Quality sorting and trade: Firm-level evidence for French...

Quality sorting and trade:Firm-level evidence for French wine∗

Matthieu Crozet† Keith Head‡ Thierry Mayer§

November 19, 2008

Abstract

Investigations of the effect of quality differences on heterogeneous performancein exporting have been limited by lack of direct measures of quality. We examineexports of French wine, matching the exporting firms to producer ratings from twowine guidebooks. We show that high quality producers export to more markets,charge higher prices, and sell more in each market. Our model predicts qualitysorting: the more difficult a market is to serve, the better on average will be thefirms that serve it. Our findings point to the empirical importance of quality sortingin one industry and could be extended to other industries.

∗We thank Isaac Holloway for his very efficient research assistance. Participants in conferences andseminars in Louvain-la-Neuve, Nottingham, NOITS, ERWIT, LSE... provided very helpful helpful sug-gestions.

†CEPII and University of Reims.‡Sauder School of Business, University of British Columbia, [email protected]§Paris School of Economics (Universite de Paris 1), CEPII, and CEPR.

1 Introduction

Why do some firms export more intensively and extensively than others? In the seminalpapers of Melitz (2003) and Bernard, Eaton, Jenson, and Kortum (2003) the answeris productivity differences. However, measures of physical output per unit of input arerarely available at the firm level,1 forcing reliance on proxies like domestic market shares orvalue-added per worker. These variables can be driven by primitives other than physicalproductivity, such as product quality. A separate literature on quality and trade relies onnoisy proxies (unit values). We study French wine exports, where we are able to matchfirm-destination-level export flows to firm-level quality ratings from wine guides.

Prior work on quality and trade has examined both the supply side and demand side.Supply side research asks what makes a country export higher quality goods (as inferredfrom unit values)? Schott (2004) finds that within goods categories, unit values tend toincrease with the exporters’ per capita income, capital to labor ratio, skill ratio, and thecapital intensity of production. Hummels and Klenow (2005) find that, within categories,price and quantity indexes rise with origin-country income per capita. The elasticitiesare 0.09 (price) and 0.34 (quantity). The authors interpret their price result as showingwhy big countries do not suffer from a negative terms of trade effect (as they would in amodel without quality differentiation). Rather than drive down the value of their singlevariety, large countries export more varieties and also higher quantities and prices of eachvariety. Hummels and Klenow also argue in favor of a model with Romer (1994) fixedcosts per export market.

Demand-side papers ask what makes country demand a larger share of high qualitygoods (again inferred from unit values)? Hummels and Skiba (2004) find that averageFOB export price rise with freight costs to destination market. They interpret thisas a confirmation of the Alchian-Allen (1969) effect (“shipping the good apples out”).2

Hallak (2006) estimates destination-country income effects and find evidence supportingthe hypothesis that richer countries have relatively high demand for high quality. Hallakestimates an interaction between unit values (based on the US import data) and incomeper capita.3

This paper contributes to the quality and trade literature in terms of data and method.“Direct” quality measures compared to “inferred” quality (unit values, market shares).Firm-level quality measures matched to firm-level destination-specific exports. Our modelcombines the Hallak assumption on preferences for quality with the Baldwin and Harrigan

1Foster, Haltiwanger and Syverson (2008) is a notable exception, where the authors observe firm-levelquantities and prices separately for a number of industries. They show that traditional TFP estimatesconfound the effect that physical productivity and demand shocks have on the survival probability offirms, and that demand shocks are important in practice. Note that they deliberately exclude qualitysorting from their analysis by selecting quasi-homogenous goods.

2The Alchian-Allen effect relies upon freight costs that are less than proportional to product value.An increase in freight costs therefore lowers the relative price of high quality goods leading to an increasein their relative demand.

3The majority of the coefficients estimated are insignificant or negative and significant. Hallak’s“confirmation” of the theory is based upon finding more significant positive than significant negativecoefficients.

1

(2007) assumption on the cost of quality. Methodologically, we develop new predictionsfor the heterogeneous quality model, relating conditional means to market attractivenessmeasures.

The paper proceeds as follows. We first derive new testable predictions from a modelof firm-level heterogeneity in quality. Then we explain why applying this model to cham-pagne and burgundy producers makes sense. Next we estimate the firm-level equationsof that model and back out the implied values of the key structural parameters. Utilizingfixed effects estimated in the firm-level regressions, we estimate the conditional meanrelationships implied by the model. Our conclusion suggests a research program basedon the success of the quality sorting model as well as the empirical anomalies we find.

2 Theory

The theory examined in this paper is based on work by Baldwin and Harrigan (2007),who introduced a cost-quality tradeoff in the model of Melitz (2003), who introducedproductivity-heterogeneity in the model of Krugman (1980), who introduced trade coststo the monopolistic competition model of Dixit and Stiglitz (1977). We also draw onEaton, Kortum, and Kramarz (2006).

2.1 General Set-up

We consider a category of goods (in our case, an 8-digit goods classification) with a sub-utility function that is assumed to have a constant elasticity of substitution (CES), σ > 1,over the set, Bj, of all varieties, i available in country j:

Uj =

(∫i∈Bj

[s(i)γq(i)]σ−1

σ di

) σσ−1

. (1)

In this expression q(i) denotes quantity of variety i consumed and s(i) denotes its mea-sured quality.4 Following Hallak (2006), the intensity of the consumers’ desire for qualityis captured in parameter γ. The sub-utility enters full utility with a Cobb-Douglas ex-penditure parameter denoted µj. The foreign country comprises Mj individuals with yj

income per capita.We assume that, within a detailed product classification, each firm exports a single

variety.5. The solution to the consumers’ utility maximization is usually expressed interms of trade-cost inclusive export values. For data reasons, we want to work with FOBvalues. Hence, we divided the market j consumers’ desired expenditures on firm i by atrade cost factor, τj(i), to obtain FOB exports. Using xj(i) to denote FOB exports, weobtain

xj(i) =[pj(i)τj(i)/s(i)

γ]1−σ∫`∈Bj

[pj(`)τj(`)/s(`)γ]1−σd`µjyjMj/τj(i). (2)

4In our application “star” ratings in wine guides provide s(i).5The single-variety assumption is standard in the theory but is counterfactual for wine exporters, who

often export multiple varieties. We will return to this issue in the empirical section

2

In the above expression prices paid by consumers in j are given by pj(i)τj(i), whereτj(i)− 1 is the ad valorem tariff equivalent of all trade costs incurred by firm i to sell inmarket j.

Using w(i) to denote the factor price index and z(i) to denote factor productivity,a firm’s unit costs of production are given by w(i)/z(i). We make the non-standardassumption of firm-varying factor prices to take into account the idea that a firm makinghigh-quality output might be required to use more expensive inputs. The model entailsa constant mark-up, σ/(σ − 1), which can be factored out of the numerator and thedenominator of equation (2). Taken together, these assumptions imply export revenuefrom market j is given by

xj(i) =

(w(i)/z(i)

s(i)γ

)1−σ

µjyjMjτj(i)−σP σ−1

j , (3)

where the price index is defined in terms of quality-adjusted costs,

Pj ≡

(∫`∈Bj

[τj(`)w(`)/z(`)

s(`)γ

]1−σ

d`

)1/(1−σ)

.

It is useful to collect all country-specific determinants of exports into a single factor.To do, we specify τj(i)

−σ in terms of a country-level factor and an idiosyncratic firm-destination factor. Thus, we assume

τj(i)−σ = φjηj(i), (4)

There are a variety of possible interpretations for ηj(i). It might represent the firm’snetwork of connections with purchasers in each destination country. Alternatively, itcould represent country-specific differences in tastes that impact firm-level demand. Theimportant thing is that it allows the model to accommodate the fact that the two firmswith the same observed quality, s, may export differing amounts to the same country.It also allows for violations in the hierarchy of markets served. Without a stochasticcomponent in trade costs, all French firms that serve Thailand for instance, a remote andrelatively small market, should also export to all “easier” countries. Eaton et al. (2005)show that this hierarchy does not hold in its strict version, a finding we can confirmfor wine exporters. Firm-specific variation in trade costs are one way to account for thisfinding. As shown in subsection 2.7, heterogeneous ηj(i) introduce a structural error termfor firm-level regressions.

