Trade and Prices in the Melitz Model∗

Robert C. Johnson†

University of California - Berkeley

October 22, 2007

JOB MARKET PAPER(PRELIMINARY AND INCOMPLETE)

Abstract

What determines who a country trades with? How much they trade? The price atwhich they trade? This paper marshals disaggregated data on export prices and tradeflows to estimate the Melitz model and study these three related features of the data. Inconstrast to previous work, I focus on exploiting information contained in the patternof export prices, in addition trade flows themseleves, to identify the role of produc-tivity versus quality heterogeneity in explaining trade patterns. Empirically, qualityheterogeneity both within and across countries is essential to understanding robustpatterns in the data. To draw out the implications of price differences across countries,I perform a series of accounting exercises using estimates from the structural modeland construct estimates of unobserved product variety and quality across countries.

∗I am grateful to Pierre-Olivier Gourinchas for many productive discussions regarding this work. Ialso thank Chad Jones, Chang-Tai Hsieh, Guillermo Noguera, Jonathan Rose, and participants in the UCBerkeley International Economics Seminar for helpful comments. I also thank Marc Melitz for providingdata on trade costs.

†Department of Economics, University of California-Berkeley, 512 Evans Hall #3800, Berkeley, CA 94720-3880. E-mail: rjohnson@econ.berkeley.edu

1

What determines who a country trades with? How much they trade? The price at

which they trade? Recent trade models emphasizing firm-level selection into exporting and

endogenous non-tradability – typified by Melitz (2003) – make strong predictions regarding

these three related features of the data. With fixed costs of serving foreign markets, the

model predicts that only large, high productivity firms find it profitable to export. This

implies that there is a hierarchy among exporting firms and destination markets, with only

the largest, most capable firms exporting to ‘hard-to-reach’ markets. As a result, both the

number of exporters (exported varieties), the volume of exports, and the average price of

exports vary with the implicit productivity threshold for exporting to each market.

This paper marshals disaggregated data on export prices and trade flows to estimate

the Melitz model and study the the joint behavior of participation in trade, trade volumes,

and trade prices. The empirical approach is motivated by the insight that variation in traded

goods prices contain valuable information that allows us to distinguish between competing

theories and identify fundamental determinants of trade. As Schott (2004) and Hummels

and Klenow (2005) report, export prices are systematically correlated with source country

characteristics, such as income per capita and the capital/skill intensity of production. This

observation suggests that they contain important information about the extent of vertical

specialization and quality heterogeneity within sectors and across countries. To unlock the

information in prices, we need to move beyond correlations toward careful estimation of

structural models of the sort employed in this paper.

To that end, I bring together sector-level data on prices, participation, trade to esti-

mate the three main structural components of the model. Following Helpman, Melitz, and

Rubinstein (2007), I exploit binary, sector-level data on participation in trading relation-

ships to estimate thresholds for selection into exporting. I then proceed to estimate joint

structural equations that relate both export volumes and export prices to variation in the

endogenous export thresholds across markets within each sector. As in Helpman et al., the

2

export equation is an augmented, gravity-style specification derived from the demand struc-

ture that accounts for both variation in the set of firms engaged in trade across partners

and endogenous selection into bilateral trade relationships. The price equation, based on

the aggregation of firm-level optimal pricing decisions, relates aggregate sector-level prices

to home country characteristics and partner specific export thresholds. In specifying these

structural relationships, I augment the standard model to flexibly allow for quality hetero-

geneity both across countries and within sectors. This augmented model nests a number of

different hypotheses about the relative roles of heterogeneity in physical productivity versus

product quality in explaining firm level decisions to export.

Empirically, quality heterogeneity is essential to understanding robust pricing patterns

in the data. Specifically, whereas the standard model with productivity heterogeneity alone

predicts that export prices for a given exporter should be decreasing in the export threshold

across destination markets within a given sector, the data suggest otherwise. Rather, in the

majority of sectors, the largest exporting firms appear to charge higher absolute prices on

average than their competitors. This can be rationalized in the model if quality is hetero-

geneous within sectors and large exporters produce higher quality goods on average. This

general conclusion masks some interesting heterogeneity in the empirical results, however.

Whereas the majority of sectors appear to have upward sloping price schedules with respect

to firm size, a cluster of sectors including apparel and footwear for example, demonstrate

a different price pattern whereby larger exporting firms appear to charge lower prices on

average, consistent with the pure productivity version of the model. Thus, the data is

characterized by meaningful sectoral heterogeneity with regard to the relationship between

productivity, quality, and export prices.

Despite the identifiable role of within-sector quality heterogeneity in the data and

large variation in export thresholds across destination markets, within-country heterogene-

ity plays a relatively small role in understanding average prices across countries. Rather,

3

cross-country variation in prices is primarily due to differences that are common to prices

across to all destinations. That is, to a first approximation, the price schedule with respect to

export thresholds across markets for a rich country is simply a vertical translation of the price

schedule of a poor country. As such, this suggests large variation in average product quality

across countries within sectors.1 To draw out the implications of price differences across coun-

tries, I perform a series of accounting exercises using estimates from the structural model.

Combining estimated components of the structural model with auxiliary assumptions, I use

price data to recover a quality/variety composite from the exporter-specific component of

the endogenous non-tradability augmented gravity equation. Exploiting changes in prices

over time to infer changes in product quality, I further decompose this composite into quality

and variety subcomponents and track their movements through time.

In contrast to the emphasis on prices in present paper, previous empirical work on

models with endogenous non-tradability has mostly been confined to studying trade flows

and export participation decisions in isolation. Recent papers have used firm-level data to

document selection into exporting based on firm productivity, studied the response of trade

flows and aggregate industry productivity following trade liberalization or other market

access shocks, and attempted to match observed firm-level and aggregate export volumes

and dynamics. Bernard, Jensen, Redding, and Schott (2006) provide a survey of a selection

of this rapidly growing volume of work.2 Within this literature, this paper draws most heavily

on the insights and estimation framework of Helpman, Melitz, and Rubinstein (2007). This

paper extends Helpman et al.’s methodology to include information on prices, as well as

shifts emphasis from aggregate trade patterns to disaggregated sectoral flows that more

closely match the microeconomic industrial structure in the model.

Relatively less work has been dedicated to the price implications of this class of mod-

1This accords well with work by Hallak and Schott (2007) and Khandewal (2007) that emphasizes qualityheterogeneity as the prime determinant of cross country price differences.

2Several other papers, including Ruhl (2005) and Alessandria and Choi (2007), have studied the effectsof sunk export costs and hysteresis on trade dynamics.

4

els. Melitz and Ghironi (2005), Bergin and Glick (2006), and Bergin, Glick, and Taylor

(2006) study the behavior of the real exchange rate in a model with both endogenous non-

tradability.3 Atkeson and Burstein (2006) use a model with endogenous non-tradability, im-

perfect competition, and pricing to market to study short run fluctuations of cross-country

consumer and producer prices. Importantly, these contributions have focused primarily on

calibration and simulation to study aggregate empirical predictions. This paper is among

the first to exploit disaggregated unit value price data to assess the empirical plausibility of

the price predictions of these models.

Most closely related to this paper, contemporaneous independent work by Baldwin

and Harrigan (2007) explores how one can use information contained in the incidence of

export zeros and export prices in US bilateral data to distinguish between alternative mod-

els of international trade. Most relevant to my work, the authors report that both US

exports prices and the incidence of zero-export observations are increasing in distance to

foreign markets, and that the incidence of zeros is negatively related to destination income.

Concluding that these facts are inconsistent with standard models in the literature, they

propose a simple extension of the Melitz model similar in spirit to that proposed in this

paper.4 Whereas Baldwin-Harrigan confine themselves to documenting correlations in US

data, I use disaggregate worldwide trade data to explicitly estimate a structural model to

explain the behavior of prices and selection rules across countries and sectors. Estimation

of the structural model permits me to test hypotheses and perform accounting exercises not

possible in their less structured framework. Also related to this paper is work in progress

by Hallak and Sivadasan (2007) that incorporates endogenous quality choices into a Melitz

style model of trade with minimum quality requirements for exporting in order to study

3An important difference between these papers is that Melitz and Ghironi focus on an environment withendogenous variety, whereas the others do not. Corsetti, Martin, and Pesenti (forthcoming) also studyinternational relative prices with endogenous variety, but in a model with traded goods only.

4Specifically, Baldwin and Harrigan focus on using the US data to distinguish between Helpman-Krugman,Eaton-Kortum, and Melitz style trade models. They find that all three models are rejected by the data, butthat a quality-augmented Melitz model similar to that employed in this paper can rationalize the data.

5

microdata on the characteristics of exporting versus non-exporting firms. Importantly, they

present firm-level evidence from Chile, Colombia, and India suggesting that exporters in

these countries produce higher quality goods than non-exporting firms. Their paper thus

provides micro-based evidence that corroborates the type of mechanism emphasized in this

paper for understanding sector-level aggregates in a multi-country world.

The structure of the paper is as follows. Section 1 lays out an augmented version

of the Melitz model with heterogeneous quality and productivity and draws out the main

implications of the model for international prices and trade flows. Section 1 outlines how one

can take the structural model to the data. Section 3 implements the procedure and discuss

results. Section 4 discusses robustness of the empirical results.

1 Theory

In this section I introduce a multi-country model of sector-level trade in a continuum of

differentiated products. The basic setup of the model follows Melitz (2003) and Helpman,

Melitz, and Rubinstein (2007) closely in conceptualizing the firm level decision to export

to foreign markets. The model here deviates from this previous work by allowing for two

dimensions of firm-level heterogeneity – firms are heterogeneous both in the physical produc-

tivity with which they turn inputs into output and the quality of that output. To simplify

presentation of the model and highlight the main results, I describe a one-sector version (e.g.,

aggregate manufacturing) version of the model. In the empirical work, I straightforwardly

extend the model to allow for multiple sectors within aggregate manufacturing to allow for

sector-specific heterogeneity and concord with the manner in which data is collected.

6

1.1 Consumption

To begin, we assume that there is a representative consumer in each country with CES,

Love-of-Variety preferences over consumption differentiated varieties of manufactures given

by:

C =

(∫

ω

[λ(ω)c(ω)](σ−1)/σdω

)σ/(σ−1)

, (1)

where ω indexes the variety, λ(ω) is the quality of variety ω, and σ > 1 is the elasticity

of substitution between different goods. Product quality here enters as a demand shifter in

preferences, such that higher quality goods (higher λ(ω)) yield higher consumption utility

all else equal. As a result, if two varieties with different quality levels have identical prices,

a maximizing consumer allocates a larger share of expenditure to the higher quality good.

