Trade, Reallocations and Productivity: A
Bridge between Theory and Data in ÖresundAnders Akerman
Stockholm University*** REVISED VERSION ***July 24, 2009

Abstract
The paper estimates the causal e¤ect of trade liberalisation on aggregate productivity through mechanisms related to …rm selection. The construction of a bridge in 2000 across the Öresund Strait linking Copenhagenwith Malmö, Sweden’s third largest city, provided a natural experimentwith which to analyse this e¤ect. A di¤erence-in-di¤erence methodology
is applied using both geographic and sectoral variation in how much thebridge a¤ected export patterns and productivity. Firms based in Malmöraise exports to Denmark substantially, mostly by …rms selecting into exporting, and the aggregate productivity in Malmö increases. I …nd that
almost all of Malmö’s productivity growth is due to the reallocation of
production from less productive to more productive …rms. When decomposing the productivity gain, I …nd that these e¢ ciency gains comemostly from the exit of the least productive …rms but also from …rms
with an above-average productivity that start to export and therefore expand their output share. The two largest sectors in Malmö are wholesaletrade and manufacturing. Exports by the wholesale sector in Malmö arestrongly a¤ected by the bridge whereas those of manufacturing are not.
The productivity e¤ects are also the strongest in the wholesale sector.
I am grateful for comments from seminar participants at the International Monetary
Fund, the ETSG Meeting in Athens 2007, NOITS in Bergen 2008, EIIE in Ljubljana 2009 andfor helpful comments by Richard Baldwin, Karolina Ekholm, Doireann Fitzgerald, Rikard
Forslid, Nicola Fuchs Schündeln, Elhanan Helpman, Martin Bech Holte, Marc Melitz andDiego Puga. Financial support from the Jan Wallander’s and Tom Hedelius’ Foundation is
gratefully acknowledged.

1

1

Introduction

Understanding the welfare e¤ects of globalisation requires knowing how international trade a¤ects aggregate productivity. This paper estimates the causale¤ect from a speci…c mechanism through which this can occur: the reallocationof production among …rms that are heterogeneous in productivity levels. This
link is important to understand for two reasons. First, aggregate productivity
is crucial in determining an economy’s welfare since it is a main determinant ofreal wages. Second, much recent empirical work has highlighted the substantial
heterogeneity in …rm characteristics in virtually all sectors and countries. Theoretical work has built on this evidence and has shown how this heterogeneity
can play an important role in determining aggregate productivity in an open
economy.
Melitz (2003)1 argues that two processes raise aggregate productivity when
trade costs decrease: a) the output of non-exporters decreases due to foreigncompetition, and b) existing exporters expand their output. Because exporters
are more productive than non-exporters, a decrease in trade costs reallocatesproduction from less productive to more productive …rms. Although ample
empirical evidence traces the static di¤erences between exporters and nonexporters, it has been more di¢ cult to test the causality of these links when
trade costs decrease. This stems from the di¢ culty in …nding exogenous reductions in trade costs. Trade agreements and trade liberalisation policy are rarely
determined in isolation from unobserved industry variables; moreover, tradeliberalisation is often associated with other types of economic liberalisation intime.
This paper provides an analysis of how trade a¤ects aggregate productivity
through …rm selection, using a truly exogenous change in trade costs. It examines the natural experiment arising from the 2000 construction of the Öresund
bridge linking the Swedish city Malmö with the Danish capital Copenhagen.
1 Other important theoretical contributions showing similar dynamics include Bernard,
Eaton, Jensen, and Kortum (2003) and Yeaple (2005).

2

Data at the …rm level is available for all Swedish enterprises during the years
before and after construction, making it possible to study how dynamics at the…rm level drive aggregate variables. Before 2000, the Öresund Strait separating
Sweden and Denmark could only be crossed by ferry or commuter passenger
boats; now, however, the trip can be made in 20 minutes by car or lorry. The
fall in trade costs caused by the bridge is exogenous for two main reasons. First,
its construction was decided six years prior to its completion and can therefore
not be related to temporary unobserved shocks in productivity. Second, except for the fact that sectors depending on road transport bene…t the most, abridge cannot intentionally be designed to favour trade in certain sectors morethan others (trade policy, for example, is often designed to protect vulnerable
and less competitive sectors). Moreover, macroeconomic policy and regulation
related to productivity, such as labour market and other industry regulation,
are relatively stable in Sweden and uniform across the country. This makes it
possible to compare Malmö, which is situated right next to the bridgehead, withthe two other large cities, Stockholm and Gothenburg (located about 610 and
270 kilometers away).
I apply a di¤erence-in-di¤erence methodology using geographic and sectoralvariation. Exports to Denmark by …rms in Malmö increase by more than by…rms in other cities and the main sector that is a¤ected is the wholesale industry;
manufacturing seems not to be a¤ected (wholesale and manufacturing accountfor about 70% of output in these cities). I …nd evidence of a causal e¤ect oftrade liberalisation on aggregate productivity. The main mechanism that drives
aggregate productivity is the reallocation of production across existing …rms; thee¢ ciency of allocation improves. More speci…cally, the least productive …rms
exit and …rms with high productivity enter into exporting and therefore capturea larger output share.
I begin by describing the previous literature and empirical issues involvedin estimating causal e¤ects of international trade in Section 2. Section 3 describes the natural experiment and how it can be used to overcome many of the3empirical problems discussed in Section 2. Section 4 presents the model, which
is based on Melitz (2003)2 , and derives the main predictions from falling trade
costs according to the model. Section 5 describes my method for estimating…rm productivity. I use the semiparametric method from Levinsohn and Petrin(2003) to …nd unbiased estimates of sector speci…c production functions thatgenerate measures of total factor productivity for each …rm and year. Section 6
describes the data set and …nds that patterns of heterogeneity related to tradeand productivity observed in previous literature exist also in the Swedish data.
Section 7 describes my empirical method and the results. Section 8 concludes
the paper.

2

Previous literature

The literature on how trade drives aggregate productivity through …rm selection
originates in an empirical literature that has focused on how …rm characteristics correlate with trade patterns. These results are by now …rmly established.
Bernard and Jensen (2004), Aw, Chen, and Roberts (2001) and Clerides, Lach,
and Tybout (1998) among others …nd that exporters are on average more productive and larger than non-exporters3 . Also, the e¤ect of turnover of …rms (inthe sense of …rm entry and exit) on aggregate productivity growth is large asshown in Foster, Haltiwanger, and Krizan (1998). They show that the simplifying assumption that the economy consists of identical …rms disregards dynamics
related to …rm heterogeneity that a¤ect aggregate productivity levels. It is also
shown in Bernard and Jensen (2005) that signi…cant …xed costs are involved inexporting, and that these are larger than …xed costs involved in entering the…rm’s domestic market. Roberts and Tybout (1997) estimates these costs for
Colombia and …nd them to be of substantial size. Finally, Helpman, Melitz, and
2 My simplifying assumptions are from Helpman, Melitz, and Yeaple (2004) and consistof using a homogenous sector that equalises wages across countries and parameterising theprobability distribution of productivity across …rms to a Pareto distribution.
3 See Tybout (2003) for a survey and also Schank, Schnabel, and Wagner (2007) for aliterature overview on wage premia paid to workers in exporting …rms in a large set of countries.

4

Rubinstein (2008) show that …rm heterogeneity are important also for understanding aggregate trade ‡ows since the productivity distributions of …rms help
explaining bilateral trade links without any trade at all. Several papers havebuilt general equilibrium models incorporating these facts, such as Bernard,
Eaton, Jensen, and Kortum (2003), Yeaple (2005) and Melitz (2003). The common feature used for this analysis is that they build on …rm selection as thedriving channel for how trade a¤ects aggregate productivity. What this literature shows is that …rm heterogeneity in productivity is of substantial size, thatcertain patterns relating to trade hold across countries and that it is important
to incorporate …rm heterogeneity to explain trade patterns and the evolution of
aggregate productivity.
There have been previous studies on how trade liberalisation a¤ects productivity through the reallocation of production. Pavcnik (2002) estimates thee¤ect of trade liberalisation in Chile in the 1970s. During this period, Chile
liberalised its trade regulation dramatically and she …nds strong e¤ects on reallocation of production across …rms in import-competing sectors. Also, Loecker
and Konings (2006) …nd similar results for Slovenia in the 1990s, where themain drivers are job destruction at state …rms and reallocation of employment
to private …rms. Tre‡er (2004) estimates the e¤ect of the Free Trade Agreement(FTA) between the United States and Canada. This paper has many advantages. Industry in all of Canada was a¤ected by the FTA and the cut in tari¤levels was substantial. However, I argue that my experiment builds on a fall intrade costs that was more exogenous in nature than in the papers mentioned
here. I will outline my argument in the following passages.
Empirical research on the e¤ect of a trade liberalisation is often susceptible
to a problem of endogeneity. The decision to reduce tari¤s is likely to coincidewith other reforms that have e¤ects on production choices and productivity.
Several countries have, for example, liberalised trade at the same time as they
have removed domestic regulatory and taxation barriers to productivity growthsuch as India in 1990s. Using these would overestimate the true e¤ect due to5the inclusion of productivity increases that come from other sources than lower
trade costs alone.
Also, trade policy is frequently e¤ected by industry lobbying (see for example
Grossman and Helpman (1994) and Koujianou Goldberg and Maggi (1999)).
The size of a tari¤ cut in a speci…c sector could in such a setting be correlatedwith other characteristics that a¤ect production and productivity. This would
bias the estimates for the e¤ect of trade liberalisation on productivity. For
example, a sector with, in an international context, relatively unproductive …rms
may lobby its government to retain tari¤ protection while a sector with somevery productive …rms may want the government to sign free trade treaties withcountries to which these …rms can successfully export. Both of these problems
would bias the estimates upward. I claim, however, that the natural experiment
in my paper provides a setting where the fall in trade costs is more exogenous
than in the previously mentioned papers since policy plays a very limited role.
Both the timing and the selection of industries to be exposed are very unlikely to
be a¤ected by unobserved shocks to productivity in the a¤ected region aroundthe time of the bridge being opened. This is discussed in more detail in thefollowing section.