The net contribution to firm profits of market j is given by

πj(i) = xj(i)/σ − F = ([z(i)/w(i)]s(i)γ)σ−1Ajηj(i)/σ − F, (5)

where Aj is a factor that aggregates the determinants of the attractiveness of country jdefined as

Aj ≡ µjyjMjφjPσ−1j .

Attractiveness depends positively on the size (µjyjMj) and relative accessability (φjPσ−1j )

of the market.

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2.2 The cost-quality tradeoff

We have so far allowed for heterogeneity in productivity (the standard approach followingMelitz (2003)), factor prices, quality, and trade costs. Four sources of heterogeneity istoo many for a tractable model. One option is to hold w/z constant and have a modelof pure (costless) quality variation. The problem with this is that in the Dixit-Stiglitzframework, mark-ups do not vary across firms and so quality has no independent effecton price. In this framework the only way to make prices depend on quality is to havea relationship between costs and quality. We follow Baldwin and Harrigan (2007) inassuming that this relationship takes the form of a deterministic parametric tradeoff. Inparticular, we assume that when firms draw high quality, a cost must be paid in terms ofhigher unit costs (either because of higher factor prices or lower productivity or both):6

w(i)

z(i)= ωs(i)λ, (6)

with λ ≥ 0.We discuss the reasons to expect such a relationship for wine in section 3.Using equation (6), we can express the key behavioural equations of the model in

terms of the remaining sources of heterogeneity. Export values are given by

xj(i) = ω1−σs(i)(γ−λ)(σ−1)Ajηj(i). (7)

Individual firms charge FOB prices of

pj(i) =σ

σ − 1ωs(i)λ. (8)

Thus, the model predicts that firms charge the same FOB prices to all destinations andthat these prices increase in quality with elasticity λ. A more general model mightincorporate pricing-to-market via cross-country differences in σ, and hence the mark-up.

Export quantities can be obtained by dividing (7) by the equation for FOB prices,(8):

qj(i) =σ − 1

σω−σs(i)(σ−1)γ−λσAjηj(i) (9)

The parameterization of our model in terms of γ and λ is useful because when setγ = 0 and λ = −1, utility does not depend directly on s and costs are inversely relatedto s, i.e. w(i)/z(i) = ω/s(i). Hence, we can reinterpret s(i) as a productivity draw. Thisallows us to compare the results of the quality-sorting model (γ > λ ≥ 0) with the originalMelitzian productivity sorting model (γ = 0, λ = −1). As can be seen in equation (9),both models predict that higher s leads to higher export quantities. However, the priceeffects differ in sign. When s is interpreted as costly-quality it causes higher prices butwhen s is a productivity draw, it causes low prices. This distinction is important laterbecause it leads to contrasting predictions for conditional mean prices and quantities.

6Because we observe quality directly, and therefore want to focus on that variable, we have modifiedthe parameterization of the cost-quality tradeoff relative to Baldwin and Harrigan (2007). They assumethat firms draw a unit labour requirement (1/z) which implies a level of quality. Our cost-qualityparameter, λ, is related to their θ as follows: λ = 1/(1 + θ).

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2.3 Entry threshold quality

The next step is to determine which firms export to a given destination. Substituting (6)into (5), we obtain

πj(i) = ω1−σs(i)(γ−λ)(σ−1)Ajηj(i)/σ − F, (10)

For any given value of η we can solve for the critical level of quality below which entryinto market j becomes unprofitable:

sj(η) =

(Ajη

σFωσ−1

) −1(σ−1)(γ−λ)

. (11)

Equation (11) shows the level of quality needed to enter market j is a decreasing functionof how “easy” this market is for the average French exporter, which is captured by Aj

and the firm’s idiosyncratic access to the market, captured in η. On the flip-side, higherfixed (F ) or variable (ω) costs increase the quality cut-off, which means that lower qualityfirms will not be able to sell abroad.

We assume that s(i) and ηj(i) are independently distributed with probability densityfunctions (PDFs) denoted g(s) and h(η), respectively. The probability of entering is givenby

Pr[πj(i) > 0] =

∫ ∞

0

Pr[s(i) > sj(η)]h(η)dη =

∫ ∞

0

(1−G[s(η)])h(η)dη. (12)

The precise functional of h(η) can be left unspecified for the moment. However, to obtainclosed form solutions, we have to adopt a tractable distribution for s. We follow muchof the recent literature in assuming a Pareto distribution for firm-level heterogeneity s.Thus, assume that the CDF, G(s), and PDF, g(s), take the forms

G(s) = 1− (s/s)−κ, and g(s) = κsκs−κ−1. (13)

Plugging in equation (11) for sj(η) and assuming s is Pareto, we can express the proba-bility of exporting to a market as a function of its attractiveness:

Pr[πj(i) > 0] = s(1)−κsκη1 =

(Aj

σFωσ−1

) κ(σ−1)(γ−λ)

sκη1, (14)

where s(1) is the quality cut-off for a firm with η = 1 and η1 is defined as

η1 ≡∫ ∞

0

ηκ

(σ−1)(γ−λ) h(η)dη.

The total pool of firms that might export to market j is given by Nx, which wetreat as an exogenous variable. The share of firms exporting to a market j is Nj/Nx ≈Pr[πj(i) > 0]. The approximation operator, ≈, is used because Nj/Nx only converges onthe probability in the limit. We refer to Nj as the “popularity” of market j. Equation (14)shows that popularity is predicted to be a power function of the attractiveness of themarket, Aj.

We now proceed to specify predictions for measurable aggregate statistics: the averagequality, average price, and average quantity for each destination market j. We showthe relationship between the conditional expected values of these variables and bothattractiveness, Aj, and popularity, Nj.

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2.4 Conditional expected quality

The average quality of exporters to a given market is E[s | πj(i) > 0]. The general formfor the expected value is

E[s | πj(i) > 0] =

∫∞0

∫∞sj(η)

sg(s)h(η)dsdη

Pr[πj(i) > 0](15)

To obtain the numerator, we start by integrating over s, conditional on η:∫ ∞

sj(η)

sg(s)ds = sj(η)1−κsκ κ

κ− 1. (16)

Substituting the expression for sj(η) shown in (11) and integrating over all values of η,the numerator of (15) is∫ ∞

0

∫ ∞

sj(η)

sg(s)h(η)dsdη = sj(1)1−κsκ κ

κ− 1η2, (17)

where η2 is defined as

η2 ≡∫ ∞

0

ηκ−1

(σ−1)(γ−λ) h(η)dη.

Dividing (17) by the probability of entry obtained from equation (14), the expected valueof quality exported to a given market is

E[s | πj(i) > 0] =

(Aj

σFωσ−1

) −1(σ−1)(γ−λ) κ

κ− 1(η2/η1), (18)

We can estimate the expected value of quality using the observed average quality level ofexporters to a given market:

sj ≡ (1/Nj)∑i∈Hj

s(i) where Hj is set of French exporters to j (19)

The testable predictions are straightforward. Anything that makes a market more attrac-tive (higher Aj) will reduce sj, the average level of quality (in the quality sorting model)or the average level of productivity (in the productivity sorting model). In a reducedform equation Aj can be approximated as a positive function of market size and a neg-ative function of distance (or any other measurable proxy for trade costs to j). Averageperformance (quality or efficiency) of French exporters in j should therefore decrease withpopulation and average income in j and increase with distance to j. Note that if fixedcosts were also increasing in distance, the overall prediction is unchanged: more distantmarkets should exhibit higher average performance (quality or productivity).

The preceding approach to testing the theory relies upon specifying Aj as a parametricfunction of observables. This may be problematic because Aj collects a potentially largeset of variables, some of which (e.g. the trade costs that determine φj) are difficult to

6

measure. We also use a method described below to estimate Aj directly as a destinationfixed effect in a firm-level quantity regression. A third approach is to express conditionalexpected quality in terms of the observable number of firms that actually enters a market,Nj.

