Trade and Labor Market Outcomes

Elhanan Helpman
Harvard University and CIFAR
Oleg Itskhoki
Princeton University
Stephen Redding
Princeton University
December 1, 2010

Abstract
This paper reviews a new framework for analyzing the interrelationship between inequality,
unemployment, labor market frictions, and foreign trade. This framework emphasizes …rmheterogeneity and search and matching frictions in labor markets. It implies that the opening oftrade may raise inequality and unemployment, but always raises welfare. Unilateral reductions
in labor market frictions increase a country’s welfare, can raise or reduce its unemployment rate,
yet always hurt the country’s trade partner. Unemployment bene…ts can alleviate the distortions
in a country’s labor market in some cases but not in others, but they can never implement theconstrained Pareto optimal allocation. We characterize the set of optimal policies, which requireinterventions in product and labor markets.
Keywords: inequality, unemployment, trade, labor market policy
JEL Classi…cation: F12, F16, J64

We thank the National Science Foundation for …nancial support and Eliav Danziger for research assistance. This
paper is based on the Frisch Memorial Lecture from the World Congress of the Econometric Society 2010 in Shanghai.
We are grateful to conference participants for their comments.

1

Introduction

For understanding the causes and consequences of international trade, recent research has increasingly focused on individual …rms. While this research emphasizes reallocations of resources acrossheterogeneous …rms, it typically assumes frictionless labor markets in which all workers are fully
employed for a common wage. In reality, labor markets feature both unemployment and wage
inequality, and labor market institutions are thought to play a prominent role in propagating theimpact of external shocks. In this paper, we draw on recent research in Helpman and Itskhoki(2010) and Helpman, Itskhoki and Redding (2010), to discuss interdependence across countries.
This framework incorporates a number of features of product and labor markets. Firms areheterogeneous in productivity, which generates di¤erences in revenue across …rms. There are search
and matching frictions in the labor market, which generate equilibrium unemployment, and giverise to multilateral bargaining between the …rms and their workers. While workers are ex antehomogeneous, they draw a match-speci…c ability when matched with a …rm, which is not directly
observed by either the …rm or the worker. Firms, however, can invest resources in screening theirworkers to obtain information about ability. Larger, more productive …rms, screen workers more
intensively to exclude those with low-ability. As a result, they have workforces of higher averageability and they pay higher wages. These di¤erences in …rm characteristics are systematicallyrelated to export participation. Exporters are larger and more productive than nonexporters; theyscreen workers more intensively; and they pay higher wages in comparison to …rms with similar
productivity that do not export. The resulting framework highlights a new mechanism throughwhich trade a¤ects inequality, based on variation in wages across …rms and the participation of
only the most productive …rms in exporting.
We use a simpli…ed version of this framework to examine interdependence across countries
through labor market frictions. Cross-country di¤erences in labor market characteristics shapepatterns of comparative advantage. A reduction in a country’s labor market frictions in the di¤erentiated sector reduces unemployment within that sector and expands the share of workers searching for employment there, which a¤ects aggregate unemployment through a change in sectoralcomposition. Depending on the relative values of unemployment rates across sectors, aggregate unemployment may rise or decline. The expansion in a home country’s di¤erentiated sector increases

1its welfare, but enhances the degree of product market competition faced by foreign …rms, whichleads to a contraction in the foreign country’s di¤erentiated sector and a reduction in its welfare.
Unilateral labor market reforms, therefore, can have negative externalities across countries, whereas
coordinated reductions in labor market frictions raise welfare in every country.
As well as providing a platform for analyzing the positive economic e¤ects of trade and labormarket characteristics, our framework can be used to address normative issues. We …rst examine
the impact of unemployment bene…ts on resource allocation and welfare, and show that they raise
welfare in some circumstances and reduce welfare in other. We also present new results on policies
that implement a constrained Pareto optimum. When the Hosios (1990) condition is satis…ed, thesepolicies do not require intervention in the labor market. Otherwise, a combination of subsidies tothe cost of posting vacancies/hiring, subsidies to output/employment, and a common subsidy to all…xed costs (entry, production and exporting) implement the constrained Pareto optimal allocation.
These product market policies apply equally to exporting and nonexporting …rms. Unemployment
bene…ts can be part of the optimal policy package under some circumstances, but even then more
direct interventions in the labor market are preferable on informational grounds.
The remainder of the paper is structured as follows. In Section 2 we discuss the motivationfor our approach and some of the related literature. In Section 3 we introduce our frameworkand examine the relationship between inequality, unemployment and trade. In Section 4 we use
a simpli…ed version of the model to explore how changes in labor market frictions in one countrya¤ect its trade partners and how the removal of trade impediments a¤ects countries with di¤erent
labor market frictions. Section 5 examines unemployment bene…ts and optimal policies. Section 6
concludes.

