’s GEV distribution has dispersion θq for q, this yields anested-logit demand system in which the fraction of consumers with income y buying variety
j of quality q can be expressed as ρj (y) = ρj|q · ρq (y). ρq (y) is the fraction with income yP
who choose a product of quality q, and ρj|q = exp (−pj q/θq ) / j 0 :qj0 =q exp (−pj 0 q/θq ) is thefraction buying j among those buying quality q. The latter is income-invariant.
This demand system has two important properties. First, the complementarity betweenz and qj in equation (1) makes higher-income consumers more likely to choose higher-quality
16

Factor mobility would be relevant in considering counterfactuals, since individuals may migrate acrosscities in response to economic changes. My empirics characterize the equilibrium observed in the data, andthere is substantial variation in both skill distributions and income levels across US cities.
17
I make extensive use of log-supermodularity as an analytical tool; see Costinot (2009) for an introduction.
In R2 , a function f (ω, k) is log-supermodular if ω > ω 0 , k > k 0 ⇒ f (ω, k)f (ω 0 , k 0 ) ≥ f (ω, k 0 )f (ω 0 , k) andstrictly log-supermodular when the inequality is strict. Using educational attainment data, Davis and Dingel(2014) provide evidence that US cities’ skill distributions are broadly consistent with this assumption.

7q (y)
varieties. Market share ρq (y) varies with income according to ρq1(y) ∂ρ∂y= q − qa (y), whereqa (y) is the average quality consumed by individuals with income y. Second, if firms ignore∂ ln ρ (y)their own effect on the price index, the elasticity of demand is ∂ lnjpj = −pj qj /θq , so
producers of quality q charge a constant additive markup of mq ≡ θq /q.18

3.2

Production

Production involves employing workers of heterogeneous skills, so relative factor supplies may
be a source of comparative advantage. The homogeneous good is competitively produced andfreely traded. Differentiated varieties are produced by monopolistically competitive firms.
Production of the homogeneous good exhibits constant returns to scale, so the total costof producing quantity x(z, k) at unit cost c(z, k) is x(z, k)c(z, k).19 Skill ω in location kcommands wage w(ω, k). Hiring `(ω) units of skill ω per unit of output, the unit cost isZZc(z, k) = min`(ω)`(ω)w(ω, k)dωb(ω, z)`(ω)

s.t.

σ−1
σ

σ
 σ−1

≥ 1.

dω

ω∈Ω

ω∈Ω

The technological coefficients b(ω, z) describe the contribution of each skill type in production
and therefore characterize the homogeneous good’s skill intensity. The elasticity of substitution across inputs σ is greater than one and finite. Cost minimization yields per-unit input
demands `(ω, z, k) = w(ω, k)−σ b(ω, z)σ wherever x(z, k) > 0.
Firms may produce a differentiated variety of quality q by paying fixed cost fq in unitsof the numeraire. The constant marginal cost of producing quality q in location k is
ZZc(q, k) = min`(ω)`(ω)w(ω, k)dωb(ω, q)`(ω)

s.t.

σ−1
σ

σ
 σ−1

dω

≥ 1.

ω∈Ω

ω∈Ω

Thus, unit input demands are `(ω, q, k) = w(ω, k)−σ b(ω, q)σ c(q, k)σ , with marginal costZc(q, k) =σ

1−σb(ω, q) w(ω, k)

1
 1−σ

dω

.

ω∈Ω

A firm producing x(q, k) units of quality q in location k hires x(q, k)`(ω, q, k) of skill ω.
Firms producing a differentiated variety in location k can export one unit to destination
0
k at marginal cost c(q, k) + τqkk0 , where the trade cost τqkk0 is incurred in units of the18

I use the nested-logit demand system in part because the constant-additive-markup property makes themodel analytically tractable. Only the first property, that high-income consumers are more likely to purchasehigh-quality varieties, is necessary for the home-market effect to influence the pattern of specialization.
19
I abuse notation using z to index the homogeneous good. In equation (1), z denotes the quantity of this
good.

8

numeraire. Taking competitors’ behavior as given, the profit-maximizing prices charged byfirm j producing quality q in k are a constant markup over cost, pjk0 = c(q, k) + τqkk0 + mq .
We can now identify the equilibrium sales level in location k 0 for a variety of quality
q produced in k, which I denote dqkk0 . If k 0 has Nk0 consumers with income distributionRg(y, k 0 ), this is dqkk0 = Nk0 ρj (y)g(y, k 0 )dy. Denote the number of firms producing varietiesof quality q in location k by nq,k . Plugging in optimal prices, sales dqkk0 can be written interms of (vectors of) the number of firms (n), unit costs (c), and trade costs (τ ).
Z
dqkk0 = Nk0

ρj (q)ρq (y)g(y, k 0 )dy = exp(−(c(q, k) + τqkk0 )/mq )Nk0 Γk0 (q, n, c, τ )The function Γk0 (q, n, c, τ ) describes the share of demand in location k 0 for quality q given
the equilibrium prices and locations of all producers. A firm’s sales of quality q to k 0 from kdepend on this demand share, population Nk0 , marginal cost c(q, k), and trade cost τqkk0 .20

3.3

Equilibrium

In equilibrium, labor markets clear and firms earn zero profits. The full-employment condiPtion for each skill ω in each location k is f (ω, k) = x(z, k)`(ω, z, k)+ q∈Q nq,k x(q, k)`(ω, q, k).
Plugging in firms’ labor demands and defining nz,k = 1, we can write this asf (ω, k) = w(ω, k)−σXnr,k x(r, k)b(ω, r)σ c(r, k)σ ,

(2)

r∈z∪Q

where I use r to sum both the homogeneous good and qualities of the differentiated good.
The free-entry condition says that the profits from producing quality q in location k are
non-positive everywhere and zero where firms are active: πq,k ≤ 0 ∀k and nq,k > 0 ⇒ πq,k = 0.
πq,k =

X
X(pqkk0 − c(q, k) − τqkk0 )dqkk0 − fq = mq
dqkk0 − fqk0=mq exp(−c(q, k)/mq )k0Xexp(−τqkk0 /mq )Nk0 Γk0 (q, n, c, τ ) − fq

(3)

k0

3.4

Equilibrium pattern of specialization and trade

Given the geographic distribution of skills, individuals’ preferences, and the production technology, the equilibrium pattern of production and trade depends on two forces. Trade costs
The model therefore implies a gravity equation for exports of q from k to k 0 , but q is not an observablecharacteristic. Since gravity equations do not aggregate by summation, the model does not deliver a closedform gravity equation for total exports of differentiated varieties from k to k 0 .
20

9shape the pattern of market access and therefore the home-market effect. Skill intensities,
governed by b(ω, r), link output composition to skill supplies through labor-market clearing.
I consider two cases for each force. The two trade-cost matrices are costless trade andtrade costs that are small but positive, τqkk0 > 0 for k 6= k 0 and τqkk = 0. The two skillintensity cases are uniform skill intensities, b(ω, r) = b1 (ω)b2 (r), and skill intensities that are
increasing in quality, b(ω, r) weakly log-supermodular.21
I analyze the four cases in turn. When neither mechanism is active, the pattern ofproduction is indeterminate. Section 3.4.1 characterizes equilibrium when only the factorabundance mechanism is active, while Section 3.4.2 does likewise for the home-market effect.
In each case, high-k locations both export and import high-q varieties. Thus, each mechanism
alone could account for previously documented empirical patterns. Section 3.4.3 describes
equilibrium when both mechanisms are active and shows how to identify the home-market
effect after conditioning on plants’ skill intensities.
To facilitate the analysis, define a skill-intensity index i(r) such that i(r) = i(r0 ) ⇐⇒b(ω, r) ∝ b(ω, r0 ) and i(r) > i(r0 ) ⇒ r > r0 . This index groups together products so that
producers in the higher-i group employ relatively more skilled labor. Let i(r) equal thelowest r in this set of products, so that b(ω, i) is strictly log-supermodular by definition.
3.4.1

Skill-intensive quality and costless tradeFirst, consider the case when trade is costless and b(ω, r) is weakly log-supermodular. Costless trade (τqkk0 = 0 ∀q ∀k ∀k 0 ) means that πq,k in the zero-profit condition (3) depends on
k only through the c (q, k) term. In the absence of trade costs, variation in demand acrossdestinations k 0 is orthogonal to the location of production. Producing quality q is mostprofitable wherever its unit cost c(q, k) is lowest.
Skill abundance governs the pattern of production through labor-market clearing. Equation (2) and the strict log-supermodularity of f (ω, k) imply, for k > k 0 and ω > ω 0 ,w(ω, k)−σEω0 ,kw(ω 0 , k)−σb(ω, i)σb(ω 0 , i)σw(ω, k 0 )−σ>Eω0 ,k0
w(ω 0 , k 0 )−σb(ω, i)σb(ω 0 , i)σ


,

(4)

where Eω0 ,k [α(i)] is an output-share-weighted average of α(i) for production in k, with outputb(ω,i)σshares weighted by use of skill ω 0 .22 Since b(ω, i) is strictly log-supermodular, b(ω
0 ,i)σ is strictlyσb(ω,i)
increasing in i, and Eω0 ,k b(ωis a measure of the average skill intensity of output in k.
0 ,i)σ21

When b(ω, q) is log-supermodular, quality is skill-intensive. By allowing z to take any value, I makeno assumption on the skill intensity of the homogeneous good, but I assume that there is a value z makingb(ω, r) a log-supermodular function.
(ω,k)
f (ω,k0 )22
For expositional convenience, I assume f (ω, k) > 0 ∀ω ∈ Ω ∀k, so that k > k, ω > ω 0 ⇒ ff(ω0 ,k) > f (ω 0 ,k 0 ) .

10This inequality means that more skill-abundant (higher-k) locations produce more skillintensive
products. By skill abundance, products made in k are more skill-intensive (higher-i)w(ω,k)−σb(ω,i)σ(Eω0 ,k b(ω0 ,i)σ is greater) and/or skilled labor in k is relatively cheaper ( w(ω0 ,k)−σ is greater).
The latter implies skill-intensive products’ unit costs are relatively lower in k, and thus
k’s output must be more skill-intensive in equilibrium. When b(ω, q) is log-supermodular,
higher-quality varieties are more skill-intensive, so we interpret inequality (4) as saying thatk absorbs its greater supply of higher skills by producing higher-quality varieties.23
This result describes the factor-abundance mechanism for quality specialization. Notethat specialization across qualities of the same skill intensity is indeterminate in this case,because inequality (4) depends on i(q), not q. Skill-abundant locations produce higherquality varieties only because such products are more skill-intensive.24
What about the equilibrium pattern of demand? Since trade is costless, varieties’ prices
and income-specific market shares do not vary across locations. Denoting the equilibrium
variety counts and factor prices by the vectors n̄ and c̄, sales volumes Γk (q, n̄, c̄, 0) vary withlocation k solely due to differences in the composition of income. Demand for higher-quality
varieties is relatively greater in higher-income locations.
Result. When trade is costless, there is no home-market effect. When quality is skillintensive and skill-abundant locations are higher-income locations, higher-income locations
both produce more of and have greater demand for higher-quality varieties in equilibrium.
3.4.2

Uniform skill intensities and costly trade

When skill intensities are uniform, unit costs are multiplicatively separable in (r, k) and canσ
be written as c(r, k) = b2 (r) 1−σ c(k). The labor-market clearing condition (2) becomesf (ω, k) = b1 (ω)σ w(ω, k)−σ c(k)X

σnr,k x(r, k)b2 (r) 1−σ .

r∈z∪QSince nothing inside the sum depends on skill ω, the factor-abundance mechanism imposes norestrictions on the equilibrium composition of local production nr,k x(r, k). Any observed re23

This interpretation neglects the skill intensity of the homogeneous good. If the homogeneous good ismore skill-intensive, skill-abundant locations may produce more of the homogeneous good rather than higherquality varieties. When factor intensities vary both across and within goods, the factor-abundance mechanism
may operate along both margins. Empirically, Schott (2004) documents that there is little correlation
between countries’ factor supplies and across-good specialization. Assuming that the homogeneous good is
the least skill-intensive product is sufficient to guarantee that high-k locations specialize in high-q varieties.
24
This result has been derived without any reference to the demand system beyond the fact that costlesstrade makes consumers’ locations irrelevant to the optimal production location. Thus, the empirical investigation of whether the factor-abundance mechanism alone can explain the pattern of specialization does notdepend upon the functional form of the preferences in equation (1).

11

lationship between f (ω, k) and the pattern of specialization results from the demand channel
and reflects the connection between g(y, k) and f (ω, k).
To characterize how specialization is determined by demand, I follow the approach taken
by FGH to determining the equilibrium pattern of production when trade costs are small
and locations specialize.25 With uniform skill intensities, the zero-profit condition isσπq,k = mq exp(−b2 (q) 1−σ c(k)/mq )X

exp(−τqkk0 /mq )Nk0 Γk0 (q, n, c, τ ) − fq ≤ 0.

k0

Through this condition, demand governs the location of production in equilibrium. Consider
two cases, depending on whether wages vary across locations.
When factor prices equalize, c(k) = 1 ∀k and πq,k varies only with demand. If trade
costs are uniform (τqkk0 = τq ∀k 0 6= k), then profits vary only with home demand, πq,k >
πq,k0 ⇐⇒ Nk Γk (q, n, c, τ ) > Nk0 Γk0 (q, n, c, τ ). Provided that wages are increasing in skill,
high-k locations are high-income because they are skill-abundant, and they have greater
demand for high-q varieties. This makes producing high-q varieties more profitable in high-k
locations. When population sizes are equal, Proposition 6 of FGH describes the resulting
equilibrium: if location k produces quality q and location k 0 < k produces quality q 0 , thenq 0 < q. Similarly, since higher-k locations have greater demand for higher-q varieties, theirimports are higher-quality (see Proposition 7 of FGH). In the case of σ = ∞ and Nk = 1 ∀k,
the model under consideration reduces to that in section VII of FGH.
When factor prices do not equalize, the location with the lowest c(k) is the most attractive
cost-wise for all producers. Firms locate in higher-cost locations only if these locations havegreater demand for their output so that they save on transport costs. In other words, when
trade costs are uniform, if nq,k > 0 and c(k) > c(k 0 ), it must be that Nk Γk (q, n, c, τ ) >Nk0 Γk0 (q, n, c, τ ). When population sizes are equal and trade costs are sufficiently low, thisdifference in demand is due solely to the income composition of the two locations. Thus,
higher-income locations specialize in producing higher-quality varieties and export them.
Result. Suppose that population sizes are equal, skill intensities are uniform, and trade
costs are uniform and small. If k > k 0 , nq,k > 0, and nq0 ,k0 > 0, then q > q 0 and nq,k0 = nq0 ,k =0. Higher-income locations are net exporters of higher-quality varieties because demand forsuch qualities is greater in such locations. If consumers in k and k 0 import varieties ofqualities q and q 0 with q > q 0 , then k imports relatively more of quality q.
Thus, the home-market effect yields equilibrium trade patterns that match the empiricalevidence summarized in section 2. Since we obtained the same result in the previous section
via the factor-abundance mechanism, quality specialization is overdetermined.
25

Appendix section A.4.2 discusses the case when trade costs are large and production is diversified.

12

Result. Higher-income locations both exporting and importing higher-quality varieties is
consistent with the factor-abundance mechanism or the home-market effect operating alone.
3.4.3

Skill-intensive quality and costly trade

Now suppose both mechanisms are active. When quality is skill-intensive and trade is costly,
the labor-market clearing condition (2) and the zero-profit condition (3) jointly govern thepattern of quality specialization. The critical result that underlies my empirical investigationis that demand alone determines specialization across varieties of the same skill intensity.
First, consider the labor-market-clearing inequality, which is governed by the factorabundance mechanism. As shown previously, inequality (4) implies that output of higher-ivarieties is relatively greater in higher-k locations. Thus, skill intensities govern the broad
pattern of production.
Second, consider the zero-profit condition, which depends on potential customers’ incomesthrough demand levels. To summarize demand, define a market-access term
Mq,k (τ ) ≡X

exp(−τqkk0 /mq )Nk0 Γk0 (q, n̄, c̄, 0),k0where the costless-trade-equilibrium demand levels Γk (q, n̄, c̄, 0) were found in section 3.4.1.
When trade costs are small, the profits from producing a variety of quality q in location k
are approximately
πq,k ≈ mq exp(−c(q, k)/mq )Mq,k (τ ) − fq .
(5)With small trade costs, profits are not sensitive to the locational decisions of other firms.26
This means that all varieties of a given quality are produced in a single location, and we canidentify production locations using the profits expression.
Within skill intensities, demand determines where varieties are produced. When two
qualities have the same skill intensity, i(q) = i(q 0 ), the location that minimizes the cost of
producing a variety of quality q also minimizes the cost of a variety of quality q 0 . Thus, if
varieties of the same skill intensity are produced in different locations, this must be due todifferences in market access, Mq,k (τ ). In particular, if c(q, k) 6= c(q, k 0 ), then firms produce inthe higher-cost location because its market-access advantage outweighs its cost disadvantage.
Proposition 1 (Within-intensity market access). When trade costs are small, if nq,k > 0,
nq0 ,k0 > 0, and i(q) = i(q 0 ), then Mq,k ≥ Mq,k0 or Mq0 ,k ≤ Mq0 ,k0 .
Proposition 1, proved in appendix A, establishes that market access alone governs specialization within qualities of the same skill intensity. An important component of Mq,k (τ ) is26

With large trade costs, Γk0 (q, n, c, τ ) and thus profits depend on competition through firms’ locations n.

13demand in the location of production, Nk Γk (q, n̄, c̄, 0).27 This is the home-market effectexplanation for why high-income locations specialize in high-quality products.
This yields an empirical strategy for distinguishing the two mechanisms. Both the factorabundance mechanism and the home-market effect cause high-k locations to specialize inhigh-q varieties, so variation across skill intensities is overdetermined. Variation withinskill intensities is driven by market access alone. We can therefore identify a lower boundon the home-market effect by examining the pattern of specialization conditional on skill
intensities.28 My empirical strategy is to relate the pattern of specialization across locations
to variation in market access after controlling for plants’ factor usage.29

3.5

Taking the theory to plant-level data

The theory describes relationships between product quality (q), location (k), skill intensity(i), and market access (Mq,k (τ )). These objects can be inferred from observables using themodel and some auxiliary assumptions. The following results are derived in appendix A.
I infer product quality from shipments’ prices. Assume that b(ω, q) is strictly decreasing
in q, so that higher qualities have higher costs. If c(q, k) increases in quality faster than
mq declines in quality, the price of a variety pjk0 = c(q, k) + τqkk0 + mq is informative about
its quality. I validate this approach in appendix E.3 by calculating demand shifters to inferproduct quality. Prices and shifters are strongly positively correlated in my data.
I infer locations’ rankings from their per capita incomes, denoted ȳk . Under the assumption that g(y, k) is log-supermodular, average income is a sufficient statistic for k.
I infer skill intensities from the composition and wages of plants’ workers. The composition measure assumes that non-production workers are more skilled than production workers.
The wage measure assumes that wages are increasing in skill. When factor prices equalize,
ranking plants by their share of non-production workers or their average wage is equivalent
to ranking them by their factor intensities. When labor is cheaper where it is abundant,
plants of all intensities use more skilled workers in skill-abundant locations, so I include themeasure and its interaction with ln ȳk to control for skill intensity.
My empirical counterpart to the model’s market-access term Mq,k (τ ) is the average of27

When trade costs are uniform, as in FGH, differences in Mq,k (τ ) are due solely to differences in demandin the location of production, Mq,k (τ ) > Mq,k0 (τ ) ⇐⇒ Nk Γk (q, n̄, c̄, 0) > Nk0 Γk0 (q, n̄, c̄, 0).
28
The strategy of using variation in demand within a set of goods of the same factor intensity is similar
to the approach used by Davis and Weinstein (2003) to integrate factor-abundance and home-market-effectmodels. We differ when we go to the data. Whereas Davis and Weinstein (2003) assume that factor intensities
are fixed within 3-digit ISIC industries, I use plant-level information to infer factor intensities.
29
Proposition 1 implies cross-sectional comparisons of market access in levels. It does not, for example,
imply that I could exploit changes in market access over time, since nq,k is not a continuous function of Mq,k .
If πq,k > πq,k0 both periods, q is not produced in k 0 both periods, regardless of the change in πq,k − πq,k0 .