This achieved by first inverting equation (14) to obtain Aj as a function of Pr[πj(i) >0]. Then one substitutes this value into equation (18) and simplifies to obtain

E[s | πj(i) > 0] = (Pr[πj(i) > 0])−1/κ κ

κ− 1sη2η

(1−κ)/κ1 (20)

If the sample is large enough, Nj/Nx should approximate Pr[πj(i) > 0]. The observedconditional mean quality of exporters to a market, sj should be approximately a powerfunction of the observed number of entrants:

sj ≈(

Nj

Nx

)−1/κ

sκ

κ− 1η2η

(1−κ)/κ1 (21)

It is very easy to investigate the performance of this prediction graphically without theneed for any data on the destination countries. One simply graphs average quality of theexporters to a destination against the number of exporters, with both variables shown ina log scale. There should be a negative linear relationship between the two variables witha slope given by −1/κ. The same prediction applies to average productivity if one wereworking with the original Melitz model. Thus one cannot use the relationship between theaverage performance indicator and market popularity to discriminate between the models.However, performance has differing implications for price and quantity in the quality andproductivity sorting models. Hence, one can use the signs of the relationships betweenaverage price and quantity to attractiveness and popularity to discriminate between thealternative types of sorting.

2.5 Conditional expected price

The expected price conditional on exporting closely is given by

E[p | πj(i) > 0] =

∫∞0

∫∞sj(η)

p(s)g(s)h(η)dsdη

Pr[πj(i) > 0](22)

To obtain the numerator we start by plugging in equation (8) for p(s) and integratingover s, conditional on η:

σω

σ − 1

∫ ∞

sj(η)

sλg(s)ds = sj(η)λ−κsκ σωκ

(σ − 1)(κ− λ). (23)

For the integral to be finite we need κ > λ. Substituting the expression for sj(η) shownin (11) and integrating over all values of η, the numerator of (22) is∫ ∞

0

∫ ∞

sj(η)

p(s)g(s)h(η)dsdη =ωσκsκ

(σ − 1)(κ− λ)s(1)λ−κη3, (24)

7


η3 ≡∫ ∞

0

ηκ−λ

(σ−1)(γ−λ) h(η)dη.

Dividing (24) by the probability of entry obtained from equation (14), the expected valueof price exported to a given market is

E[p | πj(i) > 0] =

(Aj

σF

) −λ(σ−1)(γ−λ)

ωγ

(γ−λ)σκ

(σ − 1)(κ− λ)(η3/η1), (25)

We can estimate the expected value of price using the observed average price level ofexporters to a given market:

pj ≡ (1/Nj)∑i∈Hj

pj(i) where Hj is set of French exporters to j (26)

Recall that attractiveness, Aj ≡ µjyjMjφjPσ−1j . In the quality sorting model, where

γ > λ > 0, the average price should therefore be a negative function of population (Mj),income per capita (yj) and taste for wine (µj). It should however be increasing in distancedj, which enters τj positively. A reduced form equation of the quality sorting model canbe estimated in the following form:

ln pj = β0 + β1 ln Mj + β2 ln yj + β3 ln dj + εj, (27)

where α1, α2 < 0 and α3 > 0. This is a reduced form equation since i) not all componentsof trade costs are controlled for, ii) the fixed cost is left constant7, iii) the unobservablepreference parameter µj and price index Pj are left in the disturbance term. The effi-ciency sorting model calls for opposite coefficients on all those variables, enabling for adiscriminating test between those two views of exporters’ sorting.

We can also express the conditional mean of price in terms of popularity.

pj ≈(

Nj

Nx

)−λ/κωσκ

(σ − 1)(κ− λ)sλη3η

λ/κ−11 (28)

As with mean quality, the mean price conditional on exporting is decreasing in Nj/Nx forthe quality sorting model. However, the prediction is opposite for the efficiency sortingmodel, which you obtain by setting γ = 0 and λ = −1. When quality sorting takes place,only high quality varieties get exported to difficult countries, and those are high pricevarieties, because high quality is associated with high costs in our setting. When efficiencysorting is the driver of firms’ selection into export markets, only the most productive firmswith low marginal cost make it to difficult markets, and—with a constant markup—thosehave a low price.

7As mentioned above however, if fixed costs of serving j are increasing in distance dj , the predictionon the signs of coefficients is left unaffected.

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2.6 Conditional expected quantity exported

The expected quantity, conditional on exporting profitably to market, is given by

E[q | πj(i) > 0] =

∫∞0

∫∞sj(η)

q(s)g(s)h(η)dsdη

Pr[πj(i) > 0](29)

Substituting in equation (9) for q, we start by evaluating∫∞

sj(η)q(s)g(s)ds:∫ ∞

sj(η)

q(s)g(s)ds =κsκω−σAjη

κ− (σ − 1)γ + λσ

σ − 1

σsj(η)(σ−1)γ−λσ−κ. (30)

For the integral to be finite, we assume κ > γ(σ − 1) − λσ. This expression is morecomplex than the corresponding equation, (23) obtained for prices. In particular, bothAj and sj enter average exports, while only sj(η) enters average price. The reason hasto do with the intensive and extensive margins of trade increases in this model. In aDixit-Stiglitz setup, prices are a constant markup over marginal costs, and in particulardo not depend on market size or anything that enters Aj. Therefore, a rise in marketattractiveness Aj impact prices only through the extensive margin, the entry of firms intoexport market j, the sj(η) term in (23). Quantities sold by each firm that exports to jdo however depend on Aj. Consequently, (30) depends on the extensive margin sj(η),but also on the intensive one through the independent impact of Aj.

Next, we substitute (11) into (30) and integrate over η to obtain∫ ∞

0

∫ ∞

sj(η)

q(s)g(s)h(η)dsdη =κsκω−σAj

κ− (σ − 1)γ + λσ

σ − 1

σsj(1)

(σ−1)γ−λσ−κη4. (31)


η4 ≡∫ ∞

0

ηκ+λ

(σ−1)(γ−λ) h(η)dη.

The final step is to divide (31) by (14), the probability of being a profitable exporter toj , yielding

E[q | πj(i) > 0] =

(Aj

σ

) λ(σ−1)(γ−λ)

F(σ−1)γ−σλ(σ−1)(γ−λ) ω

−γ(γ−λ)

κ(σ − 1)

κ− (σ − 1)γ + σλ(η4/η1). (32)

We can estimate the expected value of quantity as the average of the observed averagequantity of exporters to a given market:

qj ≡ (1/Nj)∑i∈Hj

qj(i) where Hj is set of French exporters to j (33)

The power on Aj is positive as long as quality is “worthwhile,” i.e. γ > λ. Under theparameterization corresponding to productivity sorting (γ = 0, λ = −1), the power on

9

Aj is negative since −1/(σ − 1) < 0. Again, with Aj ≡ µjyjMjφjPσ−1j , a reduced form

equation of the quality sorting model can be estimated in the following equation:

ln qj = β0 + β1 ln Mj + β2 ln yj + β3 ln dj + εj. (34)

When F does not vary across countries, the prediction is very simple and opposite tothe one on prices: β1, β2 > 0 and β3 < 0. This is a reduced form equation for the samereasons as the price equation. Again, the Melitzian productivity sorting model calls foropposite coefficients on all those variables, enabling a discriminating test between thosetwo types of exporter sorting. In the quality sorting model, easy markets see lower qualityfirms on average export high quantities of low price goods. In the productivity sortingcase, those same high Aj countries face exports by less efficient firms on average thatcharge high prices and sell less.

There appears to some ambiguity regarding the F term. Suppose that Fj is a positivefunction of dj. In the average price equation, the sign prediction on α3 is unchanged sinceτj and Fj are raised to the same power in (25). This is not the case in the mean quantityequation (32) since (σ − 1)γ − σλ > 0 as long as γ > λ > 0 and σ > 1. In that case, dj

has a positive influence on average quantity through Fj and a negative one through τj inAj. In the productivity sorting parameterization, expected quantity is increasing in bothτ and F . Therefore distance should unambiguously raise average quantity.

Note the powers on Aj and ω in equation 32 are equal in absolute values, but ofopposite sign to the corresponding powers int expected price equation (25). Using thesame steps to derive the expected export value, E[x | πj(i) > 0], leads to the strikingresult that it is independent of Aj. Thus, the average firm exports the same value (pq)to large and small markets. This feature of the model, which appears to be driven byfunctional forms was also obtained independently by Eaton et al. (2005) and Lawlessand Whelan (2007) for the productivity sorting model.

