What’s Behind the Figures? Quantifying the
Cross-Country Exporter Productivity Gap∗
Kozo Kiyota †Toshiyuki Matsuura ‡Lionel Nesta §December 26, 2018

Abstract
We present a simple framework that allows us to examine the cross-country
exporter productivity gap without accessing confidential firm-level data. This gap
depends on the three readily available statistics: the productivity gap between two
countries; the export participation rates; and export premia. This gap holds irrespective of the distribution underlying firm productivity and irrespective of thepresence of fixed costs. Under specific conditions, allocative efficiency may affect the exporter productivity gap. The empirical analysis globally validates thisexercise.

Key words: International productivity gap; Export premia; Competitiveness; Meta
analysis.
JEL classification code: F1, D24∗

This study is conducted as a part of the Project “Microeconomic Analysis of Firm Growth” undertaken at Research Institute of Economy, Trade and Industry (RIETI). This study utilizes the micro dataof the questionnaire information based on the Basic Survey of Japanese Business Structure and Activities
which is conducted by the Ministry of Economy, Trade and Industry (METI). We benefited from helpfulcomments on earlier drafts from Hirokazu Ishise and seminar participants at Hokkaido University, Keio
University, Kindai University, Kyoto University, Okayama University, RIETI, the University of Niigata
Prefecture, the University of Tokyo, and participants at CAED2015, JSIE2015, JEA2016, ETSG2016
conferences/meetings. Kiyota and Matsuura gratefully acknowledge the financial support received froma JSPS Grant-in-Aid (JP16H02018, JP18H0367). Kiyota also acknowledges financial support received
from the JSPS Grant-in-Aid (JP26220503). The usual disclaimers apply.
†
Department of Economics, University of Hawai‘i, Mānoa, 2424 Maile Way, Saunders 534, Honolulu,
HI, 96815, USA, Keio University, and RIETI, Japan. E-mail: kiyota@sanken.keio.ac.jp‡
Keio University, Japan. E-mail: matsuura@sanken.keio.ac.jp§
Université Côte d’Azur, CNRS, Gredeg, OFCE SciencesPo and SKEMA Business School, France.
Email: lionel.nesta@unice.fr

1

1

Introduction

How can one compare the performance of exporters from different countries? This
question has gained enormous momentum in the past decade [e.g., 9], first and foremost
because exporting firms are regarded as the key actors in economic recovery. Consider
the Eurozone countries. Since the financial turmoil of 2008, Eurozone countries havefound it difficult to return to their pre-crisis level of economic activity. Austerity policies
have depressed internal demand, making it key for the country to recover growth via
distant markets. A better understanding of the behaviour and performance of exporters
is therefore needed for policy makers to implement successful export policies.
Increased awareness of the benefits of exports for economic growth is accompanied
by a broadening reliance on firm-level information (International Study Group on Exports and Productivity (ISGEP), 2008). The well-documented productivity premium has
made it clear that in many respects, exporters outperform non-exporters within a given
country. However, it is difficult to provide an economic interpretation for the magnitudeof the productivity premium enjoyed by exporters, and a large export premium does notmechanically imply a productivity advantage of these exporters relative to their foreigncompetitors. In other words, little can be said about how exporters from one country
perform with respect to exporters from other countries.
The main contribution of this paper is to encourage economists to use readily available data to actually assess and compare the performance of exporters from different
countries. Our intuition is that readily available figures conceal additional informationthat allows one to compare exporters from different countries. Our paper is similar in
spirit to that of [1]. However, whereas [1] focus on families of theoretical models, ourpaper concentrates on families of empirical papers analyzing the exporters’ premium.
In a similar fashion, we come up with the conclusion that, without direct access to firmlevel data, three descriptive statistics are sufficient to allow the comparison of exporters’level of productivity across countries.
We advance three propositions. The first proposition is based on a simple identity toshow that the productivity gap between exporters can be assessed by using three basic
statistics. Proposition 2 states that Proposition 1 holds irrespective of the distribution
underlying firm productivity and irrespective of the presence of fixed costs. Proposition
3 raises concerns about the use of aggregated statistics and shows that our frameworkholds either when the productivity gap between exporters is of significant magnitude or,if this gap is narrow, when market structures are similar across countries. The paper
then empirically explores our propositions by using readily available, aggregated data
and testing the validity of the framework by accessing confidential firm-level data.
The remainder of the contribution is structured as follows. The next section presents
the literature review. Section 3 explains our analytical framework and explores various
dimensions such as concerns regarding the use of aggregated data. Section 4 presents2

empirical results based on the use of readily available data and on confidential, firmlevel data from France and Japan. A summary of our findings and their implications ispresented in the final section.

2

Literature Review

The international competitiveness of industries has long been a central issue in the business literature [e.g., 32] and in the economics literature [e.g., 11, 9].1 In measuring theinternational competitiveness of industries, previous studies have focused primarily on
two aspects. One is productivity (e.g., the comparison of industry-average productivity),
and the other is exports (e.g., the comparison of export shares in the world market using
revealed comparative advantage). After [27] succeeded in developing a model to explain
the systematic link between firm productivity and exports, a number of studies have examined the relationship between these two values in various countries.2 However, thefocus of the previous studies is limited to the relationship between firm productivity andexports within a country. Although the productivity of exporters certainly reflects theinternational competitiveness of the firms in a country, little attention has been paid tothe comparison of the productivity gap across exporters between countries.
Some studies such as that conducted by the [20] and by [7] have examined the crosscountry differences in export premia (i.e., the productivity difference between exporters
and non-exporters within a country). However, high export premia do not necessarily
imply that exporters will be competitive on international markets. To the best of ourknowledge, only [4] directly compare the productivity of exporters from two different countries.3 In other words, although we now know that exporters outperform nonexporters, we do not know much about whether exporters from one country outperform
those from another country. The cross-country comparison of exporter performance has
not yet been fully explored in the literature.
Focusing on the productivity of exporters is nontrivial. Table 1 presents the rankingof labour productivity for 11 developed countries. One interesting finding is that the
1 In this paper, we focus on competitiveness as measured by productivity, and do not analyze othercompetitiveness measures such as unit labour cost. Accordingly, our empirical analysis focuses on advanced countries exclusively. The comparison between advanced and developing countries is beyond thescope of our paper.
2 See [16, 35, 17] for surveys and [5] and [24] for evidence from France and Japan, respectively.
3 Using confidential firm-level data from the French and Japanese manufacturing industries, [4] reportthat the productivity gap across French and Japanese exporters systematically differed from the averageindustry productivity gap: it is wider in industries in which Japan has a productivity advantage and it isnarrower in industries in which France has a productivity advantage. This is due to the differences in theselection effect between Japan and France. As a consequence of the stronger selection of Japanese firms
into export markets, the productivity gap between Japanese and French exporters becomes larger than the
average productivity gap in industries in which Japan has a productivity advantage.