3

The Öresund bridge as a natural experiment

The natural experiment used in this study is the construction of the Öresund
bridge. The Öresund bridge connects the Danish capital of Copenhagen with
Sweden’s third largest city of Malmö. These two cities are separated by the Öresund Strait which was previously only connected by large ferries and somewhat
smaller but faster boats that only carried people. The region was, however,already before the bridge was constructed, well integrated due to free trade,similar cultures, similar and mutually comprehensible languages and the factthat passing the border did not require a passport. In 2000, the metropolitan

6population of Copenhagen was 495,699 and that of Malmö 259,579.4
There are several advantages of this experiment. First, the timing can beassumed to be exogenous for reasons that will be discussed shortly. Second,the countries involved have similar relative factor endowments and access tosimilar technology as shown by the similarities in the GDP per capita levels.
Firm dynamics can therefore be assumed to be related to intraindustry trade
which is the focus of Melitz (2003). Third, there is …rm-level data available for
Swedish …rms for both the time before and after the bridge was constructed.
Regarding the exact timing of the bridge, it is important to note that whether
to build the bridge was a controversial issue in both Danish and Swedish politics.
It was discussed for a very long time. But it was only in 1991 that decisions
in the Danish and Swedish parliaments were taken. However, due to publicconcern and tensions within the Swedish coalition government regarding possible
environmental e¤ects, the bridge was only accepted by the Swedish government
in 1994 and …nally completed in June 2000. The long construction time is usefulfor this paper because politicians at the time in 1994 and even less in 1991 could
only have had a very vague idea of what the business cycle would be in 2000
and what other industrial policies would be implemented in 2000. Policy makers
could not know how such variables would change from 1998 to 2002, which isthe sample period that I will focus on. I therefore claim the timing of theconstruction of the bridge to be largely exogenous.
The endogeneity problem when the selection of which sectors that are exposed is correlated with their productivity levels is unlikely to be present in thisexperiment. It is di¢ cult to design a bridge so that sectors are protected in a
way that is related to variables a¤ecting productivity. A lorry carrying goods
from any industry is able to drive across the bridge. It is probably the case,however, that a bridge of this type favours certain sectors more than others.
Some trade, for example, is simply transported through information technology
communication and not subject to any change due to a bridge. Sectors with
4 Statistics Denmark and Statistics Sweden.

7goods that are very costly to transport by sea but not by road might, however,be greatly e¤ected. But since which sectors bene…t from a bridge is largely
exogenous, the productivity levels in those sectors at the time of construction
cannot be related to the bridge actually being constructed.
A possible criticism speci…cally against the experiment used here could bethat rational …rms change their behaviour in advance since they are expecting
the bridge to open in 2000. This might mean that I do not fully capture the truee¤ect of the bridge by simply looking at levels before and after the experiment
happened. This would cause a downward bias in the results. In terms of thesigni…cance of an e¤ect existing at all, however, it is not that problematic since
this phenomenon would only make it more di¢ cult to …nd signi…cant results.
Another issue is that labour markets in the region change. There is strong
evidence of this in the region. During the very …rst years, this mostly involved
skilled Swedish labour starting to work in Copenhagen, somewhat draining …rms
in Malmö of skilled labour. Since I use Swedish data this factor would, again,
make it more di¢ cult for me to …nd signi…cant results. If I …nd productivity
to increase in Malmö due to an increased exposure to foreign competition anda larger market, this would happen despite any movement of skilled labour to
Copenhagen.
The Malmö city region is therefore selected as the “treatment” area since
it is the geographic area closest to the bridgehead. In proportional terms, thelargest decrease in trade costs should be for areas closest to the bridge. The
control group should be one that faces the same macroeconomic or national
shocks as Malmö. I therefore pick the two largest cities in Sweden: Gothenburg and Stockholm (located about 270 and 670 kilometers from the bridge,
respectively). Any national policy or national economic shock should theoretically a¤ect Malmö, Gothenburg and Stockholm in the same direction. Other
control groups could, of course, be considered. But these three cities are usually referred to as the only “large” cities of Sweden. Any smaller towns would
probably be much more limited as regards what sectors are active there Also,

8

using only …rms located within the city boundary somewhat narrows down thesample since large cities are typically surrounded by smaller cities that participate in the economy of the big city. However, it would be di¢ cult to expand thede…nition of Malmö, Stockholm and Gothenburg to include surrounding cities
without introducing an arbitrary and questionable selection system. Where theboundary of the “larger city area”ends is di¢ cult to de…ne in a consistent way.
Therefore only …rms actually registered in the city area of the three cities areincluded.
Finally, it could be argued that this experiment is more focused on the e¤ectof infrastructure improvements and cuts in transport costs rather than the e¤ectof tari¤ cuts. It is true to the extent that the paper uses a decrease in transport
costs but in terms of external validity this is not so problematic. Theoreticallyin the trade literature, the e¤ect of transport costs versus tari¤s of a variable
type is almost never treated di¤erently. This is because transport costs map
into the cost of trade in exactly the same way as tari¤s. As long as the cost is
proportional to the value of goods being transported, it does not matter for theactions of …rms whether the costs is accrued to the government or spent on theactual transportation of the good.

4

Model

4.1

Basic setup

The model outlined here is a simpli…ed version of Melitz (2003) in the sensethat it uses a homogenous sector (here labelled as agriculture) with constantreturns to scale and parameterises the probability distribution of productivity
to a Pareto distribution5 . The model has two countries, Home and Foreign(marked with an asterix “ ”). There is one factor of production, L and L .
Production is composed of two di¤erent industries: agriculture, A, and manu5 Helpman, Melitz, and Yeaple (2004) introduces these assumptions as well as foreign direct
investment (which I do not).

9Figure 1: Map of the Öresund region.

facturing, M . The agricultural sector is characterised by costless trade, a unit
input requirement of labour and constant returns to scale. The prices of thehomogenous agricultural good is therefore equalised across countries and chosen
as the numeraire: pA = pA = 1. Due to the unit labour requirement it also follows that w = w = 1. The manufacturing sector is characterised by increasing
returns due to positive …xed costs and has a monopolistic competition setting
as in Dixit and Stiglitz (1977). The marginal cost is heterogeneous across …rms.
International trade in manufacturing varieties is costly with an iceberg trade
cost of> 1.6

There are three types of …xed costs that …rms have to pay: fE is the innovation cost for starting a new …rm, fbX is a …xed cost a …rm has to pay only if theyexport to the other country and fbD is a …xed cost which the …rm has to pay forentering the domestic market. The marginal cost is wai where ai is the labour
requirement for producing one unit of the good xi and is speci…c to …rm i. In
equilibrium, there is a constant rate of entry and exit of …rms due to an exogenous per period death probability< 1. Potential entrants do not know theirlabour requirement ai but instead face an ex ante probability distribution G (a).
6 A …rm has to shipy units for y unites to arrive at the destination.

10

Having sunk the entry cost, fE , …rms learn their labour requirement and decide
whether they exit immediately, serve the domestic market (for which they haveto sink an entry cost of fbD ) or serve both the domestic and foreign markets (forwhich they have to invest both fbD and fbX ). The value of a …rm, in the absenceof intertemporal discounting, is bounded from above by the exogenous death
probability .