2

Background and Motivation

Traditional explanations of international trade have emphasized comparative advantage based on
variation in technology across countries and industries (Ricardo 1817) or the interaction between
cross-country di¤erences in factor abundance and cross-industry di¤erences in factor intensity(Heckscher 1919, Ohlin 1924, Jones 1965 and Samuelson 1948). In the 1980s, economies of scale andmonopolistic competition were merged with factor proportions-based explanations for trade in Dixit

2and Norman (1980), Helpman (1981), Krugman (1981) and Lancaster (1980). While economies ofscale and love of variety preferences together generated two-way trade within industries, as observed
empirically, the assumption of a representative …rm implied that all …rms exported.
More recently, …rm heterogeneity has been introduced into general equilibrium trade theory
following Melitz (2003) and Bernard, Eaton, Jensen and Kortum (2003). The resulting models of…rm heterogeneity and trade provide a natural explanation for empirical …ndings from micro datathat only some …rms within industries export and these exporters are larger and more productive
than non-exporting …rms. Table 1 reports some representative evidence on export participationfrom the World Trade Organization (2008). In each of the countries considered, only a minority of…rms export. Furthermore, even within exporters, there is tremendous heterogeneity in productivity
and size. As reported in Table 2, the top 1 percent of …rms account for 81 percent of U.S. exports
and a substantial percentage of exports in all countries.
Country
U.S.A.
NorwayFranceJapan
Chile
Colombia

Year
2002
2003
1986
2000
1999
1990

Exporting …rms, in percent
18.0
39.2
17.4
20.0
20.9
18.2

Table 1: Share of manufacturing …rms that export, in percent (Source: WTO 2008, Table 5)
Country
U.S.A.
Belgium
FranceGermany
Norway
U.K.

Year
2002
2003
2003
2003
2003
2003

Top 1% of …rms
81
48
44
59
53
42

Top 10% of …rms
96
84
84
90
91
80

Table 2: Share of exports of manufactures, in percent (Source: WTO 2008, Table 6)This new theoretical literature on …rm heterogeneity and trade emphasizes the self-selectionof more productive …rms into exporting and foreign direct investment (FDI). As a result of this3

self-selection, reductions in trade costs have uneven e¤ects across …rms, as low-productivity …rms
exit and high-productivity …rms expand to serve foreign markets. The resulting changes in industry
composition raise aggregate productivity, consistent with empirical …ndings from trade liberalization episodes, as reported in Pavcnik (2002) and Tre‡er (2004). Firm heterogeneity and selection
also in‡uence cross-section patterns of trade and FDI. For example, the ratio of exports to foreign subsidiary sales depends not only on the trade-o¤ between proximity and concentration, butalso on the dispersion of …rm productivity, as shown in Helpman, Melitz and Yeaple (2004) andYeaple (2009). Similarly, the decision whether to o¤shore stages of production within or outside
the boundaries of the …rm is systematically related to …rm productivity, as shown theoretically in
Antràs and Helpman (2004) and empirically in Nunn and Tre‡er (2008) and Defever and Toubal(2010).
Although this theoretical literature emphasizes reallocations across …rms, the modelling of thelabor market has, until recently, been highly stylized. All workers are fully employed at a common
wage and hence are a¤ected symmetrically by the opening of trade. These model features sit
uncomfortably with a large empirical literature that …nds an employer-size wage premium (seethe survey by Oi and Idson 1999) and with extensive evidence that exporters pay higher wages
than non-exporters (see in particular Bernard and Jensen 1995, 1997). While this theoretical
literature assumes no labor market frictions and costless reallocations across …rms, search andmatching frictions occupy a prominent position in macroeconomics (following Diamond 1982a,b,Mortensen 1970, Pissarides 1974, and Mortensen and Pissarides 1994). More generally, labor market
institutions have been found to be in‡uential in shaping the responses of European countries toexternal shocks (Blanchard and Wolfers 2000) and in understanding the evolution of unemployment
rates in OECD countries over time (Nickell, Nunziata, Ochel and Quintini 2001).
Evidence on the magnitude of cross-country di¤erences in labor market institutions is presented
in Table 3. Even among countries at similar levels of economic development, such as OECD
countries, there are substantial di¤erences in the ease of hiring and …ring workers and the rigidityof hours worked. In the European Union, member states have focused on labor market policies
for more than a decade following the Luxembourg Extraordinary European Council Meeting on
Employment in 1997. This meeting produced the European Employment Strategy, which wasincorporated into the broader Lisbon Strategy, designed to turn Europe into a more competitive4and dynamic economy. To address such policy issues, we require theoretical models that pay morethan usual attention to features of labor markets. And the high levels of international integrationin the contemporary world economy suggest the need for frameworks within which it is possible toexamine interdependence in labor market outcomes across nations.
Country
United States
UgandaRwandaUnited Kingdom
Japan
OECD
Italy
MexicoRussiaGermany
FranceSpain
MoroccoDi¢ culty of Hiring
0
0
11
11
11
27
33
33
33
33
67
78
89