3

United States ranks eighth out of these 11 countries. This low rank is puzzling because
it is widely believed that US firms represent the productivity frontier and are therefore
the most competitive firms in the world. We argue that this puzzle comes from thegap between the productivity of exporters and industry-average productivity (i.e., theproductivity of exporters and non-exporters). The average productivity of an industry
certainly affects the productivity of exporters. However, as we will show, the productivity of exporters is also the product of the selection of firms into foreign markets and ishence determined by the export participation rate. It follows that high (low) average productivity in an industry does not mechanically imply a high (low) level of productivity
for exporting firms.
[Table 1 about here.]
Clarifying the cross-country exporter productivity gap is not an easy task. Somestudies have compared the international productivity gap at the firm level.4 However,most of them have focused on large, listed firms. This choice precludes the ability toaddress the issue of heterogeneity in the export behaviour of firms, simply because thevast majority of listed companies are exporters. One thus needs access to confidential
firm-level data from different countries, which implies that one faces several confidentiality restrictions. For example, Japanese confidential firm-level data are available only
within Japan. Similarly, French confidential firm-level data are available only within
France. Because of data confidentiality restrictions, one cannot simply merge two or
several datasets into one unique dataset.
One additional difficulty remains. To compare productivity levels between different
countries, one needs to address the issue of the comparability of inputs and outputs.
First, one needs to ensure that the accounting definitions of many firm-level variables
stemming from the financial statements are similar, if not identical. Second, the exchange rate between any two currencies does not necessarily yield the proper relative
price between countries, due, for example, to short-term capital movements. One needs
information on purchasing power parity (PPP) for inputs and outputs [e.g., 22, 19] if
one is to address the issue of the cross-country exporter productivity gap.
Our main contribution is to develop a simple framework that allows one to examine
the cross-country exporter productivity gap without directly accessing confidential firmlevel data. This framework is based on three propositions that are empirically tested. We
show that the average international productivity gap between exporters (PXb ) depends onthe following three sufficient statistics:
1. The industry-average productivity gap between two countries (Pb ), which is defined as the average productivity of all firms (exporters and non-exporters);
4 See, for example, [2], [14], and [23].

42. The export participation rate (Ω), which is defined as the ratio of the number ofexporters to the number of all firms (exporters and non-exporters);
3. The export premium (PXw ) within a country, which is defined as the productivity
difference between exporters and non-exporters.
The above three variables can be relatively easily obtained from the literature allowing, for example, the implementation of a meta analysis.
Our framework does not depend upon the productivity distribution so long as the
distribution has a mean.5 Many studies on firm heterogeneity and trade assume thatthe productivity and/or size of firms follow a Pareto distribution.6 Some recent studies
depart from this assumption. For example, [12] and [29] explore the properties of abounded (or truncated) Pareto distribution, while [18], [37], and [4] examine those of alog-normal distribution. Our study goes one step further without assuming any specificdistribution while addressing the issue of firm heterogeneity and trade.7
We apply our framework to cross-country comparisons across 11 advanced countries, such as Japan, the United Kingdom, and the United States, obtaining the relevant
information from the literature. The major findings of our paper are twofold. First, theaverage exporter productivity gap between two countries does not necessarily reflect
the industry-average productivity gap due to the differences in export participation rates
and export premia between countries. Second, higher export premia do not necessarilyreflect higher performance in exporter productivity.

3

Statistical Framework

3.1

A simple identity

Consider a population that consists of two groups 1 and 2. Let x̄i be the mean of group i,with i = (1, 2). The mean of the sample x̄, as the weighted average of x1 and x2 , reads asx̄ = sx1 + (1 − s)x2 , where s is the share of group 1 in the overall population. Subtracting
x1 from both sides and rearranging terms yields:
x1 = x̄ + (1 − s)dx,(1)

5 Some distributions such as the Cauchy distribution do not have a mean. However, such distributions

are rarely used in economic studies.
6 See, for example, [27].
7 [4] also present a simple framework to relate cross-country productivity gaps to the export status offirms. However, the scope of their framework is limited in the sense that it relies on the assumption thatfirms’ productivity is distributed log-normal. Therefore, our paper is a generalizatoin of their study.

5where dx = x1 − x2 . Identity 1 holds if the overall population and its subgroups admit amean. Now this very simple, if not tautological, identity provides a useful starting point
to analyse the exporter productivity gap.
Let µX and µD be the average productivity gap for exporters and domestic firms(firms focusing on the domestic market), respectively. Let N, NX and ND be the numberof all firms, exporters, and non-exporters, respectively, where N = NX + ND . Similar
to the above general example, the overall industry-average productivity µ reads as theweighted average of the levels of productivity of domestic and exporting firms µ =ΩµX + (1 − Ω)µD , where Ω = NX /N is the export participation rate, i.e., the shareof firms exporting to foreign markets. Now write the overall level of productivity µ
as the weighted average of the levels of productivity of domestic and exporting firmsµ=ΩµX + (1 − Ω)µD . Subtracting µX from both sides and rearranging terms yields:µX = µ + (1 − Ω)(µX − µD ) = µ + (1 − Ω)PXw ,(2)

w is the well-documented – generally positive – export premium, that is, thewhere PX,cproductivity difference between exporters and non-exporters. The superscript w denotes the export premium computed using firms active within the same domestic market.
Equation (2) states that the mean level of productivity of exporting firms is a function of
the overall level of productivity of active firms µ and the product of the domestic participation rate (1 − Ω) and the export premium PXw = µX − µD . We call the first component(µ) the competitiveness effect and the second component ((1 − Ω) · PXw ) the selection
effect. Although the former effect is pervasive in the literature on cross-country competitiveness, the selection effect provides information about the threshold productivity
levels that companies must reach to cope with sunk costs of entering export markets.

The above general framework is useful if one wishes to establish cross-country comparisons in competitiveness with readily available statistics in the empirical literature on
the firm export premium. For any pair of countries, we have the following proposition:
Proposition 1: The average international exporter productivity gap (PXb ) depends
on three sufficient statistics: 1) the industry-average productivity gap (Pb ); 2) the export
participation rate Ω; and 3) the export premium in each country (PXw ).
Proof: Let µX,1 and µX,2 , be the mean productivity of exporters in country 1 andcountry 2, respectively. Using equation (2), the following is immediate:w
w
PXb ≡ µX,1 − µX,2 = µ1 + (1 − Ω1 )PX,1− µ2 + (1 − Ω2 )PX,2w
w= Pb + (1 − Ω1 )PX,1− (1 − Ω2 )PX,2,

where (µ1 − µ2 ) represents the productivity gap between the two countries. 
6(3)

Proposition 1 is admittedly very simple. However, conditional upon the availabilityof information on Pb , Ω and PXw , it allows for the comparison of country performancein export markets without accessing confidential firm-level data in countries 1 and 2. A
direct implication is that, given the same benchmark, pairwise comparisons involving
several countries can be recovered. Hence, we have Lemma 1:
Lemma 1: Given three countries 1, 2 and 3, if the international exporter producb ) and the international exporter productivity
tivity gap between countries 1 and 3 (PX,13b ) are known, then the international exporter progap between countries 2 and 3 (PX,23b ) can be recovered.
ductivity gap between countries 1 and 2 (PX,12bb
Proof: Let PX,13≡ µX,1 − µX,3 and PX,23≡ µX,2 − µX,3 ; the following is immediate:

b
b
PX,13
− PX,23= (µX,1 − µX,3 ) − (µX,2 − µX,3 )= µX,1 − µX,2 .
b= PX,12(4)

Depending on data availability, pairwise comparisons can be performed. 
The decomposition presented above excludes more sophisticated phenomena suchas firm entry into and exit from foreign and domestic markets. In this respect, ouranalysis is based on a simple static framework rather than a more complex dynamic one.
Nonetheless as presented here, a part of the extensive margin effects can be captured by
the changes in the export participation rate because firm entry and exit directly affects
the share of exporters.8

3.2

Heterogeneous firms and trade model

Although useful, the above framework does not assume any distribution of firm-levelproductivity, nor is it based on any formal international trade model à la [27]. In fact,
this simple framework is consistent with the heterogeneous firm trade model. To thisend, we make the simplifying assumption that firms cope with sunk costs of entering
domestic and foreign markets that are common to all firms. Obviously, such costs are
firm specific and follow a given distribution, as is the case in [28]. Therefore in ourframework, such costs should be viewed as the industry average of a distribution ofheterogeneous, firm-specific sunk costs of entering markets, whether domestic or international.
8 A caveat is that the export participation rate can only capture the net entry effects.