The last step is to substitute for Aj as a function of the probability of entry andthen plug the result into equation (32) as we did with prices. Again recognizing that wecan approximate the unobservable entry probability with the observed popularity of themarket, we obtain an expression for the conditional expectation of quantity with respectto popularity:

qj ≈(

Nj

Nx

)λ/κF

ω

s−λκ(σ − 1)

κ− (σ − 1)γ + σλη4η

−λ/κ−11 . (35)

Average quantity exported to j is a positive function of popularity, Nj/Nx, in the case ofthe quality sorting model, and again the sign of the relationship is reversed when in theproductivity sorting model.

Table 1 summarizes the predicted elasticities derived from equations (14), (18), (21),(25), (28), (18) and (21). We contrast the predictions for quality sorting with theMelitzian productivity sorting parameterization. The key takeaways are that measuredattractiveness, Aj, and popularity, Nj, have the same signs for all their predicted effectson average quality, price, and quantity. The table highlights the opposing signs for priceand quantity and the way the signs flip when one goes from the quality sorting case to theproductivity sorting case. These predictions allow for testing the general validity of the

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approach and also give the potential to discriminate between quality and productivitysorting.

Table 1: Predicted elasticities in two sorting models

Sorting model: Explanatory variable: Dependent variable:Nj sj pj qj

s = quality “popularity” (Nj)−1κ

−λκ

λκ

(γ > λ ≥ 0) “attractiveness” (Aj)κ

(σ−1)(γ−λ)−1

(σ−1)(γ−λ)−λ

(σ−1)(γ−λ)λ

(σ−1)(γ−λ)

s = productivity “popularity” (Nj)−1κ

1κ

−1κ

(γ = 0, λ = −1) “attractiveness” (Aj)κ

σ−1−1

(σ−1)1

σ−1−1σ−1

2.7 Firm-level predictions

We can estimate the model using firm-level data for three different dependent variables:the probability of exporting, the FOB price, and exported quantity. Taking logs ofequations (10), (8), and (9) we can obtain estimating equations.

The probability of exporting is given by

Pr(qj(i) > 0) = Pr(πj(i) > 0) = Pr(ln xj(i)− ln σ − ln F > 0).

Using equation (7) to express xj(i) in terms of its determinants, firm i will export to jwith probability:

Pr(πj(i) > 0) = Pr[(γ−λ)(σ−1) ln s(i)−(σ−1) ln ω−ln(F/σ)+ln Aj+ln ηj(i) > 0]. (36)

The parameters of this probability can be estimated using a binary choice model whoseform depends on the assumption made on the distribution of the unobserved heterogeneityterm ηj(i). Assuming log-normality for ηj(i) implies a probit form. This is the assumptionmade in Helpman, Melitz, and Rubinstein (2007). Assuming log-normal η also impliesthat OLS will be the maximum likelihood estimator for the firm-level quantity equation.On the other hand, if we let η be distributed log-logistic (also called the Fisk distribution),then we can use the fixed effects logit which has the advantage of absorbing the country-year fixed effects for the Aj.

8

8The Stata command is “xtlogit, fe”

11

From (8), the price charged by firm i takes the following estimable form:

ln pj(i) = λ ln s(i) + ln ω + ln[σ/(σ − 1)]. (37)

The price equation in this model lacks an error term. However, for parallelism withthe quantity equation, we add a normally distributed (in log scale) error with country-year specific fixed effects. One possible interpretation of the fixed effects are that σ variesacross markets and the fixed effects estimate ln[σj/(σj−1)]. However, this is unattractivebecause it implies country-specific elasticities with respect to quality in the quantity andexport equations.

From (9), the firm-level exported quantity is

ln qj(i) = [(γ − λ)(σ − 1)− λ] ln s(i) + ln[(σ − 1)/σ]− σ ln ω + ln Aj + ln ηj(i). (38)

For export probabilities and quantities, ln Aj appears on the RHS. Rather than at-tempt to estimate this term as a parametric function of country j primitives, we absorbit with country-year-specific fixed effects.

We have also estimated a semi-parametric form of these regressions in which we replaceln s(i) with a set of indicator variables corresponding to the number of stars accorded tothe producer. Our initial assessment was that the gain from more flexibility was not highenough to offset the cost in terms of the inability to extract estimates of γ and λ and thegreater number of coefficients to report and discuss.

A last important comment is in order with respect to a potential selection bias inthe estimate of the quality coefficient in equation (38). Inspecting equation (36) revealsa negative relationship between the quality observed among exporters (s(i)), and theunobserved idiosyncratic shock that firms experience when considering exports to eachmarket (ηj(i)). Consider firms with identical quality level, the probability of passing thecutoff and therefore actually exports increases with (ηj(i)). It follows that firms with highobserved quality will become exporters even with relatively low draws of ηj(i), while lowquality firms need high draws of ηj(i) to be observed as positive exporters. This negativecorrelation will tend to drive the estimates of s(i) toward zero, since low quality firmswill tend to do better (and high quality firms worse) than expected from their observedquality level. Going back to Helpman et al. (2008), this is a usual “sample selection”issue, which is directly implied from the theoretical framework of trade by heterogenousfirms, and it can be addressed by Heckman-type correction, here as in Helpman et al(2008) paper.9

Empirically, what is needed is an variable explaining firm-level decision to export toindividual markets. This variable has to exhibit variance across the firm-market dimen-sion, and also has to be excluded from the second stage where we estimate determinantsof trade volumes. Helpman et al (2008) use overlap in religion memberships in tradepartners, as well as measures of entry costs based on world bank data. We need an

9Helpman et al (2008) have an additional, non-linear, correction term accounting for the fact that “alarger fraction of firms export to more attractive export destinations”, while they only observe aggregatetrade flows in their data. Since we work with firm-level exports, this second term is not needed here.

12

additional firm-level dimension here, that we find using the financial structure of groupsin France. Our data enables us to find whether our exporters belong to a larger finan-cial group. Those groups are generally large (greater than XXX mn euros in our case)and diversified, and enable scope economies that can be particularly useful for reducingfixed costs to export. Our assumption is that the reduction in fixed export costs willparticularly valuable for entering in countries characterized by large entry costs. Our ex-cluded variable therefore interacts entry costs already used by Helpman et al (2008) witha dummy for group membership. Practically, a first stage probit estimation is run addingthe variable just described to equation (36). The second stage simply adds a mills ratiovariable, calculated from the probit results, into equation (38). We have a clear expec-tation on the quality variable coefficient. Since the selection bias comes from a negativecorrelation between s(i) and ηj(i), the Heckman correction should raise the estimate ons(i). We also run the same exercise on the price equation, although as stated above, theerror term does not enter fob price in the Dixit-Stiglitz framework. Our expectation istherefore that that change in the quality coefficient should be smaller in magnitude thanfor shipments.

3 Why Champagne?

Wine in general and Champagne in particular provide an excellent industry for an empir-ical application of our theoretical predictions. The way we proceed is the following: Weconcentrate in the body of the paper on Champagne (nc8 22041011) for reasons that arelisted below. However, we also carry out the analysis on red burgundy (nc8 22042143),notably because it is a type of wine where far more firms are listed in wine guides. Whilethere are several reasons to expect red burgundy to perform worse than Champagne thatwe list below, our primary results are common to both wines. There are several reasonsfor the relevance of wine and Champagne in particular to our framework:

• The first is the fact that the wine industry combines differentiation by place ofproduction with heterogenous quality across producers of the same origin.

Champagne and red burgundy have built reputations for non-replicable attributes.Thus, they exhibit Armington-style differentiation by place of origin. With Cham-pagne this is an organized legal and promotional effort. To qualify as champagne inthe EU (and Canada), a wine must be produced within the Champagne geographicappelation.