Preferences are assumed to be identical across countries (hence, I intentionally omit

country subscripts here for simplicity).5 With a price p(ω), the consumer will allocate

consumption across varieties according to:

c(ω) = [λ(ω)]σ−1

(p(ω)

P

)−σ

C, (2)

where P is the CES aggregate price level of consumption. The consumer inelastically supplies

L units of labor, receives wage w. Aggregate spending PC equals aggregate labor wL.

1.2 Production

Each variety of the differentiated good is produced by an individual monopolistically compet-

itive firm. These firms are heterogeneous with respect to idiosyncratic physical productivity

z(ω) and the quality of the good they produce λ(ω). Shifting notation, we can equivalently

characterize each firm by the duple {z, λc(z)}, where λc(z) is the quality of the product

5Implicitly, these preferences assume that individuals everywhere have identical perceptions of productquality and/or “tastes” for each variety. Allowing for different “tastes” for quality is a natural direction forfuture work.

7

produced by firm with productivity level z in country c. We denote the number of firms in

each country as Nc.

A firm in country c employs labor L(z) to produce output qc(z) according with the

production function q(z) =(

Zczλc(z)b

)

L(z), where Zc is aggregate productivity in country

c. Equivalently, denoting the price of labor as wc, firm z produces with marginal cost

MCc(z) = wcλc(z)b

Zczand the coefficient b indexes the elasticity of marginal cost with respect

to quality.

As in Helpman, Melitz, and Rubinstein (2007), we assume that firms pay a fixed cost

to enter and then draw their individual z from a truncated Pareto distribution.6 The CDF

and PDF of the distribution in each country c is given by:

Gc(z) =z−k − z−k

L

z−kH − z−k

L

(3)

gc(z) =kz−k−1

z−kL − z−k

H

, (4)

with finite support z ∈ [zL, zH ] and shape parameter k that governs the distribution of

productivities. A larger value of k indicates a “thinner” tail to the distribution and less

dispersion overall in productivities across firms. We assume k is common across countries

within an industry.7 For simplicity, we also assume that the upper bound on the distribution

of relative productivities (zH) is equal across countries. Since variation in zH across coun-

tries is observationally equivalent to allowing aggregate productivity to be country specific,

restricting zH in this manner does not result in loss of generality.

6Note that all firms that choose to enter and draw a productivity level actually produce ex post. Thus,the minimum productivity cutoff in the model is exogenous, unlike in Melitz (2003). This may be relaxedwithout changing the main implications of the model for export prices.

7Note that as zH → ∞, then the distribution approaches G(z) = 1 −(

zmin

z

)k. This is simply a special

case of this formulation, but one that has counterfactual implications for export participation. Namely,zH → ∞ implies that we should observe every country trading with every other country – a result clearlyat odds with the data.

8

1.3 Selection into Exporting and Export Prices

In addition to the fixed entry cost and variable production cost, firms pay additional costs

to export their output. In particular, they face both a fixed cost to enter each specific export

market and a variable iceberg trade cost to serve that market. Specifically, for a firm from

country c to export to country d it must pay a fixed cost equal to fxcd and must ship τcd

units of the good for one unit to arrive for consumption in d.8 If the factory gate price

for produced output is pc(z) then the price of one unit of consumption of that good in the

foreign country is effectively pcd(z) = τcdpc(z). Firm revenue from exporting is then given

by:

Rxcd(z) = pc(z)qcd(z) =

(pc(z)τcd

Pd

)1−σ

Ed (5)

where Pd and Ed are the sectoral price index and sectoral expenditure in country d, Ed =

PdCd, and pc(z) = pc(z)/λc(z) is a quality adjusted price. Naturally, with σ > 1, firms that

have relatively low quality-adjusted prices enjoy high revenues.

Firms select into exporting to market d if they earn positive profits from exporting.

That is, if

Rxcd(z) −

(wcλc(z)b

Zcz

)

qcd(z) ≥ fxcd. (6)

For each market, this condition implies that there exists a marginal firm with threshold

productivity zxcd such that 1σRxcd(zxcd) = fxcd. This condition holds for a firm with quality

adjusted price given by:

pc(zxcd) =

(τ 1−σcd P σ−1

d Ed

σfxcd

)1/(σ−1)

. (7)

Note that revenue and selection into exporting depend on a firm having a low quality adjusted

price. Only low quality-adjusted price firms are able sell enough to recoup the fixed costs

fxcd of entering the foreign market. Conditional on fixed costs, foreign markets that are

8One standard assumption here worth noting is that both the fixed and variable cost of exporting arecountry-pair specific, and independent of individual firm characteristics.

9

either larger (higher Ed), less competitive (higher Pd), or have lower variable trade costs

(τcd) generate higher revenue for any given firm that enters then, and thus these features of

the destination market allow firms with higher quality adjusted prices to recoup the fixed

costs of entry. The existence of a cutoff quality-adjusted price for exporting similarly implies

that there is a threshold productivity for exporting to market d that satisfies:

zxcd =σ

σ − 1

wc

Zc[λc(zxcd)]

b−1

[σfxcd

τ 1−θcd P θ−1

d Ed

]1/(σ−1)

. (8)

In the standard formulation of the model in the literature, λc(z) = 1 ∀ c, z and therefore

the cutoff is explicitly a function of aggregate productivity-adjusted wages, trade costs of

exporting, and destination specific market conditions only. In contrast, the more general

formulation here recognizes the role of product quality via the term [λc(zxcd)]b−1, where

the exponent (b − 1) reflects the net effect of marginal cost effects and preference effects

on quality-adjusted prices. Whether quality relaxes or tightens the productivity threshold

depends on whether b > 1 or b < 1. For now, we leave this parameter unrestricted.

In the data, we do not observe either quality adjusted prices or the prices of individual

firms. Rather we observe aggregate bilateral unit values (total exports/total quantity). To

move toward predictions for observed prices, we need to (1) specify how λc(zxcd) varies

with zxcd, and (2) aggregate firm level prices. A natural way to parameterize λc(z) is to

assume that λc(z) = λcza. In this formulation, λ(z) may be increasing in, decreasing in, or

independent of z. Moreover, quality is separable into a country-specific component and a

firm specific component. The important restriction here is that λ(z) is weakly monotone in z.

While this restriction is likely not literally true, this characterization is useful to analytically

characterize the main results that emerge from the model with heterogeneous quality.9 With

9This specification of the quality-productivity schedule can be thought of as a reduced form way of con-ceptualizing a deeper process in which firms draw both productivity and quality randomly from a joint

distribution (with arbitrary correlation between quality and productivity) such that the ratio λc(z)z

– andhence quality-adjusted prices – follow a Pareto distribution so as to match evidence on the firm size distri-

10

this specification, we can write absolute and quality adjusted prices for an individual firm

as:

pc(z) =

(σ

σ − 1

wc

Zc

)(λb

c

z1−ab

)

(9)

pc(z) =

(σ

σ − 1

wc

Zc

)(λb−1

c

z1+a−ab

)

. (10)

The key point is that the unit price of firm z’s good is falling in z if ab < 1 and increasing in

z if the opposite holds. The quality adjusted price is falling in productivity if 1+a−ab > 0.

This formulation collapses to the standard formulation of the model, if λc = 1, a = 0,

and b = 0. In this special case, quality adjusted prices are identical to unit prices. More

generally, there is a wedge between these prices. At this point, I leave the parameters a and

b unrestricted. However, it is useful to point out that to the extent that firms have some

control over the quality level of their products that it is easy to write down models in which

high productivity firms will choose to produce high quality products. Thus, theory suggests

that a ≥ 0 is the most relevant case to consider. The intuitive positive link between quality

and marginal cost implies that b ≥ 0 is also a weak and plausible restriction.10

With this formulation, we can explicitly solve for the threshold productivity required

to export to each market:

zxcd =

[

σ

σ − 1

wcλb−1c

Zc

(σfxcd

τ 1−θcd P θ−1

d Ed

)1/(σ−1)]1/(1−ab+a))

. (11)

Up to this point, I have placed no explicit restriction on the sign of 1 − ab + a. Thus,

the productivity threshold could in principal be increasing or decreasing in fixed costs of

bution. I choose not to take this route because this more complicated model does not provide additionaluseful empirical implications.

10Whether b < 1 holds is a stronger assumption, but again one that is reasonable in models in which firmschoose their quality level. Since the main text does not work explicitly with such a model, I do not imposethat assumption here.

11

accessing foreign markets (for example). However, the data (as will be explained later)

imply that generically 1 − ab + a > 0, and hence the relevant case is one in which the

productivity threshold is increasing in fixed trade costs, decreasing in variable trade costs,

decreasing in foreign market size/competitiveness, increasing in the productivity adjusted

wage, and ambiguous in country-specific quality.

Now we turn to aggregation and construct aggregate unit values that correspond to

what we observe in the data.11 This requires constructing aggregate bilateral export values

and quantities in the model. Aggregate exports from country c to country d are given by:

EXcd =

∫ zHc

zxcd

Rxcd(z)NcdG(z)

=

∫ zHc

zxcd

(pc(z)τcd

Pd

)1−σ

EdNcdG(z)

= NcVcd

(σ

σ − 1

wcλb−1c

Zc

)1−σ

τ 1−σcd P σ−1

d Ed,

(12)

where Vcd =∫ zHc

zxcdz(1−ab+a)(σ−1)dG(z) is a country-pair specific term that quantifies the influ-

ence of the endogenous cutoff on export volumes. Similarly we can characterize the quantity

of goods shipped from c to d as:

Qcd =

∫ zHc

zxcd

qxcd(z)NcdG(z)

=

∫ zHc

zxcd

(τcdcd(z))NcdG(z)

= NcVcd

(σ

σ − 1

wcλb−1c

Zc

)−σ

τ 1−σcd P σ−1

d Ed

(13)

where Vcd =∫ zHc

zxcdzσ(1−ab+a)−adG(z) quantifies the effect of endogenous cutoffs on the quanity

of exports.

The unit value export price for trade between c and d is then defined as pcd = EXcd

Qcd. To

11These aggregate unit values are proportional to the prices of the “representative exporting firm” em-phasized in the work of Melitz (2003).