7Let ωi be the logarithm of the productivity of firm i in an industry. Firm productivity
is assumed to follow a distribution ω ∼ g(ω), with ω and ω̄ representing the minimum
and maximum values of firm productivity. For the sake of generality, we do not need toassume any specific parametric distribution.
Firms cope with two types of sunk entry costs. We define cD as the cost associated with entering the domestic market and cX as sunk costs of entering export markets.
To cope with cD and cX , firm efficiency must exceed the threshold productivity levels
ωD to enter the domestic market and ωX to enter foreign markets. Strictly speaking,export costs cX include not only sunk entry costs into export markets but also periodby-period fixed costs. Moreover, assuming that firms face a common threshold (i.e.,cD and cX ) may seem highly simplistic. In a more realistic fashion, one could think ofexport thresholds as being composed of four components: a firm-specific component
ci ; a sector-specific component cs , a region-specific component cr , and a domestic –economy-wide – component cw , so that cX = ci + cs + cr + cw . By analyzing the conditions under which cross-country comparisons can be performed, we naturally equatecX with cw (cX = cw ). When cross-country comparisons can be performed by industry,
our framework equates cX with both cs and cw (cX = cs + cw ). However, this framework
cannot include firm-specific thresholds to perform cross-country comparisons. What is
important is that our framework can only address comparisons based on the part of sunk(and fixed) costs which is common to the set of companies to which the comparisonsapplies.
The literature generally reports that the vast majority of firms focus on domestic
markets and fewer export part of their production to foreign markets. Accordingly, werank the threshold values as follows: 0 < ω < ωD < ωX < ω̄ < ∞. Given this setting,the average productivity of firms active in the market reads as follows:R ω̄ωµ = E(ω|ωD < ωi < ω̄) = R Dω̄ωg(ω)dωωD g(ω)dω.

(5)Under perfect sorting, all firms exceeding the threshold value export, whereas firms
failing to reach the threshold focus on the domestic market. The expected productivityof domestic and exporting firms µD and µX then read, respectively, as:R ωX

ω ωg(ω)dωµD = E(ω|ωD < ωi < ωX ) = R DωX,ωD g(ω)dω

and

R ω̄
ω

µX = E(ω|ωX < ωi < ω̄) = R Xω̄ωg(ω)dωωX g(ω)dω.

Given this very general framework, we propose the following:

8

(6)

(7)

Proposition 2: Proposition 1 holds irrespective of 1) the truncation of the productivity distribution due to sunk costs of entering the domestic market and 2) the data
generating process, that is, the distribution of the productivity distribution so long as
the distribution has a mean.
Proof: Write the overall level of productivity µ as the weighted average productivityof domestic and exporting firms:
R ωX
ω g(ω)dωωX g(ω)dωµX + R ω̄DµD ,µ = R ω̄ωD g(ω)dωωD g(ω)dω
R ω̄

(8)

where ωω̄X g(ω)dω/ ωω̄D g(ω)dω is the share of firms active in export markets (the exRRport participation rate) and ωωDX g(ω)dω/ ωω̄D g(ω)dω is the share of firms focusing on
the domestic market (the domestic participation rate). Now let Ω be the export participation rate. The domestic participation rate reads as follows:
R

R

R ωX

R ω̄
R ω̄
ωD g(ω)dωωD g(ω)dω − ωX g(ω)dω== 1 − Ω.
R ω̄R ω̄ωD g(ω)dωωD g(ω)dω

Inserting Ω and (1 − Ω) into equation (8), subtracting µX from both sides and rearranging terms yieldsµX = µ + (1 − Ω)(µX − µD ) = µ + (1 − Ω)PXw .

(9)Whether the data generating process is identical or different across any two countries
does not affect equation (9) and, therefore, does not affect equation (3). In the same vein,
whether there exist significant differences in fixed costs CD between countries does notaffect the feasibility of the comparison. 

3.3

Aggregation issues

Thus far, the average productivity is the simple, arithmetic mean of the (log of) the
productivity parameter of all firms within an industry µ = (1/N) ∑i ωi . Because we do
not weight observations, µ represents the unweighted productivity average. However inthe literature, most figures stem from industry-level data, meaning that when computing
productivity, one necessarily computes the ratio of two sums:
Ψ=

∑i Qi
,
f (∑i Vi )(10)where Qi and Vi are output and input for firm i and f (∑i Vi ) may represent various
combinations of inputs. Because larger firms will account for a larger share of the9industry summation for both Q and V , Ψ represents the weighted average of the firmspecific productivity terms. Only under very specific market structures in which all firms
have a strictly identical use of inputs and equal market shares will the two productivity
averages coincide: µ = Ψ. Because this is very unlikely to hold in practice, one must
address the additional issue of aggregate productivity.
By aggregate productivity, we mean the summation of individual, firm-specific measures of some productivity performance ωi using specific weights, the choice of which
is far from univocal. Firms are heterogeneous in their use of inputs and in market shares,
and whether one chooses to weight firms using their output shares or their input use does
not yield a similar relationship between the unweighted productivity average used in ourframework and aggregate productivity [see 34, for a discussion]. In this subsection, we
follow [31] and choose to use output weights.
Define the log of weighted average productivity as Ψ ≡ ∑i vi ωi , where vi (= Yi /Y ) is
the market share of firm i; Yi and Y (= ∑i Yi ) are the output of firm i and that of all firms,
respectively. Let v̄ and ω̄ be the simple average of the output share and productivity. As[31] show, the weighted average productivity can be decomposed into the unweighted
average productivity and the overall covariance term:Ψ = ω̄ + ∑ ∆vi ∆ωi ,

(11)

i

where ω̄ = (1/N) ∑i ωi , ∆vi = vi − v̄ and ∆ωi = ωi − ω̄.
Note that ω̄ equates with µ, the unweighted average productivity of all firms. Henceω̄ is also the weighted average of the productivity of exporters and that of non-exporters:ω̄ = µ = ΩµX + (1 − Ω)µD .

(12)

The so-called covariance term ∑i ∆vi ∆ωi is an indicator of allocative efficiency. If
firms with higher market shares are also the most productive, the covariance term exceeds zero. A negative covariance term indicates that the least-productive firms are also
those with the larger market shares, thus indicating a misallocation of resources acrossfirms active in the market. Therefore, allocative efficiency must reflect institutional andregulatory features that may distort the functioning of markets [3]. Note that the covariance term can also be written as follows:∑ ∆vi ∆ωi

∑ ∆vi∆ωi = N i N= Ncov(∆v, ∆ω),

(13)

i

where cov(∆v, ∆ω) ≡ (1/N) ∑i ∆vi ∆ωi . We thus have
Ψ = µ + Ncov(∆v, ∆ω).