“The important thing to remember is that while some processes of Cham-pagne production may be duplicated, the terroir is unique, original, andimpossible to replicate.” (www.champagne.us)10

10This quote comes the offical Champagne promotion agency. Some wine critics do agree with theproposition that sparking wine from Champagne is distinct:

“The Champagne region has certain natural advantages that no amount of money, ambition,or talent can surmount: The combination of chalky soil and fickle northern European weather

13

www.champagne.us

Burgundy producers do not invest in such overt promotion of their regional identity.However, wine critics tend to judge pinot noir wines relative to the Burgundian style.Furthermore, the most expensive wines in the world are red burgundies.

The relevance for this study is that Melitz (2003) model, upon which we base ouranalysis, assumes that firms face only the option of exporting or not to a givenmarket. They cannot relocate production as in the Helpman, Melitz, Yeaple (2004)framework. With footloose production, the implications for quality sorting could bequite different. Thus, the geographic definition of champagne and burgundy makesthese goods particularly appropriate for studying the effect of heterogeneity on thecomposition of exporters by destination.

While the model rests upon a product that is not reproducible in the export market,it also insists on firm-level differentiation within each country. Champagne fitsthis assumption well. Geographic distinctions within champagne region (a singleappelation) are not emphasized.

“[E]ssence of champagne is that it is a blended wine, known in all but ahandful of cases by the name of the maker, not the vineyard.” (Johnsonand Robinson, 2005)

Quality determined by cellar-master’s talent at blending, “dosing,” etc. Sales policyemphasizes the brand.

In Burgundy, on the other hand, there are many small appelations, each of which issupposed to have distinct properties. Within the appelations, vineyards are furtherstratified into village wines, premier cru and grand cru. Many different producerstypically make wine from grapes from the same grand cru vineyard. Converselymost producers obtain grapes from multiple vineyards. Burgundians attribute mostquality variation to place-specific terroir : the soil, topography, and microclimate.Comparing across wines from the same vineyard, they also emphasize vintage: year-specific weather. Since our data does not report the vineyard or the vintage of thewine exported, it would appear ill-suited to capture quality variation in burgundywine. However, Robert Parker, the most influential wine critic in the world, assertsthat there are large within-vineyard quality differences due to firm-specific variationin viticulture and vinification practices.

“Knowing the finest producers in Burgundy is unquestionably the mostimportant factor in your success in finding the best wines.”

• There are several mechanisms supporting a cost-quality tradeoff in wine of theBaldwin-Harrigan type. First there is the cost of acquiring land with the desirableterroir properties. In Burgundy “village vineyards” cost e150–500K/ha (Robinson,

yields sparkling wines that simply can’t be replicated anyplace else, or at least anyplace that’sbeen tried.” (Steinberger, 2005)

14

20??). Assuming an interest rate of 5% and a typical yield of 5000 bottles perhectare, this corresponds to a unit land cost of e1.5–5 per bottle. On the otherhand, land that has been designated as a grand cru vineyard costs over e2M/ha, ormore than e20 per bottle. In the Champagne region the major, where the qualityof land has been built into the price of grapes through the system called echelle descrus. Thus if we think of w(s) as the factor costs embodied in wine of quality s, wehave good reasons to expect w′ > 0.

Wine is also believed to exhibit a trade-off between yield and quality. Low-yieldviticulture, which involves pruning back vines from 40 hectolitres per hectare (theaverage in Burgundy) to 20 hl/ha (the yield at the Romanee Conti vineyard) doublesunit land costs. However, Parker and most other wine experts argue that this raisesflavor concentration. Indeed the importance of yield is recognized in much of theAOC regulation in France which sets allowable yield levels by appelation.

The process of winemaking itself also exhibits cost-quality tradeoffs. One familiarexample is the use of new oak barrel. The advantage of new oak is that imparts moreflavour into the wine. However, our calculations indicate that it adds something inthe neighborhood of e2 to the cost of each bottle.

Champagne has additional features that make it even better than other wines as acase study:

• The market organization in Champagne is such that the actual producers are theones that make most of the export value of the industry, contrary to other wines.Customs data lists exports by a firm for each nc8 product. However, in other firm-level sources of data, the same firms are classified according to a“primary” activity.It appears actually that a large proportion of wine exporters are not referenced asproducers. Some of those “non-producing” exporters are dealers who mainly labeland distribute wine made by other firms (as is the case for Bordeaux). Other firmsare mainly dealers, but are also vertically integrated backwards into vinification andeven viticulture (as is the case for Burgundy). Table 2 provides the share of exportsfor Champagne and Red Burgundy according to primary activity. For Champagne,the growers and makers add up to 76% of the total, only 28% for Burgundy and avery small 9% for Bordeaux, where most of exports is channeled through large scalewholesalers (85%). The problem with exports by dealers is that it is hard to assessthe exact wine and therefore the exact quality exported by the firm. In fact, forBordeaux it is impossible to assess quality because those dealers do not seem to beproducers themselves for the vast majority of them. For Burgundy, a much largerproportion of dealers exports, and we are able to find quality ratings for them inthe guides. This is why we keep exports of red burgundy as a robustness check inthe appendix. Note however that the large proportion of dealers in total exportvalue is likely to add a substantial amount of noise in the measurement of firm-levelquality, and therefore in all of our regressions for Burgundy.

15

Table 2: Who exports wine?

activity code description Export shr.Cham. Burg. Bord.

growers 011G viticulture (grapes) 2% 24% 7%makers 159F/G vinification (wineries) 74% 4% 2%dealers 513J bev. wholesalers 7% 62% 85%others — admin., interm., ... 16% 10% 6%

• The quality of Champagne is much more stable over time. Champagne producers,as stated above, blend several years of grapes to reproduce the same taste (andtherefore quality associated with their brand). This is a big advantage over Bor-deaux or Burgundy wines for instance, where vintage matters a lot in the qualityof the product. Since we observe yearly exports by a firm, but not the precise mixof vintages of the bottles exported, having much less quality variance over vintageshelps our analysis greatly.

4 Data

4.1 Trade data

We use the micro-data collected each year based on export declarations submitted toFrench Customs. It is an almost comprehensive database which reports annual shipmentsby destination at the 8-digit product level for each French exporting firm. The “almost”is due to EU legislation following the implementation of the single market, which setsdifferent thresholds for compulsory declarations inside and outside the customs union.Inside the EU, shipments are reported if their annual trade value exceeds 250,000 euro.Exports outside the EU are recorded unless their value is smaller than 1000 euros orone ton. For each firm, Customs record FOB values and quantities exported to 216importing countries, and 11,578 8-digit product classifications (combined nomenclature,which is abbreviated as “nc8”). We have observations for the six years from 1998 to2003. We calculate firm-destination-level FOB prices (often referred to as “unit values”)as pj(i) = xj(i)/qj(i).

The nc8 is the harmonized system 6-digit (hs6) code with a 2-digit suffix that isparticular to the European Union. Wine has hs4 of 2204. Sparkling wine is 220410 andstill red wine less in less than two liter containers is 220421. For our purposes is fortunatethat the last two digits of nc8 distinguish important wine-growing regions in the EU. Thuschampagne, the sparkling wines of the official Champagne region are recorded as nc8 #22041011.

Champagne accounts for 0.45% of French exports. This might not seem large, but is infact impressive when compared to other goods. The mean good-level contribution to total

16

trade is less than 0.01% and the largest exporting industry at this level of disaggregation(aeroplanes and other aircraft exceeding 15 tons) accounts for only 3.24%. Champagneis clearly among the largest contributors to French exports, and is also a strong outlier inother dimensions. When ranking nc8 products according to number of exporting firms,champagne ranks 21st out of 11,578 products. Its importance is even more striking interms of the number of destination countries. As figure 1 shows, this industry exports toa much larger number of countries than the typical French industry. The actual rank is7th, with an average of 171 countries served in our sample years (the top industry servesan average of 179 countries).

Number of destination markets (average per year)

prob

abili

ty d

ensi

ty

0.00

00.

005

0.01

00.

015

0.02

00.

025

0 25 50 75 100 125 150 175

050

010

0015

00fr

eque

ncy

Exponential PDF

ChampagneRed Burgundy

Figure 1: Champagne is an outlier in the distribution of destinations per product

The export declaration data provides us with firm identification numbers, or SIREN,for all 12,314 firms who exported any form of wine (hs4 = 2204) between 1998 and 2003.Of those, the French National institute (INSEE) provides us with the names, addresses,main industry code, and other attributes of 10,341 firms in existence as of June 2007. Weused the firm-level information to match our exporters with wine producers that wererated in two guidebooks.