12

solve for this price, we evaluate Vcd and Vcd using the Pareto distribution (3). First solving

for the functions of the cutoff terms in the export values and quantity equations:

Vcd =k

δ1

(z−δ1

xcd − z−δ1H

z−kL − z−k

H

)

(14)

Vcd =k

δ2

(z−δ2

xcd − z−δ2H

z−kL − z−k

H

)

, (15)

where δ1 = k − (σ − 1)(1 − ab + a) and δ2 = k − σ(1 − ab + a) + a are both assumed to be

greater than zero.12 Using these, we can then solve for the unit value price:

pxcd =

[σ

σ − 1

wcλbc

Zc

]Vcd

Vcd

= pc(zH)

(δ2

δ1

)

(zxcd

zHc

)−δ1

− 1(

zxcd

zHc

)−δ2

− 1

(16)

The interpretation of this expression is that the average export price is proportional to the

absolute price of the most productive firm. Whether it is higher or lower than this price

depends on the values of δ1 versus δ2. Notice that δ1 − δ2 = 1− ab, and recall that firm level

prices are decreasing in the productivity if and only if ab < 1. Naturally, this case implies

that every firm charges prices that are equal to or higher than the most productive firm. As

a result, the average export price to any given destination is higher than the price of the

most productive firm. Hence, in this case

(zxcdzH

)−δ1

−1(

zxcdzH

)−δ2

−1> 1. In the opposite case, price are

increasing in productivity and hence the average price is lower than the price of the most

productive firm.

The fact that the correlation between the aggregate export price and the export cutoff

depends only on whether ab > 1 or ab < 1 suggests that there are a number of different

12These conditions require that the productivity distribution is not “too disperse” relative to consumer’swillingness to substitute across goods. More technically, these conditions are necessary for an equilibriumto exist.

13

scenarios in which we could observe that export prices are decreasing in the export threshold.

For example, if marginal cost does not depend on quality at all (b=0), then prices are

automatically declining in the cutoff. Further, if quality is uniform across firms with different

productivity levels (a=0), then prices will also be declining in the cutoff. Moreover, even if

both a > 0 and b > 0, we can still observe prices decreasing in the threshold if either a or b is

small enough to ensure that ab < 1. That is, if prices are only weakly increasing in quality

and/or quality is only weakly positively related to productivity then prices will be declining

in the cutoffs. Thus, there is a relatively high bar to cross to observe prices that increase in

the cutoff to different destination markets.

1.4 Additional Implications: Trade Volumes and Export Partici-

pation

As emphasized by Helpman et al., this framework also yields novel predictions for export

participation and export volumes. First, the model predicts that the volume of bilateral trade

depends directly on the export threshold. Thus, export thresholds are of interest not only in

studying prices as in the previous section but also in understanding trade volumes directly.

Second, the model makes very specific predictions about when two countries should trade

with one another. That is, unlike traditional variety-based trade models, this framework is

able to make sense of the fact the vast majority of country pairs in fact do not trade with

one another either in any given sector, or even in the aggregate. Using this aspect of the

model, Helpman et al. outline a method via which we can use binary data on the existence of

bilateral trade to infer information about export cutoffs. This section briefly exposits these

features of the model.

The role of variation in export thresholds in driving export behavior is obvious upon

examination of the export equation (12). Export cutoffs play a rather complex role in driving

exports, since they determine both the number and identity of exporting firms. To clarify

14

this point, it is helpful to rewrite the bilateral export equation using several useful facts. We

start by rewriting (12) and manipulating the definition of Vcd:

EXcd = Nc [1 − G(zxcd)]︸ ︷︷ ︸

Nxcd

∫ zH

zxcd

(pc(z)τcd

Pd

)1−σ

Edg(z|z > zxcd)dz

︸ ︷︷ ︸

exports per firm

(17)

This reformulation highlights that there are two margins on which the endogenous cutoff

effects total exports. First, the number of exporting firms – denoted Nxcd – is decreasing in

the productivity threshold. Thus, holding exports per firm constant, increasing the export

threshold depresses aggregate exports. Aggregate exports do not fall one or one with the

number of firms exporting, however, because as the threshold rises the smallest exporters

are the first to fall out of the foreign market. Thus, exports per remaining firm actually

rises. To see this clearly, we evaluate the integral representation of exports per firm to show

that the exports of the average firm are simply a scaled version of the exports of the most

productive firm:

EXcd

Nxcd=

k

δ1

(zxcd

zHc

)−δ1

− 1(

zxcd

zHc

)−k

− 1

(pc(zH))1−στ 1−σ

cd P σ−1d Ed, (18)

with pcd(zH) defined as the quality-adjusted price of the most productive firm. It is important

to note here that there are multiple sources of variation in average exports per firm across

countries. First, changes in average exports per firm across different markets arises due to

changes in the identity of which firms are exporting to which markets. As it becomes more

difficult to penetrate foreign markets (zxcd rises), the weakest firms are weeded out and the

remaining firms are naturally larger, more productive, and sell larger volumes one average.

Second, holding the export threshold constant, exports per firm will be higher when there

are lower trade costs or the destination market is larger (higher Ed) or less competitive (Pd

15

is higher). Decomposing these sources of variation is a worthy goal for empirical work.

In this discussion, it is important not to lose sight of the fact that overall aggregate

exports across markets are always decreasing in the threshold. Further manipulating the

equation for exports, canceling terms where appropriate, leads to a simple expression that

quantifies the net effect of variation in cutoffs on aggregate export volumes:

EXcd = Nc

[(pc(zH))1−στ 1−σ

cd P σ−1d Ed

]

[

k

δ1

((zxcd

zH

)−δ1

− 1

)]

. (19)

And exports are increasing in the cutoffs because δ1 > 0. As emphasized by Helpman et

al. and detailed in the following section section, this specification leads naturally to an

augmented gravity equation that allows us to estimate the net effect of endogenous cutoffs

on exports.

Obviously, export productivity thresholds are generally not directly observable. Thus,

estimating the relationship between prices and exports requires a procedure to infer these

cutoffs from available data. Helpman et al. describe one such procedure exploiting data

on bilateral export participation that arises naturally out of the model described above.

To see the implications of the model for bilateral export participation, note that the fact

that firm productivity is drawn from a truncated Pareto distribution means that there is a

lower limit to the productivity adjusted price of the highest productivity firm. Further, note

that we observe trade between two countries if and only if the most productive firm in any

given sector finds it profitable to export to that market. That is, if Rxcd(zH)− wcλbc

Zcz1−abH

≥ fxcd.

Equivalently, if we define αcd to be the ratio of the profits of the most productive firm relative

to the fixed costs of exporting, then we observe exports if αcd ≥ 1 and zero otherwise. Thus,

define a binary variable Tcd = 1(αcd > 1) that takes the value one if c exports to d and zero

otherwise. This fact suggests that we can use the model along with data on participation to

infer the ratio of profits to fixed costs of the most productive firm in each sector. This turns

16

out to be incredibly useful.

The key insight is that the relative productivity cutoff zxcd

zHis a monotone function of

the ratio of the profits of the most productive firm relative to the fixed costs of exporting.

To see this, we follow Helpman et al. and define this ratio as:

αcd =1σ

(pc(zH))1−σ τ 1−σcd P σ−1

d Ed

fxcd(20)

Combined with the fact that the same ratio of profits to fixed costs for the marginal exporter

equals 1, it is straightforward to show that:

zxcd

zH= α

−1/[(σ−1)(1−ab+a)]cd . (21)

Thus, the relative productivity cutoff is falling in the profitability of the most productive

firm. Moreover, using binary data on participation to predict αcd offers the opportunity to

identify the relative export cutoffs that are relevant for understanding the behavior of prices

and exports.

2 Empirical Procedure

Estimation of the model proceeds by exploiting the structure that the model imposes on the

data. We start by translating the framework outlined above into a set of conditional expec-

tations for participation, export volumes, and unit value prices that characterize behavior

in the model. We then discuss details regarding how we implement this general framework,

and discuss how model estimates can be manipulated to gain insight into the deep structure

of trade.

17

2.1 Export Participation

As discussed above, we observe a binary variable Tcd that takes the value one when the

productive firm in country c finds it profitable to serve market d, and hence we observe

exports from c to d. Drawing on the notation of the previous section, we observe:

Tcd = 1(αcd > 1) = 1(log(αcd) > 0). (22)

Then taking logs of both sides of the expression for αcd yields:

log(αcd) = log(1/σ) + (1 − σ) log(pc(zH)) + (1 − σ)τcd + log(P σ−1d Ed) − log(fxcd) (23)

Following Helpman et al., we parameterize the bilateral fixed and variable trade costs:13

(1 − σ) log (τcd) = ρDcd + ucd (24)

− log(fxcd) = ξc + ξd + κϑcd + ǫcd, (25)

where Dcd and ϑcd are multidimensional, possibly overlapping sets of observable proxies for

bilateral fixed and variable trade costs (e.g., distance, common language, etc.), ucd reflects

random unobserved variation in variable trade costs, ǫcd reflects random unobserved variation

in fixed trade costs (possibly correlated with ucd), and ξc, ξd are exporter and importer specific

fixed effects. Subbing this parameterization back into the expression for log(αcd) we arrive

at a reduced form:

log(αcd) = β0 + βc + βd + ρDcd + κϑcd + ηcd, (26)

13Of course, the specification of variable costs of trade in this manner is standard in the large literatureestimating gravity-style trade models.

18

with ηcd = ucd + ǫcd, β0 = log(1/σ), βc = (1−σ) log(pc(zH))+ ξc, and βd = log(P σ−1d Ed)+ ξd.

Then substituting these expressions back, we can rewrite the expression for Tcd as:

Tcd = 1(log(αcd) > 0)

= 1(ηcd > −[β0 + βc + βd + ρDcd + κϑcd]).

(27)

With this in hand, we know that:

E[Tcd|βc, βd, Dcd, ϑcd] = Pr{ηcd > −[β0 + βc + βd + ρDcd + κϑcd]} (28)

Making an assumption regarding the distribution of the error then allows us to estimate the

(normalized) coefficients.14 For example, assuming that the underlying errors uicd and ǫicd

are distributed normally with mean zero, then ηicd is distributed N(0, σ2η) with σ2

η = σ2u +σ2

ǫ .

Then we can write:

E[Tcd|βc, βd, Dcd, ϑcd] = Φ(β∗

0 + β∗

c + β∗

d + ρ∗Dcd + κ∗ϑcd)

= Φ(Xcdβ∗) ≡ ρcd,

(29)

where x∗ indicates that that x has been divided by σ2η so that η∗

cd has unit variance, and

Xcdβ∗ ≡ β∗

0 +β∗

c +β∗

d +ρ∗Dcd+κ∗ϑcd for notational convenience. This conditional expectation

then provides an opportunity to construct one set of moment conditions using the binary

data to estimate the normalized parameters.