(14)

The term Ncov(∆v, ∆ω) is economically meaningful. The number of firms N relates10

to competition or market structure in a given market, and the covariance cov(∆v, ∆ω)
provides information on what could be thought of as normalized allocative efficiency.
Computing ∂ cov(∆v, ∆ω)/∂ ∆ω yields (1/N) ∑i ∆vi . This term can be interpreted as the
expected gain in market share for domestic firms stemming from a unit increase in thefirm’s own productivity relative to the market. In turn, knowledge about the size of themarket provides information on profit opportunities. This latter component makes thecovariance term comparable across countries and/or industries.
If Ncov(∆v, ∆ω) is large, i.e., Ψ > µ, then competition and normalized allocative
efficiency add to the overall productivity of the market. Conversely if Ψ ≤ µ, then alack of competition and misallocation problems presumably harm economic growth.
We therefore propose the following:
Proposition 3: The comparison of exporter performance between any two countries
is compatible with the use of aggregated data if allocative efficiency is similar between
the two countries.
Proof: Adding a country-specific subscript c to take into account country differences
yields Ψc = µc + Nc cov(∆vc , ∆ωc ). The weighted average productivity gap between two
countries (c = 1, 2) now reads as follows:Ψ1 − Ψ2 = µ1 − µ2 + N1 cov(∆v1 , ∆ω1 ) − N2 cov(∆v2 , ∆ω2 )= Pb + N1 cov(∆v1 , ∆ω1 ) − N2 cov(∆v2 , ∆ω2 ).

(15)

Our framework is consistent with the weighted average productivity gap if the following
relationship holds:
N1 cov(∆v1 , ∆ω1 ) = N2 cov(∆v2 , ∆ω2 ).

(16)

Differences in allocative efficiency can stem from differences in either competition or
profit opportunities. 
Whether this relationship actually holds is an empirical issue. We will address thisissue in Section 4.3.

4Empirical Analysis

4.1

Baseline analysis: labour productivity

This section examines the empirical validity of Proposition 1. It states that our analytical framework can be applied to cross-country comparisons without directly accessing
11

confidential firm-level data. To estimate the international exporter productivity gap PXb ,only the industry-average productivity gap Pb , export participation rate Ωc , and export
productivity premium PXw of each country are needed. For manufacturing as a whole, it
is relatively easy to access these data.
We focus on 11 advanced countries: Belgium, Germany, Sweden, France, Austria,
the United Kingdom, Denmark, the United States, Japan, Italy and Spain. We obtain theindustry-average labour productivity gap Pb from the Groningen Growth and Development Center (GGDC) Productivity Level Database.9 The export participation rate Ωcand export productivity premium PXw come from [20] and [4].
Ideally, we would construct these variables using firm-level data across countries
to maintain the consistency of the variables. However, firm-level data are confidential
in many countries, and thus, it is not easy to apply the same criteria across countries.
Therefore, this exercise may be helpful for those who are interested in the international
comparison of exporters’ productivity but cannot access confidential firm-level data,
although the results of this exercise should be interpreted with caution.
Table 2 presents the results using equation (3). The industry-average productivity
gaps Pb and the exporter productivity gaps PXb are measured relative to the United States.
Table 2 indicates, for example, that Belgian firms are, on average, 26.4 percent moreproductive than their US counterparts (0.264 in Belgian Pb ), whereas Spanish firms are,on average, 26.9 percent less productive than US firms (−0.268 in Spanish Pb ). Rank Pb
and Rank PXb are the rankings of the productivity gap for all firms and that for exporters,
respectively.
[Table 2 about here.]Three findings appear immediately. First, the exporter productivity gap (PXb ) for two
countries does not necessarily reflect the industry-average productivity gap (Pb ). For
example, while French exporters are 8.4 percent less productive than US firms (−0.084
in French PXb ), the industry-average productivity for France is 7.9 percent greater thanthat of the US (0.079 in French Pb ). As suggested by the fact that the export participation rate is higher in France, French firms presumably face lower trade costs thantheir US counterparts. This is indeed plausible, first because France is geographicallylocated in the centre of Europe and, second, because it shares its currency with otherneighbouring Eurozone countries, thereby decreasing export costs related to the use offoreign currencies.
Second, a higher export premium does not necessarily reflect greater performance inexporter productivity. For example, the export premium for Italy is 9.7 percent, whereasthat of the United States is 2.0 percent. Nevertheless, the average productivity of Italian
exporters is 32.8 percent lower than that of US exporters. This pattern is due both
9 We first focus on labour productivity to account for possible measurement error. As was pointed out

by [26], the measurement error tends to be most pronounced in capital variable.

12to the higher industry-average productivity of US companies and fiercer selection into
export markets due to higher trade costs in the US. This result clearly indicates that theinternational comparison of exporter productivity gaps is different from that of export
productivity premia.
Third, use of Lemma 1 allows us to recover various international productivity gaps.
For example, the performance of German exporters relative to Belgian exporters amountsbb
to PX,GER/US− PX,BEL/US= −.017 − .165 = −.182, implying that German exporters are
18 percent less productive than their Belgian counterparts. In a similar vein, the perforbb
mance of French exporters relative to Italian exporters amounts to PX,FR/US−PX,IT/US =−.084 − (−.328) = +.244, implying that French exporters are 24 percent more productive than their Italian counterparts. Through such a procedure, one can recover the
relative performance of exporters for any pair of countries.
Our finding raises the issue of policy solutions for advanced countries that face declining and aging population such as Japan, to promote export markets as a possible
alternative solution to lack of internal demand. Although little can be done in the short
run to overcome the geographic specificity of Japan, solutions can be viewed as twofold.
One would be to promote innovation and productivity growth in order to help firms exceed the productivity threshold. This would shift the productivity distribution to theright, holding the threshold ωX constant. The second policy solution is to promote exports by supporting potential exporters in the search for foreign markets. This would
shift the export threshold ωX to the left, holding the productivity distribution constant.

4.2

Robustness check I: Alternative measures of productivity andof the export participation rate

One may argue that TFP is a more appropriate productivity measure than labour productivity. We focus on France, Japan, the United Kingdom, and the United States, wheresuch information is relatively easy to access. We obtain the industry-average productivity gap Pb from (author?) [30, Table I-1-3-2].10 The export participation rates Ωc andexport productivity premia PXw are obtained from [6] for the United States, from [4] forFrance and Japan, and from [15] for the United Kingdom.
Table 3 presents the results based on TFP. Note that the ranking in the international
TFP gap differs from that using the labour productivity gap. For example, while thelabour productivity level for France is greater than that of the US, France’s TFP is lower.
This may reflect differences in working hours regulation and, primarily, differences in
the productivity of capital. Turning to the exporters’ TFP gap, the results confirm our
10 We rely on (author?) [30] rather than the GGDC Productivity Level Database. The GGDC Produc-

tivity Level Database reports manufacturing productivity while excluding electrical machinery. In contrast, (author?) [30] computes manufacturing productivity while including electrical machinery based on
the GGDC Productivity Level Database.