17

4.2 Quality ratings

Wine producer quality ratings come from two different sources: i) a French one: Burtschy,Bernard and Antoine Gerbelle, 2006, Classement des meilleurs vins de France, Revue DesVins De France (Paris), which we will refer to as RVF, ii) an internationally recognizedone: Parker, Robert, Wine Buyer’s Guide, 5th Edition, 1999, which we refer to as WBG.For each of the listed producers, the name and location were matched with the exporter’sdataset by hand.

In RVF, listed producers receive between 0 and 3 stars. We have 64 champagneproducers listed, and are able to match those with 51 exporters. For burgundy, 268 arelisted, of which 206 can be found in the customs dataset. In WBG, producers (70 forchampagne, and 159 for burgundy) are categorized as “average,” “good,” “excellent,” or“outstanding.” Of those we manage to find 47 champagne exporters and 139 burgundyexporters. Table 3 evaluates how closely those two quality ratings match for Champagne.Kendall’s τ index of concordance between ratings (given in the footnote) suggests thatwhile those two ratings are certainly not independent, they are not identical either. Wewill explain how we exploit those differences later.

Table 3: Champagne quality ratingsRVF’s Classement

Parker’s WBG n/a Incl. * ** *** Totaln/a 1724 16 6 0 0 1746Average 3 1 0 0 0 4Good 7 3 1 2 0 13Excellent 7 6 4 3 0 20Outstanding 1 0 3 4 2 10Total 1742 26 14 9 2 1793Note: Kendall’s τ measure of concordance −1 ≤ τ ≤ 1

(p-value for test for independence), all exporters:0.58 (0.000) / included in both books: 0.43(0.009).

We have to select a group of low quality producers. We cannot rely only on the groupof exporters that are excluded from the ratings. It seems desirable to exclude from ouranalysis all firms that ship wine abroad but for which we are unable to judge qualityof the wine exported. This happens for dealers that are not rated, who presumablyexport all sorts of wine. Those enter a category we refer to as “mixed” in figure 2. Forproducers, we consider as low quality firms, the ones that are unrated by either guideand located within the “right” areas, that is the relevant grape-growing departements.Unrated producers from other areas also enter the mixed category. The information usedto construct this “mixed” category is summarized in Table 4.

There are several issues that can be raised with guidebook ratings as quality measures:

1. The ratings are hard to interpret : units of measurement (stars) do not correspond

18

Figure 2: Champagne: Markets per firm and Prices (wt. avg.)

(a) RVF rating: Markets per firm (b) WBG rating: Markets per firm

1 2 5 10 20 50 100

0.00

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010

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1.00

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number (k) of markets (log scale)

shar

e of

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to k

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Quality Rating

******includedlowmixed

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Quality Rating

outstandingexcellentgoodaveragelowmixed

(c) RVF rating: Prices (d) WBG rating: Prices

mixed low included * ** ***

Pric

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mean

mean + std. dev.

mixed low average good excellent outstanding

Pric

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uros

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020

4060

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mean + std. dev.

19

Table 4: Champagne: # of exporters/destinations

Primary Quality-Rated? No YesActivity Local Dept? No Yes Yesgrower 40 392 22

76 3972 1015

maker 10 84 3350 2914 5846

dealer 346 94 101624 2229 769

other 678 101 42923 1166 824

to prices or quantities. Our theory includes parameter to measure marginal utilityof quality units. This parametric approach also has the advantage of compactnessin the presentation of the results .

2. The ratings are unreliable: authors may have idiosyncratic tastes or be influenced bynon-taste considerations.11 In order to minimize this concern, we use two completelyindependent sets of ratings, for which we have no reason to suspect that author-specific “specificities” would be correlated.

3. The ratings are incomplete: bad producers are usually omitted from the guidebooksand much wine is exported by non-producers. We try to correct for this by inferringthe set of low quality firms and eliminating firms likely to have mixed quality.

4. The ratings may influence price directly : Some wine experts have become so famousworldwide, that their opinion exerts a direct impact on the price a firm can chargefor its wine.

5. The ratings may influence demand by increasing foreign customer awareness. Forinstance, consumers in New Zealand are probably not aware of all varieties of wineproduced and available for consumption in France. A guide like Parker’s, becauseit is in English, and so widely popular will change to effective set of varieties inthe consumer’s information set. To eliminate this concern, we run a separate set ofregressions using only the French guide ratings (RVF) and restricting the sampleto non-francophone markets (RVF is not translated).

11Parker and the Faiveley affair. DETAIL OR THIS ONE

20

5 Results

We start by presenting results on our firm-level predictions about how quality affects theprobability to become an exporter, quantity shipped and price charged.

5.1 Individual level analysis

Tables 5 and 6 report results of our firm-level regressions. In each of those tables, thefirst three columns average the two quality ratings (WBG and RVF) when measurings(i). The last three columns uses only the French rating (RVF) and restricts the sampleto non-francophone countries.

Table 5: Champagne firm-level regressions

(1) (2) (3) (4) (5) (6)qjt(i) > 0 ln pjt(i) ln qjt(i) qjt(i) > 0 ln pjt(i) ln qjt(i)

ln s(i) 3.61a 0.29a 1.80a 3.23a 0.25a 1.24a

(0.03) (0.01) (0.03) (0.03) (0.01) (0.04)

constant 2.50a 6.22a 2.59a 6.87a

(0.01) (0.03) (0.01) (0.03)Ratings WBG & RVF average RVF onlyDestinations all markets non-francophone marketsObservations 405189 12426 12426 317516 8801 8801Within-jt R2 0.117 0.203 0.092 0.102ρ: frac. var. ∼ FE 0.38 0.29 0.37 0.25

Destination-year (jt) fixed effects. Standard errors in parentheses.Significance levels: c p < 0.1, b p < 0.05, a p < 0.01

These regressions can be used to reveal the structural parameters of the model. Recallthat equation (38) defines the elasticity of quantity with respect to quality as ηqs ≡(γ − λ)(σ− 1)− λ. Therefore, the implied value of γ is λ + (ηqs + λ)/(σ− 1). Parameterλ can be obtained as the coefficient on log quality in the price regression, 0.29. Andersonand van Wincoop (2004) report 5 ≤ σ ≤ 10 as a reasonable range for the CES. Pluggingin estimates obtained for the full sample, we infer γ to lie between 0.52 and 0.81. Usingthe higher of the two values, a consumer is willing to trade 3.7 bottles of low quality(s = 1) wine for one bottle of the highest quality (s = 5).

Furthermore, we can use estimates in Table 6 to test the Hallak (2006) assumption ofincome dependence of the preference for quality parameter, γj = γ0 + γ1 ln(yj/y0), wherethe income per capita of country j is normalized by the average world income (y0). Withthis specification of preference for quality, the exported quantity equation becomes:

ln qj(i) = ln[(σ−1)/σ]−σ ln ω+ln Aj+[(γ0−λ)(σ−1)−λ] ln s(i)+γ1(σ−1) ln s(i) ln(yj/y0).(39)

21

Table 6: Champagne firm-level regressions with interactions


ln s(i) 3.63a 0.31a 1.52a 3.21a 0.26a 0.83a

(0.03) (0.01) (0.04) (0.03) (0.01) (0.04)

ln s(i)× ln(yjt/y0) 0.15a -0.03a 0.39a 0.13a -0.02b 0.58a

(0.02) (0.01) (0.02) (0.02) (0.01) (0.03)

Constant 2.49a 6.40a 2.59a 7.05a


Destination-year (jt) fixed effects. Standard errors in parentheses.Significance levels: c p < 0.1, b p < 0.05, a p < 0.01.y0 = $6, 800 is the all-country average GDP per capita (1998–2003).

With estimates of λ = 0.29 from the price equation and σ = 7 from the literature,one can provide estimates of both γ0 and γ1.