14Though I proceed by assuming normally distributed errors, one could easily substitute other standarddistributions (with the leading alternative obviously being the logistic distribution). I have performed theestimation using logistic distribution, and find no appreciable differences.

19

2.2 Export Volumes

As discussed above, the model implies a “gravity”-style equation for bilateral export volumes.

To illustrate this, we return to Equation (19) and take logs of both sides:

log(EXcd) = log(Nc) + (1 − σ) log(pc(zH)) + (1 − σ)τcd + log(P σ−1d Ed)

+ log(k/δ1) + log

((zxcd

zH

)−δ1

− 1

)

. (30)

Then using the same parameterization of fixed costs and redefining terms:

EXcd = φ0 + φc + φd + ρDcd + log

((zxcd

zH

)−δ1

− 1

)

+ ucd, (31)

where φ0 = log(k/δ1),φc = log(Nc)+(1−σ) log(pc(zH)), and φd = log(P σ−1d Ed). Constructing

moments using this equation then obviously involves evaluating the expecta

To evaluate E[ucd|·, Tcd = 1] we assume that E[ucd|η∗

cd] = γη∗

cd. This implies that we

can employ the standard Heckman-style correction as follows:

E[ucd|·, Tcd = 1] = E[ucd|·, η∗

cd > −Xcdβ∗]

= γφ(Xcdβ

∗)

Φ(Xcdβ∗),

(32)

using the notation defined in the previous section.

To evaluate the conditional expectation of the cutoff term, we need to exploit the

specification of αcd to write the cutoff in terms of observables. Recalling the previous section,

we can write:

zxcd

zH= α

−1/[(σ−1)(1−ab+a)]cd

= [exp ((Xcdβ∗ + η∗

cd))]−ση/[(σ−1)(1−ab+a)]

(33)

20

Then we can insert this in the cutoff term, to get:

log

((zxcd

zH

)−δ1

− 1

)

= log (exp(θ1(Xcdβ∗ + η∗

cd))) , (34)

where we define the new parameter θ1 = σηδ1(σ−1)(1−ab+a)

. Using this substitution, we can then

exploit the fact that we have assumed that η is normally distributed and construct the

conditional expectation of the cutoff term as follows:

E

[

log

((zxcd

zH

)−δ1

− 1

)∣∣∣·, Xcd, Tcd = 1

]

=

∫∞

−Xcdβ∗

log (exp(θ1(Xcdβ∗ + η∗

cd)) − 1) dΦT (η∗

cd)

≡ F (Xcdβ∗, θ1),

(35)

where the expectation is evaluated over the truncated distribution for η∗

cd: ΦT (η∗

cd) =

φ(η∗

cd)

1−Φ(−Xcdβ∗).

With these inputs, we can generate moments off of the conditional expectation:

E[EXcd|·, Tcd = 1] = φ0 + φc + φd + ρDcd + F (Xcdβ∗) + γ

φ(Xcdβ∗)

Φ(Xcdβ∗). (36)

To be clear, the conditioning set here includes both the observables {φ0, φc, φd, Dcd} in the

export equation as well as Xcd from the specification of the participation equation above.

2.3 Export Prices

Estimation of the export price equation proceeds straightforwardly using the techniques

developed in previous sections. To translate the deterministic specification of prices into

a stochastic specification for estimation, we assume (realistically) that prices are measured

21

with error. In this case, we can take logs of the export price equation to obtain:

log(pxcd) = log(δ2/δ1) + log(pc(zH)) + log

(zxcd

zHc

)−δ1

− 1(

zxcd

zHc

)−δ2

− 1

+ νcd, (37)

where we have assumed that νcd is mean-zero measurement error. Then, we proceed to

substitute for the cutoffs as in the previous section and construct E[log(pxcd)|·, Tcd = 1]. In

doing so, we deal with the cutoff term as in the previous section by substituting for the cutoffs

and then evaluating the conditional expectation using the truncated normal distribution

ΦT (η∗

cd). We define this conditional expectation H(Xcdβ∗; θ1, θ2), with θ1 is defined as in the

previous section and θ2 = σηδ2(σ−1)(1−ab+a)

.

Further, we note that log(pc(zH)) is a constant for each country, and hence can be

absorbed by a exporter fixed effect. Then, we can write the conditional expectation of the

price equation as:

E[log(pxcd)|·, Tcd = 1] = µ0 + µc + H(Xcdβ∗; θ1, θ2), (38)

where we have defined coefficients µ0 = log(δ2/δ1) and µc = log(pc(zH)).

2.4 Estimation Details

We now turn to providing details on how we implement the estimation framework outlined

above. In principal, it is possible to estimate all three structural equations simultaneously.

In practice, this is computationally burdensome due to the high dimensionality of the pa-

rameter space. Therefore, I follow a two-step GMM procedure.15 In the first step, we use

binary participation data to estimate the export participation equation (29) within each

15In unreported results, I have compared the results from using the two-step procedure implemented inthe main text to alternative estimates for selected sectors obtained by simultaneously estimating the threeequations. The results are indistinguishable. This implies that the pattern of export participation containsall available information regarding the values of the productivity thresholds.

22

sector. With these estimates in hand, we generate values for the probit index that are then

used to construct the functions F (Xcdβ∗; θ1), G(Xcdβ

∗; θ1, θ2), and the inverse mills ratio in

expressions (36) and (38). For convenience, we rewrite the conditional expectations here as

estimating equations:

log(pxcd) = µ0 + µc + H(Xcdβ∗; θ1, θ2) + e1cd (39)

log(EXcd) = φ0 + φc + φd + ρDcd + F (Xcdβ∗) + γ

φ(Xcdβ∗)

Φ(Xcdβ∗)+ e2cd, (40)

where we have substituted the first stage estimator of β∗ for the true value and have defined:

e1cd ≡ log(pxcd) −E[log(pxcd)|·, Tcd = 1]

e2cd ≡ log(EXcd) − E[EXcd|·, Tcd = 1].

We estimate these two equations jointly using sectoral trade and prices by stacking moment

conditions and imposing the cross equation restriction that the value of θ1 is identical across

the two equations. We focus on a small set of straightforward moments to estimate these

equations, all built on the orthogonality between the errors and the regressors.16 As im-

plemented, the problem is exactly identified and hence moments are equally weighted.17 In

light of the fact that we use a two-stage estimation procedure, we construct standard error

for the second stage estimates using the large sample two-step GMM procedure laid out in

Newey and McFadden (1994).18

16The only modestly non-standard conditions worth mentioning are: E[e1cd(Xcdβ∗)] = 0 and

E[e2cd(Xcdβ∗)] = 0. These are non-standard only in the sense that they are constructed such that the

composite Xcdβ∗ is orthogonal to the error rather than the individual elements of Xcd. One could also use

these individual elements, though in practice the composite contains much more useful identifying variation.17Work in progress explores the use of additional moments and weighting schemes. To reduce the compu-

tational burden in the present scheme, I collapse the set of moments by “partialing out” the linear portionof the two equations, solve for the parameters {θ1, θ2} using the collapsed moments, and then return to thefull set of moments to compute the fixed effects.

18The two-step procedure stacks the moments from the first and second stages into a single joint vector ofmoments and computes the asymptotic variance of this full set of moments. Because the two-step procedureyields consistent estimates, this variance may be evaluated using the two-step estimates. Work in progress

23

In specifying the estimating equations above, we have assumed that the participation

equation error is normally distributed. To ensure that identification in the second stage

augmented-gravity equation does not rest on this assumption alone, we need to specify an

exclusion restriction. That is, we need to identify a variable that predicts selection into a

trading relationship, but does not directly influence the volume of exports. On theoretical

grounds, measures of fixed costs of exporting satisfy such a restriction. Helpman et al.

employ proxies for such costs using data on general firm entry costs and common religion as

exclusion restrictions when working with aggregate data.19 Neither of meets the necessary

criteria in the disaggregated sample. Instead, I propose using lagged participation in bilateral

trade. Though there is much churning in trading relationships at the disaggregate level,

participation in past trade is a strong predictor of whether two countries trade today. There

are a number of a priori grounds on which lagged participation seems well suited to be a

proxy for fixed costs of trading. To the extent that some of the fixed export cost is sunk at the

firm level, payment of this cost in the past makes it more likely firms will find it profitable in

the present to export to a given country. Abstracting beyond the level of the individual firm,

initiating trade may entail establishment of sector-wide contacts and distribution networks

whose cost does not vary with the actual volume of goods traded. These types of links are

further likely to persist through time. In this spirit, I construct measures of how frequently

two countries have traded in the past to use in estimating the participation equation. In

addition, the reasoning above also suggests that some observable variables, such as common

language or colonial history, might also satisfy the necessary exclusion restriction. As a

robustness check, we can re-estimate using these variables in place of lagged participation.

considers bootstrapped standard errors as a robustness check on this procedure.19Manova (2006) uses the a dummy variable coding whether a country is an island as an excluded variable.

24

2.5 Combining Participation, Exports, and Prices

Before moving on to the actual estimation, I pause to discuss how the estimated parameters

can be interpreted and combined draw inferences about the underlying structure of export

selection and trade patterns.

First, we can use model estimates to study the role of endogenous non-tradability in

explaining variation in prices by looking at estimated values of {θ1, θ2}. Recalling previous

results, the price schedule slopes downward with respect to the productivity cutoff only if

ab < 1. Under restrictions imposed by the model, we can identify whether this is in fact

true from the estimated parameters. Start by taking the difference between the coefficients:

θ2 − θ1 =ση

(σ − 1)(1 − ab + a)(δ2 − δ1)

=ση

(σ − 1)(1 − ab + a)(ab − 1) .

(41)

The sign of this difference is a direct indication as to whether the price schedule is increasing

or decreasing in the productivity cutoff. If θ2 − θ1 > 0, then the schedule is increasing in

the cutoff. This difference does not directly reveal whether ab > 1 because (1 − ab + a)

is unrestricted. To uncover this feature of the data, we normalize this difference by θ1 to

yield:20

θ2 − θ1

θ1=

1

δ1(ab − 1) . (42)

If this ratio is negative, then ab > 1 and the price schedule is downward sloping with respect

to firm productivity. Alternatively, if this ratio is positive, then ab < 1 and the price schedule

is downward sloping.

We can obtain additional results regarding the relative importance of cross-country

quality and variety versus price differences in explaining trade patterns by exploiting addi-

20Because we also assume δ2 > 0, we could alternatively normalize by θ2 and reach an identical conclusionto that in the main text.

25

tional elements of the model structure. First, note that by the definition of the parameters,

exp(µ0 + µc) = δ2δ1

pc(zH). As a result, if we define Mc = exp(µ0 + µc), then Mc

Md= pc(zH)

pd(zH)

allows us to recover the relative prices of the most productive exporting firm in each country.