Consumers in both countries derive utility from, …rst, an upper tier (CobbDouglas) combination of manufacturing and agricultural goods:
1
U = CM CA(1)

where CA is the consumption of the agricultural homogenous good. CM is anindex of consumption of manufacturing varieties as in Dixit and Stiglitz (1977):
2 nZ(
CM = 4 ci

1)=

0

3 =(

1)

di5

(2)

where n is the mass of varieties consumed, ci the amount of variety i consumed
and> 1 the elasticity of substitution. Consumers spendof their income on

the manufacturing varieties and this generates the following demand functions
for the domestic …rm i:

xi =

pi
P1

Y;

xi =

( pi )P 1

Y

where xi and xi are the demand levels of …rm i’s good in Home and Foreign,respectively. pi is the producer price of variety i, Y is income in Home and Y
!11
n
Rn 1
RX
1
pi di +
( pi )
diis the price index ofincome in Foreign. P
00manufacturing goods in Home where n is the number of domestic …rms serving
the domestic market and nX the number of foreign …rms exporting to Home.
This setup generates the following optimal pricing rules for …rms:

11

pijj =

1ai ;pijl =

1ai(3)where pijl is the price for …rm i based in country j but selling the good incountry l.
It can be shown that an equilibrium is characterised by six equations. The…rst four consist of “cuto¤” equations showing the labour requirement ai for a…rm that is just productive enough to serve the domestic or both markets sothat the operating pro…t is equal to the per period equivalent of the …xed costs
involved in serving that market. This has to hold for …rms in both countries.

a1D B = fD

fbD , fX

where fD

(4)

a1X

B = fX(5)

aD1

B = fD(6)

aX1

B = fX(7)

fbX , B = P 1L , B = P (1L

)

, and

1

2

[0; 1] represents trade freeness. aD denotes the cuto¤ productivity to enter thedomestic market and aX is the equivalent for the export market. It is assumed
that fX > fD always holds. The term B is best understood as a “per …rm
market potential”. Free entry into both markets generate two more equations
stating that for the potential entrant, the expected pro…t must equal the entry
cost fE .
ZaD

a1D

B

0

ZaD
0

(1
aD

fD dG(a) +

ZaX

a1X B

ZaX

aX

fX dG(a) = fE ;

(8)

0

)

B

fD dG(a) +

0

12

(1

)

B

fX dG(a) = fE .

(9)

4.2

Solution to the long run equilibrium

The probability distribution G (a) determining the labour requirement is assumed to follow a Pareto distribution. This is in line with empirical evidence,as for example in Axtell (2001).

G(a) = ak .

It is assumed that

k

(10)

1 > 1 to ensure that the integrals in the free entry

conditions (8) and (9) are bounded. Using this in the free entry conditions andsolving the equilibrium generates the following expressions for the endogenous
variables:
fE1
fD 1 +
fE1)
fX 1 +

akD = aDk = (1)

akX = aXk = (B=B =fE fD 1
1)
1+

(

(11)
(12)
!1

.

(13)

The variables do not di¤er across countries, even if these di¤er in size, because all cost parameters and determinants of the distribution are assumed tobe the same across countries. It can also be seen that since fX > fD :aD > aX .

meaning that the marginal productivity for surviving in the home market islower than the marginal productivity needed to be able to export.7 It follows
from this that exporters (which always have athan non-exporters (which have aX < aaX ) are always more productiveaD ).

The revenues from selling to the domestic market and the export market
7 This is not a strong assumption since it is generally viewed as more expensive to enter aforeign and less well-known market than the home market.

13

are:

1

yD = a

1

1
1+

1

B= a

(14)
1

1

yX = awhereh1) fE fD 1

(

i1

1

B = a

(15)

1+

. The combined revenue of an exporter (sinceaX < aD all …rms that export also serve the domestic market) is therefore
1+

yD + yX = a1

(1 +

)

1

.

(16)

Finally, using the price index together with the free entry conditions (8)and (9) and the solutions to the productivity cuto¤s and B and B I …nd theexpressions for the number of …rms:

n=
n =

fX
fD

where

1

1 (L L )2)fD (1
1 1 (L
L )
2)
fD (1

(17)
(18)

1

.

To derive the expression for total M-sector trade, I note that the export levelof an existing exporter isyX (a) = a1

B =

a
aX

1

fX

due to (5). Integrating from 0 to aX and multiplying with the number of …rms
as in (17), I …nd that the total value of M-sector exports from home, VT , isVT = nZ aXyX (a) dG (aja < aD ) =

0

fX
fD

1

(L L )
2)(1(19)

As opposed to the variables analysed so far, total exports depend also on

14

country size (L and L ). This is since population size a¤ects the total numberof …rms in each country’s manufacturing industry due to the “home markete¤ect”.8

4.3

Comparative statics when trade costs decrease

It is now possible to analyse what happens when trade costs decrease (herecharacterised by an increase in trade freeness, d > 0). First, the cuto¤s forsurvival (aD ) and exporting (aX ) change in the following way:
dakD
da k
= D =
d
d
dakX
da k
= X =
d
d

(
(

1)
1)

1

fE
fD (1 +fE
fX (1 +

2 < 0.

)(20)

1
2 > 0.

)(21)

It is the case that aD decreases in trade freeness, meaning that the least
productive …rms exit the economy when trade is liberalised. It is often argued
that this takes place due to the increase in foreign competition but what is
technically operating in the model is that there is an increase in the demand forfactors of production from existing exporters which now expand production.
The cut-o¤ for exporting increases which means that new …rms enter theexport market. These “switchers” have productivity levels which were marginally below the previous cut-o¤ for exporting but are now productive enoughto engage in exporting.
It can also be seen that the allocation of production changes from nonexporters to exporters. Equation (14) show that domestic sales, yD , decreases inand (15) shows that foreign sales, yX , increases in . Non-exporters therefore
lose market share. Exporters, however, more than makes up for the loss ofdomestic sales by increasing exports. The derivative of yD + yX as in (16) withregard tois shown in the appendix to be positive.

These are essentially the processes that raise aggregate productivity in Melitz(2003). Production is reallocated from non-exporters to exporters and the least
8 See Krugman (1980).

15

productive non-exporters exit production.
Formally, I denote aggregate productivity in home by
0

= @sD

ZaD

a1

dG(a ja < aD ) + sX

ZaX

1 11

dG(a ja < aD )A

a1

0

0

.

(22)

where sD is the share of non-exporters and sX is the share of exporters. The
ratio of exporters to non-exporters is
1
f
1+ fD

; and sX =

X

fD
fX
f
1+ fD
X

aX
aD

k

D
= ffX

so it follows that sD =. It is shown in the appendix that dd > 0 implyingthat aggregate productivity increases when trade costs decrease.
It can be seen in (19) that lower trade costs increase total manufacturingexports if the two countries are not too asymmetric in size. This is easiest shown
if I assume that the two countries are of equal size:
d
dVT
=
d L=L
d

"

L

fX
fD

1

(1 + )

#

>0

(23)

since dd > 0.

4.4

Predictions

The main analytical predictions for trade and aggregate productivity can now besummarised. As regards trade, exports always increase at the so-called intensive
margin among existing exporters and among new exporters at the extensive
margin. Moreover, if size asymmetries are not too large, exports increase also
at the aggregate level. Aggregate productivity increases through the reallocationof production from exiting …rms and non-exporters to existing exporters.

5

Estimating …rm productivity

Productivity in this analysis will be estimated by using an estimated production function to …nd the total factor productivity of each …rm and year. To …nd
this, I follow a semiparametric method outlined in Levinsohn and Petrin (2003).

16

Having estimated production function coe¢ cients for labour and capital, productivity, pist , is de…ned aspist = exp (vaist

l listk kist ) .

where vaist is the value added of …rm i in sector s in year t, list is labour used,kist is capital used. The estimation technique uses intermediate inputs (energy
and raw materials) as a proxy to control for the correlation between input levelsof factors of production and unobserved productivity shocks.
There are many di¤erent ways of estimating …rm productivity.9 To calculate
the total factor productivity of a …rm there is a need to estimate the …rm’s
production function. This involves some well known problems. There is, …rst, a
problem of simultaneity because the productivity level of a …rm could have ane¤ect on its choice of factor input levels. Olley and Pakes (1996) …nds evidence of
this using data from the US telecommunications industry in 1980s. For example,
with time varying productivity, a …rm that experiences a positive shock canbe assumed to increase its production temporarily to reap the higher pro…ts
available. If it can do this immediately by increasing for example labour (asopposed to capital, which might be assumed to take longer time to accumulate),the coe¢ cient on labour in the estimated production will have a positive bias.10
Also, productivity a¤ects entry and exit decisions by …rms. Much research
has so far used “balanced panels” when estimating production functions andhas thereby excluded all new entrants and exiting …rms. This methodology
is, however, prone to be subject to selection bias if the productivity of a …rm
a¤ects its decision of staying or exiting. If, for each productivity shock in time,the exit decision is correlated with the current capital level (it can been argued
that …rms with more capital may be less likely to default given productivity)
there will be a negative bias on the coe¢ cient on capital in the production
function if the balanced panel is used. These two biases are the reasons for
9 See Arnold (2005) for an excellent and practical summary.
1 0 This problem was …rst highlighted by Marschak and Andrews (1944).