Rigidity of Hours
0
0
0
20
7
30
40
20
40
53
60
40
40

Di¢ culty of Redundancy
0
0
10
0
30
23
40
70
40
40
30
30
50

Table
3:
Cross-countryDi¤erences
in
Labor
MarketFrictions(Source:
Botero et al.
2004).
Downloaded from the World Bank’s website
http://www.doingbusiness.org/ExploreTopics/EmployingWorkers/ on September 25, 2009.

Our analysis builds on a long line of research on trade and labor market frictions. This literature has considered a number of di¤erent sources of labor market frictions, including minimum
wages (Brecher 1974), implicit contracts (Matusz 1986), e¢ ciency wages (Copeland 1989), fairwages (Agell and Lundborg 1995 and Kreickemeier and Nelson 2006), search and matching frictions (Davidson, Martin and Matusz 1988, 1999), and labor immobility and volatility (Cuñat andMelitz 2009). More recently, a surge of research has begun to incorporate labor market frictions
into theories of …rm heterogeneity and trade, including models of fair wages (Egger and Kreickemeier 2009, Amiti and Davis 2008), e¢ ciency wages (Davis and Harrigan 2007), and search andmatching frictions (Helpman and Itskhoki 2010, Helpman, Itskhoki and Redding 2010, Mitra andRanjan 2010, and Felbermayr, Prat and Schmerer 2010).
Our analysis focuses on search frictions as the source of labor market imperfections and isbased squarely in the new view of foreign trade that emphasizes …rm heterogeneity in di¤erentiatedproduct markets. The discussion of inequality, unemployment and trade in Section 3 draws on
5

Helpman, Itskhoki and Redding (2010), while the analysis of interdependence in labor market
outcomes in Section 4 is based on Helpman and Itskhoki (2010). In Section 5, we present new
results on the design of labor market policies in economies with …rm heterogeneity and labormarket frictions.1

3

Inequality

The traditional framework for examining the distributional consequences of trade liberalizationis the Stolper-Samuelson Theorem of the Heckscher-Ohlin model. Recent research, however, has
identi…ed a need to rethink the links between trade and wage inequality. While the StolperSamuelson Theorem predicts that trade raises wage inequality in skilled–labor–abundant countries
and reduces wage inequality in unskilled–labor–abundant countries, empirical studies of recent
trade liberalization episodes typically …nd rising wage inequality in both developed and developing
countries (see for example the survey by Goldberg and Pavcnik 2007).2 Furthermore, whereas
the Stolper-Samuelson Theorem emphasizes changes in the relative wages of skilled and unskilledworkers, there is evidence of changes in within-group inequality for workers with the same observed
characteristics in the aftermath of trade reforms, as in Attanasio, Goldberg and Pavcnik (2004)
and Menezes-Filho, Muendler and Ramey (2008).
In contrast to the Stolper-Samuelson Theorem’s reliance on reallocations of resources acrossindustries, the key predictions of our framework relate to the distribution of wages and employment
across …rms and workers within a sector. We derive these distributions from comparisons across…rms that hold in sectoral equilibrium for any value of a worker’s expected income outside thesector, i.e., his outside option. An important implication is that the predictions of our model for
sectoral wage inequality hold regardless of general equilibrium e¤ects. Throughout this section, allprices, revenues and costs are measured in terms of a numeraire, where the choice of this numerairedepends on how the sector is embedded in general equilibrium, as discussed further in Helpman,
Itskhoki and Redding (2010).
1

See also Itskhoki (2010) for an analysis of the optimal design of a tax system in an open economy with heterogenous…rms.
2
See, however, Feenstra and Hanson (1996), Zhu and Tre‡er (2004) and Sampson (2010) for trade mechanismsthat can raise inequality in rich and poor countries alike.