In turn, this ratio allows us to learn about relative marginal costs across countries within a

sector. Similarly, we note that by definition:

exp(φ0 + φc) =kNc

δ1(pc(zH))1−σ

=k

δ1

[Nc(λc(zH))σ−1

](pc(zH))1−σ

(43)

Then, define Φc = exp(φ0 + φc) and it follows that:

Φc

Φd=

(Nc(λc(zH))σ−1

Nd(λd(zH))σ−1

)(Mc

Md

)1−σ

. (44)

Thus, with an assumption about the value of σ we can back out(

Nc(λc(zH))σ−1

Nd(λd(zH))σ−1

)

, where

Nc(λc(zH))σ−1 is a composite index of product variety and quality for each country.

Extending the analysis to the time dimension, we can separately recover measures of

changes in product quality versus product variety under some additional assumptions. [TO

BE COMPLETED]

3 Estimation Results

This section implements the estimation framework outlined in previous sections. We begin

with a discussion of the data, and then proceed to the results.

3.1 Data

The main body of data on disaggregated world trade has been compiled by Robert Feenstra

and Robert Lipsey and is available from the NBER and the Center for International Data at

26

UC Davis. Because data for the United States in the Feenstra-Lipsey data is somewhat less

reliable and comprehensive than US-sourced data, I also use United States trade value and

quantity data compiled Robert Feenstra, John Romalis, and Peter Schott. While this data

is available at the 4-digit level of disaggregation and beyond, I aggregate reported exports

and quantities into 3-digit sectors.21 Furthermore, I discard non-manufacturing trade on

the grounds that the Melitz monopolistic competition model ought to be best suited to

understanding trade in differentiated manufactures. After dropping several sectors due to

missing data, I am left with data on 141 3-digit sectors spanning SITC categories 5-8.22

From this data on values and quantities, I construct unit values for each exporter by

sector and destination market. A few comments are in order regarding the procedure I

use for dealing with several problems that arise in working with the quantity data. First,

there are several complications that arise due to differences in the way quantity units are

recorded across countries and sectors. Due to the manner in which the Feenstra-Lipsey data

are assembled, units are not always homogeneous within sectors or for individual countries.

When there are multiple units within a sector, I discard prices associated with the minority

unit. In practice, this results in a small, quasi-random loss of data.23 In addition, sometimes

quantities and units are simply missing either for part or all of a country’s trade with a

specific parter. When quantites are missing for a majority of trade for a given exporter to a

specific destination, I treat that category as if I observe no quantity and hence no price. In

addition, a further complication arises because US-sourced trade data is reported in entirely

different quantity units than the Feenstra-Lipsey data. This has two implications. First,

21Trade is quite sparse at the disaggregated level for most countries, and therefore some aggregation ishelpful to thicken the density of the network for estimation purposes.

22For reference, the 1-digit category headings are as follows: 5-“Chemicals and related products”;6-“Manufactured goods, classified chiefly by material”; 7-“Machinery and transport equipment”; 8-“Miscellaneous manufactured articles”.

23In the vast majority of sectors, this results in a loss of somewhere between 1-5% of price observations.Some sectors lose no data, and the maximum loss is around 25% in the Feenstra-Lipsey data. In the USdata, the problem is somewhat larger because the US simply has a larger number units categories. Usuallythe problem manifests itself as observing two different prices for exports to each destination in a sector. Inthis event, I drop the minority set of units.

27

the US fixed effect in the price equation picks up both variation in average prices in the

US relative to the rest of the world as well as differences in units. As a result, all the

analysis below that uses the estimated fixed effects omits the US. Second, I include a US

importer fixed effect as well in the price regression to purge the effects of units differences

from prices associated with exports to the US. 24 Finally, the price data contains a small but

influential number of outlying prices. These appear to be due almost entirely to measurement

error in the data, and therefore I purge these observations from the data.25 In practice, I

have experiemented with alternative procedures dealing with these problems and found the

reported results to be robust to the exact procedure used.

In addition to this trade data, I use data on standard proxies for bilateral trade costs

as in Helpman et al.26 The data includes physical impediments to trade including measures

of distance between capital cities, and dummies for whether two countries share a border,

whether one partner is landlocked, and whether one partner is an island. Further, the data

includes measures of cultural and historical ties that may facilitate or impede trade, in-

cluding measure of the commonality of religion affiliation, and dummies for past colonial

relationship, common legal origin, and common language. As mentioned above, I also con-

struct an additional variable based on previously trading experience to use in estimating

the participation equation. In the year 2000 base estimation, I construct a variable for each

pair equal to the fraction of years between 1985-1995 in which the two countries engaged in

trade.27 In analyzing prices and cutoffs, we also employ data on real GDP per capita and

24Whereas quantities/prices are available for nearly all US trade, quantity data is somewhat patchier inthe Feenstra-Lipsey data. Missing data appears to be due principally to quasi-random reporting gaps anddoes not follow obvious systematic patterns. Nearly all countries in the sample have prices for upwards of80-90% of the value of exports.

25Specifically, I purge the data of observations that differ from the median price in a sector by more thana factor of five. Purging observations that differ by more than a factor of ten yields similar results.

26In addition to the variables used in the main text, I have experimented with policy-type variables,including free trade areas, WTO membership, and currency unions and obtained roughly identical resultsto those reported.

27In current work, I am studying the robustness of the results to alternative specifications of this laggedparticipation variable.

28

population across countries from the Penn World Tables (Version 6.2).

The final estimation sample includes the 125 countries listed in Table 1 for which I

have data on trade, prices, and trade costs. The exact estimation sample obviously varies

from sector to sector depending on whether countries engage in trade in a given sector. The

main body of results are obtained from the cross-section for the year 2000. In extensions

tracking estimates through time, I use data from three additional years – 1985, 1990, 1995.

3.2 Estimating the Participation Equation

Turning to discuss results of this procedure, Table 2 includes select results from the first

stage probit regression for eight representative sectors.28 We naturally omit from the table

estimates for typically 200+ coefficients on the exporter and importer fixed effects. Suffice

it to say that the vast majority of these coefficients are significantly different from zero

and that they account for large portion of the variation in the data. As for the remaining

proxies for trade costs, the probability of trade between two countries is strongly and robustly

decreasing in the distance between them. This accords with the theory given that distance is

a robust determinant of bilateral variable costs, and that higher trade costs lower demand for

exports in the foreign market all else equal. The probability of trade also tends to increase

if the countries share a common border, common language, or common legal system. These

coefficients are sensible as well when interpreted via the theory. A common border is plausibly

associated with lower variable and/or fixed costs. While the link between common language

and common legal system on variable trade costs is less direct, they both are plausibly related

to the fixed costs of establishing a trading relationship. The effects of being an island, being

landlocked, or of sharing common colonial history and religion are more mixed. The fact

that these coefficients vary from sector to sector is not surprising to the extent that the

28These sectors were chosen according to a mechanical rule and are representative of the overall estimationresults.

29

estimation sample varies substantially across sectors. The probability of engaging in trade

today is also strong related to the average propensity of the two countries to trade in the

past.29

To check the plausibility of the estimated cutoffs, we can explore whether the predicted

indices adhere to the theoretical prediction that foreign market size will be a crucial determi-

nant of the cutoff for exporting to a given market. This is in general true in the data as the

predicted probability of trade is increasing in the aggregate GDP of the destination market.

For example, Figure 1 constructs the trade-weighted average predicted probit index (Xcdβ∗)

for each importing country in two sectors, and plots the result against aggregate GDP of

the importer. Clearly, larger importers have higher predicted values for Xcdβ∗ on average,

which means they have higher predicted probabilities of trade with their partners, and in

turn means that they will have lower predicted export thresholds on average. A further

interesting fact to note is that the predicted probability of trade is generally higher for large

and wealthy exporters. For example, Figure 2 constructs a similar trade weighted predicted

probit index for each exporter in the same two sectors above and plots the result against

GDP per capita of the exporter. The figures clearly suggest that poorer countries tend to

have lower indices on average, lower predicted probabilities of trade with their partners, and

hence fact higher export thresholds on average. Though the theory does not directly indicate

the origins of this statistical relationship, a plausible conjecture would be that lower income

countries face higher thresholds due to either higher fixed costs of accessing foreign markets

or due to lower average product quality.30

29Results are broadly similar for the other variables if this lagged participation measure is omitted fromthis specification.

30For average product quality to lower thresholds in this manner requires b < 1.

30

3.3 Estimating the Trade and Price Equations

With the first stage estimates in hand, we move on to discuss estimates of the second stage

trade and price equations. Estimates for the values of {θ1, θ2} are listed with standard errors

by sector in Table 3 and plotted by sector in Figure 3. Although these estimates move around

quite a bit from sector to sector, they are in general centered around one throughout the

entire dataset. Moreover, the absolute value of the difference between θ1 and θ2 is quite

small. As discussed earlier, this difference and the normalized difference in (41) and (42)

provide evidence on the slope of the price equation. These estimates with standard errors

are presented in Table 4. The point estimates indicate that the price schedule is positively

sloped in 61% of sectors, and significantly positive (at the 10% level) in 48% of sectors. The

remaining sectors have a negative slope, and this slope is significantly negative in 21% of

the sectors. Thus, positive price slopes are in general more prevalent in the data, and only

a fifth of the sectors can be said with any certainty to have a negative slope.

In the context of the model, the prevalence of positive point estimates suggests that

typically ab > 1. That is, quality is both on average positively associated with the physical

productivity of the firm and producing higher quality goods entail higher marginal cost.

Furthermore, given that the sign of θ2 − θ1 tracks the sign of θ2−θ1

θ1

one for one, this implies

that (1− ab + a) > 0 in the data. In the model, this means that quality adjusted prices are

decreasing with respect to physical productivity on net.

To illustrate the sectoral pattern of the estimates, Figure 4 plots point estimates for

θ2 − θ1 by SITC 3-Digit sector. An interesting cross-sector pattern emerges in this figure.

Specifically, nearly all the significant negative estimates are clustered on the right end of the

figure, in the upper end of SITC category 7 and into category 8. In SITC category 8, these are

clustered in categories 831-881, which span the apparel and footwear categories along with

categories for optical and medical instruments. Khandelwal (2007) argues that apparel and

footwear are sectors characterized by relatively small dispersion in quality internationally.

31

As an analog, the finding here suggests that they may be characterized by relatively low

quality dispersion within countries as well, which means that large exporting firms are high

physical productivity firms that sell at low prices.