14potential customers’ per capita incomes, weighted by population size and distance from thelocation of production. In the model, per capita income is a sufficient statistic for relative
demand for qualities when trade costs are low.30 Weighting these incomes by population sizeand distance reflects the fact that it is more profitable to produce in locations that are more
proximate to a larger number of consumers due to distance-related trade costs.
I construct two such market-access measures. Denote log income per capita in destinationcity d in year t by ln ȳ dt , population size by Ndt , and the mileage distance from origin o by
milesod . The first measure describes the composition of potential customers not residingP
N miles−ηodin the origin location Mot1 = d6=o P dtN miles−η ln ȳdt . The second market-access measured0 6=o d0 t
od0P
N miles−η31
odincludes all potential customers, consistent with the model, Mot2 = d P dt
−η ln ȳdt .
d0 Nd0 t milesod0
In constructing each measure, I use a distance elasticity of unity, η = 1. This is based on theempirical relationship between transaction volumes and distance, which I estimate using agravity model in appendix C. These gravity estimates for trade between metropolitan areas
are consistent with the findings of the vast gravity literature on trade between nations.
I now turn to the data to characterize the empirical relationships linking product qualities,
skill intensities, and market access following the model’s guidance.

4

Data and empirical settingThis section introduces the empirical setting in which I conduct my investigation. First,
I describe the data that I use to characterize the pattern of specialization and exchange
between US cities. Additional details are in appendix B. Second, I document that bothoutgoing shipments and incoming shipments within fine product categories exhibit higher
prices in higher-income cities. Thus, this empirical setting is suitable for testing theories ofquality specialization.

4.1

Data

I combine microdata on US manufacturing plants’ production and shipments with data
describing cities and sectors. The two confidential microdata sources used are the 1997,
30
This exploits spatial variation in income levels to capture demand Γk0 (q, n̄, c̄, 0). With high trade costs,
this may be a poor approximation due to Γk0 (q, n, c, τ ) also depending on firms’ equilibrium locations. Tradecosts between US cities are lower than those between countries due to the common currency, language, andpolicy environment. Glaeser and Kohlhase (2004) estimate that incurred transport costs are less than
4% of shipment value for most manufactures. My empirical results suggest that approximation (5) is notunderpowered in practice.
31
2
1
Mot
can be written as a weighted average of Mot
and ln ȳot . A city’s own income per capita has greater
weight in this average when it is more populous than and more distant from other metropolitan areas.

15

2002, and 2007 Commodity Flow Survey (CFS) and Census of Manufactures (CMF).The
CFS describes commodity shipments by a sample of business establishments in terms of
their value, weight, destination ZIP code, and transportation mode.32 Products are describedusing the Standard Classification of Transport Goods, a distinct scheme that at its highest
level of detail defines 512 5-digit product categories. Each quarter of the survey year, plants
report a randomly selected sample of 20-40 of their shipments in one week.The CMF describes
a plant’s location, industry, employees, payroll, material inputs, and revenues. It covers theuniverse of manufacturing plants, which are classified into 473 6-digit NAICS manufacturingindustries.33
In most of the analysis, I define a product as the pairing of a 5-digit SCTG commodity
code and a 6-digit NAICS industry code. This results in more narrowly defined products
when the NAICS industry scheme is more detailed than the SCTG commodity scheme.
For example, footwear (SCTG 30400) produced by an establishment in “men’s footwear(except athletic) manufacturing” (NAICS 316213) is distinct from footwear produced byan establishment in “women’s footwear (except athletic) manufacturing” (NAICS 316214).
There are more than 5,000 commodity-industry-year triplets in my estimation sample.34
The empirical analysis describes core-based statistical areas (CBSAs), which are 366
metropolitan and 576 micropolitan statistical areas defined by the Office of Management
and Budget. I refer to these geographic units as cities. Appendix B describes how datausing other geographies were assigned to CBSAs.
I calculate cities’ per capita incomes using data on CBSAs’ total populations and personal incomes from the Bureau of Economic Analysis’s regional economic profiles for 1997,
2002, and 2007. In my baseline specification, I exclude the employees and income of all
establishments in the same 6-digit NAICS industry as the shipping plant when calculating
the population and per capita income of its CBSA.35 Since most manufacturing sectors’
workforces and payrolls are small relative to the total populations and incomes of the cities
in which they are located, the results obtained without making this adjustment to the percapita income and population measures are very similar.
32

The Census Bureau defines an establishment as “a single physical location where business transactions
take place or services are performed.”The CFS covers manufacturing, mining, wholesale, and select retailand services establishments. I analyze shipments by manufacturing establishments, which I call “plants.”
33
Information on small establishments is estimated from administrative records, not reported by the establishment. I exclude these administrative records and imputed observations. See appendix B for details.
34
My results are robust to defining products using only the SCTG commodity codes.
35
There is therefore variation across industries within a CBSA in the regressors I call “log origin CBSA
population” and “log origin CBSA per capita income.”

16

4.2

Pattern of specialization and tradeThis section describes variation in manufacturing shipment prices across US cities.36 The
patterns mirror those found in international trade data. First, outgoing shipments exhibit
higher prices in higher-income cities. This pattern is consistent with quality specialization inwhich higher-income cities produce higher-price, higher-quality varieties.37 Second, incoming
shipments exhibit higher prices in higher-income cities. This pattern is consistent with
non-homothetic preferences in which higher-income consumers demand higher-price, higherquality varieties.
One concern with inferring qualities from prices is that products may be horizontally differentiated, as in the model. With horizontal differentiation, two varieties of the same quality
can sell at different prices in the same destination, with the high-price variety simply obtaining a smaller market share (Khandelwal, 2010). This raises the concern that high-income
locations’ specialization in high-price products may only reflect higher costs. However, thisobjection is unlikely to be problematic for the empirical investigation here.
Unit values are likely to be informative about product quality in this context for four
reasons. First, investigations of international trade data distinguishing between raw unit
values and quality-adjusted prices have shown unit values to be a meaningful, though imperfect, proxy for quality (Khandelwal, 2010; Feenstra and Romalis, 2014). I obtain similar
results in section E.3, where I find that demand shifters are positively correlated with unit
values. Moreover, these demand shifters exhibit patterns of specialization and factor usage
consistent with those found for unit values. Second, my empirical setting allows me to check
whether differences in prices across locations only reflect higher costs. Using plant-level dataon wages and workers, I can test whether plants shipping from high-income locations chargehigher prices only because they have higher labor costs. They don’t. Third, consistent
with the international evidence presented by Hallak (2006), I find a positive relationshipbetween shipment prices and destinations’ per capita income, suggesting that higher-priceproducts are those preferred by higher-income consumers.38 Fourth, in barcode-level retail data, Hottman, Redding, and Weinstein (2016) and Faber and Fally (2016) find thathigher-price products have higher sales or appeal to consumers.
The first feature of the US data matching international findings is that shipments origi36

Recall that all observed “prices” are in fact unit values, the ratio of a shipment’s value to its weight inpounds. See data appendix B for details of the sample selection and variable construction.
37
I follow Schott (2004), who characterized specialization across products using quantities and specialization within products using average prices. The latter is necessary because quantities are reported by product,so by definition we do not observe the quantities of different qualities within narrowly defined products.
38
A potential concern is that higher-income consumers pay higher prices for identical products because
higher-income consumers are less responsive to price changes (Simonovska, 2015). This would be a concern
if the observed price variation were primarily within-plant. Table 2 below shows that this is not the case.

17

nating from higher-income cities exhibit higher prices. To characterize how shipment prices
vary with origin characteristics, I estimate linear regressions describing a shipment s of product k by plant j from origin city o to destination city d by transport mode m in year t of
the formln pskjodmt = β ln ȳokt + α1 ln Nokt + α2 ln milesskjodmt + γmt + γkdt + skjodt ,(6)where pskjodmt is the shipment’s unit value, ȳokt and Nokt are per capita income and total
population in the origin CBSA excluding the industry of the shipping plant, milesskjodmt
is the ZIP-to-ZIP mode-specific mileage distance of the shipment, γmt are mode-year fixed
effects, and γkdt are product-destination-year fixed effects. Including both per capita income
and total population allows me to distinguish between income composition and scale, sincethese are positively correlated across cities. The mileage and mode covariates allow prices
to vary with transport costs.39 The product-destination-year fixed effects mean that I am
comparing prices of the same product shipped to the same metropolitan area in the same year,
such as shipments of beer by breweries to Chicago in 1997. This is akin to the comparisonof US import prices with product-year fixed effects in Schott (2004).40
Table 1 characterizes how variation in outgoing shipments’ unit values relates to origin
characteristics. The first column reports a large, positive origin-income elasticity of shipment
prices of 44%. Higher-income cities specialize in the production of higher-price varieties of
products, and this pattern is highly statistically significant. Conditional on the level of percapita income, there is no economically meaningful correlation between origin population
size and outgoing shipments’ prices.
I proceed to interact the regressors with two measures of the scope for product differentiation. The Sutton (1998) measure, industrial R&D and advertising intensity, proxies
the scope for quality differentiation by the cost shares of differentiation-related activities.
The Khandelwal (2010) measure infers the scope for quality differentiation from the rangeof estimated demand shifters in US imports. The second and third columns of Table 1
show that the positive relationship between origin income per capita and outgoing shipment prices is stronger in products with greater scope for quality differentiation, as classified
by both measures. These patterns are consistent with higher-income cities specializing inhigher-quality products. In products with greater scope for quality differentiation, income
differences correspond to greater differences in output prices.
39

In the model, the constant-markup assumption makes plants’ free-on-board prices invariant to transport
costs. Including these covariates relaxes that assumption. The main results of this paper are robust toomitting the population and mileage covariates and mode fixed effects.
40
Note that my unit of observation is a shipment. The paper’s main results are robust to aggregating tothe origin-destination-industry-product-year level.

18

Table 1: Outgoing shipment prices
Dep var: Log unit value, ln pskjodmt

(1)

(2)

(3)

Origin CBSA log per capita income, ln ȳokt

0.440**

0.411**

0.430**(0.0359)(0.0491)(0.0496)

Origin CBSA log population, ln Nokt

-0.00764

0.000175-0.000889(0.00421)(0.00540)(0.00547)

0.0404**0.0538**0.0528**(0.00280)(0.00357)(0.00365)

Log mileage, ln milesskjodmt
Per capita income (log) × differentiation

0.115*

0.191**(0.0522)(0.0733)

Population (log) × differentiation-0.000146-0.0205*(0.00533)(0.00804)

Mileage (log) × differentiation-0.00858*-0.00870(0.00376)(0.00539)

Sutton0.094
20,0003000
900,000

Khandelwal
0.094
20,0003000
900,000

Differentiation measureWithin R2
Number estab-year (rounded)
Number ind-prod-year (rounded)
Observations (rounded)

0.080
35,0005250
1,800,000

Notes: Manufacturing establishments in the CFS and CMF. All shipments are to a domestic destination
CBSA distinct from the origin CBSA. All regressions include SCTG5 × NAICS6 × destination × year
fixed effects and mode × year fixed effects. Columns 2 and 3 are estimated on a sample of observations
for which industry R&D and advertising intensity, Khandelwal (2010) ladder length, and Rauch (1999)
differentiation measures are available. Standard errors, clustered by origin CBSA × year, in parentheses.
∗∗and ∗ denote statistical significance at 1% and 5%, respectively.

The second feature of the US data matching international findings is that shipments
destined for higher-income cities exhibit higher prices. To characterize how shipment prices
vary with destination characteristics, I estimate linear regressions of the formln pskjodmt = β ln ȳdt + α1 ln Ndt + α2 ln milesskjodmt + γkt + γmt + θot + θkjt + skjodt ,where pskjodmt is the shipment’s unit value, milesskjodmt is the ZIP-to-ZIP mileage distance ofthe shipment, and ȳdt and Ndt are per capita income and total population in the destination
CBSA. γkt and γmt are product-year and mode-year fixed effects that are included in all
specifications. The θ fixed effects, which are mutually exclusive and omitted from somespecifications, are origin-year and product-plant-year fixed effects.
19

Table 2: Incoming shipment prices
Dep var: Log unit value, ln pskjodmt

(1)

(2)

(3)

Destination CBSA log per capita income, ln ȳdt

0.247**

0.159**

0.0509**(0.0213)(0.0168)(0.00586)

Destination CBSA log population, ln Ndt-0.00448*-0.00315

0.000142(0.00225)(0.00172)(0.000701)

0.0449**0.0467**0.0148**(0.00308)(0.00189)(0.000875)

Yes

Yes
Yes

0.097

0.145
35,0005250
1,800,000

Log mileage, ln milesskjodmt

Commodity × Industry × Year FE
Origin CBSA × Year FE
Establishment × Commodity × Year FE
Within R2
Number estab-year (rounded)
Number ind-prod-year (rounded)
Observations (rounded)

Yes
0.029

Notes: Manufacturing establishments in the CFS and CMF. All shipments are to a domestic destination
CBSA distinct from the origin CBSA. All regressions include mode × year fixed effects. Standard errors,
clustered by destination CBSA × year, in parentheses. ∗∗ and ∗ denote statistical significance at 1%
and 5%, respectively.

Table 2 reports regressions characterizing how variation in shipment unit values within
products relates to destination characteristics. The first column shows that the per-capitaincome elasticity of incoming shipment prices is 25%. Higher-income cities import higherprice varieties, which suggests that preferences are non-homothetic. This pattern is attributable to city income composition, not city size per se, as the coefficient on log population
reveals. The distance elasticity of incoming shipment prices is about 4%; longer shipments
exhibit higher prices.41
The second and third columns show that the large majority of the correlation between
income per capita and incoming shipment prices is attributable to cities of different income
levels purchasing goods from different cities and plants. The second column introduces
fixed effects for cities of origin, θot . The destination per capita income elasticity falls by
about 10 percentage points, indicating that about 40% of this variation is attributable to41

There are at least three possible explanations for the positive coefficient on shipment distance. First,
distance-related costs may be included in the reported shipment values. Second, the composition of plants
shipping to a destination may vary with distance. Third, plants may charge higher mark-ups when serving
more distant destinations. The third column of Table 2 suggests that this last channel could explain at most
one-third of such variation, since the within-establishment mileage elasticity is 1.5%.

20

the composition of cities trading with each other.42 The coefficients on the other regressors
are similar to those in the first column. The third column introduces fixed effects for eachplant-product, θkjt . The within-plant destination-income elasticity of shipment prices is
considerably lower, 5.1%. Selling the same product at a higher price therefore accounts
for at most one-fifth of price variation across destinations of different income levels. This
decomposition suggests that changes in markups are not responsible for the majority of theobserved correlation between shipment prices and destination incomes.
These findings demonstrate that the composition of cities’ manufactures demand isstrongly linked to their income levels. This is consistent with numerous previous empirical studies of both households and countries. Such non-homothetic preferences are necessary
for the “home-market effect for quality” hypothesis.43
Together, Tables 1 and 2 demonstrate patterns of specialization that are strongly linked tocities’ income levels. Within narrowly defined product categories, higher-income locations
both export and import higher-price products than lower-income locations. In addition,
Appendix C shows that cities with more similar incomes trade more intensely with eachother. These findings mirror those found in international trade data and could be generated
by the factor-abundance mechanism or the home-market effect. I now use data on plants’factor inputs to empirically distinguish between these potential explanations.

5

Empirical results

This section reports two main bodies of empirical evidence. First, observed factor-usage
differences explain about one quarter of the relationship between cities’ incomes and theprices of outgoing shipments. This bounds the explanatory power of the factor-abundancemechanism in terms of observed factor inputs. Second, the market-access measures describing
the income composition of proximate potential customers are strongly linked to outgoingshipment prices. The estimated home-market effect explains close to half of the observed
price-income relationship.
My regression results can be seen as decomposing the covariance between plant j’s outgoing shipment price and origin o’s per capita income. The regressions in Table 1 demonstrate apositive relationship between prices and incomes but omit both measures of factors employed42

Appendix C shows that cities with more similar incomes trade more intensely with each other.
Non-homothetic preferences alone are not sufficient to produce the home-market effect, as discussed
in section 2 and shown in section 3.4.1. The home-market effect for quality stems from non-homothetic
preferences, economies of scale, and trade costs.
43

21

and market access. This “short”specification in equation (6) can be restated asln pskjodmt = β S ln ȳokt + αS · Xskjodmt + Sskjodmt ,where the superscript S denotes the “short” regression and the vector Xskjodmt contains
origin population, shipment mileage, and destination-product-year fixed effects. The priorempirical literature has estimated β̂ S > 0, and this result has been interpreted as attributable
to differences in factor supplies or demand conditions. In the factor-supplies account, thefactor inputs employed in production are omitted variables that explain output prices andare correlated with origin income per capita. In the market-access account, origin income
has a causal effect on output prices through its effect on the composition of demand.
My empirical strategy is to introduce observable measures of both factor inputs andmarket access, described in section 3.5, in order to identify their contribution to the positivecoefficient on origin income per capita. The factor-input measures address their omission
from the short regression. The market-access measures employ spatial variation in income
levels to capture spatial variation in demand, exploiting neighboring cities’ contributions to
Mq,k (τ ).44 Consider a “long” regression that incorporates factor-employment measures Fjt
and market-access measure Mot ,ln pskjodmt = β ln ȳokt + α · Xskjodmt + δ · Fjt + λMot + skjodmt .

(7)

If this long regression is the correct specification, then the estimated β̂ S > 0 captures
how outgoing shipment prices covary with income per capita both directly (β) and indirectly
through factors of production and market access. This can be seen using the omitted variables
bias formula:
"

βS
αS

#

"
=

β
α

#

""
+E

ln ȳ
X

#

h

ln ȳ X

#
i −1

""
E

ln ȳ
X

#

h

F M

#" #
i
δ
λ

β S > β to the extent that (1) skill-intensive products have higher prices (δ > 0) andskill-intensive products are produced in higher-income locations (cov(ln ȳ, F |X) > 0) and(2) higher-price products are produced where proximate potential customers’ per capita
incomes are higher (λ > 0) and higher-income locations are more proximate to higherincome potential customers (cov(ln ȳ, M |X) > 0). Each of these channels is a potential
explanation because the economic mechanism (δ > 0 or λ > 0) is plausible, as shown by
44

While Fajgelbaum, Grossman, and Helpman (2011) derive their theoretical results from a location’s own
contribution to its market access, I exploit geographic variation in nearby cities’ income levels to addressconcerns about unobservables in the city of production relating to its income level.