17

using semiparametric methods as in Olley and Pakes (1996) or Levinsohn andPetrin (2003). The methods are fairly similar but Olley and Pakes (1996) uses
investment instead of intermediate inputs as its instrument. However, as is often
the case in many other datasets, there are more observations in my sample
that report non-zero or non-missing values for intermediate inputs than forinvestment. So since the method by Levinsohn and Petrin (2003) gives me more
observations for my dataset, I opt for this method. Production functions are
estimated at the 2 digit industry level. A more disaggregated industry level
would provide two few observations for many sectors.

6

Data

All data I use is from the Swedish database “Företagsdatabasen” except for
trade data which is collected by the Swedish Customs. Both datasets have been
provided by Statistics Sweden. It contains information on all active Swedish…rms during the time period 1996 to 2002.11 In the absence of industry-speci…cprice indices, I de‡ate all variables measured in monetary values by the national
Swedish price level. The location variable is in what city (“kommun”) the …rm isregistered so unfortunately there is not information about the location of plants.
However, for the purpose of the experiment I argue that, on average, more …rms
that have most of their plants close to the bridge should also be registered in
Malmö than in Gothenburg or Stockholm.
Generally, the data show that similar relationships between trade and productivity as found in the literature for other countries (regarding the di¤erence
between exporters and non-exporters, export intensity and which industries thatexport) hold also in Sweden. There is clear evidence of heterogeneity among…rms which is a key motivation for the model developed by Melitz (2003). In
1 1 I exclude some sectors, either because they are not a¤ected by changes in trade levels orthat they are not relevant. These include the …nancial and public sectors as well as utilities
and construction. There is also a small subset of observations for which I cannot estimate productivity due to the lack of data on either capital, labour or value added. These observations,which account for 6% of all observations with exports, are dropped from the analysis.

18

0

Number of sectors
2
4

6

Export shares in sectors

0

.2

.4
Export share.6.8

Source: Statistics Sweden. Sectors are defined at the 4-digit level.

Figure 2: Export shares in sectors.

the year of 1999, the year just before the bridge was constructed, the standard
deviation of the log of sales of …rms in Sweden was 1.98. When only including
variation within sectors, the variance is still as high as 1.84. In terms of productivity there is also substantial variance. The variance of the log of productivity
is 0.65 and when only using variation within sectors it is 0.62.
In my sample, 26% of manufacturing …rms export and 20% when nonmanufacturing sectors are included. However, of …rms with at least 50 employees,
90% of manufacturing …rms and 77% of all …rms export. There is no cuto¤ in…rm size for exporting, except that total exports to an EU country has to exceed
SEK 1.5 million to be recorded. Most exporters, as is typical in most countries,
only export a small share of their output. Moreover, most sectors export onlya smaller share of their output which con…rms the absence of a clear division
into exporting and nonexporting sectors; most sectors serve both the Swedishand the foreign market as can be seen in Figure 2. Among …rms in 1999, I …ndthat exporters are on average 26% more productive than non-exporters (33%
in manufacturing). This is in line with research using U.S. data; Bernard and190Percentage of firms
.05
.1

.15

Ratio of productivity to sector mean

0 .1 .2 .3 .4 .5 .6 .7 .8 .9

1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 2.1 2.2 2.3 2.4

Nonexporters

Exporters

Sectors are defined at the 4-digit level.

Figure 3: Ratio of productivity to sector mean.

Jensen (2004) found a 39% di¤erence in US manufacturing data. This pattern
can also be seen in more detail in Figure 3 where I divide the productivity ofeach …rm by the mean in its sector and compare non-exporters with exporters.
There are more exporters than non-exporters in all categories above 1.
Finally, a common …nding is that exporters have a lower probability of being
shut down. This can be seen as indicative of sunk costs being involved inexporting, which is assumed in Melitz (2003). Bernard and Jensen (2005) foundin US data that, after introducing controls that explain plant shutdowns, there
is a 5% reduction in the probability of the plant being shut down if the plantis exporting. Although the Swedish data is at the …rm and not the plant level,
I …nd a 4% reduction in shutdown probability for exporters as compared to
non-exporters.
These …ndings tell us that there are indeed clear signs of heterogeneity among
Swedish …rms, that exporters and non-exporters operate within the same sectors
and that there is an indication of …xed costs involved in exporting.

20

Sectoral distribution
OutputValue added

Wholesale

Wholesale

Manufacturing

Manufacturing

RetailRetailTransport

Transport

Car retail

Car retail

Hotels and restaurants

Hotels and restaurants

Communication

Communication

MiningMiningAgriculture

Agriculture
0

20

40
%

60

80

0

20

Employment
Wholesale

Manufacturing

Manufacturing

RetailRetailTransport

Transport

Car retail

Car retail

Hotels and restaurants

Hotels and restaurants

Communication

Communication

MiningMiningAgriculture

Agriculture
20

40
%

Malmö

60

80

60

80

Exports

Wholesale

0

40
%

60

80

Stockholm

0

20

40
%

Gothenburg

Source: Statistics Sweden. 1999 values. Sectors are sorted by Malmö's output share.

Figure 4: Sectoral distribution.

6.1

Comparability of cities

Figure 4 shows the sectoral composition of the three economies used for the
study. It uses the year 1999 since it is the year immediately before the bridge
is built. The industrial structure is relatively similar. Exports, value added
and the number of …rms seem to be located in about the same way in thethree cities. The largest sectors in all three economies are wholesale trade andmanufacturing; these two sectors combined account for around 70% of output
in all cities. These sectors are most likely very di¤erent in many aspects and areprobably a¤ected to a di¤erent extent by the bridge. I will therefore examine
these two sectors individually in addition to the aggregate economy. In termsof sectoral composition, Stockholm and Malmö are the most similar economies,
while Gothenburg appears to be more manufacturing intensive. When possible
in the analysis, however, I control for sectoral e¤ects at the 4-digit level.
Table 1 provides descriptive statistics for four variables in each city: output,

21

number of employees, productivity and exports. It also does so for the yearof 1999. The table shows that, also from this aspect, it seems as if the cities
are relatively comparable. It is seen that Stockholm and Gothenburg has more
and, on average, larger …rms than Malmö. The median is very similar for all
variables except exports where Stockholm has a lower median. The fact that themean is considerably larger than the median for all variables and in all cities isin line with the assumption that the distribution of …rm productivity follows aPareto distribution.12 The frequency of …rms is larger towards the lower levels of
productivity but there is a thin tail with …rms endowed with higher productivity.
If the distribution of productivity of existing …rms had been symmetric, such as
in a non-truncated normal distribution, the mean would have been the same as
the median which is clearly not the case here.

7

Results

The key assumption for examining whether any e¤ect on productivity in Malmöbuilds on the reallocation of production, as in Melitz (2003), is that there has
been a larger decrease in trade costs for the economy in Malmö, especially as
regards trade with Denmark, than in the economies of Stockholm and Gothenburg. I therefore examine the changes in exports to Denmark …rst and thenturn to the e¤ects on aggregate productivity.

7.1

The e¤ect on exports

The assumption in this experiment is that trade costs to a foreign country havebeen lowered more for …rms based in Malmö (the treatment city) than for …rms
based in either of Gothenburg and Stockholm (the control cities). I examine
this in some di¤erent ways according to the model described in Section 4. Less
formally, however, I …rst use data and a survey from Öresundskonsortiet13 that
1 2 It would also be in line with a truncated normal distribution.
1 3 The …rm owning and managing the Öresund bridge. It is jointly owned by the Danish
and Swedish governments.

22

Table 1
Descriptive statistics II
Variable

Stockholm

Gothenburg

Malmö

Observations

11 251

5 587

2 782

OutputMeanStandard deviation
Median63 331
848 660
4 129

62 576
1 177 315
4 403

29 242
128 591
4 527

Employees
MeanStandard deviation
Median

22
228
3

19
223
3

14
60
3

Value added(Levinsohn Petrin)
MeanStandard deviation
Median

12 579201 633
1 042

12 070207 363
1 148

6 374
28 160
1 131

ExportMeanStandard deviation
Median

13 24190 016625

9 328
36 334950

4 863
10 463936

Note: The table describes properties of important variables in 1999, thelast year before the construction of the bridge. Output, value addedand exports are reported with a multiplier of 1000 Swedish kronor.
Source: Statistics Sweden.