To drill down into individual sectors and get a sense of how the model fits that data, I

focus on studying two sectors –SITC 511: “Acyclic Hydrocarbons” and SITC 776: “Cathode

Ray Television Picture Tubes” – in greater detail. The price schedule slopes upward in sector

511 and downward in 776. To see visually how the price schedules are fit to the data, I purge

prices in each sector of the estimated exporter fixed effects and plot this residual against the

associated value of the predicted probit index. I then overlay the predicted values for prices

as a function of the predicted index. Figure 5 plots the results. Clearly there is a large

amount of residual variation in the data even after purging the data of the fixed effects, but

there is a discernible slope in both pictures. Figure 6 performs a similar exercise with the

trade equation, where I purge log exports of the exporter and importer fixed effects along

with the estimated direct effects of trade costs. In this figure, the fit is quite good. Indeed,

the only place where the fit is poor in the lower left tail of the figure. However, the fit should

be poor here because this lower left tail is where the selection term bites. Specifically, the

coefficient on the inverse mills ratio is essentially chosen so as to bring the lower tail of the

cumulated sum of the cutoff function and the inverse mills ratio into line with the data. As

illustrated in the figures, this typically means the selection term is estimated to be negative.31

To get a sense of how the variance in prices within each sector is divided between

the exporter specific component and the function of the cutoffs, I turn to examining the

predicted price schedules for individual exporters within each sector. Figure 7 plots the

predicted price schedules in these same two sectors for five countries: South Korea, India,

China, Belgium, and the UK. As the figure illustrates, the prices schedules of these different

countries are shifted relative to one another, and these translations seems to account for

31This contrasts somewhat with the results of Helpman et al. in aggregate data where the selection termis positive. More work is needed to understand this result fully.

32

significant variation in the data. In sector 776, the ordering of the exporters confirms to

intuition. The UK and Belgium charge the highest prices in the sector, while China and

India charge lower prices. Somewhat surprisingly, South Korea is the low cost supplier in

this group. The ordering in sector 511 is somewhat different. In this sector, China is the

high cost supplier, though Belgium and the UK then follow with South Korea and India at

the bottom of the ladder. The fact that China is a high cost supplier in this specific sector

should not prevent us from drawing the conclusion that price levels are generally highly

correlated with exporter income per capita.

To document these patterns more systematically across a broad range of sectors, we

turn to summary statistics. [TO BE COMPLETED]

3.4 Cross-Country Quality and Variety

Recalling the model, we can combine estimated coefficients from the gravity and price equa-

tions to back out a composite index of latent product variety and country-specific product

quality within each sector. Product variety and aggregate quality both shift the aggregate

demand for exports. Given that the gravity equation is derived from a structural equation

that characterizes this aggregate demand, we can use information in prices along with ex-

ternal estimates of the elasticity of demand to pin down the location of the demand curve.

Specifically, as discussed in Section 2.5, we can use the estimated price of the most productive

firm in each sector to calculate a variety/quality index using the estimated exporter fixed

effect in the augmented-gravity equation. To perform this calculation, we set the elasticity

of substitution equal to 4 in line with estimates by Broda and Weinstein (2006) for US SITC

3-Digit imports. Further, in each sector, we normalize the quality-variety composite of the

United Kingdom to one and report proportional deviations from this numeraire country.

In line with intuition, the estimated quality-variety composite covaries strongly with

exporter income per capita. For reference, Figure 8 plots the quality-variety composite

33

versus exporter income for the same sectors used in previous figures. In both cases, we find

a statistically significant positive slope. This result is not specific to this sector. Extending

the calculation to all sectors, 95 of of the 141 have a statistically significant positive slope

at the 5% level. Further, only 2 sectors have a statistically significant negative slope.

To understand the origins of this result, it is useful to look at the exporter fixed effects

separately from average prices. Figure 9 plots both individually versus exporter income. The

estimated fixed effect in the trade equation is generally unrelated to GDP per capita, whereas

the estimated price fixed effect is strongly correlated with income. As such, variation in the

estimated quality-variety composite is nearly entirely due variation in average prices across

countries.

To gain further insight, we move to longitudinal data to decompose this composite into

quality and variety subcomponents. [TO BE COMPLETED]

4 Robustness

[TO BE COMPLETED]

5 Conclusion

[TO BE COMPLETED]

34

References

[1] Anderson, James and Eric van Wincoop (2004). “Trade Costs.” Journal of Economic

Literature, Volume 42, Number 3, pp.691-751.

[2] Alessandria, George and Horag Choi (2007). “Do Sunk Costs of Exporting Matter for

Net Export Dynamics.” The Quarterly Journal of Economics, Volume 122, Issue 1,

pp.289-336.

[3] Atkeson, Andrew and Ariel Burstein (2006). “Trade Costs, Pricing-to-Market, and In-

ternational Relative Prices.” UC-Los Angeles Working Paper.

[4] Baldwin, Richard and James Harrigan (2007). “Zeros, Quality, and Space: Trade Theory

and Trade Evidence.” NBER Working Papers 13214, National Bureau of Economic

Research.

[5] Bergin, Paul and Reuven Glick (forthcoming). “Tradability, Productivity, and Under-

standing Economic Integration.” Journal of International Economics.

[6] Bergin, Paul, Reuven Glick, and Alan Taylor (forthcoming). “Productivity, Tradability,

and the Long Run Price Puzzle.” Journal of Monetary Economics.

[7] Bernard, Andrew, Jonathan Eaton, J. Bradford Jensen, and Samuel Kortum (2003).

“Plants and Productivity in International Trade.” The American Economic Review,

Volume 93, Number 4, pp. 1268-1290.

[8] Bernard, Andrew, J. Bradford Jensen, Stephen Redding, and Peter Schott (2006).

“Firms in International Trade.” The Journal of Economic Perspectives, Volume 21,

No. 3, pp.105-130.

[9] Chaney, Thomas (2006). “Distorted Gravity: Heterogeneous Firms, Market Structure,

and the Geography of International Trade.” University of Chicago, mimeo.

35

[10] Corsetti, Giancarlo, Philippe Martin, and Paolo Pesenti (forthcoming). “Productivity

Spillovers, Terms of Trade and the Home Market Effect.” Journal of International Eco-

nomics.

[11] Eaton, Jonathan and Samuel Kortum (2002). “Technology, Geography, and Trade.”

Econometrica, Volume 70, Issue 5, pp. 1741-1779.

[12] Feenstra, Robert (2003). Advanced International Trade: Theory and Evidence. Prince-

ton University Press (Princeton, New Jersey).

[13] Ghironi, Fabio and Marc Melitz, (2005). “International Trade and Macroeconomic Dy-

namics with Heterogeneous Firms.” The Quarterly Journal of Economics, Volume 120,

Number 3, pp. 865-914.

[14] Hallak, Juan Carlos and Jagadeesh Sivadasan (2006), “Productivity, Quality and Ex-

porting Behavior under Minimum Quality Requirements.” University of Michigan,

mimeo.

[15] Helpman, Elhanan, Marc Melitz, and Yona Rubinstein (2007). “Estimating Trade

Flows: Trading Partners and Trading Volumes.” NBER Working Paper No. 12927.

[16] Hummels, David and Peter Klenow (2005). “The Variety and Quality of a Nation’s

Exports.” The American Economic Review, Volume 95, pp. 704-723.

[17] Khandewal, Amit (2007). “The Long and Short (of) Quality Ladders.” Columbia Uni-

versity, mimeo.

[18] Melitz, Marc (2003). “The Impact of Trade on Intra-Industry Reallocations and Aggre-

gate Industry Productivity.” Econometrica, Volume 71, Issue 6, pp. 1695-1725.

[19] Ruhl, Kim (2005). “Solving the Elasticity Puzzle in International Economics.” Univer-

sity of Texas, Austin Working Paper.

36

[20] Schott, Peter (2004). “Across-Product versus Within-Product Specialization in Interna-

tional Trade.” The Quarterly Journal of Economics, Volume 119, Issue 2, pp. 647-678.

37

Table 1List of Countries Included in Estimation Sample

AFGHANISTAN GUATEMALA PANAMAALBANIA GUINEA PAPUA N.GUINEAALGERIA GUINEA-BISSAU PARAGUAYANGOLA GUYANA PERUARGENTINA HAITI PHILIPPINESAUSTRALIA HONDURAS POLANDAUSTRIA HONG KONG PORTUGALBANGLADESH HUNGARY ROMANIABELGIUM-LUX ICELAND RUSSIABELIZE INDIA SAUDI ARABIABENIN INDONESIA SENEGALBOLIVIA IRAN SEYCHELLESBRAZIL IRAQ SIERRA LEONEBULGARIA IRELAND SINGAPOREBURKINA FASO ISRAEL SOUTH AFRICABURUNDI ITALY SOUTH KOREACAMBODIA JAMAICA SPAINCAMEROON JAPAN SRI LANKACANADA JORDAN ST KITTS NEVCENTRAL AFR REP KENYA SUDANCHAD KIRIBATI SURINAMCHILE KUWAIT SWEDENCHINA LAOS SWITZERLANDCOLOMBIA LEBANON SYRN ARAB RPCOSTA RICA MADAGASCAR TAIWANCOTE D’IVOIRE MALAWI THAILANDDENMARK MALAYSIA TOGODJIBOUTI MALI TRINIDAD-TOBDOMINICAN RP MAURITANIA TUNISIAECUADOR MAURITIUS TURKEYEGYPT MEXICO UGANDAEL SALVADOR MONGOLIA UNITED KINGDEQ. GUINEA MOROCCO UNTD ARAB EMETHIOPIA MOZAMBIQUE UNTD RP TANZFIJI NEPAL URUGUAYFINLAND NETHERLANDS USAFRANCE NEW ZEALAND VENEZUELAGABON NICARAGUA VIETNAMGAMBIA NIGERIA YEMENGERMANY NORWAY ZAMBIAGHANA OMAN ZIMBABWEGREECE PAKISTAN