22the model, and higher-income US metropolitan areas are both populated by more skilled
manufacturing workers and more proximate to high-income consumers.45
In the model, these mechanisms are the only forces for specialization across income levels,
so β should be zero. In practice, prices and and incomes may be correlated after accounting
for factor inputs and market access due to additional omitted regressors or causal effectsof local income. The former might include unobserved differences in production conditions,like entrepreneurial zeal or exogenous technological advantages, that could plausibly both
explain output prices and correlate with local income. The latter would be mechanisms
through which higher incomes cause locals to supply higher-quality varieties. Measurement
error in the observables Fjt and Mot may also leave residual covariance captured by β.
I decompose β S by first introducing factor inputs F and then introducing market access
M . Introducing measures of plants’ employment of factors of production decomposes thecovariance between outgoing shipment prices and origin per capita income into betweenintensity variation and within-intensity variation.46 While the factor-abundance mechanism
operates exclusively through the former, the home-market effect may manifest in both, sincehigher-income locations have greater demand for higher-quality varieties, regardless of qualities’ skill intensities. Section 5.1 shows that the measured across-skill-intensities component
is modest, constituting 27% of the covariance between outgoing shipment prices and income
per capita.
Introducing a measure of market access yields the long regression specified in equation(7). Following Proposition 1, the coefficient λ describes how outgoing shipment prices covary
with potential customers’ income levels, conditional on differences in factors employed in
production. The coefficient β captures the residual covariance between prices and incomes
attributable to neither differences in skill intensity nor the market-access measure. In section
5.2, I find that within-skill-intensity variation in market access accounts for about 58% of the45
In terms of skills, higher-income cities’ manufacturing plants exhibit higher non-production worker sharesand their manufacturing employees exhibit more years of schooling and higher wages. In terms of market
1
access, cities’ income levels are spatially correlated, such that regressing Mot
on log per capita income yields a2
positive relationship with an R of about 20%. Note that these patterns only imply β < β S if the associatedmechanism also accounts for price variation conditional on per capita income, that is, if δ > 0 or λ > 0.
46
Using the law of total covariance and omitting notation indicating that moments are conditional on X,
the covariance between plant j’s outgoing shipment price and origin o’s per capita income can be written ascov(ln pj , ln ȳo ) = cov [E(ln pj |Fj ), E(ln ȳo |Fj )] + E [cov(ln pj , ln ȳo |Fj )]
|
{z
} |
{z
}
between-intensity variation

within-intensity variation

My regressions are linear projections that approximate these conditional moments.

23

observed price-income relationship.47 This makes β̂ small relative to β̂ S and, in a number of
specifications, statistically indistinguishable from zero.
After estimating this decomposition, I provide additional empirical evidence to support
these results. Section 5.3 summarizes two pieces of further evidence, which are describedat length in appendix E, that support an economically large role for home-market demandin determining the pattern of quality specialization. First, the second moment of the local household income distribution is linked to outgoing shipment prices. Second, demand
shifters exhibit the same patterns as outgoing shipment prices. Section 5.4 reports a seriesof robustness checks that yield results consistent with the claim that market access explains
as much of the covariance of shipment prices and income levels as observed factor usage.

5.1

The factor-abundance hypothesis

This section identifies the share of within-product specialization attributable to differencesin observable plant-level factor usage. The canonical factor-abundance theory posits thatdifferences in locations’ outputs are explained by differences in the factors employed by theirproducers. Within groups of products of the same factor intensity, the location of production
is indeterminate. That is, under the null hypothesis that differences in factor supplies are
the only source of comparative advantage, there should be no correlation between locational
characteristics and plants’ outputs after controlling for plant-level factor usage. In fact,
there is a very strong relationship between income per capita and outgoing shipments prices
after controlling for factor inputs. Observed factor usage explains only 27% of the observed
covariance between cities’ per capita incomes and outgoing shipment prices.
To characterize how shipment prices vary with origin characteristics, I estimate linear
regressions describing a shipment s of product k by plant j from origin city o to destinationcity d by transport mode m in year t of the formln pskjodmt = β ln ȳokt + α · Xskjodmt + δ1 ln shareN jt + δ2 ln+ δ4 ln shareN jt ln ȳot + δ5 ln
47

Kjt+ δ3 ln w̄jt
Ljt

Kjt
ln ȳot + δ6 ln w̄jt ln ȳot + skjodt
Ljt

(8)

Following footnote 46, we can write the within-intensity variation as E [cov(ln pj , ln ȳo |Fj )] =EF [covM (E(ln pjo |Fj , Mo ), E(ln ȳo |Fj , Mo ))] + EF [EM (cov(ln pj , ln ȳo |Fj , Mo ))]
|
{z
} |
{z
}
within-skill-intensity market accessresidual covariance

Using regressions to approximate these conditional moments, the market-access component accounts forabout 58% of the overall cov(ln pj , ln ȳo ).

24

K

where shareN jt is the ratio of the plant’s non-production workers to total employees, Ljtjt
is gross fixed assets per worker, and w̄jt is average pay per employee.48 The interactions ofplant-level factor-usage measures with origin income per capita address the case in which
factor prices do not equalize, as described in section 3.5.49 In theory, either ln shareN jt
and its interaction with ln ȳot or ln w̄jt and its interaction with ln ȳot would be sufficient tocharacterize plants’ skill intensities. In practice, I include both and the capital measure to
maximize the potential explanatory power of observed factor-usage differences.
Table 3 characterizes how variation in shipment unit values relates to origin characteristics
and plant-level observables. The first column relates outgoing shipment unit values to origin
characteristics controlling for destination fixed effects, as in Table 1. The next two columns
incorporate the plant-level measures of factor usage and their interactions with income perKcapita. The second column introduces quantity measures of capital intensity ( Ljtjt ) and labor
usage, the non-production employment share (shareN jt ). The third column adds the average
wage measure and therefore corresponds to the regression specified in equation (8).
These measures of factor usage are informative predictors of a plant’s shipment prices,
but they explain only a modest share of the observed origin-income elasticity of outgoingshipment prices. Consistent with the premise that higher-price, higher-quality varieties are
more skill-intensive, the coefficients on log non-production worker share and log pay per
worker are positive and economically large. The negative coefficient on log assets per worker
is inconsistent with a model in which higher-price, higher-quality varieties are more capitalintensive.50 The observed variation in factor usage helps explain some of the total variationin outgoing shipment prices, but only a small share of the income-linked variation. While
introducing the quantity measures in the second column increases the R2 , it only reduces
the origin-income elasticity from 44% to 40%. Incorporating the wage measure in the thirdcolumn reduces this elasticity to 35%. Thus, the observed factor-usage differences can explain
about one-fifth of the origin-income elasticity of shipment prices in this specification.
The fourth through sixth columns of Table 3 incorporate the control variables in more
flexible functional forms. The mileage, non-production worker share, assets per worker,
and pay per worker covariates now enter as cubic polynomials that vary by 3-digit NAICS
48

The theoretical model emphasized differences in the composition of skill across locations. I also include
gross fixed assets per worker as a measure of capital intensity, since this variable has been emphasized in priorempirical work both across countries (Schott, 2004) and across plants (Verhoogen, 2008). Since I cannot
construct capital stocks using the perpetual-inventory method with quinquennial data, I use the book valueof assets as my measure of plant capital.
49
Bernard, Redding, and Schott (2013) infer that relative factor prices do not equalize within the US when
considering two factors, production and non-production workers.
50
Using very aggregate data, Torstensson (1996) obtains a negative partial correlation between prices andcapital per worker when distinguishing between human and physical capital.

25

Table 3: Shipment prices and factor usage
Dep var: Log unit value, ln pskjodmt
Origin CBSA log per capita income
Origin CBSA log population

(1)

(2)

(3)

(4)

(5)

(6)
0.311**

0.440**

0.401**

0.353**

0.413**

0.362**(0.0359)(0.0350)(0.0345)(0.0345)(0.0334)(0.0330)-0.00764-0.0111**-0.0136** -0.00652-0.0104**-0.0133**(0.00379)√(0.00365)

√

√

√

√

(0.00421)(0.00408)(0.00398)

Log mileage (ZIP-ZIP-mode-specific) 0.0404**

0.0418**0.0413**(0.00280)(0.00275)(0.00269)

Non-production worker share (log)0.135**

0.113**(0.00692)(0.00695)

Assets per worker (log)-0.0369**-0.0540**(0.00391)(0.00404)

Pay per worker (log)(0.00393)√√√

0.217**(0.0180)

Non-production worker share× income per capita
Assets per worker
× income per capita
Pay per worker
× income per capita
Within R2
Number estab-year (rounded)
Number ind-prod-year (rounded)
Observations (rounded)

0.080

0.05710.00606-0.000645-0.0387(0.0315)(0.0327)(0.0298)(0.0307)-0.0320*-0.0619**-0.0106-0.0253(0.0155)(0.0161)(0.0165)0.088(0.0168)

0.336**

0.198**(0.0686)(0.0699)

0.091
0.084
35,0005250
1,800,000

0.100

0.106

Notes: Manufacturing establishments in the CFS and CMF. All shipments are to a domestic destination
CBSA distinct from the origin CBSA. All regressions include SCTG5 × NAICS6 × destination × year fixed
effects and mode × year fixed effects. The fourth through sixth columns include 3-digit-NAICS-specificcubic polynomials in log mileage (4,5,6), log non-production worker share (5,6), log assets per worker (5,6),
and log pay per worker (6). Standard errors, clustered by origin CBSA × year, in parentheses. ∗∗ and ∗denote statistical significance at 1% and 5%, respectively.

industry. Since there are 21 3-digit industries, this introduces 63 regressors for each control
variable, yielding a total of 252 regressors.51 I refrain from reporting the coefficients on these√controls and indicate their inclusion by in the relevant rows of tables.
The results obtained using these more flexible functional forms are similar to those in thefirst three columns of Table 3. The origin-income elasticity of 41% is reduced to 36% by the
introduction of the quantity controls and further to 31% by the full battery of plant-levelfactor-usage measures. Thus, differences in plants’ observed factor usage explain about onequarter of the correlation between cities’ incomes per capita and outgoing shipment prices.
This suggests that the factor-abundance hypothesis has meaningful but modest explanatory
power for the pattern of within-product specialization across US cities.
51

Using a 3-digit-NAICS-specific translog approximation with the input measures and a 3-digit-NAICSspecific quadratic in log mileage yields very similar results.

26

These factor-input covariates may be imperfect measures of plant-level factor usage,leaving residual variation in shipment prices that is correlated with cities’ incomes. WhileI cannot directly rule out measurement error, these plant-level input measures are far more
precise than the country-level covariates typically used to evaluate factor-abundance theories
of comparative advantage, which aggregate over plants, cities, and industries. Moreover,
the observed factor inputs are informative about outgoing shipment prices. There is aconsiderable increase in the R2 between the fourth and sixth columns in Table 3. However,these factor inputs do not vary across cities in a way that accounts for the link between
city-level income and shipment prices.
Could city income per capita be informative about plant-level factor usage conditionalon the plant-level covariates? Plants with observationally equivalent workforces in termsof non-production-to-production-worker ratios may exhibit unobserved differences in worker
quality. In particular, prior research has documented weak but systematic sorting of workers
across cities on unobservable characteristics correlated with higher wages (Davis and Dingel,2012; De la Roca and Puga, 2013). However, these differences between workers should
appear in the plant-level wage measures included in the third and sixth columns of Table
3. The posited unobserved differences in input factor quality would therefore have to be
characteristics of workers that raise output quality, are not priced into their wages, and aresystematically correlated with city-level incomes, which seems an unlikely explanation for
the findings.
These results are robust to introducing further information on the skills employed inthese plants. I construct city-industry-level measures of employees’ schooling from publicuse microdata from the Census of Population and American Community Survey. These
measures are available for a subset of the observations in the main estimation sample. The
results are reported in Appendix Table D.1. The partial-correlation origin-income elasticityof 30.5% is quite similar to the 31% obtained in Table 3.
Another potential concern is aggregation bias. Though my data describe hundreds ofmanufacturing product categories, these are less detailed than the most disaggregated product categories in international trade data. I address this concern using data from the Census
of Manufactures product trailer, which describes comparable number of product categories
and reports quantities for a subset of them. Appendix Table D.2 describes establishments’
average unit values from Census of Manufactures data on products for which quantities arereported and reports results that are consistent with those reported in Table 3.52 Though
the origin-income elasticity is lower than that found in the CFS data, observed plant-levelfactor usage explains only a small fraction of the total variation.
52

These plant-level average unit values necessarily include shipments destined for the origin CBSA.

27

This section has shown that a modest share of the observed within-product variation in
outgoing shipment prices across cities of different income levels is attributable to observabledifferences in plants’ factor usage. Under the null hypothesis that differences in factor
abundance alone explain within-product specialization, the partial correlation between origin
income per capita and outgoing shipment prices conditional on plant-level factor usage would
be zero. In the presence of a rich set of plant-level controls, the estimated coefficient β̂1 incolumn six of Table 3 is 31%, roughly three quarters of its value in the absence of plant-level
controls. If we were to attribute the full decrease in the value of the coefficient on ln ȳot to thefactor-abundance mechanism, it would explain about one quarter of the observed variation.53

5.2

The market-access hypothesis

This section identifies the share of the covariance between incomes and prices not explainedby factor-usage differences that is attributable to home-market demand. I find that cities
with greater market access to higher-income households produce higher-price manufactures.
This within-intensity market-access variation explains more of the covariance between incomes and prices than differences in plants’ factor inputs.
The “home-market” effect in fact depends on the composition of demand in all locations
potentially served from a location of production, as described in the model by market access
Mq,k (τ ). A city that is more proximate to another city with many high-income residents
has higher relative demand for higher-quality manufactures, ceteris paribus.54 Section 3.5
P
N miles−ηoddescribed two market-access measures. The first, Mot1 = d6=o P dtN miles−η ln ȳdt , omits
d0 6=o d0 t
od0
potential customers residing in the location of production. The identifying assumption whenusing this measure is that variation across locations in neighboring cities’ incomes per capita,
after conditioning on plants’ inputs and income per capita in the city of production, is related to plants’ outputs only through variation in the composition of demand. The secondP
N miles−ηodmarket-access measure, Mot2 = d P dt
−η ln ȳdt , includes all potential customers, cond0 Nd0 t milesod0
sistent with the model. The accompanying identifying assumption is that, after conditioning
on plants’ inputs, variation across locations in potential consumers’ incomes, including res53

To the degree that differences in skill intensities are causally induced by differences in demand, thisoverstates the explanatory power of the factor-abundance hypothesis.
54
Fajgelbaum, Grossman, and Helpman (2011) assume the cost of exporting to another location is thesame across all locations. Thus, in their model the home-market effect depends only on the difference inincome composition between the location of production and the rest of the world. When trade costs are notuniform, the home-market effect depends on a production location’s access to every other market, as notedby Burenstam Linder (1961, p.87) and Behrens, Lamorgese, Ottaviano, and Tabuchi (2009). Measuringmarket access has received considerable attention in empirical assessments of the new economic geography(Redding and Venables, 2004). See Lugovskyy and Skiba (2015) for a discussion of market access in thecontext of quality specialization.

28

idents in the city of production, is related to plants’ outputs only through variation in thecomposition of demand.55
Table 4 demonstrates that market access plays a significant role in explaining the originincome elasticity of shipment prices. To facilitate comparisons, the first column is identical to
the sixth column of Table 3. The second column introduces the first market-access measure,and its coefficient is positive and highly significant. Its inclusion reduces the origin-income
elasticity from 31% to 18%. Recall that flexibly controlling for the non-production worker
share, assets per worker, and average pay per worker initially reduced the elasticity from 41%
to 31%. Thus, the income composition of proximate potential customers other than thosein the city of production explains more of the covariance of income per capita and outgoingshipment prices. In locations with better access to high-income customers, plants produce
higher-price products. This evidence suggests that the geography of demand influences thepattern of within-product specialization.56
The third column uses the second market-access measure, which includes the income ofresidents in the city of production in the weighted average. This reduces the origin-income
elasticity to 9%, a reduction of 22 percentage points compared to the first column. In thisspecification, market access explains about half of the observed relationship between income
per capita and outgoing shipment prices, which is substantially more than that attributable
to differences in plants’ factor usage.
These results can be succinctly summarized as a decomposition of the covariance between
incomes and prices.57 After controlling for population size and shipment mileage, differencesin observed factor usage are responsible for 27% of the covariance between outgoing shipment
prices and origin income per capita. Conditional on factor usage, the first market-accessmeasure, which omits residents in the city of production, accounts for 36% of the total
covariance, leaving 37% as residual variation. The second market-access measure, which
follows the model by including residents in the city of production, accounts for 58% of thetotal covariance, leaving 15% as residual variation.
The fourth column of Table 4 reports a regression that incorporates the first marketaccess measure while omitting factor inputs.58 Because market access is positively correlatedwith these omitted regressors, the positive coefficient on Mot1 is about 15% larger than in
the second column.59 While within-intensity variation in market access accounts for 36%
55

This identifying assumption would be violated by unobserved quality-improving inputs or technologies
that were correlated with city-level income per capita conditional on my plant-level measures of inputs.
56
This result reflects income composition, not total income. I have confirmed that the inverse-distanceweighted sum of total incomes, a “market potential” measure, does not explain variation in shipment prices.
57
Footnotes 46 and 47 report the decomposition that I approximate using linear regressions.
58
Table D.3 in the online appendix reports further specifications omitting factor inputs.
59
Similarly, adding classical measurement error to the factor-input covariates raises the estimated market-

29

Table 4: Shipment prices and market access
Dep var: Log unit value, ln pskjodmt

(1)

(2)

(3)

(4)

Origin CBSA log per capita income

0.311**

0.179**

0.0929*0.258**(0.0330)(0.0357)(0.0407)(0.0369)-0.0133**-0.00298-0.00847*

0.00510(0.00365)√(0.00376)√(0.00358)(0.00405)

√

√

√

√

√

√

√

√

√

Origin CBSA log population
Log mileage (ZIP-ZIP-mode-specific)
Non-production worker share (log)Assets per worker (log)
Pay per worker (log)Market access (excludes origin) Mot1√

1.103**

0.0465**(0.00187)

1.253**(0.112)Market access Mot2√

(5)

(0.115)1.015**(0.110)Destination CBSA log per capita income

0.165**

Destination CBSA log population-0.00360*(0.0171)(0.00173)
1
Destination market access Mdt-0.0535(0.0451)

SCTG5 × NAICS6 × Destination × Year FE
SCTG5 × NAICS6 × Year FE
Origin × Year FE
Within R2
Number estab-year (rounded)
Number ind-prod-year (rounded)
Observations (rounded)

Yes

0.106

Yes

0.108

Yes

0.108
35,0005250
1,800,000

Yes

0.086

Yes
Yes
0.145

Notes: Manufacturing establishments in the CFS and CMF. All shipments are to a domestic destination
CBSA distinct from the origin CBSA. All regressions include mode × year fixed effects. Standard
errors are clustered by origin CBSA × year in columns 1 through 4 and by destination CBSA × year
in column 5. Unreported controls in columns 1 through 3 are the interactions of log origin income
per capita with the three input variables and 3-digit-NAICS-specific cubic polynomials in log mileage,log non-production worker share, log assets per worker, and log pay per worker. Unreported controls
in column 4 are 3-digit-NAICS-specific cubic polynomials in log mileage. Clustered standard errors inparentheses. ∗∗ and ∗ denote statistical significance at 1% and 5%, respectively.

30

of the total covariance, unconditional variation in market access can explain about 47% of
the price-income covariance.60 This result might reflect spurious correlation or an economic
relationship. If the correlation between market access and factor input usage is spurious,
then the regression in column four is misspecified and overstates the role of market access in
explaining the price-income covariance. If differences in market access cause firms to produce
varieties of different factor intensities, then market access explains more of the price-income
covariance than suggested by the conservative specification in column two that exploits only
within-intensity variation in market access.
Market access does not predict incoming shipments’ prices. This is shown by the fifth
column of Table 4, which introduces the destination city’s income level and market accessas regressors and uses product-year and origin-year fixed effects rather than destinationproduct-year fixed effects. Thus, it is the second column of Table 2 augmented by destination
market access. While higher-income destinations purchase higher-price incoming shipments,
destinations with higher-income neighbors do not exhibit higher incoming prices. The coeffi1
is a precisely estimated zero.61 Since better market access predicts higher-pricecient on Mdt
outgoing shipments and unchanged incoming shipments, better market access is associatedwith net exporting of higher-price varieties.
Appendix section E.1 shows that the patterns found in domestic shipments are also
found in export shipments destined for foreign markets. The origin-income elasticity ofexport prices is 42%. After controlling for plants’ factor inputs, this elasticity is 30%. After
controlling for both factor inputs and market access, this elasticity becomes negative andstatistically indistinguishable from zero.
This section has established the role of market acess in explaining the pattern of outgoing shipment prices. The income composition of proximate potential customers is strongly
associated with outgoing shipment prices. Consistent with the model, plants located nearhigher-income potential customers sell products at higher average prices. The income composition of potential customers other than those in the location of production is quantitatively
more important for explaining the origin-income elasticity of outgoing shipment prices thanobserved plant-level factor usage. When including individuals residing in the city of production, the income composition of potential customers explains about half of the observed
origin-income elasticity of shipment prices. Incoming shipment prices are invariant to destiaccess coefficient.
60
2
The respective numbers when using Mot
are 58% and 77%.
61
This result also demonstrates the point made in footnote 45 that introducing Mot to equation (7) only
1
1
implies β < β S if λ > 0. The correlation between Mdt
and ln ȳdt is identical to that between Mot
and ln ȳot ,yet the coefficient on ln ȳdt in the fifth column of Table 4 is statistically indistinguishable from its value inthe second column of Table 2.