23

describes the changes in tra¢ c across the Strait over time and of what characteristics their corporate customers are. Then, turning to the dataset describedin Section 6, I, …rst, examine the changes in aggregate exports from the threecities. Second, I look at the per-…rm increase in exporting and likelihood of
being an exporter; while doing this I control for any sectoral changes that might
confound the results. Finally, I look at how much of the changes in exportinglevels come from the intensive versus extensive margin in the three cities.
Data from Öresundskonsortiet shows that there has been an increase in traf…c across the Öresund Strait since the bridge was constructed. Figure 5 demonstrates the sharp increase since the construction of the bridge from a largely
stable level. The light grey bars show the ferry tra¢ c between Swedish Helsingborg and Danish Helsingör, two smaller towns slightly north of Malmö and
Copenhagen. The black bars show ferry tra¢ c between Malmö and Copenhagen
before the bridge and dark grey shows the new tra¢ c across the bridge. It is evident from the …gure that tra¢ c between Malmö and Copenhagen has increased
rapidly. However, from this we do not know the purpose of the tra¢ c. But
Figure 6 shows that the proportion of tra¢ c by car which travel in “business”,
including transportation of goods, is relatively stable. This indicates that the
total number of vehicles crossing the bridge on business purposes has increased.
Figure 7 shows the number of trucks crossing the bridge. Since I do not know
the destination of the goods being transported, it can of course be argued thatthe goods are destined further south in Europe or to large ports. But it is atleast an indication that the bridge has had an e¤ect on trade patterns.
There has also been more detailed studies done by Öresundskonsortiet into
the characteristics of their corporate customers. The report Öresundsbrokonsortiet (2006) describes how the patterns of trade change after the construction of
the bridge after interviewing 2000 randomly selected corporate customers (1000
customers each from Sweden and Denmark, although the results are sometimes
pooled) in 2006. First, they …nd that, among Swedish …rms, only 29% of …rms
using the bridge in 2006 had any activity (of what kind is not speci…ed) on the248Millions of vehicles crossing the bridge per year
02461990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004
Old Malmö Copenhagen ferryÖresund Bridge

Helsingborg Helsingör ferry

Figure 5: Millions of vehicles crossing the Öresund Strait per year. Source:Öresundsbrokonsortiet.

2001

19%

2004

13%

29%

29%

15%
19%

5%
23%

28%

20%

2010 (forecast)

9%

26%

13%

Business
Commuting

20%

Leisure32%

Short Vacation
Long vacation
Graphs by year

Figure 6: Car tra¢ c across the bridge broken down by purpose. Source: Bridge
Authorities.

25

300000
Number of trucks crossing the bridge per year
0
100000200000

2000

2001

2002

2003

2004

2005

Figure 7: Number of trucks crossing the bridge per year. Source: Öresundsbrokonsortiet.

other side of the Strait before the decision to build the bridge was taken. Of
the remaining 71%, 26% initiated their activities after the decision was taken
to build the bridge but before it was completed (1991 - 1999) and 45% started
after the bridge was constructed (2000 and afterwards).14 In the pooled sample
of …rms that started their activities on the other side after 2000, smaller …rms
are more common. 53% of …rms employing 0-5 people initiated their activities
on the other side of the Strait after 2000, 44% of …rms employing 6-10 people
and only 19% of the largest …rms employing more than 1000 people.15 Thismeans that, …rst, most Swedish …rms that today use the bridge did not haveany activity on the other side of the Strait prior to the bridge’s construction.
Second, the report tells us that smaller …rms were a¤ected more by the bridge
than larger …rms. The group of large …rms seemed to have initiated their activities abroad already before the bridge was constructed whereas small …rms
to a greater extent chose to do so only after the bridge was constructed. This
is what would happen, on average, across sectors according to the model. If
1 4 Öresundsbrokonsortiet (2006), p. 15.
1 5 Ibid, p. 13.

26

.8

1

1.2

1.4

1.6

Exports to Denmark

1997

1998

1999

2000

2001

2002

Year
Malmö
Gothenburg

Stockholm

Source: Statistics Sweden. Data include all exporting to Denmark by firms located in either of the threecities. Levels rebased to 1997 levels.

Figure 8: Exports to Denmark.

there was some sector-speci…c productivity cuto¤ prior to the bridge and that
this was lowered by the bridge, then the larger …rms would be less a¤ected thansmaller or medium-sized …rms.
Having discussed these less formal indications of an e¤ect from the bridge, I
now turn to the formal analysis using the dataset from Statistics Sweden.
Here, I can examine the e¤ect on aggregate exports by summing the export of each …rm to get a measure of VT . The prediction from the model, as
shown in (23), is that total exports from Malmö will increase more than from
Stockholm and Gothenburg. First, I plot graphically the sum of total exports
to Denmark per city during the sample period in Figures 8 and 9. It can beseen that the aggregate series is, …rst, more volatile than one might expect and,second, that both Stockholm and Malmö have large increases starting in 1999.
After 2000, however, Malmö’s growth continues and stays at a high level while
Stockholm’s level drops a little bit. Proportionally, however, if I compare theyears 1998-1999 with 2001-2002, i.e. the four years around the construction of
the bridge, exports from Malmö increase by around 42% which is more than27

Exports to Denmark by the two largest sectors

Exports to Denmark
1.5
2
1
.5

.5

1

Exports to Denmark
1.5
2

2.5

Wholesale

2.5

Manufacturing

1997

1998

1999

2000

2001

2002

Year

1997

1998

1999

2000

2001

2002

Year

Malmö
Gothenburg

Stockholm

Source: Statistics Sweden. Data include all exporting to Denmark by firms located in either of the threecities. Levels rebased to 1997 levels.

Figure 9: Exports to Denmark (two largest sectors).

Stockholm’s 30% and Gothenburg’s 5% (see Table 2). A comparison of the twolargest sectors, manufacturing and wholesale trade, reveal large di¤erences in
how these two sectors are a¤ected. While it is di¢ cult to detect any e¤ect inmanufacturing, exports to Denmark by Malmö-based …rms in wholesale tradealmost doubles (increases by 92%). Stockholm and Malmö move closely together
until 2000 when the bridge is constructed, but then Malmö continues the rapid
increase while Stockholm levels stay at the level in 2000. Summing up, it seems
as if aggregate exports to Denmark in Malmö respond to the construction of
the bridge, and most clearly so in the wholesale sector. It will be seen in analysis of productivity whether this di¤erence between the two sectors translate indi¤erent productivity e¤ects as well.
In order to make a clean comparison, I also do a di¤erence-in-di¤erenceestimation on how existing exporters change their export levels where I cancontrol for sectoral e¤ects (that are the result of, for example, changes in international demand or technology and are uniform for all …rms in Sweden). It wasseen in (15) in Section 4 that foreign sales of an existing exporter, yX , always
28

Table 2
Contributions, by margin, to thechange in exports (1998/9 versus 2001/2)

Malmö(a) All firms
Stockholm

Gothenburg

Extensive margin
Intensive margin

35%
6%

16%
13%

17%
-12%

Total change

42%

30%

5%

Malmö

(b) Manufacturing
Stockholm
Gothenburg

Malmö(c) Wholesale
Stockholm

Gothenburg

Extensive margin
Intensive margin

22%
-11%

30%
-35%

20%
1%

56%
36%

13%
38%

15%
-34%

Total change

11%

-5%

21%

92%

51%

-19%

Note: The table compares how the different categories contribute to the changes in exporting levels
between the two years following the construction of the bridge (2001 and 2002) with the two years
preceding the bridge (1998 and 1999).
Source: Statistics Sweden.

increases when trade freeness,, increases. If all exporters at a given point

in time are included, it would not necessary hold that exports in the exposed
region increases since new and less productive …rms (“switchers”) would enter
the export market with lower export levels than existing exporters.
I run a panel data regression to test the hypothesis in (15) at the level ofthe …rm with sector-speci…c controls, only including …rms that were exporting
before the bridge was constructed. This is in essence a di¤erence-in-di¤erence
estimator.

exportit =0+

M Mit +

T Tit +M T Mit Tit +it + "it(24)

where exportit denotes exports in logarithms of …rm i in year t, Mit is a dummythat takes the value 1 if the …rm is based in Malmö and 0 otherwise, Tit is atime treatment dummy that takes the value 1 if t

2001, that is if the bridge

has been constructed, tit is a linear time trend and

it is a vector of industry…xed e¤ects at the 4 digit level. More speci…cally,29

it takes into account sectoralchanges. It is constructed in the following way:

= [1

T

T]D

where T is a vector which is one for each observation where t

2001 and zerootherwise. D is a matrix with …xed sector e¤ects. Adding

to the regression

controls for time speci…c sectoral means. That is, it adjusts for the fact thatthese sectors may change export patterns in all cities across the period. A…xed e¤ect for the same sector with the same value for all years would not
capture changes in a sector that occur after the bridge is built. To control forsuch common changes in time, I use instead one …xed e¤ect per sector before
the bridge was constructed and another …xed e¤ect for the same sector after
the bridge was built. My set of dummies is therefore twice as large as theset of sectors. This allows the intercept (or average levels) to change in eachsector in order to control for common shocks due to, for example, international
demand. The error term "it is robust to heteroskedasticity. The coe¢ cientMT

is therefore a measure of how much a …rm in Malmö, on average, increases its
exports from 1996-2000 to 2001-2002 in comparison to …rms in Stockholm and
Gothenburg.
Table 3 reports the result of the regression in (24), …rst for the aggregate
economy and then separately for manufacturing and wholesale trade. The results indicate that Malmö-based exporters had a large increase in exports compared to …rms in Stockholm and Gothenburg both with and without adjustingfor sector-speci…c changes at the 4 digit level. This holds for the aggregate
economy as well as manufacturing and wholesale. The e¤ect is strongest in
manufacturing which could seem like a paradox given how little manufacturingchanged overall. This could be explained, however, by the fact that the increasein wholesale trade mainly originated in new …rms starting to the exporting, theextensive margin instead of the intensive margin. I turn to this question now.
A decomposition of the changes in exporting into the intensive and extensive