6

3.1

Model Setup

We consider a di¤erentiated-product sector. Consumer preferences take the constant elasticity of
substitution (CES) form and the real consumption index for the sector (Q) is:

Q=

Z

1=

q(j) dj

;

0<

< 1;

(1)

j2J

where j indexes varieties; J is the set of varieties within the sector; q (j) denotes consumption ofvariety j; andcontrols the elasticity of substitution between varieties.

There is a competitive fringe of potential …rms who can choose to enter this sector by incurring
a sunk entry cost of fe > 0. Once the sunk entry cost is paid, a …rm observes its productivity ,( min = )z for

which is drawn from an independent Pareto distribution, G ( ) = 1

min > 0and z > 1. Once …rms observe their productivity, they decide whether to exit, produce solely forthe domestic market, or produce for both the domestic and export markets. Production involves a…xed cost of fd > 0 units of the numeraire. Exporting involves an additional …xed cost of fx > 0
units of the numeraire and an iceberg variable trade cost, such that

> 1 units of a variety must

be exported in order for one unit to arrive in the foreign market.
There is a continuum of ex ante identical workers, who choose whether or not to search for
employment in the sector. The labor market is subject to search and matching frictions. Workers
draw a match-speci…c ability a when matched with a …rm in the di¤erentiated sector. This matchspeci…c ability, which is observed neither by the worker nor the …rm, is drawn from an independent
Pareto distribution, Ga (a) = 1(amin =a)k for aamin > 0 and k > 1.

Output of each …rm variety (y) depends on the productivity of the …rm ( ), the measure ofworkers hired (h), and the average ability of these workers (a):y = h a;

0<

< 1;

(2)

where this production technology can be interpreted as capturing either human capital complementarities (e.g., production in teams where the productivity of a worker depends on the average
productivity of her team) or a managerial time constraint (e.g., a manager with a …xed amount oftime who needs to allocate some time to each worker). A key feature of this production technol-7ogy is complementarities in worker ability, where the productivity of a worker is increasing in theabilities of other workers employed by the …rm.
Search and matching frictions in the labor market are modelled following the standard DiamondMortensen-Pissarides approach. A …rm that pays a search cost of bn units of the numeraire canrandomly match with a measure of n workers, where the search cost b is endogenously determinedby the tightness of the labor market x:
b= x :
This search technology can be derived from a Cobb-Douglas matching function;(3)
is a parameter,

which is increasing in the cost of posting vacancies and decreasing in the Hicks-neutral e¢ ciencyof the matching process;is the ratio of the Cobb-Douglas coe¢ cients on the number of workers

searching for jobs and vacancies; the tightness of the labor market, x = N=L, is the ratio of
the measure of matched workers, N , to the measure of workers searching for employment in thedi¤erentiated sector, L.
Once matched with workers, …rms can invest resources in screening them to obtain an imprecise
signal of match-speci…c ability. By incurring a screening cost of cac = , where c > 0 and> 1,

a …rm can identify those workers with an ability below ac , but cannot determine the abilities of
the individual workers with any greater precision. We focus on interior equilibria in which c issu¢ ciently small that all …rms screen their workers.
The timing of decisions is as follows. Firms and workers decide whether or not to enter thedi¤erentiated sector. The outside option of …rms is zero. The outside option of workers is expected
income in other employment, !, where workers are assumed to be risk neutral and ! is determinedin general equilibrium. After incurring the sunk entry cost for the di¤erentiated sector, …rms learn
their productivity

and choose whether to exit or produce. If …rms choose to produce, they post ameasure of vacancies and choose whether to serve only the domestic market or also export. Workers
are next matched with …rms. Unmatched workers become unemployed and receive unemployment
bene…ts of zero. Firms screen their n matched workers by choosing a screening threshold ac . Only
workers with abilities above the screening threshold are hired and those with abilities below thescreening threshold become unemployed. The …rm and its h hired workers engage in multilateralbargaining over the division of the surplus from production as in Stole and Zwiebel (1996). Finally,8

output is produced and markets clear.