31

nation market access. This is consistent with a model in which market access plays a largerole in quality specialization and makes high-income locations net exporters of high-quality
products.

5.3

Further evidenceThis section summarizes two further pieces of evidence supporting the inference that homemarket demand plays a large role in quality specialization. First, the second moment of thelocal household income distribution is linked to outgoing shipment prices. Second, I calculate
demand shifters and find that they exhibit the same patterns as outgoing shipment prices.
These findings are both described in more detail in Appendix E.
Appendix section E.2 uses another moment of the income distribution to identify therole of demand in quality specialization. Conditional on average income, cities with higher
dispersion in household income have higher incoming shipment prices. This suggests that
second moment of the income distribution is informative about the composition of demand.
I then show that cities with greater income dispersion have higher outgoing shipment prices,and this is not due to greater dispersion in the wages or skills of workers employed at theplants shipping these products. This is consistent with the home-market effect under the
Fajgelbaum, Grossman, and Helpman (2011) demand system in an equilibrium in whichmost individuals purchase low-quality varieties.
Appendix section E.3 characterizes the pattern of quality specialization using demand
shifters instead of outgoing shipments’ unit values as the dependent variable. Due to data
constraints, I am only able calculate demand shifters for shipments in 2007. In the absenceof exogenous price variation to identify the demand system, I use price-elasticity estimatesfrom Feenstra and Romalis (2014) to calculate demand shifters. The empirical results are
consistent with the unit-value findings for the influence of market access, though factor
usage exhibits greater explanatory power. The origin-income elasticity of the plant-productdemand shifter is 41%. This covariance between income per capita and demand shifter
decomposes into factor-intensity differences (46%), within-intensity market-access differences(48%), and residual variation (7%). The greater explanatory power of plants’ factor inputs
primarily reflects less residual variation, not a dramatically weakened role for the income
composition of proximate potential customers. Home-market demand plays a substantial
role in quality specialization, as large as that explained by the factor-abundance mechanism.

32

Table 5: Shipment prices and industrial rents
Dep var: Log unit value, ln pskjodmt

(1)

(2)

(3)

(4)

(5)

Origin CBSA log per capita income

0.446**

0.332**

0.231**

0.322**(0.0790)(0.0760)(0.0813)(0.0690)

Origin CBSA log population

0.01430.00555-0.00529(0.0133)(0.0129)(0.0133)

Log mileage (ZIP-ZIP-mode-specific)

0.0413**0.0375**0.0382**(0.00637)(0.00615)(0.00608)

Non-production worker share (log)0.131**

0.133**(0.0175)(0.0175)

Assets per worker (log)-0.0545**-0.0522**(0.00848)(0.00841)

0.223**

0.222**

Pay per worker (log)(0.0413)Asking rent (USD per sqft)

(6)

(7)

0.273**

0.140-0.290*(0.0731)(0.0736)(0.117)-0.00241-0.01210.000298-0.0257*(0.0123)√(0.0139)√(0.0141)√(0.0130)

√

√

√

√

√

√

√

√

√

√

√

√

√

√

√

(0.0420)0.0457**√(0.0119)

Market access (excludes origin) Mot1

1.095**(0.219)Market access Mot2

1.625**(0.309)Within R2
Number estab-year (rounded)
Number ind-prod-year (rounded)
Observations (rounded)

0.065

0.075

0.076

0.100
10,0004000
500,000

0.105

0.105

0.106

Notes: Manufacturing establishments in the CFS and CMF. All shipments are to a domestic destination
CBSA distinct from the origin CBSA. All regressions include SCTG5 × NAICS6 × destination ×
year fixed effects and mode × year fixed effects. The fourth through seventh columns include 3-digitNAICS-specific cubic polynomials in log mileage (4-7), log non-production worker share (4-7), log assets
per worker (4-7), log pay per worker (4-7), and industrial asking rent per square foot (5-7). Unreported
controls in columns 2-7 are the interactions of log origin income per capita with the three input variables.
Standard errors, clustered by origin CBSA × year, in parentheses. ∗∗ and ∗ denote statistical significance
at 1% and 5%, respectively.

5.4

Robustness checks

This section reports robustness checks motivated by potentially empirically relevant mechanisms that were omitted from the theoretical model. These include land prices, intermediate
inputs, and multi-plant firms. While the measured contributions of factor usage and market
access are not completely invariant to addressing these issues, all the robustness checks are
consistent with the claim that market access explains at least as much of the covariance of
shipment prices and income levels as observed factor usage.
The model omits land, which is an input whose price variation across metropolitan areas
is correlated with income levels. While land has not been posited as relevant for quality
specialization in the prior literature, shipment prices might covary with land prices if higherquality varieties are less land-intensive or if land costs are passed through. To address this33

omission, I use an industrial rent measure from Reis, a commercial real estate informationcompany, as an additional regressor. The measure, asking rent per square foot for industrial
properties, is available for only 44 metropolitan areas in the relevant years. Table 5 reports
the factor-usage and market-access regressions while controlling for this variation in local
industrial rents. Columns 1, 2, and 4 demonstrate that the factor-usage results for thissubsample of observations are comparable to those obtained in Tables 3. Columns 3 and5 introduce the industrial rent covariate, which reduces the income elasticity by about five
percentage points in the flexible-control specification. Plants in locations with higher land
prices have higher outgoing shipment prices, and this variation in rents is correlated withlocal income levels such that this explains some of the covariance between shipment prices
and incomes. After controlling for industrial rents, market access accounts for most of
the remaining covariance between prices and incomes, as the income elasticity becomes
statistically indistinguishable from zero. Thus, the previous results are robust to controlling
for land prices.
In section 3, all goods are final goods sold to consumers. This absence of intermediate
inputs raises two concerns for the empirical evidence presented thus far. First, outgoingshipments in the data are made up of both final and intermediate goods. Second, input
market access is an omitted variable that may be correlated with output market access.
Each of these concerns warrant additional examination.
The formal theory is narrowly written in terms of quality-differentiated final goods, as in
Fajgelbaum, Grossman, and Helpman (2011), while the evidence presented thus far includes
all manufacturing industries. Market access is potentially important for a broad class ofgoods. Burenstam Linder (1961) posited that “there must be a home market for an export
good, whether it is a consumer good or a capital good”and that “there is a strong relationshipbetween the level of per capita income, on the one hand, and the types of consumer goods
and also capital goods demanded, on the other hand.”62 And Kugler and Verhoogen (2012)suggest a complementarity between input quality and output quality that would generate
differences in demand for intermediate inputs. Nonetheless, to narrow the inquiry in linewith the final-goods-only model, Table 6 restricts the estimation sample to manufacturingindustries selling more than 50% of their output value to final consumers.
62

The relevance of the home market follows from economies of scale and trade costs. The potential rolefor per capita income in the composition of capital demand is less familiar. Burenstam Linder (1961, p. 96):
“The relative amount of capital also determines the qualitative composition of the demand for new capital
goods. A capital-abundant country, i.e., a country which, with some likelihood, finds itself on a high level ofper capita income, demands more sophisticated capital equipment than a capital-scarce country. Although
there is no direct causal relationship, we might thus expect that the differences in the level of per capita
incomes would tell us at least something about what differences there will be in the structure of demand forcapital goods.”

34

Table 6: Shipment prices for final consumer goods
Dep var: Log unit value, ln pskjodmt

(1)

(2)

(3)

Origin CBSA log per capita income

0.332**

0.246**

0.192**

0.119

0.0102(0.0658)(0.0634)(0.0656)(0.0741)(0.0813)

Origin CBSA log population
Log mileage (ZIP-ZIP-mode-specific)

(4)

(5)

0.01030.00391

0.00706

0.01290.00990(0.00765)(0.00715)(0.00708)

0.0258**√(0.00714)

0.0260**√(0.00770)

√

√

√

√

√

√

√

√

√

(0.00596)(0.00584)

Non-production worker share (log)0.0686**

Assets per worker (log)-0.00334(0.0142)(0.00766)√

Pay per worker (log)0.238**

Non-production worker share × income per capita-0.0841-0.151-0.154-0.154(0.0724)(0.0787)(0.0786)(0.0792)-0.0447-0.0320-0.0331-0.0282(0.0275)(0.0310)(0.0307)(0.0305)

0.325

0.01750.0143-0.0184(0.166)(0.151)(0.150)(0.149)(0.0351)

Assets per worker × income per capita
Pay per worker × income per capita
Market access (excludes origin) Mot1

0.622*(0.272)Market access Mot2

0.796**(0.219)Within R2
Number estab-year (rounded)
Number ind-prod-year (rounded)
Observations (rounded)

0.066

0.077

0.107
5000
750
400,000

0.107

0.108

Notes: Manufacturing establishments in the CFS and CMF. All shipments are to a domestic destination
CBSA distinct from the origin CBSA. The estimation sample is restricted to industries for which morethan 50% of value produced is sold to final consumers. All regressions include SCTG5 × NAICS6 ×destination × year fixed effects and mode × year fixed effects. The third through fifth columns include
3-digit-NAICS-specific cubic polynomials in log mileage, log non-production worker share, log assets per
worker, and log pay per worker. Standard errors, clustered by origin CBSA × year, in parentheses. ∗∗and ∗ denote statistical significance at 1% and 5%, respectively.

35

Table 6 shows that the contribution of market access to the covariance of per capita
income and outgoing shipment prices is relatively larger for final consumer goods comparedto all manufactures. The income elasticity of 33% reported in the first column falls to 19% in
the third column after flexibly controlling for observed plant-level factor usage. Introducing
Mot1 , the market-access measure that omits potential consumers in the location of production, reduces the income elasticity to 12% in the fourth column and this point estimate is
statistically indistinguishable from zero. Using the Mot2 measure reduces the point estimate
to virtually zero, so that factor usage and market access jointly explain almost all of the observed relationship between cities’ income levels and outgoing shipment prices in final goods.
Market access accounts for more than half of this covariance.
Table 7 shows that the contribution of market access to the price-income covariance isconsiderably smaller for shipments of intermediate inputs. For industries that sell less than
10% of their output to final consumers, factor inputs and within-intensity variation in market
access each explain about one-third of the price-income relationship. Unlike final consumer
goods, intermediate inputs exhibit considerable residual covariation. These findings are
consistent with the idea that household income levels better predict the composition ofdemand for consumer goods than intermediate inputs.
Another concern related to intermediate inputs is that the regressions in Table 4 do notcontrol for input market access. Plants in high-income cities may indirectly employ capitalor skill via the factor content of intermediate inputs, which would not be captured by theplant-level factor-usage measures used above. In appendix section E.4, I use plant-levelwages and input-output tables to construct measures of upstream human capital to address
this concern. The findings of Table are 4 are little changed by controlling for input market
access in this way.63
The model has single-product, single-plant firms, while in reality most manufacturing
output is produced by multi-product firms operating multiple plants. A potential concern
is that the prior regression results might reflect shipments by large, multi-plant firms whose
decisions are poorly described by the model.64 Appendix section E.5 addresses this concern
by restricting the estimation sample to non-large plants and single-plant firms. The results
are very similar to those in Tables 3 and 4. Introducing plant size as an additional regressor
also yields very similar results.
In sum, robustness checks addressing land prices, intermediate inputs, and multi-plant
63

Addressing the intermediate-inputs concern by restricting the estimation sample to establishments withhigh value-added shares also yields similar results.
64This potential concern could not simply be transfer pricing of intermediate inputs, since Atalay, Hortaçsu,
and Syverson (2014) show that a small fraction of shipments by vertically integrated establishments are todownstream units in the same firm.

36

Table 7: Shipment prices for intermediate inputs
Dep var: Log unit value, ln pskjodmt

(1)

(2)

(3)

(4)

Origin CBSA log per capita income

0.443**

0.364**

0.323**

0.169**

0.120(0.0559)(0.0543)(0.0538)(0.0574)(0.0663)-0.00940-0.0158**-0.0158**-0.00384-0.0109(0.00612)(0.00582)(0.00576)

0.0370**√(0.00573)

0.0376**√(0.00586)(0.00395)(0.00383)

√

√

√

√

√

√

√

√

√

Origin CBSA log population
Log mileage (ZIP-ZIP-mode-specific)
Non-production worker share (log)0.163**

Assets per worker (log)-0.0784**(0.0113)(0.00659)

Pay per worker (log)0.145**(5)√(0.0263)

Non-production worker share × income per capita
Assets per worker × income per capita
Pay per worker × income per capita

0.02880.02450.02210.0199(0.0432)(0.0431)(0.0432)(0.0432)-0.0756**-0.0257-0.0206-0.0174(0.0266)(0.0264)(0.0263)(0.0268)

0.597**

0.422**

0.407**

0.391**(0.102)(0.104)(0.103)(0.104)Market access (excludes origin) Mot1

1.208**(0.182)Market access Mot2

0.918**(0.184)

Within R2
Number estab-year (rounded)
Number ind-prod-year (rounded)
Observations (rounded)

0.082

0.096

0.115
15,0002250
800,000

0.116

0.116

Notes: Manufacturing establishments in the CFS and CMF. All shipments are to a domestic destination
CBSA distinct from the origin CBSA. The estimation sample is restricted to industries for which less than
10% of value produced is sold to final consumers. All regressions include SCTG5 × NAICS6 × destination
× year fixed effects and mode × year fixed effects. The third through fifth columns include 3-digit-NAICSspecific cubic polynomials in log mileage, log non-production worker share, log assets per worker, and log pay
per worker. Standard errors, clustered by origin CBSA × year, in parentheses. ∗∗ and ∗ denote statisticalsignificance at 1% and 5%, respectively.

37

firms yield results consistent with my main empirical finding that both factor abundance andmarket access shape the pattern of quality specialization, with the composition of demand
playing a large role. Attributing these results entirely to factor-usage differences rather thanspatial variation in demand composition would involve assuming two conditions. First, myplant-level microdata on factor inputs, which are relied upon in the literature to estimate
plant-level productivity and other important measures, would have to omit significant factor
usage. Second, these unobserved quality-improving inputs would have to be strongly correlated with surrounding cities’ income levels, conditional on the income level in the city of
production. While my research design cannot disprove a hypothesis positing such spatiallycorrelated unobserved factor inputs, and my decomposition results should therefore be interpreted with appropriate caution, such an argument would be quite far from the evidence
typically marshalled to support the factor-abundance hypothesis.

6

Conclusions

Two prominent theories predict that high-income locations specialize in producing and exporting high-quality products. The Linder hypothesis, formalized by Fajgelbaum, Grossman,and Helpman (2011), emphasizes the role of high-income customers’ demand for high-quality
products. The canonical factor-proportions theory focuses on the abundant supply of capitaland skills in high-income locations. Prior empirical evidence does not separate the contributions of these mechanisms because each implies the same predictions about country-level
trade flows.
In this paper, I combine microdata on manufacturing plants’ shipments and inputs withdata on locations’ populations and incomes to quantify each mechanism’s role in quality
specialization across US cities. I develop a model that nests both mechanisms to guide my
empirical investigation. The theory’s basic insight is that the factor-abundance mechanism
operates exclusively through plants’ input usage. Conditional on plant-level factor intensity,
demand determines quality specialization. I implement my empirical strategy using US
microdata because the Commodity Flow Survey and Census of Manufactures describe plants
located in many cities of varying income levels. In doing so, I document that US cities exhibit
the same patterns found in international trade data that have been interpreted as evidence ofquality specialization by income. My empirical investigation finds that home-market demand
explains as much of the specialization across US cities of different income levels as observed
differences in plants’ factor inputs. Cities with better access to higher-income customers are
net exporters of higher-price varieties.
This finding is significant because the two mechanisms have distinct implications for wel38

fare, inequality, and trade policy. The large share of quality specialization attributable tomarket access suggests that a location’s capacity to profitably produce high-quality products depends significantly on the income composition of neighboring locations. As a result,geography influences specialization in part because economic developments in neighboring
locations may shift local demand for quality. To the degree that demand shapes entry
and product availability, individuals may gain by living in locations where other residents’incomes are similar to theirs. Finally, since market access is affected by trade policy, governments may have scope to influence quality specialization.

References
Atalay, E., A. Hortaçsu, and C. Syverson (2014): “Vertical Integration and Input
Flows,” American Economic Review, 104(4), 1120–48.
Baldwin, R., and J. Harrigan (2011): “Zeros, Quality, and Space: Trade Theory andTrade Evidence,” American Economic Journal: Microeconomics, 3(2), 60–88.
Behrens, K., A. R. Lamorgese, G. I. Ottaviano, and T. Tabuchi (2009): “Beyond
the home market effect: Market size and specialization in a multi-country world,” Journalof International Economics, 79(2), 259–265.
Bergstrand, J. H. (1990): “The Heckscher-Ohlin-Samuelson Model, the Linder Hypothesis and the Determinants of Bilateral Intra-industry Trade,” Economic Journal, 100(403),
1216–29.
Bernard, A. B., S. J. Redding, and P. K. Schott (2013): “Testing for Factor Price
Equality with Unobserved Differences in Factor Quality or Productivity,” American Economic Journal: Microeconomics, 5(2), 135–63.
Bernasconi, C. (2013): “Similarity of income distributions and the extensive and intensive
margin of bilateral trade flows,” Economics Working Papers 115, University of Zurich.
Berry, S. T. (1994): “Estimating Discrete-Choice Models of Product Differentiation,”
RAND Journal of Economics, 25(2), 242–262.
Burenstam Linder, S. (1961): An Essay on Trade and Transformation. John Wiley &Sons, Ltd.