The interaction term coefficient in column (3) implies γ1 = 0.39/6 = 0.065. A doublingof GDP per capita generates a 6.5% increase in the quality preference parameter.12 Theyalso reveal γ0 = (1.81/6)+0.29 = 0.6. Finally, preference for quality parameter is revealedto be around two thirds for a country with the average income per capita (y0 = $6, 800),while for the United States in 2003 it is 0.6 + 0.065× ln(37658/6800) = 0.71. Note alsothat the interaction coefficient should be zero for the price regression and almost is.

Table 7 provides results for our two step Heckman procedure that correct for selectionbias. The two first columns are first stage results, while second stage estimates arereported in columns (3) and (4) for prices and quantities shipped respectively. The firstcolumn provides results where country fixed effects capturing Ajt are replaced by thegravity variables usually proxying for the structural attractiveness term. The secondcolumn uses fixed effects to calculate the mills ratio then used in columns (3) and (4).While column (2) is the specification that theory recommends, there are two reasonsfor having column (1). First, it is interesting to look at how gravity variables affectentry probability. Second, our excluded variable is an interaction term between groupmembership and entry costs. While the use of country-level fixed effects in column (2)makes it impossible to estimate the influence of entry costs, it is important to see whetherthose entry costs actually affect the likelihood of exporting in the expected (negative way).

12Hallak (2006) reports a median estimate that implies γ1 = 0.03 with the same assumption on σ = 7.

22

Table 7: Champagne firm-level heckman-type regressions

(1) (2) (3) (4)qjt(i) > 0 qjt(i) > 0 ln pjt(i) ln qjt(i)

ln s(i) 1.59a 1.72a 0.33a 3.30a

(0.01) (0.01) (0.04) (0.14)

groupi × ln entry costj 0.10a 0.10a

(0.01) (0.01)

ln entry costj -0.02b

(0.01)

ln popn. (Mjt) 0.31a

(0.01)

ln inc. p.c. (yjt) 0.43a

(0.01)

ln cons p.c (µjt) 0.08a

(0.01)

ln prodn (↘ Pjt) -0.02a

(0.00)

ln distance (↗ τj) -0.10a

(0.01)

French (↘ τj) 0.89a

(0.02)

Colonial link -0.17a

(0.02)

RTA 0.29a

(0.03)

GATT Member 0.29a

(0.03)

Currency union -0.01(0.02)

mills1 0.05c 1.14a

(0.03) (0.11)Observations 343720 299801 10265 10265R2 0.112 0.235rho 0.38 0.47

Note: Destination-year (jt) fixed effects for columns (2)-(4). Standard errorsin parentheses. Significance levels: c p < 0.1, b p < 0.05, a p < 0.01

23

Table 8 gives the same estimates for the sample restricted to non francophone countrieswith RVF ranking.

5.2 Conditional mean analysis

We now proceed to the conditional mean analysis that allow a discrimination betweenthe quality sorting and the productivity sorting models, based on certain contrastingpredictions, in particular on how average prices and average quantities vary according tothe popularity (Nj) and attractiveness (Aj) of each market.

The first set of relationships to examine are the relationships between conditionalmeans and popularity shown in equations (21), (28), and (35). Since these are bivariaterelationships, we can examine them directly using scatterplots of average quality, price,and quantity versus number of exporters. The quality sorting and efficiency sorting mod-els both predict that all three relationships should be linear in log scale. Furthermore bothmodels predict equal absolute slopes of opposite signs for the mean price and quantityfigures. The quality sorting model alone predicts the negative average quality-popularityrelationship, negative price-popularity relationship, and positive quantity-popularity re-lationship.

The three scatterplots shown as panels (a)–(c) of figure 3 mainly support the qualitysorting predictions. Average quality and popularity exhibit a strong negative relationshipsin panel (a)—once popularity is sufficiently high. Although the relationship is not globallylinear, this may be due to small-sample issues for the less popular markets. On the otherhand, average quantity and popularity have a strong positive relationship in panel (c)for champagne and a noisier, but still clearly positive relationship for red burgundyin the corresponding panel of figure 5 in the appendix. The mean price panels (b) isdisappointing. The slope for champagne is only mildly negative (for red burgundy it isclose to zero). Some very popular markets like Japan (JPN) have high prices that runcounter to the model.

Tables 9 (and 15 for burgundy in the appendix) estimate the reduced form predictionsbased on equations (27) and (34). The quality sorting model predicts that any of themarket primitives that raise attractiveness should lower average quality. They shouldhave the same effect on price and the opposite sign effect on quantity. For champagne theresults conform to priors remarkably well. Market size variables (population, income, highwine consumption) all raise popularity as predicted and lower average quality. Distancelowers popularity but raises quality. Speaking French (which is supposed to lower tradecosts) raises popularity and lowers quality. Having high production of wine should reducethe price index in a market. This should reduce popularity and therefore raise quality.The signs are as expected although statistical significance is lacking. The performancefor prices is disappointing as none of the size determinants enters significantly and allhave small effects in absolute magnitude, something at odds with either theory. However,the trade cost determinants enter as the quality sorting model predicts. For quantity thequality sorting model is supported by the two main market size variables (population andincome) as well as French.

24

Table 8: Champagne firm-level heckman-type regressions - RVF / non francophones

(1) (2) (3) (4)qjt(i) > 0 qjt(i) > 0 ln pjt(i) ln qjt(i)

ln s(i) 1.37a 1.45a 0.20a 2.33a

(0.01) (0.02) (0.04) (0.19)

groupi × ln entry costj 0.16a 0.16a

(0.01) (0.01)

ln entry costj -0.09a

(0.01)

ln popn. (Mjt) 0.28a

(0.01)

ln inc. p.c. (yjt) 0.38a

(0.01)

ln cons p.c (µjt) 0.05a

(0.01)

ln prodn (↘ Pjt) -0.01a

(0.00)

ln distance (↗ τj) -0.15a

(0.01)

Colonial link -0.09a

(0.03)

RTA 0.09a

(0.03)

GATT Member 0.30a

(0.03)

Currency union 0.10a

(0.02)

mills2 -0.03 0.85a

(0.04) (0.16)Observations 277620 237667 7407 7407R2 0.091 0.128rho 0.37 0.37

Note: Destination-year (jt) fixed effects for columns (2)-(4). Standard errorsin parentheses. Significance levels: c p < 0.1, b p < 0.05, a p < 0.01

25

Figure 3: Conditional mean graphs for champagne

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(c) cond. mean quantity26

Table 9: Champagne, proxies for Aj

(1) (2) (3) (4)ln Nj ln sj ln pj ln qj

ln popn. (Mjt) 0.40a -0.07a 0.01 0.37a

(0.05) (0.01) (0.01) (0.06)

ln inc. p.c. (yjt) 0.76a -0.05a 0.02 0.69a

(0.06) (0.01) (0.02) (0.06)

ln cons p.c (µjt) 0.07 -0.04a 0.00 0.03(0.05) (0.01) (0.01) (0.05)

ln prodn (↘ Pjt) -0.04 0.01c -0.00 0.01(0.03) (0.01) (0.01) (0.03)

ln distance (↗ τj) -0.03 0.07a 0.09a 0.10(0.08) (0.02) (0.03) (0.08)

French (↘ τj) 1.53a -0.22a -0.18a 0.61a

(0.18) (0.05) (0.05) (0.14)

constant -4.97a 1.17a 1.96a 0.67(0.93) (0.26) (0.32) (0.90)

Observations 168 160 168 168R2 0.654 0.529 0.212 0.741

GLS, weightj =√

Nj, Standard errors in parenthesesSignificance levels: c p < 0.1, b p < 0.05, a p < 0.01

27

Table 10: Champagne, FE estimate for Aj


ln Ajt 0.99a -0.14a -0.05b 1.18a

(0.10) (0.02) (0.03) (0.04)

Constant 3.21a 0.95a 2.86a 9.28a

(0.17) (0.03) (0.03) (0.06)Observations 176 176 176 176R2 0.525 0.347 0.046 0.855

GLS, weightj =√


The reduced form version imposes some strong assumptions on Aj, in particular re-garding the specification of trade costs and the determinants of demand for wine inimporting countries. Another path is possible using our results from the firm-level regres-sions. Equation (38) reveals that the fixed effects estimated in the regression explainingindividual export quantity corresponds to ln Aj in our model. One can retrieve those fixedeffects, and estimate conditional mean regressions directly on ln Aj, as theory suggestsshould be the case.13

These bivariate relationships between means and imputed attractiveness are reportedin Table 10 (and 16 for burgundy in the appendix). The results once again offer muchsupport for the quality sorting model. For both champagne and burgundy, popularity ismore or less proportional to attractiveness. As predicted, average quality is negativelyrelated to attractiveness. The sign on the price effect is supportive of quality sorting butit is only statistically significant for champagne. Finally the quantity relationships arestrongly significant. Indeed the result is too strong to be consistent with the theory’sprediction that the price and quantity effects be equal in absolute value. The asymmetryin magnitudes we find is also at odds with the efficiency sorting model. Taken togetherwith the previous results, it seems to us that the prices are highly noisy and appearto be driven by forces outside the basic models. Noise in unit values is to be expectedbut perhaps greater predictive power would be possible in a model with some pricingto market. The Dixit-Stiglitz-Krugman prediction of destination-invariant FOB pricesseems hard to square with the results.