13

previous findings with labour productivity: the rankings of exporters’ TFP gap PXb are
not always consistent with the rankings of the industry-average productivity gap Pb , andw across countries do not reflect greater exporter performance.
higher export premia PX,c[Table 3 about here.]
One may also be concerned about the export participation rate. Our definition ofexporters follows the standard definition of the literature [e.g., 6]. This means that exporting firms also sell domestically and thus a firm was included even if 99.9 percent
of its sales are domestic. Ultimately, what matters is not so much the number of exporters but the volume of exports. Hence, rather than using the share of exporters, one
should use the volume of exports relative to gross output. To address this concern, we
use the share of exports to gross output Ω0 in total manufacturing in 2005 obtained fromthe World Input–Output Database [33]. The result for labour productivity is presented
in the upper panel of Table 4, and that for TFP is in the lower panel. The results are
qualitatively similar to those presented in the upper panel. Even when focusing on thevolume of exports, our main message remains unchanged.
[Table 4 about here.]In sum, our framework seems relevant for a meta-analysis comparing the performance of exporters across countries. Even in the absence of firm-level data, there isindeed enough information in the economic literature to make comparisons. The productivity differences between exporters across any countries can be approximated using
readily available figures out there, that is, when one obtains the industry-average productivity gap, the export participation rate, and the export productivity premium for bothcountries.

4.3

Robustness check II: Comparing gaps using aggregate data andfirm-level data

This paper claims that one can estimate the exporters’ productivity gap between any
two countries without accessing firm-level confidential data. Yet in order to assess therelevance of this claim, we need to test whether the estimated gap P̂Xb is actually ontarget: P̂Xb = PXb . To this end, we take advantage of the fact that we can access firm-level
information for companies with at least 50 employees in both France and Japan, andcompare the firm-level exporter productivity gaps from those obtained using GGDC datafor year 1997.11 Table 5 compares PXb obtained from firm-level data and P̂Xb obtained
11 Not only are the French and Japanese firm-level data highly comparable with one another, but alsoboth countries exhibit substantial trade cost differences, which enables us to identify large differences in

14

from GGDC data.12 Since the gap is defined by subtracting French firms’ TFP fromthat of Japan, a positive productivity gap indicates a productivity advantage in favour ofJapan.
[Table 5 about here.]
Two findings are noteworthy. First, both exporter productivity gaps PXb and P̂Xb exhibit the same sign in nine out of 11 industries. Hence aggregate figures provide a
reasonably accurate picture of the direction of the exporter productivity advantage. The
same holds for the overall productivity gap Pb and P̂b , where a discrepancy in the direction of the productivity advantage is found in only three industries. Second, thecorrelation coefficient between GGDC and firm-level figures exceeds .9 for the twocomparisons concerning PXb and Pb . Overall, this exercise corroborates the idea theeconomic literature conceals valuable information about the productivity gaps acrosscountries, either for the overall manufacturing or by industry.
Nevertheless, the magnitude of the two gaps – PXb and P̂Xb – differs significantly. In
fact, the absolute value estimated P̂Xb is significantly lower than that of PXb by an averageof .2, which represents an underestimation of the actual gap of around 20 percent. In
order to better understand the reasons justifying such a gap, we estimate the following
simple regression PXb = α + β P̂Xb + ε over the 11 industries at our disposal. If the GGDC
gap P̂Xb is equal to the firm-level gap PXb , one would expect to find α̂ = 0 and β̂ = 1.
If instead α̂ 6= 0, then there is a constant bias between PXb and P̂Xb . In the same vein, ifβ̂ 6= 1, the difference between PXb and P̂Xb increases (β̂ > 1) or decreases (β̂ < 1) withP̂Xb , expressing a deviation in magnitude from PXb proportional to P̂Xb . Figure 1 displays
the comparison, exhibiting the equality between PXb and P̂Xb by a 45-degree solid line,
the dashed line exhibiting the fit where PXb = .148 + 1.708P̂Xb . Figure 1 corroborates theidea that using GGDC data produces an exporter productivity gap substantially lower
than the one obtained using firm-level data.
[Figure 1 about here.]
the export behaviour of firms from the two countries. More precisely, we use firm-level data from France
and Japan developed in [4]. To account for possible measurement errors, we exclude outliers from thedata used in [4]. We exclude firms with logs of outputs and inputs in the bottom 1 percent. Appendix
in our working paper version ([25]) provides a detailed explanation of the construction of the data, thedefinition of each variable and the methodology to ensure comparability across the two countries.
12 In some industries, the export premium Pw is negative. A negative export premium questions bothX
our statistical framework and the underlying theory, which stipulates that only the more productive firm
can make it to export markets. Our first interpretation is that some market distortions may exist, becauseof the presence of public subsidies supporting existing exporters essentially. But due to the EU regulation,
the role of public support can only be limited in time and in scope, and this conjecture should be further
confirmed. Moreover, as discussed above, one cannot rule out the possibility of measurement errors in
the data. In all cases if empirically grounded, negative premia question the sustainability of such firms tosurvive on foreign markets in the long run.

15

Why do we observe such differences? Our contention is threefold. First, one cannot
rule out the possibility of measurement errors in the data, although we have trimmed
the outliers located in the top and bottom one percent of the firm-level productivity distribution.13 Second, there may be differences in the subtleties of the TFP computation
which may affect the PXb . Indeed, looking at Pb using firm level data and P̂b using
GGDC data, we observe a significant gap. We conjecture that this change in magnitudein the two measures is likely to explain why β̂ > 1, although it is hard to explain thevery mechanics at work. One possible explanation is the fact that the use of firm-level
data implies a wider spectrum of productivity levels, thereby inflating heterogeneity inthe data, as opposed to the use of industry-level data relying on the use of a representative firm undermining heterogeneity in the data. Third, differences in data coverage
between GGDC data – with no size truncation – and firm-level data (with a size truncation of 50 employees) produce a upward bias in favour of Japan when using firm level
data, thereby explaining the positive α̂.
To see this, take equation (3) and apply it to the comparison between France andw (1 − Ω ) − Pw
Japan, yielding PXb = Pb + PX,JP
JP
X,FR (1 − ΩFR ). It is straightforward tobw
bw
show that ∂ PX /∂ ΩJP = −PX,JP < 0 and ∂ PX /∂ ΩFR = PX,FR> 0. This tells us thatbthe exporter productivity gap PX decreases when the export participation rate of Japan
increases, and PXb increases when the export participation rate of France increases. By
applying a size-threshold, one may indeed modify the export participation rates. How
this influences the exporter productivity gap ultimately depends on the export participation rates Ω of the two countries.
Figure 2 presents the relationship between the log of size and the export participation
rate.14 Figure 2 displays the observed export participation rates gradually increasing thesize truncation (i.e., the number of employees).15 Recall that in our case, we observecompanies with at least 50 employees, and discard smaller firms, symbolised in the Figure by the vertical, solid line at ln(50) = 3.91. As Figure 2 clearly shows, the difference
between the export participation rates between the two countries is greatest at around
50 employees, where the French participation rate exceeds 85 percent in France andreaches 28 percent in Japan. This implies that PXb is likely to be overestimated when
applying such a size truncation to firm-level data, and that the difference between PXb
13 Our framework does not need to assume no measurement errors in productivity measures.

But itneeds to assume that in the presence of measurement error, its underlying magnitude and direction are
similar in both countries.
14 For Japan, we apply linear approximation below 50 workers due to the lack of data.
15 Figure 2 indicates a generally positive, quasi-monotonic relationship between size truncation andthe export participation rate. But for relatively high levels of size truncation, the export participation
rate decreases. Although this may seem surprising, our contention is that this is due to changes in theindustry composition of the economy as the size truncation increases. By doing so, some industries
are being dropped from the sample, thereby affecting the size truncation-export participation rate nonmonotonically.