3.2

Firm’s Problem

Given the speci…cation of di¤erentiated-sector demand, the equilibrium domestic-market revenueof a …rm can be written as:r(j) = p(j)q(j) = Aq(j) ;where A is a demand-shifter, which is increasing in total expenditure on varieties within the sector,
E, and in the sector’s ideal price index, P , which summarizes the prices of competing varieties.
If a …rm exports, it allocates its output between the domestic and export markets to equate its
marginal revenues in the two markets, so that total …rm revenue can be expressed as:r( )where rd ( )( )1rd ( ) + rx ( ) =Ay ( ) ;Ayd ( ) is revenue from domestic sales; rx ( )(4)A [yx ( ) = ] is revenue fromexporting; yd ( ) is output for the domestic market; yx ( ) is output for the export market; andy ( ) = yd ( ) + yx ( ). The variable( ) captures a …rm’s “market access,” which depends onwhether it chooses to serve both the domestic and foreign markets or only the domestic market:( )1 + Ix ( )

1

A
A

1
1

;

(5)

where Ix ( ) is an indicator variable that equals one if the …rm exports and zero otherwise.
The solution to the bargaining game implies that the …rm receives a share 1= (1 +) of revenue,

while each worker receives a wage equal to a constant share of revenue per worker:

w( ) =

1+

r( )
:
h( )

Anticipating this outcome of the bargaining game, a …rm chooses the measure of workers to match

9with, n, the screening threshold, ac , and whether or not to export to maximize its pro…ts:

( )

(6)

max

n 0;
ac amin ;Ix 2f0;1g

where

y

(

"

1
1+

1 + Ix

1

A
A

1

1

#1

k

1
y n ac

A

c

bn

ac

fd

)

Ix fx ;

is a derived parameter and we have used the properties of the Pareto distribution ofworker ability. The latter implies that a …rm choosing a screening threshold ac hires a measureh = n (amin =ac )k of workers with average ability a = kac =(k1). Firms of all productivities havean incentive to screen for 0 < k < 1 and su¢ ciently small values of c.
As a result of …xed costs of production and exporting, a …rm’s decision whether or not to
produce and export takes a standard form. Only the most productive …rms with productivities
x export; …rms with intermediate productivities

and the least productive …rms with productivities

2 [ d ; x ) serve only the domestic market;<

d exit. The …rm market access variable istherefore determined as follows:

( )=

8
>
< 1;
>
:

<

x;
x

x;

1+

1

A
A

1

x;

1

> 1:

(7)

Using the …rst-order conditions to the …rm’s problem (6), closed form solutions for all …rm-speci…cvariables can be derived:
1r( ) =( )n( ) =( )ac ( ) =

( )

1

( )

w( ) =

( )

d

nd

d

1

1

h( ) =

rd

(1

ad

;

rd

;

nd
;

d

ad
(1 k= )

(1 k= )
)k

wd

hd

;

d
k
d

;

hd
wd

1+

h
b

fd ;
fd
b ;
k) fd
c

(1

h

fd
b

h

(1

(1
k)

i1=
k)

;
fd
camin
ik=

fd
camin

i k=
:

9
>
>
>
>
>
>
>
>
>
>
>
>
>
=

>
>
>
>
>
; >
>
>
>
>
>
>
>
;

(8)

More productive …rms have larger revenues, match with more workers and screen to higher ability
thresholds. As a result they have workforces of higher average ability and pay higher wages. As longas screening costs are su¢ ciently convex and worker ability is su¢ ciently dispersed,

10> k, moreFigure 1: Wages as function of …rm productivity

productive …rms also hire more workers, which implies that the model features the empiricallyobserved employer-size wage premium. The …xed costs of exporting imply that all …rm variables
apart from pro…ts jump discretely at the productivity threshold for exporting,from one tox > 1.

x , where( ) jumps

Exporting …rms are, therefore, more productive, larger, have workforces ofhigher average ability and pay higher wages, as found empirically using micro data on …rms andplants (e.g. Bernard and Jensen 1995, 1997) and matched employer-employee datasets (e.g. Frías
and Kaplan 2009).
The wage schedule as a function of productivity is illustrated for particular parameter values
in Figure 1. Although more productive …rms pay higher wages, they also screen more intensively,
which implies that they hire a smaller fraction of their matched workers. Using the solution to thebargaining game and the …rm’s …rst-order conditions, the higher wages of more productive …rms areexactly o¤set by the lower probability of being hired, since the Stole-Zwiebel bargaining solution
implies that a …rm’s equilibrium wage is equal to its replacement cost for each worker. As a result,the expected wage conditional on being matched is the same across all …rms:
w( )h ( )= b;n( )which implies that workers have no incentive to direct their search across …rms of di¤ering productivities.