39

Caron, J., T. Fally, and J. R. Markusen (2014): “International Trade Puzzles: A Solution Linking Production and Preferences,” The Quarterly Journal of Economics, 129(3),1501–1552.
Choi, Y. C., D. Hummels, and C. Xiang (2009): “Explaining import quality: The roleof the income distribution,” Journal of International Economics, 78(2), 293–303.
Costinot, A. (2009): “An Elementary Theory of Comparative Advantage,” Econometrica,
77(4), 1165–1192.
Davis, D. R., and J. I. Dingel (2012): “A Spatial Knowledge Economy,” NBER Working
Paper 18188.
(2014): “The Comparative Advantage of Cities,” NBER Working Paper 20602.
Davis, D. R., and D. E. Weinstein (1999): “Economic geography and regional production structure: An empirical investigation,” European Economic Review, 43(2), 379–407.
(2003): “Market access, economic geography and comparative advantage: an empirical test,” Journal of International Economics, 59(1), 1–23.
De la Roca, J., and D. Puga (2013): “Learning By Working In Big Cities,” .
Diamond, R. (2016): “The Determinants and Welfare Implications of US Workers’ Diverging Location Choices by Skill: 1980-2000,” American Economic Review, 106(3), 479–524.
Dollar, D., E. N. Wolff, and W. J. Baumol (1988): “The Factor-Price Equalization Model and Industry Labor Productivity: An Empirical Test across Countries,” in
Empirical Methods for International Trade, ed. by R. C. Feenstra, pp. 23–48. MIT Press.
Eaton, J., and S. Kortum (2002): “Technology, Geography, and Trade,” Econometrica,
70(5), 1741–1779.
Faber, B., and T. Fally (2016): “Firm Heterogeneity in Consumption Baskets: Evidence
from Home and Store Scanner Data,” mimeo.
Fajgelbaum, P., G. M. Grossman, and E. Helpman (2011): “Income Distribution,
Product Quality, and International Trade,” Journal of Political Economy, 119(4), 721 –765.
Falvey, R. E. (1981): “Commercial policy and intra-industry trade,” Journal of International Economics, 11(4), 495–511.
40

Feenstra, R. C., and J. Romalis (2014): “International Prices and Endogenous Quality,” The Quarterly Journal of Economics, 129(2), 477–527.
Fieler, A. C. (2011): “Nonhomotheticity and Bilateral Trade: Evidence and a Quantitative Explanation,” Econometrica, 79(4), 1069–1101.
Glaeser, E. L., and J. E. Kohlhase (2004): “Cities, regions and the decline of transport
costs,” Papers in Regional Science, 83(1), 197–228.
Glaeser, E. L., J. Kolko, and A. Saiz (2001): “Consumer city,” Journal of Economic
Geography, 1(1), 27–50.
Hallak, J. C. (2006): “Product quality and the direction of trade,” Journal of International Economics, 68(1), 238–265.
(2010): “A Product-Quality View of the Linder Hypothesis,” The Review of Economics and Statistics, 92(3), 453–466.
Hallak, J. C., and P. K. Schott (2011): “Estimating Cross-Country Differences in
Product Quality,” The Quarterly Journal of Economics, 126(1), 417–474.
Hallak, J. C., and J. Sivadasan (2013): “Product and process productivity: Implications for quality choice and conditional exporter premia,” Journal of International Economics, 91(1), 53 – 67.
Handbury, J. (2012): “Are Poor Cities Cheap for Everyone? Non-Homotheticity and theCost of Living Across U.S. Cities,” mimeo.
Handbury, J., and D. E. Weinstein (2015): “Goods Prices and Availability in Cities,”
The Review of Economic Studies, 82(1), 258–296.
Hanson, G. H., and C. Xiang (2004): “The Home-Market Effect and Bilateral Trade
Patterns,” American Economic Review, 94(4), 1108–1129.
Helpman, E., and P. R. Krugman (1985): Market Structure and Foreign Trade. MIT
Press.
(1989): Trade Policy and Market Structure. MIT Press.
Henderson, J. V. (1991): Urban Development: Theory, Fact, and Illusion. Oxford University Press.

41Holmes, T. J., and J. J. Stevens (2004): “Spatial distribution of economic activities inNorth America,” in Handbook of Regional and Urban Economics, ed. by J. V. Henderson,
and J. F. Thisse, vol. 4, chap. 63, pp. 2797–2843. Elsevier.
Hottman, C. J., S. J. Redding, and D. E. Weinstein (2016): “Quantifying the
Sources of Firm Heterogeneity,” The Quarterly Journal of Economics, 131(3), 1291–1364.
Hummels, D., and P. J. Klenow (2005): “The Variety and Quality of a Nation’s Exports,” American Economic Review, 95(3), 704–723.
Hummels, D., and A. Skiba (2004): “Shipping the Good Apples Out? An Empirical
Confirmation of the Alchian-Allen Conjecture,” Journal of Political Economy, 112(6),1384–1402.
Khandelwal, A. (2010): “The Long and Short (of) Quality Ladders,” Review of Economic
Studies, 77, 1450–1476.
Krugman, P. (1980): “Scale Economies, Product Differentiation, and the Pattern ofTrade,” American Economic Review, 70(5), 950–59.
(1991): Geography and trade. MIT Press.
Kugler, M., and E. Verhoogen (2012): “Prices, Plant Size, and Product Quality,”
Review of Economic Studies, 79(1), 307–339.
Lederman, D., and W. F. Maloney (eds.) (2012): Does What You Export Matter? In
Search of Empirical Guidance for Industrial Policies. World Bank.
Lugovskyy, V., and A. Skiba (2015): “How geography affects quality,” Journal of Development Economics, 115, 156 – 180.
Markusen, J. R. (1986): “Explaining the Volume of Trade: An Eclectic Approach,”American Economic Review, 76(5), 1002–11.
Murphy, K. M., and A. Shleifer (1997): “Quality and trade,” Journal of Development
Economics, 53(1), 1–15.
Rauch, J. E. (1999): “Networks versus markets in international trade,” Journal of International Economics, 48(1), 7–35.
Redding, S. (1996): “The Low-Skill, Low-Quality Trap: Strategic Complementarities between Human Capital and R&D,” Economic Journal, 106(435), 458–70.
42

Redding, S., and A. J. Venables (2004): “Economic geography and international inequality,” Journal of International Economics, 62(1), 53–82.
Schott, P. K. (2003): “One Size Fits All? Heckscher-Ohlin Specialization in Global
Production,” American Economic Review, 93(3), 686–708.
(2004): “Across-product Versus Within-product Specialization in International
Trade,” The Quarterly Journal of Economics, 119(2), 646–677.
Simonovska, I. (2015): “Income Differences and Prices of Tradables: Insights from an
Online Retailer,” The Review of Economic Studies, 82(4), 1612–1656.
Sutton, J. (1991): Sunk Costs and Market Structure: Price Competition, Advertising, andthe Evolution of Concentration. MIT Press.
(1998): Technology and Market Structure: Theory and History. MIT Press.
(2012): Competing in Capabilities: The Globalization Process. Oxford University
Press.
Torstensson, J. (1996): “Can factor proportions explain vertical intra-industry trade?,”Applied Economics Letters, 3(5), 307–309.
Verhoogen, E. A. (2008): “Trade, Quality Upgrading, and Wage Inequality in the Mexican Manufacturing Sector,” The Quarterly Journal of Economics, 123(2), 489–530.

43

The Determinants of Quality Specialization – Online Appendix
Jonathan I. Dingel, September 2016

A

Theory appendix

This appendix contains details and derivations of the theoretical results summarized in section 3. The order parallels that of the main text.

A.1

Preferences

In equation (1), hj is the individual’s idiosyncratic valuation of the variety. Varieties arethus both vertically and horizontally differentiated (Beath and Katsoulacos, 1991, p.4-6).
Conditional on h , all consumers prefer higher-q varieties. If all varieties were the same
price, consumers would not be unanimous in their ranking of them due to h , so theseproducts are horizontally differentiated.
An individual’s vector of idiosyncratich , is drawn fromh Pvaluations,
i the generalized exPθqtreme value distribution, G () = exp − q∈Q ( j∈Jq exp(−j /θq )) , where Q denotes theset of qualities, Jq ≡ {j : qj = q} is the set of varieties of quality q, and θq governs the strengthof idiosyncratic differences among varieties in Jq . As shown in Fajgelbaum, Grossman, andHelpman (2011), this specification yields a nested-logit demand system (McFadden, 1978).

iθq0exp((y
−
p
)/m
)
j
q
exp(−pj /mq )q· P hPρj (y) = ρj|q · ρq (y) = Piθq0
j 0 ∈Jq exp(−pj 0 /mq )0 )/mq 0 )exp((y−p00jj ∈Jq0qhP

A.2

j 0 ∈J

Production

Both the homogeneous good and the differentiated good are produced using a constantelasticity-of-substitution technology, yielding the unit-cost functions given in the main text.
A firm producing a variety j of the differentiated good in location k solves the following
profit maximization problem:
max πj ={pjk0 }

X

djk0 (pjk0 − cqk − cqk τqkk0 ) − fq

k0R
∂ ln d 0
with j’s sales in k 0 given by djk0 = Nk0 ρj (y)g(y, k 0 )dy. Because ∂ ln pjk0 = −pjk0 /mq , thejksolution to this maximization problem is pjk0 = c(q, k) + τqkk0 + mq . Plugging these solutions

1

into the expression for ρj (y) yields the sales for each firm to each destination as a functionof trade costs and all other firms’ costs.
Z
djk0 =Nk0iθq0 )/mq )exp((y−pjexp(−pj /mq )q
0P· P hPiθq0 g(y, k )dy0exp(−p
/m
)
0
j
q
j ∈Jq
j 0 ∈Jq0 exp((y − pj 0 )/mq 0 )q0hP

j 0 ∈J= exp(−(c(q, k) + τqkk0 )/mq )Nk0 Γk0 (q, n, c, τ )#PZ "exp(yq) [ k00 nq,k00 exp(−(c(q, k 00 ) + τqk00 k0 )/mq )]θq −1g(y, k 0 )dyΓk0 (q, n, c, τ ) ≡
P
P
θq 0
0
00
q 0 exp(yq ) [k00 nq 0 ,k00 exp(−(c(q, k ) + τq 0 k00 k0 )/mq 0 )]The function Γk0 (q, n, c, τ ) describes the share of demand in location k 0 for quality q given
the equilibrium prices and locations of all producers. Fajgelbaum, Grossman, and Helpman(2011) introduce a similar function in their equation (22). Their expression subsumes τ byadjusting n for trade costs to measure “effective varieties” and does not depend on c because
they assume factor prices equalize.

A.3

Equilibrium

In equilibrium, labor markets clear and firms earn zero profits. These conditions are givenin the main text by equations (2) and (3). The zero-profit condition for the homogeneous,numeraire good is c(z, k) ≥ 1 ∀k and x(z, k) > 0 ⇒ c(z, k) = 1. The equilibrium local
income distribution density, which depends on equilibrium wages w(ω, k), isZ
f (ω, k)dω.

g(y, k) =ω∈Ω:w(ω,k)=y

A.4

Equilibrium pattern of specialization and trade

The skill-intensity index i(r) is defined such that i(r) = i(r0 ) ⇐⇒ b(ω, r) = h(r, r0 )b(ω, r0 ) ∀ωfor some function h(r, r0 ) and i(r) > i(r0 ) ⇒ r > r0 . It is convenient to choose the labels i(r)such that i(r) is the identity of the lowest r in the set of products with this skill intensity. This
allows us to write b(ω, r) = h(r, i(r))b(ω, i(r)). It also makes b(ω, i) strictly log-supermodular
by definition, whether b(ω, r) is multiplicatively separable or weakly log-supermodular.

2A.4.1

Skill-intensive quality and costless trade

Trade is costless and b(ω, r) is weakly log-supermodular. The absence of trade costs (τqkk0 =0 ∀q ∀k ∀k 0 ) means that the zero-profit condition (3) reduces toπq,k =mq exp(−c(q, k)/mq )X

Nk0 Γk0 (q, n, c, 0) − fq ≤ 0.

k0This makes demand conditions within the summation orthogonal to the production location.
Skill abundance imposes structure on the pattern of production through the labor-market
clearing condition. In particular, equation (2), the strict log-supermodularity of f (ω, k), andf (ω, k) > 0 ∀ω ∈ Ω ∀k together imply, for k > k 0 and ω > ω 0 ,
P
P
0
0 −σ
−σ
b(ω, r)σ c(r, k 0 )σb(ω, r)σ c(r, k)σr∈z∪Q nr,k0 x(r, k )w(ω, k )r∈z∪Q nr,k x(r, k)w(ω, k)
P
P
>
.
0
−σ b(ω 0 , r)σ c(r, k)σ000 −σ b(ω 0 , r)σ c(r, k 0 )σr∈z∪Q nr,k x(r, k)w(ω , k)r∈z∪Q nr,k0 x(r, k )w(ω , k )This inequality can be rewritten asw(ω, k)−σ X b(ω, r)σw(ω, k 0 )−σ X b(ω, r)σ0
φ(r, ω , k) >φ(r, ω 0 , k 0 ),
0
−σ
0
σ
0
0
−σ
0
σ
w(ω , k) r∈z∪Q b(ω , r)w(ω , k ) r∈z∪Q b(ω , r)nx(r,k)b(ω 0 ,r)σ c(r,k)σwhere φ(r, ω 0 , k) ≡ P r,knr,k x(r,k)b(ω0 ,r)σ c(r,k)σ dr is akin to a probability mass function. φ(r, ω 0 , k)r∈z∪Q
describes the output share of quality (product) r in location k when shares are weighted byP
their production costs and use of skill ω 0 . Similarly, define φi (ω 0 , k) ≡ r:i=i(r) φ(r, ω 0 , k),which describes the output share of products with skill intensity i in location k, and thePb(ω,r)
related expectation operator Eω0 ,k [α(i)] ≡ i α(i)φi (ω 0 , k). Using the fact that b(ω0 ,r) is thesame for all r with i(r) = i, the inequality can then be written as expression (4) in the main
text:




w(ω, k)−σb(ω, i)σw(ω, k 0 )−σb(ω, i)σEω0 ,k>Eω0 ,k0.
w(ω 0 , k)−σb(ω 0 , i)σw(ω 0 , k 0 )−σb(ω 0 , i)σInequality (4) says that skill-abundant locations specialize in skill-intensive products. To
arrive at the result, we’ll first consider the case of factor-price equalization and then describe
the more general case.
When wages are equal across locations, w(ω, k) = w(ω) ∀k, this inequality simplifies toEω0 ,kIn this case, φ(r, ω 0 , k) = Pb(ω, i)σb(ω 0 , i)σ> Eω0 ,k0

nr,k x(r,k)b(ω 0 ,r)σ c(r)σ0σσr∈z∪Q nr,k x(r,k)b(ω ,r) c(r) dr3b(ω, i)σb(ω 0 , i)σ
= P


.

nr,k x(r,k)`(ω 0 ,r)
0r∈z∪Q nr,k x(r,k)`(ω ,r)dr

describes ω 0 -use-weighted shares of total output of r in location k. The inequality says that the averageskill intensity of output is higher in k than k 0 . This requires that φi (ω 0 , k) put more weight
on some higher values of i than φi (ω 0 , k 0 ) does so that the average skill intensity of output
produced in k is higher than in k 0 .65 This is the factor-abundance mechanism for quality
specialization.
In the absence of factor-price equalization, a slightly longer chain of reasoning delivers
the same conclusion. Suppose that inequality (4) were true but φi (ω 0 , k) did not place greater
weight on higher values of i in higher-k locations (i.e. φi (ω 0 , k) = φi (ω 0 , k 0 )). If so, w(ω, k)−σmust be strictly log-supermodular to satisfy this inequality. If w(ω, k)−σ is log-supermodular,Rthen c(r, k)−σ is log-supermodular, since c(r, k)1−σ = ω∈Ω b(ω, r)σ w(ω, k)1−σ dω and b(ω, r) is
log-supermodular (Lehmann, 1955). In the absence of trade costs, varieties of skill intensity
i are only produced in location k when c(i, k) = mink0 c(i, k 0 ). Thus, log-supermodularityof c(i, k)−σ and thecondition
implythat φi (ω 0 , k) is log-supermodular in (i, k).
 zero-profitb(ω,i)σb(ω,i)σ> Eω0 ,k0 b(ω. Therefore skill-abundant locations specialize
As a result, Eω0 ,k b(ω0 ,i)σ0 ,i)σin skill-intensive products.
A.4.2

Uniform skill intensities and costly trade

When skill intensities are uniform, b(ω, r) = b1 (ω)b2 (r), unit costs are multiplicatively separable in (r, k) and can be written asc(r, k) = b2 (r)

σ
1−σ

Z

b1 (ω)σ w(ω, k)1−σ dω

1
 1−σ

σ

≡ b2 (r) 1−σ c(k)ω∈ΩThe main text considers the case of trade costs that are small and uniform, τqkk0 =τq ∀k 0 6= k and τqkk = 0. When factor prices equalizes, profits vary only with home demand,
πq,k > πq,k00 ⇐⇒ Nk Γk (q, n, c, τ ) > Nk00 Γk00 (q, n, c, τ ). When trade costs are sufficiently low,demands approach their costless-trade equilibrium levels Γk (q, n̄, c̄, 0). Provided that wages
are increasing in skill, demand share Γk (q, n, c, 0) is strictly log-supermodular in (q, k).
Lemma 1. When factor prices equalize and wages are increasing in skill, Γk (q, n, c, 0) is
strictly log-supermodular in (q, k).
Proof. The proof of this lemma is quite similar to the proof of Lemma 1 in Fajgelbaum,σb(ω,i)
Note that the inequality of expectations holds for an arbitrary ω > ω 0 . Therefore, { b(ω0 ,i)σ }ω,ω 0 ∈Ω,ω>ω 0
is a class of strictly increasing functions. If this class were all increasing functions, we would conclude thatφi (ω 0 , k) stochastically dominates φi (ω 0 , k 0 ), since Ex̃ (u(x)) ≥ Ex̃0 (u(x)) ∀u0 (x) > 0 ⇐⇒ Fx̃ (x) ≤ Fx̃0 (x) ∀x,
where F is the cumulative distribution function.
65

4

Grossman, and Helpman (2011). The demand level isZΓk (q, n, c, 0) =P
exp(yq) [ k00 nq,k00 exp(−c(q, k 00 )q/θq )]θq −1g(y, k)dy
P
P
θq0
0
00 0
q 0 exp(yq ) [k00 nq 0 ,k00 exp(−c(q, k )q /θq 0 )]|{z}≡Ψ(y,q,n,c,0)

exp(yq) is strictly log-supermodular (SLSM), so Ψ(y, q, n, c, 0) is SLSM in (y, q). Since w(ω)
is increasing and f (ω, k) is SLSM, g(y, k) is SLSM. Since Ψ(y, q, n, c, 0) is SLSM in (y, q)
and g(y, k) is SLSM in (y, k), Γk (q, n, c, 0) is strictly log-supermodular in (q, k) (Lehmann,
1955).
This property yields the result reported in the main text that high-k locations are highincome because they are skill-abundant, and this causes them to have greater demand forhigh-q varieties.
Consider another case, in which trade costs are large and uniform. When trade costs
are sufficiently high, production is diversified, with every quality segment produced in every
location. With an additional assumption, that θq is increasing in q, Fajgelbaum, Grossman,and Helpman (2011) characterize the pattern of trade that arises when factor prices equalize.
It can be shown that all firms producing a quality q make the same local sales and export
sales. Therefore, k is a net exporter of q if it has more firms producing q than the worldPaverage, nq,k > K1 k0 nq,k0 . Lemma 2 and Proposition 5 in FGH show that, in this diversified
equilibrium, higher-income locations consume relative more of higher-quality varieties andtherefore host relatively more firms producing higher-quality varieties, making them net
exporters.
A.4.3

Skill-intensive quality and costly trade

Proof of Proposition 1:
Proof. Suppose not. That is, suppose Mq,k < Mq,k0 and Mq0 ,k > Mq0 ,k0 . If c(q, k) ≥ c(q, k 0 ),then by approximation (5) πq,k0 > πq,k , which contradicts nq,k > 0 by the free-entry condition.
Similarly, if c(q, k) ≤ c(q, k 0 ), then by πq0 ,k > πq0 ,k0 , which contradicts nq0 ,k0 > 0.