16

and P̂Xb is exacerbated by the 50-employee size truncation.
[Figure 2 about here.]
The conclusion of this exercise is that our estimated P̂Xb is likely to be more reliable
that firm level data imposing a size truncation in the measures. It corroborates the use ofaggregate data which presumably covers all firms within an economy (or an industry).
The caveat is that the proposed premium in the literature relies on the use of arithmetic
productivity averages whereas industry-level productivity gaps produced by the GGDC
database stem from aggregated output and input with a weight in favour of larger firms.
Next Subsection investigates this avenue explicitly.

4.4

Robustness check III: The incidence of the market selection
mechanism on the exporter productivity gap

One may be concerned that the aggregate productivity documented in the literature does
not compare with the unweighted productivity average µ that we have used thus far.
As discussed in Section 3.3, our framework is consistent with the weighted average
productivity if equation (16) holds. However, whether this relationship actually holds
is an empirical question. The contribution of the gap between the unweighted average
productivity Pb and that of the covariance term Ncov(∆v∆ω) and the weighted average
productivity gap Ψ is computed by dividing equation (15) by ΨJ − ΨF : 
NJ cov(∆vJ , ∆ωJ ) − NF cov(∆vF , ∆ωF )
Pb
+
.
(17)
1=
ΨJ − ΨF
ΨJ − ΨF
Because of the covariance term, the computation of equation (17) necessitates theuse of firm-level data. Thus, we examine this issue by using our firm-level data from
France and Japan. Table 6 reports the decomposition of weighted average productivity
Ψ into the unweighted average productivity µ and the term Ncov(∆v∆ω), what [31] callthe covariance term. It also exhibits the number of observations N for both countries,
the differences in Ψ and in µ, and the contributions of both µ and the covariance term
to the weighted average productivity gap ΨJ − ΨF .
[Table 6 about here.]Five findings are notable. First, the covariance terms Ncov(∆v, ∆ω) in France andJapan are not negligibly small. Market structures (N) and the size productivity advantage cov(∆v, ∆ω) account for less than 10 percent of the aggregate productivity. The
unreported Student t-tests of equality of the covariance terms between the two countries reveal that the means are significantly different between the two countries for allindustries. This suggests that the nature of competition is country-specific.
17

Second, the difference in the productivity premium in size cov(∆v∆ω) between
France and Japan is relatively small, and the unreported Student t-test reveals no significant differences in the covariance terms. This implies that the difference in the covariance term comes essentially, if not exclusively, from the difference in the numberof firms N, that is, differences in market structures between the two countries.16 The
fact that the size advantage does not appear to be significantly different between the twocountries may come as a surprise. The rise and growth of the Japanese economy was
initially export driven, based on the capacity of few yet remarkably successful companies in gaining international market shares. This relatively accepted story could produce
results whereby Japanese companies should enjoy a larger size advantage. A more detailed observation of the covariance term shows that in 14 industries, the covarianceterm is larger in Japan. Whether these differences are statistically significant is one issue. Economically, however, they suggest that, indeed, Japanese companies have been
more successful at exploiting economies of scale than their French counterparts.
Third, the contribution of the covariance term Ncov(∆v∆ω) to the aggregate productivity gap is rather small for most industries when the productivity gap between thetwo countries is large. This is mainly due to differences in technologies µ. When the
gap is small, the role played by differences in the nature of competition mechanicallyinflates, as is the case for Fabricated metal prod and in Machinery & equip industries.
This is why in All Manufacturing the contribution of the covariance term is relatively
large, amounting to 72 percent. This is because the performance of countries in manufacturing conceals important sectoral specialization where productivity differentials are
more pronounced. It also implies that sector specialization should be taken into accountwhen comparing the productivity performance of countries.
Fourth, although similar in size, allocative efficiency (the covariance term) in France
and Japan do not equate. This may be due to differences in market structures, in the nature of the underlying technology and, inter alia, in the regulation of the sector by the
local authorities. In order to assess the degree of competition per industry across countries, one possibility would be to use the information provided by OECD on ProductMarket Regulation. Such database provides insightful information on entry barriers,
price regulation, competition law and policy, among other dimensions.17 Although potentially fruitful, this line of inquiry lies beyond the scope of this paper.
16 Although we take into account the differences in market structures by measuring the number of firms(N), the productivity should also be measured in a consistent manner across countries, which appears as
a demanding necessary condition. If the industry average productivity is measured under the assumptionof perfect competition (like GGDC Productivity Level Database), the export premium also embodies thesame assumptions. In other words, in order to take into account differences in market structures, export
productivity premia and industry average productivity levels should be measured assuming away perfectcompetition.
17 See the OECD homepage of OECD entitled “Indicators of Product Market Regulation Homepage”
at http://www.oecd.org/eco/growth/indicatorsofproductmarketregulationhomepage.htm.

18

Finally, in all sectors and for both countries, the market selection mechanism seems
to operate in conformity with what economic theory tells us: firms with higher productivity levels enjoy larger market shares. Allocative efficiency seems to perform better inJapan for all manufacturing. Yet this overall difference conceals sector-specific differences that are much larger in magnitude. We do not observe any specific link between
profit opportunities for domestic firms and a productivity advantage. Again, this corroborates the idea that allocative efficiency reflects more institutional aspects of thefunctioning of markets that cannot be reflected in a simple productivity term.

5

Conclusion

Social scientists increasingly rely on the use of confidential data on individual companies or employees, and rightly so. For example, in the realm of economics, increased
reliance on firm-level information has produced a series of results across countries andindustries regarding the export behaviour of companies that are readily available to all
economists. However, this information is generally dispersed, difficult to compare andconceals differences in data generating processes that reflect differences in countryspecific institutions. These caveats often cast doubt on the comparability of such simple
statistics across countries.
This paper stems from the intuition that under specific yet generally satisfied conditions, such comparisons can be performed. Importantly, such statistics can be used
to infer additional features, notably that of the cross-country exporter productivity gap.
Our simple framework allows for the computation of the cross-country exporter productivity gap without directly accessing confidential firm-level data. We have shown thatthe average international productivity gap between exporters depends on the following
three sufficient statistics: 1) the industry-average productivity gap between any pair ofcountries, 2) export participation rates, and 3) within-country export premia.
We applied our framework to cross-country comparisons across 11 advanced countries such as Japan, the United Kingdom, and the United States. We found that the average exporter productivity gap between two countries does not necessarily reflect theindustry-average productivity gap, due to the differences in export participation rates
and export premia across countries. Our simple framework performs well with the useof such readily available information and is robust to various measures of productivity
and alternative definitions of the export participation rate. Our methodology relies on
the assumption that the differences in allocative efficiency, namely the product of competition and the expected gains in market shares stemming from productivity growth,
are small. However, when the productivity gap between two countries is large, differences in allocative efficiency do not matter. Altogether, these results suggest that, while
caution is needed, our framework is useful as a first order approximation.
Greater access to detailed information can help social scientists to depict new causal19

ities. However, our experience also tells us that the use of large databases entails important computational costs. One should not ignore the alternative possibility of deriving
additional stylized facts from simple, existing information. This paper is a first step
towards such a research strategy. We believe that our framework can be extended tovarious other issues, such as, the analysis of international wage or price differentials
that may help to explain the international allocation of resources.

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23

1

Figure 1: Observed and Estimated Productivity Gaps PXb and P̂Xb between France and
Japan

-1

Observed Exporter Producivity Gap
0

TextilesTransport

Electric
Pulp
Basic
Metal
Machinery
Manufacturing nec
Chemicals
Wood
Non-metalic

Rubber-1

0
Estimated Exporter Producivity Gap

1

Notes: The dashed line represents predictions from the regression PXb = α + β P̂Xb + ε, whereα̂ = .148 and β̂ = 1.708, with respective p-values pα = .072 and pβ = .000. Adjusted
R2 = .819 and N = 11 industries.