38

Table 2Representative First Stage Probit Regression Results

sector1 sector20 sector40 sector60 sector80 sector100 sector120 sector140Coef./se Coef./se Coef./se Coef./se Coef./se Coef./se Coef./se Coef./se

log distance -.614*** -.580*** -.689*** -.491*** -.392*** -.476*** -.485*** -.395***(.057) (.070) (.053) (.075) (.057) (.068) (.050) (.049)

language .202* .213 .363*** -.026 .398*** .231 .358*** .390***(.112) (.144) (.102) (.169) (.113) (.140) (.090) (.100)

legal system .117 .174* .073 .453*** .033 .418*** .156** .056(.080) (.103) (.078) (.120) (.089) (.107) (.072) (.080)

religion .133 .027 -.169 -.518* .220 -.142 .239* .290*(.169) (.229) (.157) (.305) (.187) (.222) (.138) (.149)

colonial -.295 .361 .003 .376 .178 -.085 .261 .442**(.205) (.252) (.190) (.292) (.189) (.267) (.180) (.183)

common border .288* .642*** .286* .117 .396** .342 .612*** .065(.174) (.237) (.167) (.290) (.196) (.232) (.166) (.182)

landlock .558 .744 -.353 -.280 -.091 -.733 .879 .727(.559) (.652) (.469) (.616) (.415) (.466) (.669) (.676)

island -.308 -.250 .194 -.002 .065 -.456 .145 .152(.301) (.314) (.240) (.356) (.259) (.342) (.214) (.218)

lagfrac 2.117*** 2.296*** 2.101*** 2.094*** 2.230*** 1.820*** 2.504*** 2.689***(.140) (.175) (.138) (.196) (.148) (.177) (.141) (.142)

Pseudo R2 .654 .650 .643 .618 .657 .641 .711 .699Obs. 6772 3948 7884 2865 6893 4086 11712 9266

Notes: Exporter and Importer fixed effects included in all regressions. Standard Errors in Parentheses. * p<.10, ** p<.05, *** p<.01

39

Table 2Estimates and Standard Errors of Parameters

SITC3-Digit θ1 SE(θ1) θ2 SE(θ2) SITC3-Digit θ1 SE(θ1) θ2 SE (θ2) SITC3-Digit θ1 SE(θ1) θ2 SE(θ2)511 1.299 0.279 1.535 0.270 665 1.269 0.255 1.274 0.260 751 0.809 0.429 0.775 0.437512 0.644 0.423 0.775 0.409 666 0.634 0.339 0.677 0.338 752 1.085 0.274 1.025 0.281513 0.726 0.402 0.841 0.388 671 1.286 0.363 1.307 0.367 759 0.582 0.226 0.321 0.270514 0.864 0.244 0.859 0.248 672 1.899 0.384 2.006 0.381 761 2.007 0.349 1.983 0.353515 1.544 0.346 1.657 0.344 673 1.177 0.255 1.245 0.254 762 1.809 0.478 1.616 0.496516 0.688 0.391 0.874 0.373 674 1.424 0.245 1.494 0.242 763 0.941 0.348 0.895 0.358522 1.008 0.295 1.135 0.289 676 0.898 0.564 1.022 0.561 764 1.092 0.288 1.047 0.294523 1.031 0.249 1.158 0.245 677 0.696 0.297 0.764 0.291 771 1.211 0.279 1.063 0.295531 1.054 0.311 1.186 0.301 678 1.166 0.213 1.231 0.214 772 0.825 0.228 0.741 0.236533 0.917 0.195 0.948 0.195 679 1.060 0.313 1.122 0.311 773 0.975 0.245 0.892 0.253541 0.843 0.204 0.809 0.208 682 1.189 0.302 1.289 0.296 774 0.923 0.366 0.762 0.391551 0.956 0.223 1.001 0.222 683 1.272 0.449 1.322 0.445 775 1.023 0.262 1.045 0.261553 1.191 0.230 1.238 0.232 684 1.288 0.198 1.407 0.195 776 1.353 0.355 1.096 0.385554 0.933 0.217 1.016 0.214 685 0.589 0.847 0.786 0.788 778 0.737 0.375 0.677 0.387562 1.130 0.283 1.220 0.282 686 1.266 0.383 1.331 0.379 781 1.537 0.264 1.515 0.265572 1.150 0.402 1.295 0.407 687 1.245 0.464 1.332 0.459 782 1.562 0.298 1.590 0.296582 1.034 0.245 1.022 0.246 689 1.137 0.536 1.021 0.559 783 1.478 0.441 1.577 0.436583 1.015 0.237 1.047 0.236 691 1.171 0.299 1.295 0.292 784 0.985 0.267 1.062 0.262584 0.997 0.350 1.043 0.347 692 0.873 0.307 0.937 0.305 785 1.123 0.319 1.034 0.326585 0.370 0.593 0.306 0.622 693 0.961 0.275 1.051 0.271 786 1.051 0.369 0.978 0.378591 0.907 0.274 0.953 0.272 694 0.666 0.205 0.723 0.202 791 1.317 0.487 1.443 0.481592 1.016 0.246 1.179 0.239 695 0.562 0.368 0.474 0.386 792 1.361 0.387 1.305 0.393598 0.785 0.284 0.911 0.275 696 0.719 0.402 0.677 0.411 793 0.844 0.551 0.835 0.563611 1.369 0.280 1.508 0.277 697 1.116 0.247 1.101 0.249 812 0.716 0.244 0.736 0.244612 1.062 0.284 0.887 0.302 699 0.925 0.208 0.898 0.211 821 0.884 0.242 0.899 0.242613 1.434 0.469 1.173 0.508 711 0.316 0.963 0.315 0.969 831 0.902 0.442 0.812 0.459621 0.722 0.273 0.770 0.269 712 0.899 0.670 1.096 0.654 842 2.020 0.371 1.952 0.375625 1.643 0.255 1.640 0.255 713 1.409 0.220 1.613 0.216 843 1.595 0.260 1.530 0.264628 0.625 0.385 0.689 0.376 714 1.169 0.419 1.147 0.426 844 1.342 0.312 1.237 0.321633 0.704 0.644 0.662 0.650 716 1.233 0.329 1.277 0.327 845 1.392 0.257 1.269 0.267634 1.259 0.249 1.344 0.247 718 0.726 0.398 0.830 0.386 846 1.567 0.373 1.492 0.379635 1.154 0.263 1.280 0.259 721 1.009 0.366 1.171 0.353 847 0.986 0.330 0.905 0.342641 1.216 0.211 1.303 0.207 722 1.899 0.402 1.828 0.409 848 1.060 0.315 0.868 0.339642 1.082 0.235 1.116 0.235 723 1.645 0.318 1.720 0.316 851 1.117 0.373 1.013 0.387651 1.235 0.220 1.296 0.218 724 0.843 0.411 0.889 0.408 871 0.628 0.482 0.496 0.521652 1.695 0.256 1.757 0.255 725 0.629 0.378 0.787 0.355 872 0.773 0.285 0.672 0.301653 1.504 0.223 1.533 0.222 726 0.859 0.308 0.906 0.305 873 1.337 0.410 1.218 0.428654 1.468 0.355 1.552 0.353 727 0.473 0.328 0.478 0.330 874 0.802 0.375 0.753 0.383655 1.573 0.256 1.567 0.259 728 0.368 0.331 0.393 0.327 881 0.831 0.563 0.638 0.610656 0.998 0.362 1.045 0.360 736 0.932 0.403 0.981 0.399 882 1.213 0.359 1.274 0.357657 1.001 0.281 1.060 0.278 737 0.694 0.483 0.784 0.467 884 0.394 1.028 0.089 1.260658 1.363 0.257 1.327 0.261 741 1.288 0.309 1.349 0.305 892 0.749 0.222 0.890 0.215659 1.729 0.358 1.723 0.363 742 1.121 0.324 1.204 0.319 893 0.861 0.281 0.856 0.283661 1.143 0.283 1.268 0.282 743 1.109 0.344 1.137 0.343 894 0.683 0.321 0.634 0.329662 1.280 0.211 1.341 0.210 744 1.072 0.351 1.231 0.338 895 0.552 0.378 0.528 0.385663 0.761 0.286 0.891 0.279 745 0.751 0.287 0.803 0.284 898 0.556 0.362 0.577 0.361664 1.203 0.277 1.275 0.278 749 0.879 0.285 0.978 0.277 899 0.664 0.365 0.734 0.359

Notes: Based on author’s calculations. See main text for details.