30

Table 3
Changes in exporting
1a

1b

2a
2b
Manufacturing

All sectors
0.2705**[0.1055]

0.2301[0.1474]

0.1154[0.1653]3a3bWholesale

Malmö

0.3007***[0.0963]

Treat

0.0171[0.0780]

Malmö * Treat

0.2879*[0.1568]

0.4495***[0.1679]

0.3945*[0.2394]

0.7240***[0.2733]

0.3494[0.2226]

0.4363**[0.2221]

Fixed industry effects(changes)

NO

YES

NO

YES

NO

YES

Observations

5637

5637

1950

1950

3109

3109

-0.0986[0.1404]

0.4644***[0.1378]

0.4225***[0.1438]

0.0972[0.1014]

Note: The export level of firms is regressed on a dummy for w hether the firm is based in Malmö, a treatment dummy if the year isafter the bridge w as built and an interaction term of these tw o. The interaction term show s the difference in difference estimate of
how much export changed per firm in Malmö after compared to before the bridge and compared to the tw o other cities. Robust
standard errors in brackets. Industry fixed effects at the four-digit level control for changes in export levels in sectors.
* significant at 10%; ** significant at 5%; *** significant at 1%
Source: Statistics Sw eden.

margins is reported in Table 2. Section 4 describes that exports increase dueXto (i) an increase in the exporting level of existing exporters ( dyas discussed)dand (ii) a selection of new …rms, “switchers”, into the export market. This isdue to the change in the productivity cut-o¤ for exporting, aX , which increases
as shown in (21) in Section 4. Table 2 shows that Malmö’s increase mostly
originates from changes at the extensive margin. It has a much larger increase
due to switchers (new exporters). When looking at the two largest sectors,
manufacturing does not show any of this pattern whereas it is strong in wholesale(where two thirds of the increase is due to changes at the extensive margin).
The importance of the extensive margin is also tested by running a linear
probability regression similar to equation (24) above, but changing the dependant variable to a dummy for whether the …rm i is exporting in year t. The
results are reported in Table 4.
There is evidence at the aggregate level that the likelihood of exporting
has increased in Malmö more than in the control cities, even if the coe¢ cientis rather small. In wholesale, the coe¢ cients are, as expected from Table 2,larger than in both the aggregate economy and in manufacturing, although the31Table 4
Changes in the share of firms that export
1a

1b

2a
2b
Manufacturing

All sectors
0.0122***[0.0013]

Treat

0.0080***[0.0009]

Malmö * Treat

0.0061**[0.0028]0.0046*[0.0026]

0.0064[0.0079]

0.0075[0.0075]0.0106*[0.0064]0.0092[0.0063]

NO

YES

NO

YES

NO

YES

221196221196

43865

43865

67873

67873

Observations

0.0281***[0.0040]0.0180***[0.0038]

3b
Wholesale

Malmö

Fixed industry effects(changes)

0.0088***[0.0013]3a0.0141***[0.0026]

0.0116***[0.0030]0.0103***[0.0030]

0.0159***[0.0022]

Note: The export level of firms is regressed on a dummy for w hether the firm is based in Malmö, a treatment dummy if the year isafter the bridge w as built and an interaction term of these tw o. The interaction term show s the difference in difference estimate of
how much export changed per firm in Malmö after compared to before the bridge and compared to the tw o other cities. Robust
standard errors in brackets. Industry fixed effects at the four-digit level control for changes in export levels in sectors.
* significant at 10%; ** significant at 5%; *** significant at 1%
Source: Statistics Sw eden.

standard errors become larger due to smaller sample size and the coe¢ cient istherefore insigni…cant when sector-speci…c e¤ects are accounted for.
Taken together, the results show strong evidence that there has been a reduction in trade costs for exporters based in Malmö which is larger than thatfor exporters in Stockholm and Gothenburg. The e¤ect seems to be stronger for
the wholesale sector than manufacturing and is mainly driven by the extensive
margin.

7.2

Changes in aggregate productivity

Having established that there has been a reduction in trade costs for …rms basedin Malmö but not to the same extent for …rms in Stockholm and Göteborg, I
turn to the see how this has a¤ected the main variable of interest: aggregate
productivity. First, however, I want to describe the method used to aggregate
productivity across …rms to the level of the city. I follow the methodology
described in Olley and Pakes (1996).
The aggregate productivity in each economy is calculated as the average

32

productivity weighted by output in the following way:pt =where sit

yit
yt

i sit pit

(25)

and pit are the market share and productivity, respectively, of…rm i in year t. I want to see how much that is due to average productivity
levels across …rms and how much is due to the e¢ ciency in the allocation of
production, namely how much more of production is performed by the moreproductive …rms. This can be seen by decomposing the measure in the following
way:

pt =

Nt
i=1 sit pit

(26)

=

Nt
i=1 (

sit + st ) ( pit + pt )

=

Nt
i=1 (

sit pit +=Nt
i=1 st pt += pt +

Nt
i=1

Nt
i=1

sit pt + st pit + st pt )sit pitsit pitwhere

sit = sitstpit = pit

pt

where st and pt denote unweighted means of market share and productivity,
respectively. The …rst term in the expression above, pt , represents how aggregate
productivity is explained by the average productivity across …rms. The second
term,

Nt
i=1

sit pit , is the “allocation e¢ ciency” of production.

The model predicts that if trade freeness, , increases, then aggregate productivity,, increases.16 First, I look at the aggregate level in the three cities.

Table 5 contains information about how aggregate productivity changes between
1 6 This is formally shown in the Appendix.

33

the two years before 2000 and the two years after. The …rst column con…rms
that Malmö experiences the sharpest rise in aggregate productivity (10% versus
small or no changes). The wholesale sector in Malmö seems to be strongly affected and its aggregate productivity increases by as much as 47%. This should
be compared with the e¤ects on trade, where wholesale was found to have amuch stronger e¤ect than manufacturing and the economy as a whole.
To see whether this is due to an average increase (a change in pt ) or a change
in the e¢ ciency of allocation (a change in

Nt
i=1

sit pit ), the rate of increase inboth of these terms is reported in the second and third columns. It is clear thatthe change in average unweighted productivity is small and there does not seemto be large di¤erences across the cities. However, allocation e¢ ciency increases
more in Malmö than in the control cities (where it actually decreases slightly).
That production is shifted towards more productive …rms is the main cause
for the rapid change in productivity growth in Malmö. Again, this mechanism
appears most strongly in wholesale which had the largest trade e¤ect.
The change in aggregate productivity is in line with the prediction by Melitz(2003) if Malmö has been exposed to a decrease in trade cost: that althoughproductivity is relatively constant within …rms, the reallocation of production
raises aggregate productivity. And as the model predicts, almost all of theincrease comes from a reallocation of production across …rms (shown in thethird column in Table 5).
I have now analysed changes at the aggregate level but I also want to look at
a decomposition of aggregate productivity which lies closer to the model. While
the result above is a general outcome of the model, the speci…c mechanism
relates to the partitioning of …rms into exporters and non-exporters and thefact that some production is reallocated towards more productive exporters.
This can be examined in more detail by decomposing the change in aggregate
productivity into speci…c groups based on exporting status.

34

Table 5
Changes in aggregate productivity
Totalchange%Mean
productivity%

Allocation
efficiency
%

Malmö

10%

1%

9%

Stockholm

0%

1%

-2%

Gothenburg

-2%

2%

-4%

Malmö

6%

0%

5%

Stockholm

-30%

1%

-31%

Gothenburg

-8%

1%

-9%

Malmö

47%

5%

42%

Stockholm

27%

5%

23%

Gothenburg

20%

4%

16%

All firms

Manufacturing

WholesaleNote: The table show s the difference in productivity betw een 1998 and 1999 versus 2001 and2002 (before and after the construction of the bridge). The change in aggregate productivity is
calculated as described in the text and seperated into how much of the change that is attributed
to a change in the unw eighted average productivity and the change in the "allocational
efficiency" of production.
Source: Statistics Sw eden.

35

Grouping of …rms

Name

Explanation

SwitcherFirms that did not export before 2000 but do so after.

Export_before

Firms that exported before 2000.

Entrants

Firms that did not exist before 2000.

Exiters

Firms that cease to exist duringsome time during or after 2000.

Neither

Firms that belong to neither of the above categories.