24

.6
.4
0

.2

Export Participation Rate

.8

1

Figure 2: Export Participation Rates for France (dashed line) and Japan (solid line)

048Size Truncation (Log of number of employees)

12Notes: Based on our appreciative knowledge, we arbitrarily set the export participation rate for
all firms to 5% in France and 1% in Japan. Values for France for firms with less than 50
employees are obtained from FICUS data. In the case of Japanese firms with less than 50
employees, we use a log-linear approximation of the relationship between size truncation andexport participation rate. The vertical, solid line indicates the size truncation of 50 employees(ln(50) = 3.91) used in the firm-level analysis.
Sources: Firm-level data obtained from national statistical offices for Japan and France.

25

Table 1: Ranking of Labour Productivity Relative to the US for the year 2005
Pb
Rank Pb
Belgium
0.264
1
Germany
0.149
2
Sweden0.139
3France0.079
4Austria
0.073
5United Kingdom 0.067
6Denmark
0.066
7
United States
0.000
8
Japan
-0.1809
Italy-0.23910
Spain-0.268
11
Notes: Labour productivity is measured by value added per hours worked. Pb is theindustry-average labour productivity gap, based on year 2005 PPP, relative to theUnited States.
Source: Pb is obtained from the GGDC Productivity Level Database.

26

Table 2: Productivity of Exporters: Labour Productivity
Pb
Ω
PXw
PXb
Rank Pb Rank PXb
Belgium
0.264 0.803 0.578 0.165
1
1
Germany
0.149 0.693 0.154 -0.017
2
3
Sweden0.139 0.830 0.067 -0.063
35France0.079 0.748 0.200 -0.084
46Austria
0.073 0.714 0.175 -0.090
57
United Kingdom 0.067 0.695 0.099 -0.116
68
Denmark
0.066 0.772 0.385 -0.059
74
United States
0.000 0.180 0.260 0.000
8
2
Japan
-0.180 0.275 0.210 -0.241
9
9
Italy
-0.239 0.693 0.403 -0.328
10
10
Spain
-0.268 0.747 0.275 -0.412
11
11
Notes: Pb is the industry-average productivity gap, based on year 2005 PPP, relative to theUnited States; Ω is the ratio of the number of exporters to the total number of firms; PXw is theexport productivity premium; and PXb is the productivity gap between exporters acrossw (1 − Ω ) − Pw (1 − Ω ).
countries. PXb is obtained from equation (3): PXb = Pb + PX,c
c
US
X,US
Sources: See main text27

Table 3: Productivity of Exporters: Total Factor Productivity (TFP)
Pb
Ω
PXw
PXb
Rank Pb Rank PXb
United States
0.000 0.180 0.020 0.000
11France-0.104 0.748 0.014 -0.117
2
4
United Kingdom -0.110 0.695 0.097 -0.097
3
2
Japan
-0.139 0.275 0.056 -0.115
43Notes: Pb is the industry-average TFP gap, based on year 2005 PPP, relative to the UnitedStates; Ω is the ratio of the number of exporters to the total number of firms; PXw represents theexport productivity premia; and PXb is the productivity gap between exporters across countries.
w (1 − Ω ) − Pw (1 − Ω ).
PXb is obtained from equation (3): PXb = Pb + PX,c
c
US
X,US
Sources: See main text.

28

Table 4: Alternative measure of export participation rate
Pb
Ω
PXw
PXb
Rank Pb Rank PXb
United States
0.000 0.151 0.020 0.000
11France-0.104 0.422 0.014 -0.113
2
4
United Kingdom -0.110 0.420 0.097 -0.071
3
2
Japan
-0.139 0.187 0.056 -0.110
43Notes: This table uses an alternative measure of the export participation rate. Ω0 is the ratio ofexports to gross output.
Sources: See main text.

29

30

Notes: The comparison pertains to year 1997 only, and covers 11 industries only, due to the adequacy of the industry breakdown
between GGDC data and the national statistical offices.
Sources: Firm-level data obtained from national statistical offices for Japan and France.

Table 5: Productivity of Exporters: Firm-level Analysis for France and Japan
France-Japan firm-level data
GGDC
FranceJapan
Japan-France
Pb
PXb
P̂b
P̂Xb
Ω
PXw
GGDC industriesΩ
PXw
Textiles, textile products, leather & footwear
0.797 0.019 0.099 0.103 0.709 0.798 0.097 0.186
Wood & products of wood & cork
0.730 -0.027 0.064 0.030 -0.376 -0.341 -0.311 -0.276
Pulp, paper, paper products, printing & publishing 0.785 -0.024 0.066 0.041 0.100 0.141 -0.003 0.040
Chemicals & chemical products
0.942 0.006 0.458 0.047 -0.297 -0.272 -0.254 -0.229
Rubber & plastics products
0.857 0.045 0.245 0.041 -1.064 -1.039 -0.816 -0.792
Other non-metallic mineral products
0.868 0.007 0.212 0.039 -0.004 0.026 -0.287 -0.270
Basic metals & fabricated metal products
0.760 0.042 0.187 0.033 -0.565 -0.548 -0.052 -0.022
Machinery, nec
0.886 0.007 0.454 0.050 -0.028 -0.002 0.000 0.026
Transport equipment
0.911 0.009 0.271 0.050 0.556 0.592 -0.012 0.024
Electrical & optical equipment
0.873 0.044 0.390 0.070 0.288 0.323 0.152 0.188
Manufacturingnec; recycling
0.927 0.023 0.291 0.048 -0.270 -0.237 -0.190 -0.158

31

ΨJP
1.162
1.37
1.375
0.832
1.161
1.088
1.020
0.579
0.815
1.104
1.029
1.103
1.537
1.427
1.500
1.383
1.437
1.337
1.076

µFR
1.034
0.599
0.626
1.190
0.903
1.006
1.198
1.580
1.278
0.949
1.039
1.047
0.929
0.963
1.205
0.950
0.689
0.683
1.181

µJP
1.049
1.321
1.248
0.783
1.081
0.959
0.910
0.494
0.732
1.025
0.956
1.002
1.398
1.288
1.340
1.269
1.324
1.242
0.905

OPFR
0.075
0.046
0.101
0.012
0.039
0.122
0.119
0.039
0.121
0.049
0.023
0.055
0.116
0.067
0.126
0.118
0.027
0.129
0.043

OPJP
0.113
0.049
0.127
0.049
0.080
0.129
0.110
0.085
0.083
0.079
0.074
0.100
0.139
0.139
0.161
0.114
0.113
0.095
0.171
NFR
85,848
4,890
5,377
2,183
3,396
5,565
7,516
7,248
3,891
3,151
10,960
11,237
340
5,653
1,128
3,822
2,945
1,765
4,781

NJP
87,406
2,715
2,695
1,128
3,294
6,034
7,571
5,383
4,398
5,910
7,715
10,8401,245
10,463
1,798
4,106
7,210
1,730
3,171

covFR
0.9
9.4
18.8
5.5
11.5
21.9
15.8
5.4
31.1
15.6
2.1
4.9
341.2
11.9
111.7
30.9
9.2
73.1
9.0

covJP
1.3
18.0
47.1
43.4
24.3
21.4
14.5
15.8
18.9
13.4
9.6
9.2
111.6
13.3
89.5
27.8
15.7
54.9
53.9