A.5

Taking the theory to plant-level data

Denote the plant index j, so that, for example, plant j’s skill intensity is i(j).
If b(ω, q) is strictly decreasing in q, higher-quality varieties are more costly to produce,5c(q, k) > c(q 0 , k) ⇐⇒ q > q 0 .
Z∂b(ω, q)∂c(q, k)−σσ=c(q, k)b(ω, q)σ−1 w(ω, k)1−σ
dω
∂q
σ−1
∂q
ω∈Ω
∂b(ω, q)∂c(q, k)< 0 ∀ω ⇒>0∂q∂q
If g(y, k) is log-supermodular, average income is a sufficient statistic for k. k > k 0 if andonly if g(y, k) likelihood-ratio dominates g(y, k 0 ), so Ek (y) > Ek0 (y) ⇐⇒ k > k 0 .
The composition measure assumes that non-production workers are more skilled than
production workers. Denote the fraction of workers of skill ω labeled as non-production byl(N, ω) and the fraction labeled production as l(P, ω) = 1−l(N, ω). Denote the share of nonproduction
workers employed in a plant with skill intensity i in location k by shareN (i, k) ≡Rω `(ω,i(q),k)l(N,ω)dωR. If l(N, ω) is strictly increasing in ω, then shareN (i, k) is strictly increasω `(ω,i(q),k)dωing in i.66 Inside the factor-price equalization (FPE) set, `(ω, q, k) = `(ω, q) ∀k and therefore shareN (i, k) = shareN (i) ∀k. Outside the FPE set, if w(ω, k)−σ is log-supermodular,
shareN (i, k) is strictly increasing in k.67 I therefore use shareN (j) × ln ȳk as an additional
control for skill intensity.
The wage measure assumes that wages are increasing in skill, ω.68 If wages are increasing
in skill, we can infer the skill intensity of a plant’s variety from its average wage. The average
wage at a plant producing quality q with skill intensity i(q) in location k isZw(ω, k)`(ω, i(q), k)Rdω =w̄(i, k) = w̄(q, k) =00
ω ω 0 `(ω , i(q), k)dωZw(ω, k)ϕ(ω, i, k)dω,ω`(ω,i(q),k)where ϕ(ω, i(q), k) ≡ R 0 `(ω
0 ,i(q),k)dω 0 is a density that is strictly log-supermodular in (ω, i),ωwhich means that ϕ(ω, i, k) likelihood-ratio dominates ϕ(ω, i0 , k) if and only if i > i0 .69 The
average wage w̄(i, k) is therefore strictly increasing in skill intensity i. We can similarly
66This assumption is analogous to Property (28) in Costinot and Vogel (2010), which connects observable and unobservable skills. If l(N, ω) is strictly increasing in ω, then choosing the labeling schemeof worker type t = N or t = P with N > P makes l(t, ω) a strictly log-supermodular function.
Since `(ω, i, k) is strictly
R log-supermodular in (ω, i) and strict log-supermodularity is preserved by integration,
theintegralRR ω `(ω, i, k)l(t, ω)dω is strictly log-supermodular in (t, i). As a result, the ratio`(ω,i,k)l(N,ω)dω/`(ω, i, k)l(P, ω)dω is strictly increasing in i. Therefore shareN (i, k) is strictly inωωcreasing in i.
67
This follows from `(ω, i, k) log-supermodular in (ω, k) and l(t, ω) log-supermodular in (t, ω).
b(ω,q)f (ω,k)68= ∂ ln∂ω− σ1 ∂ ln ∂ω> 0 ∀q∀k. Informally, more skilled individuals
A sufficient condition is ∂ ln w(ω,k)∂ω
have greater absolute advantage than local abundance.
69w̄(i, k) and ϕ(ω, i, k) can be written in terms of the skill intensity i(q) because i(q) = i(q 0 ) ⇒0R `(ω,q,k)R `(ω,q ,k)
0
0 =
0 0
0.
0 `(ω ,q,k)dω0 `(ω ,q ,k)dωωω

6define the average wage of production workers byZw̄P (i, k) =w(ω, k)`(ω, q, k)l(P, ω)Rdω =`(ω 0 , q, k)l(P, ω 0 )dω 0Zw(ω, k)ϕP (ω, i, k)dω,and an analogous average wage w̄N (i, k) for non-production workers with density ϕN (ω, i, k).
ϕP (ω, i, k) and ϕN (ω, i, k) are strictly log-supermodular in (ω, i), so these average wages arestrictly increasing in skill intensity i.
Inside the FPE set, wages equalize across locations, w̄(q, k) = w̄(q) ∀k, and ranking
plants by their averages wages is equivalent to ranking them by their factor intensities,w̄j > w̄j 0 ⇐⇒ i(j) > i(j 0 ). w̄P (q, k) and w̄N (q, k) also have these properties. This motivatesusing these average wages as establishment-level controls for skill intensity. Outside the FPE
set, if w(ω, k)1−σ is log-supermodular, w(ω, k)ϕ(ω, i, k) is strictly log-supermodular in (ω, i)
and in (ω, k). As a result, w̄(i, k) is increasing in i, increasing in k, and log-supermodular.
I therefore use w̄j × ln ȳk as an additional establishment-level control for skill intensity.
The approximation Mq,k (τ ) and its empirical counterparts describing the composition ofdemand using per capita incomes exploit the fact that this is a sufficient statistic for relative
demand for qualities under the model’s assumptions. Lemma 1 in Fajgelbaum, Grossman,and Helpman (2011) shows that, when g(y, k) is log-supermodular and trade costs are small,
relative demand for higher-q varieties is greater in the higher-k location. That is, when g(y, k)is log-supermodular, Γk0 (q, n̄, c̄, 0) is log-supermodular in (q, k). As mentioned previously,
when g(y, k) is log-supermodular, income per capita is a sufficient statistic for k.
If trade costs were large, expression (5) may not be a good approximation of profits.
The approximation characterizes market access Mq,k (τ ) using the composition of demandΓk (q, n̄, c̄, 0) when trade is costless. When trade costs are high, Γk0 (q, n, c, τ ) also varies
across k 0 due to the equilibrium locations of firms. To the degree that trade costs are large,
Γk0 (q, n, c, τ ) may not be well predicted by Γk (q, n̄, c̄, 0) and therefore not well predicted byvariation in income per capita alone. In my empirical work, I find that my market-accessmeasures explain much of the variation in outgoing shipment prices that is related to origin
incomes, so they do not seem to be underpowered in practice.
Mot2 can be written as a weighted average of Mot1 and ln ȳot . A city’s own income percapita has greater weight in this average when it is more populous than and more distantfrom other metropolitan areas.
1
Mot2 = P−ηd Ndt milesod"#X

Nd0 t miles−ηod0

d0 6=o7!
Mot1 + Not miles−η
oo ln ȳot

BData appendix

B.1

Public data

B.1.1

Geography

All the reported results describe core-based statistical areas (CBSAs). ZIP-code tabulation
areas (ZCTAs), counties, and public-use microdata areas (PUMAs) were assigned to OMBdefined CBSAs using the MABLE Geocorr2K geographic correspondence engine from theMissouri Census Data Center. I use the CBSA geographies as defined in November 2008.
These consist of 366 metropolitan areas and 574 micropolitan statistical areas.
In the gravity regressions and in constructing the market-access measures, I define themileage distance between two CBSAs as the geodetic distance between their population
centers. These population centers are the population-weighted average of the latitude andlongitude coordinates of all ZCTAs within the CBSA, using population counts from the2000 Census. I define the mileage distance from a CBSA to itself as the population-weighted
average of the pairwise geodetic distances between all the ZCTAs within the CBSA. For
five CBSAs containing only one ZCTA, I generated this mileage distance to self using thepredicted values obtained by projecting mileage distance to self for the other 935 CBSAs
onto their land areas.
B.1.2

Locational characteristics

Data on CBSAs’ aggregate populations and personal incomes come from the BEA’s regional
economic profiles for 1997, 2002, and 2007, data series CA30.
Data on the distribution of household incomes for the 1997 and 2002 samples were constructed from county-level estimates reported in U.S. Census Bureau, 2000 Census Summary
File 3, Series P052. Data on the distribution of household incomes at the CBSA level forthe 2007 sample were obtained from U.S. Census Bureau, 2005-2009 American Community
Survey 5-Year Estimates, Series B19001.
City-industry college shares were constructed from the 2000 Census and 2005-2009 American Community Surveys microdata made available via IPUMS-USA (Ruggles, Alexander,
Genadek, Goeken, Schroeder, and Sobek, 2010). City-industry means and standard deviations of years of schooling and wages from the 2000 Census and 2005-2009 American Community Surveys microdata made available via IPUMS-USA (Ruggles, Alexander, Genadek,
Goeken, Schroeder, and Sobek, 2010).
Locations’ latitudes and longitudes were compiled from various sources. Latitude andlongitude coordinates for US ZIP-code Tabulation Areas (ZCTAs) were obtained from the8

2000 Census.70 The geodetic distances for export shipments in appendix section E.1 were
calculated using latitude and longitude coordinates for major Canadian cities, which wereconstructed by aggregating Canadian dissemination areas’ populations and coordinates in
the 2006 Census Geographic Attribute File from Statistics Canada, and coordinates of eachnation’s capital or main city from Mayer and Zignago (2011).
B.1.3

Industrial and product characteristics

The Sutton (1998) R&D and advertising intensity measure of scope for vertical differentiation
is provided at the SIC72 level in Federal Trade Commission (1981). These were mapped to1987 SIC codes using the Bartlesman, Becker, and Gray concordance from Jon Haveman’s
website and to 1997, 2002, and 2007 (via 2002) NAICS codes using concordances from the
US Census. For industries to which multiple SIC72 industries were mapped, I calculated theweighted average of intensities, using 1975 sales as weights.
The Khandelwal (2010) ‘ladder’ measure of scope for vertical differentiation was mappedfrom HS10 product codes to 6-digit NAICS codes using the Pierce and Schott (2012) concordance. For industries to which multiple commodities were mapped, I calculated the weighted
average of ladder lengths, using the initial period import values reported by Khandelwal asweights.
I use the Bureau of Economic Analysis Benchmark Input-Output Data to distinguishbetween final consumer goods and intermediate inputs and to construct input-market accessmeasures. I use the 1997 and 2002 Standard Make and Use Tables at the detailed level tocompute each industry’s fraction of value produced that is sold to final consumers. I also
use them to construct input-market-access measures based on industries’ expenditure sharesfor purchased inputs. I calculate share-weighted average wages using the input-output tableshares and local wages from the Longitudinal Business Data microdata.
In calculating demand shifters, I mapped the Feenstra and Romalis (2014) estimatesof σ̂ and λ̂ from SITC revision 2 commodity codes to 5-digit SCTG product codes usinga United Nations SITC-HS concordance and a Statistics Canada HS-SCTG concordance.
When multiple parameter estimates mapped to a single 5-digit SCTG product code, I used
the median values of σ̂ and λ̂. The results are robust to using the arithmetic mean.

B.2

Confidential Census data

I use establishment-level microdata from the 1997, 2002, and 2007 editions of the Commodity
Flow Survey (CFS) and Census of Manufactures (CMF).
70

Downloaded from http://www.census.gov/tiger/tms/gazetteer/zcta5.txt in December 2012.

9B.2.1

Commodity Flow Survey

I use data describing shipments by manufacturing plants from the Commodity Flow Survey,
a component of the quinquennial Economic Census. Each quarter of the survey year, establishments report a randomly selected sample of 20-40 of their shipments from a given week
and describe them in terms of commodity content, value, weight, destination, transportation mode, and other characteristics. The approximately 100,000 establishments sampled
by the CFS were selected using a stratified sampling design reflecting the Commodity Flow
Survey’s objectives (Bureau of Transportation Statistics and US Census Bureau, 2010); of
the approximately 350,000 manufacturing establishments in the United States, about 10,000
per year appear in my estimation sample.71
These data are analogous to firm-level customs data with four important distinctions.
First, the data describe shipments at the establishment level rather than at the firm level.
Second, the geographic detail of ZIP-to-ZIP shipments is orders of magnitude more precise
than the distance measures used to describe international transactions. Each shipment’s
mileage was estimated by BTS/Census using routing algorithms and an integrated, intermodal transportation network developed for that purpose. Third, establishments report asample of their shipments in the survey, not a complete record of all transactions. Eachquarter of the survey year, establishments report a randomly selected sample of 20-40 of
their shipments in one week. The CFS data include statistical weights that can be used toestimate aggregate shipment flows. Fourth, the CFS uses a distinct product classification
scheme, the Standard Classification of Transport Goods, that is related to the Harmonized
System used in international trade data. At its highest level of detail, five digits, the SCTG
defines 512 product categories.72
The Commodity Flow Survey microdata include statistical weights so that observations
can be summed to obtain estimated totals that are representative. Each shipments’ associated “tabulation weight” is the product of seven component weights (Bureau of Transportation Statistics and US Census Bureau, 2010, Appendix C). The products of four ofthese weights (shipment weight, shipment nonresponse weight, quarter weight, and quarter
nonresponse weight) scale up an establishment’s shipments to estimate the establishments’total annual shipments. The other three component weights (establishment-level adjustment
weight, establishment weight, industry-level adjustment weight) scale up establishments’ total shipments to estimate national shipments. The 1997 and 2002 microdata report only the71

The 2002 CFS sample is roughly half that of the 1997 and 2007 surveys, sampling about 50,000 establishments in total and a proportionate number that appear in my estimation sample (Bureau of Transportation
Statistics and US Census Bureau, 2004).
72
By comparison, the HS scheme has 97 2-digit and about 1400 4-digit commodity categories.

10tabulation weights, while the 2007 microdata report all seven component weights.
The demand estimation performed in section E.3 requires measures of establishments’market shares, which are calculated from estimates of their total sales of that product ina destination market. These shares are estimated using the first four component weights.
These establishment-level measures should not be scaled up by the latter three component
weights, such as the probability of the establishment being selected into the CFS sample.
As a result, it is only possible to calculate the plant-product demand shifters using the 2007
microdata, which include the component weights required to estimate market shares.
The CFS classifies shipments’ commodity contents using the Standard Classification ofTransported Goods (SCTG), a coding system based on the Harmonized System (HS) classification that was introduced in the 1997 CFS. At its highest level of detail, five digits, the
SCTG defines 512 product categories. By comparison, the HS scheme has 97 2-digit andabout 1400 4-digit commodity categories. I exclude from my analysis all SCTG productcategories whose 5-digit product codes end in 99, since these are catch-all categories such as
24399 “Other articles of rubber.”
I calculate shipment unit values by dividing shipment value by shipment weight. All myanalyses of these unit values are within-product comparisons or regressions incorporatingproduct fixed effects. These unit values are proxies for producer prices, because they do notinclude shipping costs or shelving costs that may appear in the retail consumer price.
Each shipment is reported to have been sent by any combination of eight transportation
modes. In much of the analysis, including all the shipment price regressions, I restrict attention to unimodal shipments and the five most common multimodal shipments. Unimodal
shipments constitute more than 80% of shipments by value and 90% by weight (Bureau ofTransportation Statistics and US Census Bureau, 2010).
B.2.2

Census of Manufactures

Each manufacturing plant appearing in the Commodity Flow Survey also appears in the Census of Manufactures, which describes plant-level characteristics such as wage bills, production
and non-production employees, and capital stocks. The CMF also identifies the county inwhich an establishment is located. Very small establishments do not report detailed production data to the CMF. Instead, the Census Bureau uses data from administrative records
from other agencies, such as tax records, to obtain information on revenues and employment.
It then imputes other variables.
The product trailer of the CMF describes the products produced at each establishment.
For all products, establishments report the total value of their annual output. For a subset

11

of products, establishments report both values and quantities.73 I calculate unit values bydividing product value shipped by product quantity shipped; these unit values are used inappendix Table D.2.
B.2.3

Longitudinal Business Database

I also use information from the Longitudinal Business Database (LBD), which is a census of
US business establishments and firms with paid employees. Microdata from the 1997, 2002,
and 2007 editions are a combination of survey and administrative records. I use the LBD
for three purposes. First, I use the records in linking establishments across the 2002 CFS
and CMF data sets. Second, I use an establishment’s first year appearing in the LBD, which
is a comprehensive census, to calculate plants’ ages. Third, I use the LBD in constructing
input-market-access measures.
B.2.4

Combining the CFS and CMF

I matched shipment-level observations in CFS data to establishment-level characteristics in
CMF data using unique establishment identifiers called Census File Numbers (1997) and
Survey Unit Identifiers (2002, 2007). I also used information in the LBD to address theswitch from CFNs to SUIs in 2002.
Each data source contains information on the geographic location of an establishment.
The CMF reports the county in which an establishment is located. The CFS reports the ZIP
code and state in all survey years and some information about core-based statistical areas
in 2002 and 2007.
B.2.5

Sample selection

Though the CFS and CMF data are very rich descriptions of establishments and their shipments, some of the observations exhibit limitations that warrant their exclusion from theestimation sample.
CFS & CMF: I exclude SCTG5-NAICS6 pairs in which fewer than five establishments
report shipping a commodity.
CFS: I restrict the sample to shipments whose mode of transportation is unimodal or
one of the five most common multimodal combinations. I exclude shipments with unit
values more than two standard deviations from the product mean. I exclude destinationproduct pairs for which only one establishment ships that product to that destination. I
73

The set of products for which product quantity shipped data are collected has shrunk over time.

12exclude shipments that are the unique instance of that commodity being shipped by that
establishment.
CMF: I exclude establishments not belonging to a OMB-defined CBSA as identified
by their county location in the CMF and the November-2008-vintage CBSA definitions. I
exclude establishments whose information in the Census of Manufactures are derived fromadministrative records rather than directly reported. I exclude establishments whose employment levels or wage bills are imputed in the 2002 and 2007 CMF.74 I exclude establishmentswith wages that lie below the 1st percentile or above the 99th percentile of the wage distribution for manufacturing establishments.

C

Gravity regressions appendix

This appendix characterizes the pattern of manufactures shipments between US cities usinga gravity model of shipment volumes. Gravity regressions relate the volume of trade to theorigin’s economic size in terms of output produced, the destination’s economic size in termsof consumer expenditure, and trade frictions between the origin and destination.75 Hallak(2010) and Bernasconi (2013) use gravity models of trade flows between countries to assess
whether locations with more similar income levels trade more with each other, controlling fororigin characteristics, destination characteristics, and bilateral trade frictions. They find thatcountries with more similar income distributions trade more with each other, as predicted
by Burenstam Linder (1961). I find a similar pattern of trade flows between US cities.
The baseline gravity specification isln Xodt = −η · ln milesod + β · | ln ȳot − ln ȳdt | + γot + γdt + odt
where Xodt is the volume of manufactures shipments from origin o to destination d in yeart, milesod is the distance between the two locations, | ln ȳot − ln ȳdt | is the difference in theirlog per capita incomes, γot and γdt origin-year and destination-year fixed effects, and odt isa residual reflecting both random sampling and potential measurement error.76
This baseline specification is estimated using observations with strictly positive shipment
74

The 1997 CMF does not identify variables that have been imputed, so I am unable to exclude suchobservations.
75
See Anderson (2011) and Bergstrand and Egger (2011) for surveys of the gravity literature. Importantly,
the correct notions of economic size account for “multilateral resistance” terms that depend on the locations’bilateral trade frictions with all trading partners. These are captured by fixed effects in my regressions.
76
Observations of Xodt include sampling error since a representative sample of shipments is used to estimate
the total shipment volume. See the data appendix B for details. Noise in the dependent variable will notbias the estimated coefficients of interest.

13

volumes. In fact, there are many zeros in the trade matrix, and these non-positive shipment
volumes reflect economic mechanisms, like trade costs. For example, every city ships a
positive amount to itself Xoot > 0 ∀o∀s∀t.
I use two approaches to correct for the non-random nature of zeros. First, I implement
the Heckman (1979) two-step selection correction. The first-step probit regression, which
has the same regressors on the right-hand side, yields an estimated probability of a strictly
positive shipment volume for each origin-destination-sector-year. The second-step estimating
equation isln Xodt = −η · ln milesod + β · | ln ȳot − ln ȳdt | + δ

φ(Φ−1 (ρ̂odt ))+ γot + γdt + odt ,ρ̂odstwhere ρ̂odt is the predicted probability from the probit regression, φ and Φ are the probability−1 (ρ̂
odt ))
is the inverseand cumulative density functions of the normal distribution, and φ(Φ ρ̂odt
Mills ratio. The second approach I use to address zeros is the Poisson pseudo-maximum
likelihood estimator introduced by Silva and Tenreyro (2006) to estimate the gravity equationin levels.
βE(Xodt ) = miles−ηod | ln ȳot − ln ȳdt | exp(γot + γdt )This estimation approach allows me to include observations for which Xodt = 0.77
Table C.1 reports the result of estimating this gravity regression for aggregate manufactures shipment volumes. The first column reports the result of estimating the baseline
gravity specification via OLS. The second column uses the squared difference in incomes,(ln ȳot − ln ȳdt )2 , as a regressor instead of the absolute difference. The third column adds thetwo-step Heckman (1979) correction for selection into strictly positive trade flows. The fourthcolumn uses the Silva and Tenreyro (2006) Poisson pseudo-maximum likelihood estimator
for all observations. This final estimator is my preferred specification.
In all specifications, the difference between two cities’ average income levels is negatively correlated with the level of trade between them. The Linder pattern of trade, inwhich locations with more similar incomes trade more intensely with each other, holds true
for manufactures shipments between US cities. The finding that locations disproportionately demand products that are produced in locations of similar income levels suggests twoelements that any model explaining within-product specialization must incorporate. First,
preferences are non-homothetic, so the composition of demand varies with locations’ incomes.
77

Silva and Tenreyro (2006) emphasize that their estimation procedure addresses a concern that higher
moments of exp(odt ) are correlated with the regressors, which would cause the estimated coefficients in the
log-linear specification to be inconsistent.