Each of these categories of groups can a¤ect aggregate productivity in two
ways. First, a group’s market share can change and its e¤ect on aggregate productivity will then be determined by the change of the market share multipliedby the relative productivity of the group versus the aggregate productivity of
the region as a whole. This is denoted as “between-group changes”.17 Second,
the aggregate productivity within the group can change and its e¤ect on aggregate productivity in the region will then be determined by the group’s market
share multiplied by the change in its productivity. This I call a “within-group”
change.18
As shown in Section 4, the model predicts that aggregate productivity increases due to three “between-group e¤ects”. First, exporters expand their shareof production and since these …rms are relatively more productive than nonexporters, this increases aggregate productivity. Second, some non-exporters
exit and since these are the least productive …rms this has a positive e¤ect on
aggregate productivity. Third, surviving non-exporters who do not select into
exporting reduce their share of production and since they are less productive
1 7 This is related to “allocational e¢ ciency” but describes instead whether the change ina group’s market share generates an increase or decrease in aggregate productivity. This isdetermined by how high the group’s productivity is compared to aggregate productivity.
1 8 This decomposition is di¤erent from the previous one which is due to Olley and Pakes(1996). The previous one described how much aggregate productivity changes due to a change
in average productivity versus how productivity and production is correlated, respectively.
The current one describes how di¤erent groups of …rms contribute to the change in aggregate
productivity. The productivity of every group, however, is still calculated as in Olley andPakes (1996) above.

36

than exporters this also raises aggregate productivity. The model assumes constant productivity within …rms and that all reallocation of production across…rms is due to exporting status. Therefore, the prediction is that I should not
see any “within-group”e¤ects since the decomposition separates …rms based onexporting status. Regarding the “between-group”e¤ect of switchers, the model
does not give clear predictions. If this group’s initial productivity is above (below) average, then its expansion would generate an increase (decrease) in aggregate productivity. The uncertainty is because switchers are at an intermediate
range in the productivity distribution of …rms.
Formally, I decompose the change in productivity as follows, using i to denotea group of …rms and pit the aggregate productivity in that group in year t:

pt

pt 1
1
=
pt 1
pt 1
1
=
pt 1
1
=
pt 1
1
=
pt 1
1
=
pt 1

Nt
i=1 sit pit

Nt
i=1 sit 1 pit 1

Nt
i=1 sit pit

Nt
i=1 sit 1 pit 1 +(27)
Nt
i=1 sit 1 pit

Nt
i=1 (sit

sit 1 ) pit +Nt
i=1 sit 1 (pitNt
i=1 (sit

sit 1 ) (pitpt ) +

Nt
i=1 (sit

sit 1 ) (epit ) +In the fourth equality I use the fact that pt

pit 1 )

Nt
i=1 sit 1 (pitNt
i=1 sit 1 (pitNt
i=1 (sit

Nt
i=1 sit 1 pit

pit 1 )

pit 1 ) .

sit 1 ) = 0 and I denotethe di¤erence in group i’s productivity from that of the economy as a whole by
peit

pit

pt . Then the contribution of a speci…c group to the total change inaggregate productivity can be denoted as:
Between-group changez(sit

W ithin-group change

}|

{ z
}|
{
sit 1 ) (epit )sit 1 (pit pit 1 )
+
.
pt 1
pt 1

(28)

Each group listed in the table above therefore a¤ects aggregate productivity in two ways. First, the change in allocation of production that is due to37

Table 6aContributions, by firm category,
to changes in aggregate productivity (1998/9 versus 2001/2)
Malmö
BetweenWithinStockholm
BetweenWithinGothenburg
BetweenWithinAll firms
Switchers

2%

1%

-3%

1%

1%

0%

Exporter_before

0%

2%

-2%

1%

0%

0%

Entrants

-1%

0%

0%

Exiters

5%

4%

0%

Neither

0%

Total

1%

0%

10%

1%
0%

0%

-2%
-2%

Note: The table compares how the different categories of firms contribute to the change in aggregate
productivity between the two years following the construction of the bridge (2001 and 2002) and thetwo years preceding the bridge (1998 and 1999).
Source: Statistics Sweden.

the change in market shares between groups with di¤erent productivity levels.
Second, the productivity also moves within groups.19
The contribution of the groups at the aggregate level is reported in Table 6a.
The decomposition follows equation (28) above. Both the contribution throughbetween-group and within-group changes are reported for each city and categoryof …rms.
Table 6a shows that what drives the results in Malmö is mainly what is
described in Melitz (2003): the exit of the least e¢ cient …rms (the between-e¤ectof exiters) and the expansion of …rms with above average productivity as they
enter the export market (the between-e¤ect of switchers). There is, however, nosign of a productivity increase originating in the expansion of existing exporters,
instead there is an increase in the allocation e¢ ciency among these but inside
the group. The strongest e¤ect, however, is from …rms with low productivity
1 9 I do not have estimates for p for exiters after the 2000 and not for new entrants beforet2000 (these …rms did not exist at these times). I therefore assume that the productivity of
the groups in the period for which there is no estimate would have been the same as in the
period for which I have estimates, i.e. I assume constant productivity within these groups.

38

Table 6bContributions, by firm category,
to changes in aggregate productivity (1998/9 versus 2001/2)
Malmö
BetweenWithinStockholm
BetweenWithinGothenburg
BetweenWithinManufacturing
Switchers

-1%

1%

-2%

1%

6%

0%

Exporter_before

-1%

7%

-2%

-25%

1%

-8%

Entrants

0%

0%

0%

Exiters

1%

1%

0%

Neither

0%

Total

0%

0%

6%

0%

0%

-30%

-6%
-8%

Wholesale
Switchers

11%

4%

-7%

-1%

-2%

-3%

Exporter_before

1%

8%

0%

33%

0%

23%

Entrants

0%

0%

1%

Exiters

15%

5%

2%

Neither

1%

Total

6%

0%

47%

1%
27%

0%

2%
20%

Note: The table compares how the different categories of firms contribute to the change in aggregate
productivity between the two years following the construction of the bridge (2001 and 2002) and thetwo years preceding the bridge (1998 and 1999).
Source: Statistics Sweden.

39

closing down.
Given the di¤erences between sectors noted above, it is instructive to see if
the results di¤er according to the extent that the export pattern was a¤ected
for these sectors. These results are reported in Table 6b for the manufacturing
and wholesale sectors. While the manufacturing sector does not show any ofthe model’s mechanism, the wholesale sector does so in the same way as theaggregate economy but with larger numbers. A large share of the increase inaggregate productivity in wholesale stems from the exit of the least productive…rms and expansion by …rms that enter into exporting. The two strongeste¤ects are exactly these two mechanisms described by Melitz (2003). Existing
exporters, however, do not expand as a group, but they experience an increasein productivity due to reallocation within the group as was observed in theaggregate economy. There is to some extent also an e¤ect from the reallocationof production among nonexporters.
This analysis on aggregate productivity has so far not controlled for sectorale¤ects. In the analysis in Tables 6a and 6b, I cannot do this. However, theprocess of …rms closing down or exiting, which was seen to a¤ect productivity,
can be analysed when controlling for sectors. The logarithm of (11) in Section
4 givesaDk = (
k log

where c

log (

1)

1
aD

1 fD
fE

1)

1 fD

fE

1+

= c + log 1 +(30)

and a1D is the productivity (the inverse of mar-

ginal cost) cut-o¤ for survival. It is now seen that if
1
00
aD

(29)

00

>

0

> , then also

> a10 > a1D , i.e. the productivity cut-o¤ moves more in an economy inDwhich the trade cost moves more.
However, to test if this happens for Malmö compared to Stockholm and
Gothenburg, I have to assume that the initial trade cost is the same for all of
the three economies. This is due to the fact that40

enters nonlinearly in (30) andthe change therefore not only depends on the change inbut also on its initiallevel. If this is assumed I can test the hypothesis that the reduction in trade
costs has caused the least productive …rms to exit also controlling for sectorale¤ects. I do this by comparing the means in productivity of …rms exiting after
the year 2000 with the surviving …rms in the years before the bridge, 1998 and1999. From (30), it is seen that if

moves to0

and Gothenburg it only moves to

00

in Malmö but in Stockholm, then mean productivity of exiting …rms

in Malmö should be higher than those in Stockholm and Gothenburg since
1
1
00 >
0
aD
aD

and productivity follows the same distribution in all cities.

I test this by running the following regression:

pit =

0+

X EXITit +M Mit +XM EXITit Mit +it + "it(31)

for the years 1998 and 1999. The variable EXITit takes the value 1 if the …rm is
exiting after the bridge is constructed. Mit takes the value 1 if a …rm is locatedin Malmö and

it is a sector …xed e¤ect. The interesting coe¢ cient is therefore

XM which is multiplied with the interaction term EXITit Mit . This comparesthe di¤erence in productivity among exiters relative to surviving …rms in Malmöwith that in Stockholm and Gothenburg. This is a test of (30) saying that the
reduction in trade costs has increased the productivity cut-o¤ in Malmö morethan in Stockholm and Gothenburg.
Table 7 shows that it seems that even with sectoral controls at a very disaggregated level, there is evidence that exiters in Malmö are more productive on
average than in Stockholm and Gothenburg. The results hold in the aggregate
economy both with and without sector …xed e¤ects. For manufacturing thecoe¢ cients are close to zero but there are positive coe¢ cients in the wholesale
sector. These are, possibly due to the smaller sample size, not signi…cant, however. The aggregate results support the notion that the e¤ect of a decrease intrade costs forces out the least productive …rms.