DiffΨ
0.053
0.725
0.648
-0.3710.220-0.040-0.297-1.040-0.5840.106-0.033
0.001
0.493
0.397
0.169
0.315
0.721
0.525
-0.148

Diffµ
0.015
0.721
0.622
-0.4070.178-0.047-0.288-1.085-0.5460.076-0.084-0.045
0.470
0.326
0.135
0.319
0.634
0.559
-0.276

Contµ
0.275
0.995
0.961
1.098
0.811
1.169
0.969
1.044
0.935
0.717
2.536
−∞
0.953
0.819
0.796
1.015
0.881
1.065
1.861

Contcov
0.725
0.005
0.039
-0.0980.189-0.1690.031-0.0440.065
0.283-1.536
+∞
0.047
0.181
0.204
-0.0150.119-0.065-0.861

Notes: the figures are the averages across years. OP stands for the Olley and Pakes covariance term measuring allocative efficiency,
while cov stands for the covariance measuring the expected gains in market share (×106 ) for a one-unit increase in productive
efficiency. Contributions were computed using equation (17). See also the footnote to Table 5 for the computation of sector averages.
Sources: Firm-level data obtained from national statistical offices for Japan and France.

ΨFR
1.109
0.645
0.727
1.203
0.942
1.128
1.317
1.619
1.399
0.998
1.062
1.102
1.044
1.030
1.331
1.068
0.716
0.812
1.225

Table 6: Decomposition of the Weighted Average Productivity Gap Between France and Japan

Industry
All manufacturing
TextileClothing
Manufacture of wood
Pulp & paper
Printing & publishing
Chemical prod
Rubber & plastic
Non-metallic mineral prod
Basic metal prod
Fabricated metal prod
Machinery & equip
Machinery for officeElectric machinery
Communication equip
Medical & precision inst
Motor vehicles
Other transport equip
Furnitures & other mfg

Appendix A.

Sources of firm-level data and construction of variable

The French and Japanese firm-level data used in this study were collected by their respective national statistical offices. Both the French and Japanese firm-level data usedin this study were collected by national statistical offices. Data for France were drawn
from the confidential Enquête Annuelle d’Entreprises (EAE) jointly prepared by the Research and Statistics Department of the French Ministry of Industry (SESSI) and the
INSEE. This survey was conducted annually from 1984 until 2007. It gathers information from the financial statements and balance sheets of individual manufacturingfirms and includes all of the relevant information to compute productivity indices andinformation on the international activities of the firms surveyed.
Data for Japan were drawn from the confidential micro-level database of the Kigyou Katsudou Kihon Chousa Houkokusho (Basic Survey of Japanese Business Structure and Activities: BSJBSA) prepared annually by the Research and Statistics Department, METI (1994–2006). This survey was first conducted in 1991 and then annuallyfrom 1994. The main purpose of the survey is to statistically capture the overall pictureof Japanese corporate firms in light of their activities in diversification, globalization,and strategies for R&D and information technology.
France and Japan conduct very similar types of firm-level surveys, thus allowing us
to build a relevant set of comparable variables for the TFP computations using firm-level
information: nominal output and input variables, industry-level data for price indices,
hours worked, and depreciation rates.18 The data-implementation step allows us to construct two separate, unbalanced panel datasets with the same coverage: the same period(1994–2006), the same industries, the same employment threshold (over 50 employees),
and the same definition of inputs and output to estimate the production function.19 To
convert the input and output series in France and Japan into common units, we use theindustry-specific PPP series from the GGDC Productivity Level Database, which provides comparisons of output, inputs, and productivity at a detailed industry level for aset of 30 OECD countries.20
Our baseline estimation of TFP is calculated by the index approach, which is consistent with that in GGDC database.21 To compare firm-level productivity levels fromtwo different countries, the vectors of inputs and output of firms must be directly comparable.
18 Because of the high comparability of the firm-level data in Japan and France, a recent international

comparative study by [10] also used the EAE and the BSJBSA data.
19 Our data cover the period 1995–2006 because the variables in 1994 are used only for lagged variables in the estimation.
20 See [19] for a comprehensive description of the database and the methodology followed to construct
the PPP series.
21 We also estimate TFP based on a production function developed by [36] and [8], which confirms therobustness of our findings. These results are available from the authors upon request.

32

Output is defined as total nominal sales deflated using the industry-level gross output
price indices drawn from INSEE for France and from the Japan Industrial Productivity(JIP) 2009 database for Japan.22
Labour input is obtained by multiplying the number of employees by the average
hours worked by industry. Industry-level hours worked data are drawn from the EUKLEMS dataset of the GGDC for France and from the JIP 2009 database for Japan.23
Note that in France, a large decline in hours worked occurred from 1999 onwards because of the 35-hour/week policy: worked hours fell from 38.39 in 1999 to 36.87 in
2000.
The variables for intermediate inputs are available in both the EAE and BSJBSA
surveys. In both surveys, intermediate inputs are defined as operating cost (= sales cost
+ administrative cost) − (wage payments + depreciation cost). The inputs are deflatedusing the industry price indices for intermediate inputs published by INSEE for France
and by the JIP 2009 database for Japan.
The capital stocks are computed from investments and book values of tangible assets following the traditional perpetual inventory method (the industry subscript j andcountry superscript c are discarded to simplify the notation):
Kit = Kit−1 (1 − δt−1 ) + Iit /pIt ,(1)

where Kit is the capital stock for firm i operating in year t; δt−1 is the depreciation rate
in year t − 1; Iit is the investment of firm i in year t;24 and pIt is the investment goods
deflator for industry j.25 Both investment price indices and the depreciation rates areavailable at the two-digit industrial classification level. They are drawn from the JIP
2009 database for Japan and from the INSEE series for France. The investment flows
are traced back to 1994 for the incumbent firms and back to the entry of the firm into
our dataset for the firms that entered our dataset after 1994.
The cost of intermediate inputs is defined as the nominal cost of intermediate inputs,
while that of labour is the wage payments. To compute the user cost of capital (i.e., therental price of capital) in country c, we use the familiar cost-of-capital equation given
by [21] (the industry subscript j and country superscript c are discarded to simplify the
22 The JIP database was compiled as a part of a research project by the Research Institute of Economy,

Trade, and Industry (RIETI) and Hitotsubashi University. For further details about the JIP database, see[13].
23 The concordance between the industry-level EU-KLEMS database and the firm-level EAE databaseis achieved through the use of ISIC codes.
24 Investment data are not available in the BSJBSA. We thus use the difference in nominal tangible
assets between two consecutive years as a proxy for nominal investment.
25 If firm i’s investment was missing in year t, we consider firm i as having made no investment: I = 0.
it33

notation):26
pKt = pIt−1 p̃Kt + δt pIt − (pIt − pIt−1 ).

(2)This formula shows that the rental price of capital pKt is determined by the nominal
rate of return ( p̃Kt ), the rate of economic depreciation and capital gains. The capital
revaluation term can be derived from investment price indices. To minimize the impact
of sometimes volatile annual changes, three-period annual moving averages are used.
The nominal rates of return are yields on 10-year government bonds of France andJapan.

26 Ideally, this equation would be augmented to take into account business income tax. However, as

taxation regimes differ between France and Japan, we prefer, as in [19], to rely on a simpler common
formula abstracting from taxation34