40

Table 3Estimates and Standard Errors for Slope of Price Equation

SITC3-Digit Diff SE Ratio SE SITC3-Digit Diff SE Ratio SE SITC3-Digit Diff SE Ratio SE511 0.24 0.04 0.18 0.05 665 0.00 0.04 0.00 0.03 751 -0.03 0.05 -0.04 0.06512 0.13 0.05 0.20 0.18 666 0.04 0.04 0.07 0.08 752 -0.06 0.03 -0.06 0.04513 0.11 0.04 0.16 0.12 671 0.02 0.05 0.02 0.04 759 -0.26 0.07 -0.45 0.26514 -0.01 0.04 -0.01 0.04 672 0.11 0.04 0.06 0.02 761 -0.02 0.04 -0.01 0.02515 0.11 0.06 0.07 0.05 673 0.07 0.03 0.06 0.03 762 -0.19 0.07 -0.11 0.05516 0.19 0.05 0.27 0.20 674 0.07 0.02 0.05 0.02 763 -0.05 0.05 -0.05 0.06522 0.13 0.05 0.13 0.06 676 0.12 0.09 0.14 0.14 764 -0.05 0.03 -0.04 0.03523 0.13 0.04 0.12 0.06 677 0.07 0.03 0.10 0.07 771 -0.15 0.05 -0.12 0.05531 0.13 0.03 0.13 0.06 678 0.06 0.03 0.06 0.03 772 -0.08 0.03 -0.10 0.05533 0.03 0.02 0.03 0.03 679 0.06 0.04 0.06 0.05 773 -0.08 0.03 -0.09 0.04541 -0.03 0.05 -0.04 0.05 682 0.10 0.02 0.08 0.03 774 -0.16 0.06 -0.17 0.11551 0.05 0.03 0.05 0.03 683 0.05 0.03 0.04 0.03 775 0.02 0.03 0.02 0.03553 0.05 0.03 0.04 0.03 684 0.12 0.02 0.09 0.02 776 -0.26 0.08 -0.19 0.09554 0.08 0.02 0.09 0.03 685 0.20 0.09 0.34 0.60 778 -0.06 0.05 -0.08 0.08562 0.09 0.04 0.08 0.04 686 0.06 0.03 0.05 0.03 781 -0.02 0.02 -0.01 0.01572 0.14 0.10 0.13 0.10 687 0.09 0.05 0.07 0.05 782 0.03 0.04 0.02 0.02582 -0.01 0.02 -0.01 0.02 689 -0.12 0.10 -0.10 0.11 783 0.10 0.06 0.07 0.05583 0.03 0.02 0.03 0.02 691 0.12 0.03 0.11 0.04 784 0.08 0.02 0.08 0.03584 0.05 0.04 0.05 0.04 692 0.06 0.03 0.07 0.05 785 -0.09 0.04 -0.08 0.04585 -0.06 0.10 -0.17 0.43 693 0.09 0.03 0.09 0.05 786 -0.07 0.04 -0.07 0.05591 0.05 0.04 0.05 0.05 694 0.06 0.03 0.09 0.06 791 0.13 0.06 0.10 0.06592 0.16 0.03 0.16 0.06 695 -0.09 0.05 -0.16 0.15 792 -0.06 0.06 -0.04 0.04598 0.13 0.03 0.16 0.08 696 -0.04 0.05 -0.06 0.08 793 -0.01 0.10 -0.01 0.12611 0.14 0.03 0.10 0.03 697 -0.01 0.03 -0.01 0.02 812 0.02 0.03 0.03 0.05612 -0.18 0.05 -0.17 0.07 699 -0.03 0.02 -0.03 0.03 821 0.02 0.02 0.02 0.02613 -0.26 0.11 -0.18 0.11 711 0.00 0.11 0.00 0.36 831 -0.09 0.04 -0.10 0.08621 0.05 0.03 0.07 0.05 712 0.20 0.12 0.22 0.23 842 -0.07 0.02 -0.03 0.01625 0.00 0.02 0.00 0.01 713 0.20 0.03 0.14 0.04 843 -0.06 0.03 -0.04 0.02628 0.06 0.04 0.10 0.10 714 -0.02 0.06 -0.02 0.05 844 -0.10 0.04 -0.08 0.04633 -0.04 0.08 -0.06 0.13 716 0.04 0.03 0.04 0.03 845 -0.12 0.03 -0.09 0.03634 0.08 0.03 0.07 0.03 718 0.10 0.05 0.14 0.12 846 -0.07 0.03 -0.05 0.02635 0.13 0.03 0.11 0.04 721 0.16 0.04 0.16 0.08 847 -0.08 0.04 -0.08 0.05641 0.09 0.02 0.07 0.02 722 -0.07 0.06 -0.04 0.03 848 -0.19 0.06 -0.18 0.09642 0.03 0.02 0.03 0.02 723 0.07 0.04 0.05 0.02 851 -0.10 0.04 -0.09 0.05651 0.06 0.02 0.05 0.02 724 0.05 0.06 0.05 0.07 871 -0.13 0.09 -0.21 0.25652 0.06 0.03 0.04 0.02 725 0.16 0.05 0.25 0.20 872 -0.10 0.05 -0.13 0.09653 0.03 0.03 0.02 0.02 726 0.05 0.04 0.05 0.05 873 -0.12 0.08 -0.09 0.07654 0.08 0.04 0.06 0.03 727 0.00 0.04 0.01 0.08 874 -0.05 0.03 -0.06 0.06655 -0.01 0.03 0.00 0.02 728 0.02 0.04 0.07 0.12 881 -0.19 0.08 -0.23 0.23656 0.05 0.04 0.05 0.05 736 0.05 0.04 0.05 0.05 882 0.06 0.05 0.05 0.04657 0.06 0.03 0.06 0.04 737 0.09 0.05 0.13 0.14 884 -0.30 0.27 -0.77 2.62658 -0.04 0.03 -0.03 0.02 741 0.06 0.02 0.05 0.02 892 0.14 0.03 0.19 0.08659 -0.01 0.05 0.00 0.03 742 0.08 0.03 0.07 0.04 893 0.00 0.02 -0.01 0.03661 0.12 0.05 0.11 0.05 743 0.03 0.03 0.02 0.03 894 -0.05 0.04 -0.07 0.07662 0.06 0.04 0.05 0.03 744 0.16 0.03 0.15 0.07 895 -0.02 0.05 -0.05 0.09663 0.13 0.05 0.17 0.10 745 0.05 0.03 0.07 0.05 898 0.02 0.04 0.04 0.09664 0.07 0.04 0.06 0.04 749 0.10 0.03 0.11 0.05 899 0.07 0.05 0.11 0.10

Notes: Diff is defined as θ2 − θ1 and is positive when the slope of the price schedule with respect tothe productivity cutoff is positive. Ratio is defined as (θ2 − θ1)/θ1.

41

−4

−2

02

4W

eigh

ted

Ave

rage

Pro

bit I

ndex

Acr

oss

Tra

de P

artn

ers

7 8 9 10 11Log GDP of the Importer

SITC 511: Acyclic Hydrocarbons

−2

02

4W

eigh

ted

Ave

rage

Pro

bit I

ndex

Acr

oss

Tra

de P

artn

ers

6 7 8 9 10 11Log GDP of the Importer

SITC 776: Cathode Ray Tel. Pict. Tubes

Figure 1: Log Prices Purged of Fixed Effects versus Predicted Function of the Productivity Cutoffs

42

−2

02

46

Wei

ghte

d A

vera

ge P

robi

t Ind

ex A

cros

s T

rade

Par

tner

s

7 8 9 10 11Log GDP of the Exporter

SITC 511: Acyclic Hydrocarbons

−6

−4

−2

02

4W

eigh

ted

Ave

rage

Pro

bit I

ndex

Acr

oss

Tra

de P

artn

ers

6 7 8 9 10 11Log GDP of the Exporter

SITC 776: Cathode Ray Tel. Pict. Tubes

Figure 2: Log Exports Purged of Fixed Effects and Trade Costs versus Predicted Function of the Productivity Cutoffs

43

0.5

11.

52

500 600 700 800 900SITC 3−Digit Category

Theta One Theta Two

Figure 3: Point Estimates of Theta Parameters by SITC 3-Digit Sector

44

−.3

−.2

−.1

0.1

.2T

heta

Diff

eren

ce

500 600 700 800 900SITC 3−Digit Category

Solid point indicates point estimate is significant at 10% level of higher in one−sided test.

Figure 4: Point Estimates of Difference Between Theta Parameters by SITC 3-Digit Sector

45

−2

−1

01

−4 −2 0 2 4 6Predicted First Stage Probit Index

SITC 511: Acyclic Hydrocarbons

−2

02

4−4 −2 0 2 4 6

Predicted First Stage Probit Index

SITC 776: Cathode Ray Tel. Pict. Tubes

Log Price Purged of FE Pred. Cut Func.

Figure 5: Log Prices Purged of Fixed Effects versus Predicted Function of the Productivity Cutoffs

46

−5

05

10

−4 −2 0 2 4 6Predicted First Stage Probit Index

SITC 511: Acyclic Hydrocarbons

−10

−5

05

10−5 0 5

Predicted First Stage Probit Index

SITC 776: Cathode Ray Tel. Pict. Tubes

Log Trade Purged of FE & Grav. Var. Pred. Cut Func.

Figure 6: Log Exports Purged of Fixed Effects and Trade Costs versus Predicted Function of the Productivity Cutoffs

47

66.

57

7.5

Pre

dict

ed P

rices

−2 0 2 4 6Predicted First Stage Probit Index

SITC 511: Acyclic Hydrocarbons

910

1112

13P

redi

cted

Pric

es

−1 0 1 2 3 4Predicted First Stage Probit Index

SITC 776: Cathode Ray Tel. Pict. Tubes

S. Korea BelgiumChina IndiaUK

Figure 7: Predicted Price Schedules as a Function of the Productivity Cutoffs for Select Countries

48

GRC ITA

ISR

BGR

KWT

NLD

GER

LBN

ARG

EGY

TWN SGP

OMNMYS

RUS

NZL

IRL

JOR

CHL

DNK

PRT

AUTHUNURY

SWENORARE

JPN

COL

HKG

IND

POL

FIN

BELIDNDZA

KOR

ESPBRA

IRN

PHL

CHN

CHE

PAN

FRA

ZAF

CAF

CAN

AUS

MLITHA

VEN

SAUMEX

ZWE

ROM

ISL

ECUTUR

PRY

TUN

GBR

−5

05

Exp

orte

r C

ompo

site

Var

iety

and

Qua

lity

Inde

x

7 8 9 10 11Log GDP Per Capita of the Exporter

SITC 511: Acyclic Hydrocarbons

BEL

GBR

IND

ZAF

CHE

TWN

BGR

CHN

ISR

KNA

SWE

BLZ

MRT

ARE

JPN

PAN

DNK

TUR

GRC

RUS

NZL

ROM

HUNBRA

MARIRL

THA

VNM

AUS

FRA

MYS

IDN

POL

AUT

SGP

PRT

CAN

ESP

EGYPHL

FIN

NLD

ITA

MEX

NOR

CRI

HKG

GER

PAK

KOR

LKATUN

−10

−5

05

10E

xpor

ter

Com

posi

te V

arie

ty a

nd Q

ualit

y In

dex

7 8 9 10 11Log GDP Per Capita of the Exporter

SITC 776: Cathode Ray Tel. Pict. Tubes

Figure 8: Estimated Composite Quality-Variety Index versus Log Exporter GDP Per Capita

49

GRC

ITA

ISR

BGR

KWT

NLD

GER

LBN

ARG

EGY

TWN

SGP

OMN

MYS

RUS

NZL

IRLJOR

CHL

DNK

PRT

AUT

HUN

URY

SWE

NOR

ARE

JPN

COL

HKG

IND

POL

FIN

BEL

IDN

DZA

KOR

ESP

BRA

IRN

PHL

CHN

CHE

PAN

FRA

ZAF

CAN

AUS

THA

VEN

SAU

MEX

ZWE

ROM

ISL

ECU

TUR

PRYTUN

GBR

−1

01

23

Est

imat

ed E

xpor

ter

Exp

ort E

q. F

ixed

Effe

ct

8 8.5 9 9.5 10 10.5Log GDP Per Capita of the Exporter

SITC 511: Acyclic Hydrocarbons

GRC ITAISR

BGR

KWT

NLDGER

LBN

ARG

EGY

TWN

SGP

OMN

MYSRUS

NZL

IRL

JOR

CHL

DNK

PRT

AUT

HUN

URY

SWE

NOR

ARE

JPN

COL

HKG

INDPOL

FIN

BEL

IDN

DZA

KOR

ESP

BRA

IRNPHL

CHN CHE

PAN

FRA

ZAF CAN

AUS

THAVEN

SAU

MEX

ZWE

ROM

ISL

ECU TUR

PRY

TUN

GBR

67

89

Est

imat

ed E

xpor

ter

Pric

e E

q. F

ixed

Effe

ct

8 8.5 9 9.5 10 10.5Log GDP Per Capita of the Exporter

SITC 511: Acyclic Hydrocarbons

Figure 9: Estimated Fixed Effects in Trade and Price Equations versus Log Exporter GDP Per Capita

50