14

Estimator
Dependent variable

Table C.1: Shipment volumes (2007)
(1)
(2)
(3)
(4)
OLS
OLS
Heckman PPML w/ zeros
ln Xodln Xodln XodXod

Mileage, ln milesod
Income difference, | ln ȳo − ln ȳd |-0.916**-0.917**-1.773**(0.00745)(0.00715)(0.0104)(0.0170)-1.074**-0.430**(0.0454)(0.0840)-1.696**(0.0413)

Income difference squared, (ln ȳo − ln ȳd )2-0.952**-2.657**(0.0854)−1
Inverse Mills ratio, φ(Φ ρ̂od(ρ̂od ))2.434**(0.0222)

R2
Observations (rounded)
Origin CBSAs (rounded)
Destination CBSAs (rounded)

0.347
175,000

0.347
175,000

0.378
175,000
900
950

850,000

Standard errors in parentheses** p<0.01, * p<0.05
Notes: Aggregate shipment volume by establishments in the CFS and CMF between distinct CBSAs in 2007. All
regressions include origin and destination fixed effects. Standard errors are bootstrapped with 50 repetitions incolumns 1-3 and heteroskedastic-robust in columns 4-5.

Second, high-income locations have comparative advantage in producing products that are
particularly attractive to high-income consumers. As described in section 2, these patterns
are compatible with the factor-abundance mechanism or home-market effect determining thepattern of within-product specialization.
The distance elasticity of trade is estimated to be near negative one, although the twostep Heckman specification implies that shipment volumes are notably more sensitive to the
distance between origin and destination. An elasticity close to negative one is consistent
with the central tendency of the vast international literature summarized by Disdier andHead (2008) and the elasticity of domestic shipments reported in Table 1 of Hillberry and
Hummels (2008) for geographically aggregate shipment volumes. In section 3.5, I use thefact that sales volumes are inversely proportionate to distance to construct market-accessmeasures.

D

Tables appendix

15

16(0.0211)(0.0711)0.172*(0.0210)0.224**(0.00442)(0.00443)

0.225**-0.0499**(0.00815)(0.00809)-0.0496**0.114**(0.00305)

0.0396**(0.00586)-0.0204**(0.0444)

0.402**

0.115**(0.00302)(0.00314)(0.00553)

0.0397**(0.00583)

0.0389**-0.0224**(0.0425)(0.0435)-0.0180**0.424**

0.521**√(0.00535)-0.0165**(0.0412)0.492**

√

√

√

√

(0.00486)-0.0213**(0.0400)

0.379**

0.104

√

√

√

√

√

(0.00548)-0.0171**(0.0428)0.305**(6)

Notes: Manufacturing establishments in the CFS and CMF. All shipments are to a domestic destination CBSA distinct from the origin
CBSA. All regressions include SCTG5 × NAICS6 × destination × year fixed effects and mode × year fixed effects. Unreported controls
are the interactions of income per capita with log non-production worker share (columns 2,3,5,6), log assets per worker (2,3,5,6), log
pay per worker (2,3,5,6), and log mean years of schooling (3,6), and 3-digit-NAICS-specific cubic polynomials in log mileage (4,5,6),
log non-production worker share (5,6), log assets per worker (5,6), log pay per worker (5,6), and log mean years of schooling (6).

Within R2
0.076
0.086
0.086
0.079
0.102
Number estab-year (rounded)
30,000
Number ind-prod-year (rounded)
5250
Observations (rounded)
1,400,000
Standard errors, clustered by origin CBSA × year, in parentheses** p<0.01, * p<0.05

Mean years of schooling (log)

Pay per worker (log)Assets per worker (log)

Non-production worker share (log)

Log mileage

Origin CBSA log population

Origin CBSA log per capita income

Table D.1: Outgoing shipment prices and city-industry schooling measures
Dep var: Log unit value, ln pskjodmt
(1)
(2)
(3)
(4)
(5)

Table D.2: Establishments’ prices and origin characteristics
Dep var: CMF Log unit value(1)

Log origin CBSA income per capita
Log origin CBSA population

(2)

(3)

(4)

(5)

(6)

(7)

0.218**

0.204**

0.193**

0.192**

0.155**

0.142**

0.0591(0.0384)(0.0384)(0.0392)(0.0409)(0.0373)(0.0392)(0.0459)-0.000772-0.00120-0.00151-0.000374

0.00380

0.00345-0.00274(0.00484)(0.00481)(0.00473)(0.00501)(0.00483)(0.00492)

0.0564**0.0471**√(0.00490)

Log non-production worker share(0.00539)(0.00652)

Log assets per worker-0.0125** -0.0159**√√
0.00937(0.00395)

Log non-production share× log per capita income
Log assets per worker
× log per capita income
Log pay per worker√√√(0.00404)

0.02610.03200.01470.0125(0.0268)(0.0343)(0.0311)(0.0310)(0.0310)-0.0229-0.0183-0.0229-0.0226-0.0181(0.0226)(0.0213)(0.0198)√(0.0197)√(0.0198)

√

√

√

√

√

√

-0.07290.00495

0.00157-0.0108(0.170)(0.147)(0.146)(0.147)-0.0408-0.0751-0.0752-0.09220.109**(0.0281)Log pay per production worker-0.0411*

Log pay per non-production worker-0.0257*(0.0187)√(0.0124)

Log pay per worker
× log per capita income
Log pay per production worker
× log per capita income
Log pay per non-production worker
× log per capita income
Market access (excl origin) Mot1

(0.120)(0.101)(0.100)(0.101)-0.00298

0.008390.00891

0.00244(0.0575)(0.0531)(0.0527)(0.0531)0.564**

0.469**(0.136)(0.136)

Log std dev household income

0.0804(0.0460)

Market access Mot2

0.403**(0.113)R-squared
Observations (rounded)
Estab-year (rounded)
Ind-prod-year (rounded)
Note

0.914

0.914

0.914

0.917
0.914
10000027500
8000
ctrl all flex
Standard errors, clustered by CBSA × year, in parentheses** p<0.01, * p<0.05

0.917

0.917

ctrl all flex ctrl all flex

Notes: Manufacturing establishments in the CMF reporting a product with quantity shipped. All regressions include NAICS6×year and NAICS product code×year fixed effects. The fourth, sixth, and seventh
columns include 3-digit-NAICS-specific third-order polynomials in log non-production worker share, log
assets per worker, log pay per worker, log pay per producer worker, and log pay per non-production worker.

17

Table D.3: Shipment prices and market access (no factor input covariates)
Dep var: Log unit value, ln pskjodmt

(1)

(2)

Origin CBSA log per capita income(3)0.440**
0.266**
0.149**(0.0359) (0.0378) (0.0434)
Origin CBSA log population-0.00764
0.00517-0.00153(0.00421) (0.00432) (0.00412)
Log mileage (ZIP-ZIP-mode-specific) 0.0404** 0.0476** 0.0454**(0.00280) (0.00274) (0.00272)
Market access (excludes origin) Mot1
1.374**(0.117)
Market access Mot2
1.311**(0.118)

(4)

(5)

(6)

0.413**
0.258**
0.151**(0.0345) (0.0369) (0.0424)-0.00652
0.00510-0.00101(0.00393)(0.00405)(0.00385)√√√
1.253**(0.115)

Within R2
0.080
0.083
0.083
0.084
0.086
Number estab-year (rounded)
35,000
Number ind-prod-year (rounded)
5250
Observations (rounded)
1,800,000
Standard errors, clustered by origin CBSA × year, in parentheses** p<0.01, * p<0.05

1.194**(0.116)0.086

Notes: Manufacturing establishments in the CFS and CMF. All shipments are to a domestic destination
CBSA distinct from the origin CBSA. All regressions include SCTG5 × NAICS6 × destination × year fixed
effects and mode × year fixed effects. The third through fifth columns include 3-digit-NAICS-specific cubic
polynomials in log mileage.

E

Empirical results appendix

This appendix reports further empirical evidence consistent with the results presented in
section 5. First, export shipments exhibit patterns consistent with those found in domestictransactions. Second, cities with greater income dispersion have higher outgoing shipment
prices, consistent with the model’s demand system in an equilibrium in which most individuals purchase low-quality varieties. Third, demand shifters exhibit the same patterns
as outgoing shipment prices. Fourth, the reported results are robust to controlling for input market access. Fifth, the reported results hold in samples that exclude large plants or
multi-plant firms.

E.1

Export shipments

This section examines export shipments. My empirical investigation was motivated in partby a growing international trade literature on quality specialization. I implemented myempirical strategy using plant-level data from US cities of varying income levels. The analysis
above described shipments destined for US cities, which account for the vast majority of
US manufactures output, to characterize how shipments’ characteristics are related to the18characteristics of their production locations. This section shows that the patterns found indomestic shipments are also found in export shipments destined for foreign markets.
Export shipments by US manufacturing plants exhibit price patterns consistent withthose observed in domestic shipments. Table E.1 presents results for regressions analogous tothose presented in Tables 3 and 4 using shipments sent to foreign destinations. The sample
size is considerably smaller, since exports represent less than 8% of shipments by value
and 4% by weight (Bureau of Transportation Statistics and US Census Bureau, 2010).78 I
calculate the mileage distance from origin CBSA to foreign destination using latitude andlongitude coordinates.79
The estimated coefficients are consistent with those reported for shipments to domestic
destinations. The origin-income elasticity of export prices is 42%. After controlling for plantlevel factor usage, the origin-income elasticity is 30%. Upon introduction of the market-accessmeasures, the origin-income elasticity becomes negative and statistically indistinguishable
from zero. The dispersion of household income in the origin CBSA is positively related
to export shipment prices, though this relationship is statistically insignificant, presumably
due to the small sample size. Thus, the empirical relationships between export shipment
prices, factor usage, and the demand measures are in line with those found for shipments todomestic destinations.

78

This small sample size prevents me from calculating demand shifters using export shipments.
For Canadian destinations, I use the coordinates of major Canadian cities. For other countries, I use
the coordinates of the capital or main city. See data appendix B for details.
79

19

20
0.821

(0.0124)0.824

0.400*(0.159)0.153(0.145)0.590*(0.279)0.430(0.238)-0.485√√√(0.0541)-0.119*(0.0978)-0.0258√√√(0.0115)(0.423)0.828
qnt flex(0.0503)-0.0811(0.0839)-0.105√√√(0.0119)(0.379)0.823
miles flex

(0.105)0.304**(6)-0.000623 -0.00218(0.107)0.369**(5)-0.0302(0.0395)

0.00207(0.0623)-0.0633(0.0961)√(0.0127)0.00920(0.117)0.419**(4)

0.831
all flex

0.153(0.137)

0.187

√

√

√

√

√

√

(0.0129)-0.00998(0.135)

0.218

(8)

(0.146)√(0.0134)0.00104(0.151)0.305*

(7)

0.831
0.823
all flex miles flex
64,00010,0002,000
Standard errors, clustered by CBSA × year, in parentheses** p<0.01, * p<0.05

0.823-0.0787(0.0455)-0.0432(0.0418)0.283**-0.0296(0.0969)(0.0825)(0.0134)-0.00972(0.0128)(0.0271)-0.0601**(0.0222)-0.0451**

0.141**(0.0198)

0.0815**0.169**(0.0202)(0.0205)(0.0125)0.0812**(0.0129)0.0787**0.00333(0.114)0.334**(3)

Table E.1: Export shipments

0.831
all flex

√

√

√

√

√

√

(0.0116)-0.00337(0.106)0.312**(9)0.832
all flex(0.327)2.477**

√

√

√

√

√

√

(0.0118)

0.0288*(0.114)-0.0724

(10)

0.831
all flex(0.375)

1.961**

√

√

√

√

√

√

(0.0116)0.0112(0.138)-0.215(11)

Notes: Manufacturing establishments in the CFS and CMF. All shipments are exports to a foreign destination. All regressions include SCTG5 × NAICS6
× year fixed effects and destination × year fixed effects. The fourth through eleventh columns include 3-digit-NAICS-specific third-order polynomials in log
mileage (4-11), log non-production worker share (5, 6, 8-11), log assets per worker (5, 6, 8-11), log pay per worker (6, 8-11), log pay per production worker (6,8-11), and log pay per non-production worker (6, 8-11).

R-squared
Note
Observations (rounded)
Estab-year (rounded)
Ind-prod-year (rounded)

Log market access Mot2

Log market access (excl orig) Mot1

Log pay per worker
× log per capita income
Log pay per production worker
× log per capita income
Log pay per non-production worker
× log per capita income
Log std dev orig household income

Log pay per non-production worker

Log pay per production worker

Log non-production worker share× log per capita income
Log assets per worker
× log per capita income
Log pay per worker

Log assets per worker

Log non-production worker share

Log mileage

0.00335

0.00876(0.115)(0.117)Log origin CBSA population

0.401**

0.434**

Log origin CBSA income per capita

(2)

(1)

Dep var: Log unit value, ln pskjodmt

E.2

Income dispersion

This section documents the relationship between the second moment of the income distribution and shipment prices. Cities with greater dispersion in household income exhibit higher
prices for both incoming and outgoing shipments. The latter is not explained by dispersion
in workers’ wages or skills. These findings are consistent with a demand-side mechanism
linking local income distributions to the pattern of quality specialization.
In the Fajgelbaum, Grossman, and Helpman (2011) model, income inequality is linked toquality specialization because the income distribution determines the composition of local
demand for quality. In general, the effect of greater income dispersion on relative demandfor quality is ambiguous. The authors’ Proposition 2(iii) shows that, when there are twoqualities and the majority of individuals at all income levels consume the low-quality variety,a mean-preserving spread of the income distribution raises local relative demand for thehigh-quality variety in their demand system. Since the converse would hold if a majority
of individuals consumed high-quality varieties, there is no general theoretical result for thecorrelation between income dispersion and relative demand for quality.
A few theories link income dispersion to specialization through supply-side mechanismsthat are absent from the model in section 3. In Grossman and Maggi (2000) and Bombardini,
Gallipoli, and Pupato (2012), locations with more diverse skill distributions have comparativeadvantage in sectors in which skills are more substitutable.80 In Grossman (2004), imperfectlabor contracting causes locations with more diverse skill distributions to have comparativeadvantage in sectors in which the most talented individuals’ contributions are more easily
identified. Applying these models to the question at hand involves reinterpreting them as
theories of intrasectoral specialization. For example, if different skills were less substitutablein the production of higher-quality products, these models would predict that locations
with greater skill dispersion would specialize in lower-quality varieties.81 If they were more
substitutable, the reverse prediction would result.
In light of these theoretical ambiguities, I rely on the distinction between income dispersion among local consumers and skill dispersion among local workers to empirically distinguish between the demand-side and supply-side mechanisms. Income dispersion among
all potential customers influences the demand channel. In the supply-side theories (appro80

Though both papers describe locations with greater skill dispersion specializing in sectors with greater
substitutability of skills, these two papers differ considerably. Grossman and Maggi (2000) compare twocountries and two sectors, one in which output is supermodular in the two workers’ talents and anotherin which output is submodular in talents. They assume that talent is perfectly observed. Bombardini,
Gallipoli, and Pupato (2012) describe imperfectly observed skills and CES production functions that varyin their elasticities of substitution between skills.
81
Grossman and Maggi (2000, p.1255,1271) cite quality control as an example of supermodular productionin which less dispersion yields comparative advantage.

21

priately reinterpreted to describe specialization within sectors), only skill dispersion among
those working in the industry in question is relevant. Thus, I construct two types of empirical measures: the standard deviation of household income within each city and the standard
deviations of years of schooling and weekly wages within each city-industry pair. The former
proxies for the demand-side mechanism; the latter for the supply-side. I proceed to include
these measures, which are available for most but not all metropolitan areas in the sample,
in linear regressions describing shipment prices.
Table E.2 documents how shipment prices are related to income and skill dispersion in thedestination and origin cities. The first two columns report the result of adding the standard
deviation of household income in the shipment destination to multivariate regressions likethose appearing in Table 2. The first column includes observable origin-city characteristics;
the second column includes origin-city fixed effects. In each case, the standard deviationof household income is strongly positively related to the price of incoming shipments. Thisis consistent with an equilibrium in which a more dispersed income distribution has morehouseholds in the right tail of the distribution who purchase higher-price, higher-quality
varieties.
The next three columns of Table E.2 relate outgoing shipment prices to income and skill
dispersion in the shipment origin. These regressions all include destination-product-year
fixed effects and control variables with industry-specific third-order polynomials, like thoseregressions appearing in the last column of Table 3. The third column introduces the standard deviation of household income as a regressor alongside origin characteristics, shipment
mileage, and the three plant-level factor-usage controls. The standard deviation of household income in the shipment origin is strongly, positively related to the outgoing shipment
price. This is consistent with models in which income dispersion generates demand for highprice, high-quality varieties or skill dispersion generates comparative advantage in high-price,
high-quality varieties. The fifth and sixth columns introduce city-industry-level measures ofskill dispersion are available so that we can contrast income dispersion amongst potential
customers with skill dispersion amongst workers employed in production. The key result
is that controlling for the logs of the standard deviations of years of schooling and weekly
wages at the city-industry level leaves the coefficients on origin characteristics virtually unaltered. Skill dispersion on the supply side appears unrelated to outgoing shipment prices.
These findings suggest that a demand-side mechanism links the local income distribution to
specialization.

22

Table E.2: Shipment prices and income dispersion
Dep var: Log unit value
Destination CBSA log per capita income
Destination CBSA log population
Destination CBSA log of std dev household income
Origin CBSA log per capita income
Origin CBSA log population

(1)

(2)

0.144**(0.0224)-0.00662**(0.00211)
0.103**(0.0215)0.446**(0.0160)-0.00726**(0.00149)

0.101**(0.0195)-0.00724**(0.00181)
0.0961**(0.0186)

0.0432**(0.00258)

0.0462**(0.00188)

Origin CBSA log of std dev household income
Log mileage (ZIP-ZIP-mode-specific)

(3)

(4)

(5)

0.287**(0.0524)-0.0274**(0.00552)
0.147*(0.0595)√

0.281**(0.0525)-0.0292**(0.00575)
0.139*(0.0598)√

0.286**(0.0524)-0.0272**(0.00555)
0.147*(0.0595)√

Log of std dev weekly wage (CBSA-INDNAICS)

0.0160(0.00989)

Log of std dev years schooling (CBSA-INDNAICS)-0.000837(0.00166)

Within R2
0.102
0.145
0.102
Standard errors clusterd by
cbsa dest × year cbsa dest × year cbsa × year
Number estab-year (rounded)
35,00035,00030,000
Number ind-prod-year (rounded)
5250
5250
5250
Observations (rounded)
1.8m
1.8m
1.4m
Origin CBSA x Year FE
Yes
SCTG5 x NAICS6 x dest CBSA x Year FE
YesStandard errrors, clustered as indicated, in parentheses** p<0.01, * p<0.05

0.102
cbsa × year
30,000
5250
1.4m

0.102
cbsa × year
30,000
5250
1.4m

Yes

Yes

Notes: Manufacturing establishments in the CFS and CMF. All shipments are to a domestic
destination CBSA distinct from the origin CBSA. All regressions include mode × year fixed effects.
Unreported controls in columns 3 through 5 include 3-digit-NAICS-specific cubic polynomials in
log mileage, log non-production worker share, log assets per worker, and log pay per worker. Also
unreported in columns 3 through 5 are the interactions of log origin income per capita with thethree input variables.