13The precise implementation of this methodology involves regressing individual quantity shipped ontwo sets of fixed effects: one for firms and one for destination countries (capturing lnAjt). It amounts toreplacing measured quality with a firm dummy in equation (38). This specification has the advantage ofmaking the measurement of lnAjt unaffected by which precise variable (quality, efficiency, or anythingelse) is the true driver of firms’ performance. We are grateful to Henry Overman for pointing out thisissue in a previous version of the paper.

28

6 Conclusion

We have illustrated the importance of quality for trade by examining an industry inwhich quality can be measured (albeit imperfectly). Heterogeneous firms theory impliesa threshold quality for market entry. The result is quality sorting: good firms are betterable to serve difficult markets. We show firms with higher measured quality are morelikely to export, export more, and charge higher prices. Champagne exhibit qualitysorting using direct measures. Quantities also respond to market attractiveness withthe predicted sign. Firm-level prices exhibit much destination level variation that is notpredicted by the model. Average prices do not exhibit quality sorting.

7 References

Baldwin, R. and J. Harrigan. 2007. “Zeros, Quality and Space: Trade Theory andTrade Evidence”, NBER Working Paper No. 13214.

Bernard, A., B. Jensen, S. Redding and P. Schott, 2007, “Firms in International Trade”Journal of Economic Perspectives.

Bernard, Andrew B., Jonathan Eaton, J. Bradford Jensen, and Samuel S. Kortum,(2003) “Plants and Productivity in International Trade”, American Economic Re-view, 93(4), 1268–1290.

Chaney, T. 2008. “ Distorted Gravity: the Intensive and Extensive Margins of Interna-tional Trade”,American Economic Review, forthcoming.

Eaton J., S. Kortum and F. Kramarz, 2004, “Dissecting Trade: Firms, Industries, andExport Destinations”, American Economic Review, Papers and Proceedings, 93:150–154.

Eaton, Jonathan, Samuel Kortum and Francis Kramarz (2006), “An Anatomy of In-ternational Trade: Evidence from French Firms”, University of Minnesota, mimeo-graph.

Foster, L. J. Haltiwanger and C. Syverson, 2008, “Reallocation, Firm Turnover, and Ef-ficiency: Selection on Productivity or Profitability?” American Economic Review,98(1): 394-425.

Hallak, J-C. 2006. “Product Quality and the Direction of Trade,” Journal of Interna-tional Economics 68(1): 238–265.

Helpman, Melitz and Rubinstein, 2008, “Estimating Trade Flows: Trading Partners andTrading Volumes”, Quarterly Journal of Economics.

Hummels, D. and P. Klenow, 2005, “The Variety and Quality of a Nation’s Exports”,American Economic Review, 95, 704-723.

29

Lawless, M. and K. Whelan, 2007, “A Note on Trade Costs and Distance”, mimeoCentral Bank of Ireland.

Melitz M., 2003, “The Impact of Trade on Intra-Industry Reallocations and AggregateIndustry Productivity”, Econometrica, 71(6): 1695-1725.

Melitz, M. and G. Ottaviano, 2008, “Market Size, Trade, and Productivity,”, Review ofEconomic Studies, forthcoming.

Steinberger, Mike, 2005, “American Sparkling Wines: Are they ever as good as cham-pagne?” Slate, Posted at http://www.slate.com/id/2132509/ on Friday, Dec. 30,2005.

A Burgundy material

Table 11: Burgundy quality ratingsRVF’s Classement

Parker’s WBG n/a Incl. * ** *** Totaln/a 1389 69 44 20 4 1526Average 19 7 6 4 1 37Good 28 4 4 12 1 49Excellent 11 1 11 14 1 38Outstanding 4 1 4 3 3 15Total 1451 82 69 53 10 1665Note: Kendall’s τ measure of concordance −1 ≤ τ ≤ 1

(p-value for test for independence), all exporters:0.39 (0.000) / Included in both books: 0.22(0.023).

The results for burgundy shown in table 15 are a bit less consistent. However, for themost part they also support the quality sorting model. One perverse result is the positiveand significant effect of per capita income in the price equation (column 3).

30

http://www.slate.com/id/2132509/

Table 12: Burgundy: # exporters/destinations

Primary Quality-Rated? No YesActivity Local Dept? No Yes No Yesgrower 91 303 1 170

175 3276 2 4554

maker 21 20 5136 482 182

dealer 298 157 6 621922 3739 98 3159

other 356 143 2 301346 1112 54 643

Table 13: Burgundy firm-level regressions


ln s(i) 1.69a 0.29a 0.58a 1.35a 0.19a 0.45a

(0.02) (0.01) (0.03) (0.02) (0.01) (0.03)

constant 2.23a 6.23a 2.29a 6.34a


Destination-year (jt) fixed effects. Standard errors in parentheses.Significance levels: c p < 0.1, b p < 0.05, a p < 0.01

31

Figure 4: Burgundy: Markets per firm and Prices (wt. avg.)

(a) RVF rating: Markets per firm (b) WBG rating: Markets per firm

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Figure 5: Conditional mean graphs for burgundy

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Table 14: Burgundy firm-level regressions with interactions


ln s(i) 1.96a 0.31a 0.40a 1.73a 0.24a 0.34a

(0.04) (0.03) (0.06) (0.05) (0.04) (0.06)

ln s(i)× ln(yjt/y0) -0.25a -0.02 0.14a -0.35a -0.04 0.09b

(0.03) (0.02) (0.04) (0.03) (0.03) (0.04)

constant 2.23a 6.26a 2.28a 6.37a


Destination-year (jt) fixed effects. Standard errors in parentheses.Significance levels: c p < 0.1, b p < 0.05, a p < 0.01y0 = $6, 800 is the all-country average GDP per capita (1998–2003).

34

Table 15: Burgundy, proxies for Aj


ln popn. (Mjt) 0.56a -0.05a -0.02 0.39a

(0.07) (0.01) (0.03) (0.05)

ln inc. p.c. (yjt) 1.15a -0.03 0.24a 0.49a

(0.07) (0.02) (0.03) (0.06)

ln cons p.c (µjt) 0.03 -0.02 -0.08b -0.01(0.07) (0.01) (0.03) (0.05)

ln prodn (↘ Pjt) -0.10b 0.01b 0.05a -0.10a

(0.04) (0.01) (0.01) (0.02)

ln distance (↗ τj) 0.01 0.00 0.19a -0.12c

(0.13) (0.02) (0.05) (0.07)

French (↘ τj) 1.32a -0.18a 0.10 0.59a

(0.22) (0.04) (0.12) (0.18)

Constant -9.42a 1.36a -0.64 3.21a

(1.36) (0.31) (0.54) (0.98)Observations 148 112 148 148R2 0.688 0.235 0.451 0.639

GLS, weightj =√


Table 16: Burgundy, FE estimate for Aj


ln Aj 1.22a -0.11a 0.05 1.04a

(0.16) (0.02) (0.08) (0.06)

Constant 3.07a 0.84a 2.87a 8.12a

(0.30) (0.02) (0.10) (0.07)Observations 124 124 124 124R2 0.377 0.246 0.008 0.777

GLS, weightj =√


35

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