41

Table 7
Productivity of exiters
Productivity
All
(1)

(2)

Manufacturing(3)(4)

Wholesale
(5)
(6)

Malmö

-0.037*** -0.035***[0.008][0.008]-0.007[0.016]-0.034**[0.016]-0.045*** -0.045***[0.014][0.015]

Exiter

-0.039**[0.015]-0.042***[0.015]-0.034[0.034]-0.047[0.032]0.009[0.032]0.018[0.031]

Malmö * Exiter

0.068*[0.037]

0.091**[0.037]0.004[0.079]-0.010[0.080]0.028[0.070]0.042[0.070]

Fixed industry
effects

NO

YES

NO

YES

NO

YES

Observations

77006

77006

16266

16266

23783

23783

Note: The regressions examine if the difference in productivity between firms thatexit and firms that maintain production is different in Malmö than in the control
cities. Firms that exit after 2000 are labelled as exiters. The regressions therefore
only include the years before the bridge (1998 and 1999). Robust standard errors
in brackets. Industry fixed effects at the four-digit level.
* significant at 10%; ** significant at 5%; *** significant at 1%
Source: Statistics Sweden.

42

8Conclusion

The paper examines how aggregate productivity changes in a developed economy after a decrease in trade costs exogenous to industry-speci…c productivity
and growth levels. Due to the stability and geographic symmetry of Sweden’s
macroeconomic and industrial policies, the risk of confounding e¤ects is small
since I compare the evolution of Malmö, which faced the trade cost reduction,with the two other large cities in Sweden. Using …rm-level data, I calculate
unbiased estimates of total factor productivity growth and estimate how muchof productivity growth is due to the reallocation of production across …rms andhow much is due to average productivity growth within …rms.
I …nd substantial evidence supporting models of …rm selection such as Melitz(2003). Exports by …rms based in Malmö rise substantially, mostly due to …rms
entering into the export market that did not export before. Importantly, ofthe two main sectors manufacturing and wholesale, it is clearly the wholesale
sector that expands exports the strongest. Aggregate productivity in Malmö
also increases. I …nd that almost all of Malmö’s rapid growth in aggregate
productivity occurs because of a reallocation of production from less productive
to more productive …rms. When decomposing the productivity gain, I …nd thatthe main drivers of aggregate productivity is a) exit of the least productive …rms
and b) expansion in output of …rms with high productivity that enter the export
market. When comparing the two largest sectors, the productivity changes are
the strongest in the wholesale sector which is also the sector for which trade
increased the most.
The …ndings provide insight into the causal link from market integrationand increased trade to aggregate productivity through …rm dynamics. It largely
con…rms the …rm-selection patterns described in models such as Melitz (2003).

43

References
Arnold, J. M. (2005): “Productivity Estimation at the Plant Level: A Practical Guide,” note.
Aw, B. Y., X. Chen, and M. J. Roberts (2001): “Firm Level Evidence
on Productivity Di¤erentials and Turnover in Taiwanese Manufacturing,”
Journal of Development Economics, 66(1), 51–86.
Axtell, R. L. (2001): “Zipf Distribution of U.S. Firm Sizes,” Science, 293.
Bernard, A. B., J. Eaton, J. B. Jensen, and S. Kortum (2003): “Plants
and Productivity in International Trade,”American Economic Review, 93(4),1268–1290.
Bernard, A. B., and J. B. Jensen (2004): “Why Some Firms Export,”
Review of Economics and Statistics, 86(2), 561–569.
(2005): “Firm Structure, Multinationals and Manufacturing Plant
Deaths,” Review of Economics and Statistics, 89(2), 193–204.
Clerides, S. K., S. Lach, and J. R. Tybout (1998): “Is Learning by Exporting Important? Microdynamic Evidence from Colombia, Mexico and Morocco,” Quarterly Journal of Economics, 113(3), 903–947.
Dixit, A. K., and J. E. Stiglitz (1977): “Monopolistic Competition and
Optimum Product Diversity,” American Economic Review, 67(3), 297–308.
Foster, L., J. Haltiwanger, and C. Krizan (1998): “Aggregate Productivity Growth: Lessons from Microeconomic Evidence,”NBER Working Papers,
6803.
Grossman, G., and E. Helpman (1994): “Protection for Sale,” American
Economic Review, 84(4), 833–850.
Helpman, E., M. J. Melitz, and Y. Rubinstein (2008): “Estimating Trade
Flows: Trading Partners and Trading Volumes,” Quarterly Journal of Economics, 123.
Helpman, E., M. J. Melitz, and S. R. Yeaple (2004): “Export versus FDI
with Heterogeneous Firms,” American Economic Review, 94(1), 300–316.
Koujianou Goldberg, P., and G. Maggi (1999): “Protection for Sale: An
Empirical Investigation,” American Economic Review, 89(5), 1135–1155.
Krugman, P. R. (1980): “Scale Economies, Product Di¤erentiation, and thePattern of Trade,” American Economic Review, 70(5), 950–959.
Levinsohn, J. A., and A. K. Petrin (2003): “Estimating Production Functions Using Inputs to Control for Unobservables,” Review of Economic Studies, 70(2), 317–341.
Loecker, J. D., and J. Konings (2006): “Job reallocation and productivity
growth in a post-socialist economy: Evidence from Slovenian manufacturing,”
European Journal of Political Economy, 22.
44

Marschak, J., and W. Andrews (1944): “Random Simultaneous Equations
and the Theory of Production,” Econometrica, 12(3), 143–205.
Melitz, M. J. (2003): “The Impact of Trade on Intra-Industry Reallocations
and Aggregate Industry Productivity,” Econometrica, 71(6), 1695–1725.
Olley, G. S., and A. Pakes (1996): “The Dynamics of Productivity in the
Telecommunications Equipment Industry,” Econometrica, 64(6), 1263–1297.
Pavcnik, N. (2002): “Trade Liberalization, Exit, and Productivity Improvements: Evidence from Chilean Plants,” Review of Economic Studies, 69(1),245–276.
Roberts, M. J., and J. R. Tybout (1997): “The Decision to Export in
Colombia: An Empirical Model of Entry with Sunk Costs,” American Economic Review, 87(4), 545–564.
Schank, T., C. Schnabel, and J. Wagner (2007): “Do exporters really pay
higher wages? First evidence from German linked employer-employee data,”
Journal of International Economics, 72, 52–74.
Trefler, D. (2004): “The Long and Short of the Canada-U.S. Free Trade
Agreement,” American Economic Review, 94, 870–895.
Tybout, J. R. (2003): “Plant- and Firm-level Evidence on ‘New’Trade Theories,”in Handbook of International Trade, ed. by E. K. Choi, and J. Harrigan.
Basil-Blackwell, Oxford.
Yeaple, S. (2005): “A Simple Model of Firm Heterogeneity, International
Trade, and Wages,” Journal of International Economics, 65(1), 1–20.
Öresundsbrokonsortiet (2006): “Näringslivets Erfarenheter över Öresund,”Report.

45

9

Appendix

9.1

Proofs

9.1.1

Proof that dd > 0.
0

=@
=k

1
D
1 + ffX

ZaD

a1

0

! 1 1 0ZaD
@ ak

1
1
akD 1 + ffD

1
1

X

=

k

(

! 11

1
1
akD 1 + ffD

1

1)

X

1 11

a1

0

da +

0

1

k

ZaX

fD
g (a)
fX
da +
D
G (aD )
1 + ffX

ZaX

fD
fX

g (a)
daA
G (aD )

1 11

daA

ak

0

k (
aD

1)

(32)

fD
+
fX

k (
aX

(33)
1
1

1)

(34)
=

(

0

1

1+

k

(
k

1)
1 11

1)

C
C
A

D
1 + ffX

It must be that1)
> 0 since k
k

9.1.2

(

1)
fD
fX

B1 +
B
@

k (

1

k
k

1

1

fE
fD

+1

1+

1

(35)

.

increases in(1) > 0.

(36)

since

> 1 in the third bracket and that

Proof that d(yDd+yX ) > 0.

1

yD + yX = a

fE fD 1
1)
1+

(

!1

(1 + )

1+

= a1

(1 +

)

(37)
(38)

1

1

where

1) fE fD 1(
dd

. The derivative of

1+
(1 +

)

which is always true since
> 1.

1+
1

(1+

1

!

1

=

1+

1

with regard to

is:

)

1

>0

(39)

< 1 at trade costs strictly larger than zero and46