E.3

Demand shifters

This section characterizes the pattern of within-product specialization across US cities andits determinants using estimated demand shifters. As previously described, consumer loveof variety in the presence of horizontal differentiation breaks the price-quality mapping by
allowing high-cost varieties to sell alongside low-cost varieties of the same quality. Section
5 addresses this concern by including a variety of plant-level cost measures, which were
not available to researchers analyzing aggregate trade flows between countries. This section
addresses the concern a second time by estimating demand shifters for each plant-productpair. The empirical results are consistent with the unit-value findings.
The demand-shifter approach assigns higher quality valuations to products that havehigher market shares, conditional on price (Berry, 1994; Khandelwal, 2010; Sutton, 2012).
As described in the data appendix, it is only possible to calculate plants’ market shares in23

the 2007 edition of the Commodity Flow Survey. This considerably reduces the number ofobservations compared to the number underlying the previously presented results.
To compute demand shifters in the absence of instruments for producer prices, I use the“non-homothetic CES preferences” of Feenstra and Romalis (2014).82 In this specification,
the sales volume sjd of product j in destination market d in 2007 is described byln sjd =(σ − 1)(ln qj + λ ln ȳd ln qj − ln pjd ) + γd + jd
where qj is the product-quality shifter, pjd is price, ȳd is per capita income in market d, γdcaptures both aggregate expenditure and the price index in the destination market, and jdcaptures both idiosyncratic demand shocks and measurement error. The parameter λ governs
how consumer valuation of quality varies with income; the parameter σ is the elasticity of
substitution and price elasticity of demand. In the demand system, pjd is the price paid by
the consumer, while in my data the observed price p̌jd excludes shipping costs.83 I therefore
include the shipment mileage from establishment to destination and the shipment mileage1
ln milesjd , as additional regressors to control forinteracted with price, ln milesjd and p̌jdt
shipping costs.84 I use sectoral estimates of λ̂ and σ̂ from Feenstra and Romalis (2014) inorder to estimate qj in the linear regression
ln sjd + (σ̂ − 1) ln p̌jd
(1 + λ̂ ln ȳd )(σ̂ − 1)

= ln qj + η1 ln milesjd + η2

1
ln milesjd + γ̃d + ˜jd
p̌jd

where γ̃d and ˜jd are rescaled versions of γd and jd . These regressions are estimated productby-product, for products defined by SCTG5-NAICS6 codes, for the 2007 sample.85
Table E.3 describes how these estimated demand shifters relate to the observable characteristics of products, plants, and cities. The first column reports that the estimated demand
shifters are strongly positively correlated with plants’ prices. This validates the use of prices
82

One merit of this demand system is its computational simplicity. Because the nested-logit demand systemused in the Fajgelbaum, Grossman, and Helpman (2011) model uses quality levels as nests, its estimation
would require a computationally intensive iterative approach. Products must be assigned to quality nests inorder to estimate the demand system, and product qualities must be inferred by estimating demand.
83
In international trade parlance, demand depends on the “cost-insurance-and-freight” price while mydata reports the “free-on-board” price. If the consumer price reflects both multiplicative and additive trade
a
m
a
m
a
m
a
m
. Assuming that τjd
and τjd
costs, τjd
and τjd, then pjd = p̌jd τjd+ τjd
and ln pjd ≈ ln p̌jd + (τjd− 1) + p̌1jd τjd
1
are functions of the shipment distance motivates the inclusion of ln milesjd and p̃jd ln milesjd as regressors.
84
Omitting these regressors has very little impact on the estimated demand shifters and the subsequent
results relating these shifters to city and plant characteristics.
85
I obtain very similar results if I define products using only 5-digit SCTG codes. See the appendix section
B for details of how I mapped the Feenstra and Romalis (2014) parameter estimates to these product codes.

24

25
0.857
cl estab

0.614
cl cbsa-0.104(0.119)(0.120)0.626
cl cbsa(0.121)-0.1150.615
cl cbsa
13,00010,0001,000
Clustered standard errors in parentheses** p<0.01, * p<0.05

0.627
cl cbsa(0.148)(0.149)(0.148)-0.0965

0.626
cl cbsa

0.170

0.180

0.196

0.170
(0.231)(0.224)(0.224)(0.0232)

0.201(0.0232)(0.0232)

0.0358(0.0331)0.0844*(0.0493)0.407**(0.0590)0.0230(0.0728)

0.198

0.0363(0.0333)(0.0330)

0.03760.0844*(0.0486)(0.0485)0.0881**0.406**

0.409**

0.0136(0.0594)

0.0119(0.0592)(0.0735)(0.0727)-0.00394(0.0109)

0.003200.0106(0.0109)(0.0109)(0.0135)-0.0484**(0.0136)-0.0496** -0.0485**(0.0135)

0.615
cl cbsa(0.319)(0.277)0.0907**0.904**(0.250)(0.0119)0.0119(0.112)

0.164

(7)

0.681*(0.241)(0.0115)0.0170(0.0857)

0.265**(6)

1.034**(0.0113)0.00197(0.105)0.0856(5)0.807**(0.0109)0.0892**(0.0114)(0.0120)0.00629(0.0831)

0.157

(4)

0.0907**-0.00259

0.005770.270**(0.0819)0.412**(0.0840)(3)

Table E.3: Estimated demand shifters
(2)

0.646
cl cbsa(0.113)-0.127(0.166)0.0874(0.220)0.0201√√√(0.0623)0.0277(0.0784)

0.0212√√(0.0109)-0.000985(0.0793)0.237**(8)0.647
cl cbsa(0.112)-0.132(0.167)0.0687(0.221)

0.0224√√√(0.0624)0.0300(0.0793)0.0116√√(0.241)0.822**(0.0106)

0.00793(0.0814)

0.124

(9)

0.647
cl cbsa(0.114)-0.145(0.167)0.0571(0.226)-0.00358√√√(0.0620)0.0417(0.0786)

0.00263√√(0.278)0.715*(0.0109)

0.00375(0.101)0.0451(10)(0.0107)-0.0154(0.114)0.0401(11)

0.646
cl cbsa(0.110)-0.145(0.166)0.0819(0.220)0.0309√√√(0.0622)0.0294(0.0780)0.0152√√(0.119)0.317**

Notes: Manufacturing establishments in the CFS and CMF. All regressions include SCTG5 × NAICS6 × year fixed effects. Unreported
controls in columns 8-11 are 3-digit-NAICS-specific cubic polynomials in log non-production worker share, log assets per worker, log pay per
worker, log pay per production worker, and log pay per non-production worker.

R2 (including fixed effects)
Standard errors
Observations (rounded)
Establishments (rounded)
Ind-prod (rounded)

Log pay per worker
× log per capita income
Log pay per production worker
× log per capita income
Log pay per non-production worker
× log per capita income

Log pay per non-production worker

Log pay per production worker

Log non-production worker share× log per capita income
Log assets per worker
× log per capita income
Log pay per worker

Log assets per worker

Log non-production worker share

Log std dev origin hh income

Market access Mot2

Market access (excl origin) Mot1

Log CBSA population(0.0102)0.746**

Log unit value

Log CBSA income per capita(1)

Dep var: ln q̂jin inferring the pattern of quality specialization earlier in the paper. The second column
shows that plants with higher estimated demand shifters are located in cities with higher per
capita incomes. The 41% origin-income elasticity of the estimated demand shifter is similar to the 44% origin-income elasticity of outgoing shipment prices. The third and eighth
columns demonstrate that this positive relationship persists after controlling for plants’ input usage. Qualitatively consistent with the result in section 5.1, observed differences inplant-level factor usage explain less than half of the observed correlation between plants’
output characteristics and per capita incomes. The fourth and ninth columns replicate thefinding that the income composition of proximate potential customers, excluding those in
the city of production, is strongly positively associated with a plant’s output profile. The
11-percentage-point decline in the origin-income elasticity caused by introducing the firstmarket access measure after controlling for factor-usage differences suggests that proximity
to these customers explains at least one-quarter of the observed variation. The sixth column
demonstrates that introducing the first market-access measure prior to controlling for factor
usage would result in a change in the origin-income elasticity of essentially the same magnitude as controlling for factor usage. The fifth, seventh, and tenth columns demonstratethat the second market-access measure, which includes residents in the city of production,
has greater explanatory power. The eleventh column replicates the findings of section 5.2 bydemonstrating a positive relationship with origin CBSA income dispersion and the marketaccess measure.
These results can be succinctly summarized as a decomposition of the covariance between
incomes and shifters. After controlling for population size, differences in observed factor usage are responsible for 46% of the covariance between per capita incomes and estimateddemand shifters. Conditional on factor usage, the conservative market-access measure thatomits residents in the city of production accounts for 25% of the total covariance, leaving 30%
as residual variation. The model-consistent market-access measure that includes residents inthe city of production accounts for 48% of the total covariance, leaving 7% as residual variation.86 Thus, the observed pattern of specialization and inferences about its determinantsobtained using estimated demand shifters are similar to those obtained by examining unit
values.

E.4

Input market accessThis section demonstrates that the regression results in section 5.2 are robust to controlling for spatial differences in the factor content potentially embedded in intermediate in86

Numbers sum to 101% due to rounding.

26

Table E.4: Shipment prices and input market access(1)
Origin CBSA log per capita income
Origin CBSA log population
Log mileage (ZIP-ZIP-mode-specific)
Non-production worker share (log)Assets per worker (log)
Pay per worker (log)Log of input-weighted average wage (CBSA-NAICS6)
Log of input-weighted average wage in CBSAs within 200 miles

(2)

(3)

0.353**
0.348**
0.351**(0.0345)(0.0350)(0.0346)-0.0136** -0.0139** -0.0135**(0.00398) (0.00398) (0.00396)
0.0413** 0.0413** 0.0413**(0.00269) (0.00268) (0.00269)
0.113**
0.113**
0.114**(0.00695) (0.00696) (0.00696)-0.0540** -0.0541** -0.0541**(0.00404) (0.00404) (0.00404)
0.217**
0.215**
0.216**(0.0180)(0.0182)(0.0180)0.0140(0.0195)
0.639*(0.291)Market access (excludes origin) Mot1
Within R2
Number estab-year (rounded)
Number ind-prod-year (rounded)
Observations (rounded)

0.091

0.091

0.091

(4)

(5)

(6)

0.206**(0.0368)-0.00230(0.00404)
0.0475**(0.00264)
0.112**(0.00700)-0.0528**(0.00400)
0.205**(0.0179)

0.311**(0.0330)-0.0133**(0.00365)

0.322**(0.0340)-0.0141**(0.00365)(7)0.305**
0.178**(0.0327)(0.0353)-0.0132** -0.00296(0.00363) (0.00372)

0.300(0.289)1.187**(0.114)
0.093

0.106
35000
5250
1,800,000
Standard errors, clustered by origin CBSA × year, in parentheses** p<0.01, * p<0.05(8)

1.098**(0.114)
0.107

0.108

0.109

Notes: Manufacturing establishments in the CFS and CMF. All shipments are to a domestic
destination CBSA distinct from the origin CBSA. All regressions include SCTG5 × NAICS6 ×destination × year fixed effects and mode × year fixed effects. Unreported controls in all columns
are the interactions of log origin income per capita with the three input variables.

puts purchased from suppliers. To account for “upstream human capital”, I construct acity-industry-level measure of the average wage at potential input suppliers, using pay per
worker in the Longitudinal Business Database and the input shares reported in the BEA’s
Benchmark Input-Output data. Since the factor content embedded in inputs may be sourced
from other cities, I also calculate such an average wage using all plants in cities within 200
miles to account for input market access.
Table E.4 introduces these input-market-access measures as additional regressors andshows that the prior results are largely unchanged. The first column, included to facilitatecomparisons, is identical to the first column of Table 4. The average wage in upstream industries in the city of production, the regressor aimed at controlling for upstream human capitalthat is introduced in the second column, has little explanatory power. The input-marketaccess measure, introduced in the third column, is statistically significant as a regressor but
does not meaningfully alter the estimated income elasticity of outgoing shipment prices. The
fourth column shows that the coefficient on Mot1 , the output-market-access measure, is notsensitive to controlling for this input market access. The fourth through eighth columns
demonstrate that these findings hold when flexibly controlling for plant-level factor usage
and input market access.

27

E.5

Non-large plants and single-plant firms
Table E.5: Shipment prices for non-large and single-plant firms

Dep var: Log unit value
Origin CBSA log per capita income
Origin CBSA log population
Log mileage (ZIP-ZIP-mode-specific)

(1)

(2)

(3)

(4)

0.372**(0.0553)-0.00620(0.00640)
0.0403**(0.00351)

0.285**(0.0536)-0.0131*(0.00605)
0.0413**(0.00347)
0.0991**(0.0100)-0.0526**(0.00576)
0.260**(0.0255)
0.0267(0.0400)-0.0642**(0.0202)0.230*(0.0946)

0.153**(0.0567)-0.00308(0.00616)
0.0463**(0.00337)
0.0982**(0.0101)-0.0519**(0.00572)
0.251**(0.0256)
0.0223(0.0398)-0.0641**(0.0202)0.231*(0.0930)
0.961**(0.161)0.356**(0.0726)-0.0124(0.00793)
0.0147**(0.00534)

Non-production worker share (log)Assets per worker (log)
Pay per worker (log)
Non-production worker share × income per capita
Assets per worker × income per capita
Pay per worker × income per capita
Market access (excludes origin) Mot1

Within R2
0.072
0.081
0.083
0.060
Number estab-year (rounded)
20,00020,00020,00015,000
Number ind-prod-year (rounded)
5000
5000
5000
4500
Observations (rounded)
900,000
900,000
900,000
550,000
Sample description
Non-large Non-large Non-large
SPF
Standard errors, clustered by origin CBSA × year, in parentheses** p<0.01, * p<0.05

(5)

(6)

0.238**
0.0814(0.0706)(0.0803)-0.0178* -0.00548(0.00755) (0.00832)
0.0149** 0.0218**(0.00521) (0.00525)
0.107**
0.106**(0.0161)(0.0163)-0.0488** -0.0482**(0.00742) (0.00730)
0.273**
0.263**(0.0328)(0.0328)-0.144*-0.148*(0.0674)(0.0673)-0.0927** -0.0942**(0.0293)(0.0288)
0.473**
0.471**(0.123)(0.121)
1.143**(0.247)0.069
15,0004500
550,000
SPF

0.071
15,0004500
550,000
SPF

Notes: Manufacturing establishments in the CFS and CMF. All shipments are to a domestic
destination CBSA distinct from the origin CBSA. All regressions include SCTG5 × NAICS6 ×destination × year fixed effects and mode × year fixed effects. Columns 1 through 3 restrict the
sample to plants below the 75th percentile in plant sales and firms below the 75th percentile infirm sales. Columns 4 through 6 restrict the sample to “single-plant firms” (SPF), which areplants that are the only plant in the Census of Manufactures owned by their parent.

This section attempts to address the concern that the regression results might be driven
by shipments from plants whose decisions are poorly described by the model if, for example,
large firms impose uniform pricing across plants irrespective of local conditions. Table E.5
restricts the estimation sample to non-large plants and single-plant firms. The first throughthird columns show that findings for non-large plants owned by non-large firms are similar
to those found in the sample as a whole. The fourth through sixth columns show that
relative contributions of factor usage and market access are also similar in the subsample ofsingle-plant firms.

28

References
Anderson, J. E. (2011): “The Gravity Model,” Annual Review of Economics, 3(1), 133–
160.
Beath, J., and Y. Katsoulacos (1991): The Economic Theory of Product Differentiation. Cambridge University Press.
Bergstrand, J. H., and P. Egger (2011): “Gravity Equations and Economic Frictionsin the World Economy,” in Palgrave Handbook of International Trade, ed. by D. Bernhofen,
R. Falvey, D. Greenaway, and U. Kreickemeier. Palgrave Macmillan.
Bernasconi, C. (2013): “Similarity of income distributions and the extensive and intensive
margin of bilateral trade flows,” Economics Working Papers 115, University of Zurich.
Berry, S. T. (1994): “Estimating Discrete-Choice Models of Product Differentiation,”
RAND Journal of Economics, 25(2), 242–262.
Bombardini, M., G. Gallipoli, and G. Pupato (2012): “Skill Dispersion and Trade
Flows,” American Economic Review, 102(5), 2327–48.
Bureau of Transportation Statistics,
andUS Census Bureau(2004): “2002 Economic Census: 2002 Commodity Flow Survey,” EC02TCFUS, US Department of Transportation and US Department of Commerce,
https://1bts.rita.dot.gov/pdc/user/products/src/products.xml?p=1836.
(2010):“2007 Economic Census:
2007 Commodity Flow Survey,”
EC07TCF-US, US Department of Transportation and US Department of Commerce,
https://1bts.rita.dot.gov/pdc/user/products/src/products.xml?p=3193.
Burenstam Linder, S. (1961): An Essay on Trade and Transformation. John Wiley &Sons, Ltd.
Costinot, A., and J. Vogel (2010): “Matching and Inequality in the World Economy,”
Journal of Political Economy, 118(4), 747–786.
Disdier, A.-C., and K. Head (2008): “The Puzzling Persistence of the Distance Effecton Bilateral Trade,” The Review of Economics and Statistics, 90(1), 37–48.
Fajgelbaum, P., G. M. Grossman, and E. Helpman (2011): “Income Distribution,
Product Quality, and International Trade,” Journal of Political Economy, 119(4), 721 –765.
29

Federal Trade Commission (1981): Statistical Report: Annual Line of Business Report
1975.
Feenstra, R. C., and J. Romalis (2014): “International Prices and Endogenous Quality,” The Quarterly Journal of Economics, 129(2), 477–527.
Grossman, G. M. (2004): “The Distribution of Talent and the Pattern and Consequencesof International Trade,” Journal of Political Economy, 112(1), pp. 209–239.
Grossman, G. M., and G. Maggi (2000): “Diversity and Trade,” American Economic
Review, 90(5), 1255–1275.
Hallak, J. C. (2010): “A Product-Quality View of the Linder Hypothesis,” The Review
of Economics and Statistics, 92(3), 453–466.
Heckman, J. J. (1979): “Sample Selection Bias as a Specification Error,” Econometrica,
47(1), 153–61.
Hillberry, R., and D. Hummels (2008): “Trade responses to geographic frictions: A
decomposition using micro-data,” European Economic Review, 52(3), 527–550.
Khandelwal, A. (2010): “The Long and Short (of) Quality Ladders,” Review of Economic
Studies, 77, 1450–1476.
Lehmann, E. (1955): “Ordered Families of Distributions,” The Annals of Mathematical
Statistics, 26(3), 399–419.
Mayer, T., and S. Zignago (2011): “Notes on CEPII’s distances measures: The GeoDist
database,” Working Papers 2011-25, CEPII.
McFadden, D. (1978): “Modelling the Choice of Residential Location,” in Spatial Interaction Theory and Planning Models, ed. by A. Karlvist, L. Lundqvist, F. Snickars, and
J. Weibull, pp. 75–96. North-Holland.
Pierce, J., and P. Schott (2012): “A Concordance between Ten-Digit U.S. Harmonized
System Codes and SIC/NAICS Product Classes and Industries,” Journal of Economic andSocial Measurement, 37(1-2), 61–96.
Ruggles, S., J. T. Alexander, K. Genadek, R. Goeken, M. B. Schroeder,and M. Sobek (2010): “Integrated Public Use Microdata Series: Version 5.0 [Machinereadable database],” Minneapolis, MN: Minnesota Population Center.

30

Silva, J. M. C. S., and S. Tenreyro (2006): “The Log of Gravity,” The Review of
Economics and Statistics, 88(4), 641–658.
Sutton, J. (2012): Competing in Capabilities: The Globalization Process. Oxford University
Press.

31