11

3.3

Labor Market Equilibrium

Worker indi¤erence across sectors requires that expected income in the di¤erentiated sector isequal to workers’outside option, !, where expected income in the di¤erentiated sector equals theprobability of being matched, x, times the expected wage conditional on being matched, b:! = xb:(9)This indi¤erence condition across sectors and the search technology (3) together determine theequilibrium tightness of the labor market and hiring costs as a function of workers’outside option:

b=

1
1+

!

1+

and

x=

1
1+

!

;

(10)

where ! is determined in general equilibrium, as considered in Helpman, Itskhoki and Redding(2010).

3.4

Implications for Wage Inequality

Since wages and employment in (8) are power functions of productivity, which is Pareto distributed,
we can solve in closed form for the wage distribution. The distribution of wages across all workers
is a weighted average of the distributions of wages for workers employed by domestic …rms and forworkers employed by exporters, with weights equal to the shares of employment in the two groups of…rms: Sh;d representing the share of employment by nonexporters and Sh;x = 1

Sh;d representing

the share of employment by exporters. The distribution of wages across workers employed bydomestic …rms is a truncated Pareto distribution while the distribution of wages across workers
employed by exporters is an untruncated Pareto distribution, but these two wage distributions
have the same shape parameter, 1 + 1= , wherek=z
and we require 0 <is de…ned as:; where

1

(1

k);

< 1 and hence z > 2 for the wage distribution to have a …nite mean andvariance.

12

In both the closed economy (Sh;d ! 1) and the open economy when all …rms export (Sh;d ! 0),
the distribution of wages across all workers is an untruncated Pareto distribution. One feature ofan untruncated Pareto distribution is that all scale-invariant measures of inequality, such as theCoe¢ cient of Variation, the Gini Coe¢ cient and the Theil Index, depend solely on the distribution’s
shape parameter, which is a su¢ cient statistic for inequality. As this shape parameter is the samefor workers employed by domestic …rms and exporters, it follows that there is the same level ofwage inequality in the open economy when all …rms export as in the closed economy. In contrast,
when only some …rms export, it can be shown that there is strictly greater wage inequality in the
open economy than in the closed economy.
This result highlights a new mechanism for international trade to a¤ect wage inequality: theparticipation of some but not all …rms in exporting. This mechanism applies in any heterogeneous…rm model in which …rm wages are related to …rm revenue and there is selection into export markets.
Our result holds whenever the following three conditions are satis…ed: …rm wages and employment
are power functions of …rm productivity, there is …rm selection into export markets and exporting
increases wages for a …rm with a given productivity, and …rm productivity is Pareto distributed. An
important implication of this result, which applies for symmetric and asymmetric countries alike,is that the opening of trade can increase wage inequality in all countries. This result is therefore
consistent with empirical …ndings of increased wage inequality in developing countries following
trade liberalization. Similarly, our result is consistent with empirical evidence that much of theobserved reallocation in the aftermath of trade liberalization occurs across …rms within sectors andis accompanied by increases in within-group wage inequality.
Since sectoral wage inequality in an open economy in which all …rms export is the same as
in a closed economy, but sectoral wage inequality in an open economy in which only some …rms
export is higher than in a closed economy, it follows that the relationship between sectoral wage
inequality and the fraction of exporters is at …rst increasing and later decreasing. The intuition forthis result is that the increase in …rm wages that occurs at the productivity threshold above which…rms export is only present when some but not all …rms export. When no …rm exports, a small
reduction in trade costs that induces some …rms to start exporting raises sectoral wage inequality
because of the higher wages paid by exporters. When all …rms export, a small increase in trade
costs that induces some …rms to stop exporting raises sectoral wage inequality because of the lower
13

wages paid by domestic …rms.

3.5

Implications for Unemployment

While we have so far focused on the distribution of wages across employed workers, income inequality in this framework also depends on the unemployment rate. Workers can be unemployed either
because they are not matched with a …rm or because their match-speci…c ability draw is below thescreening threshold of the …rm with which they are matched. The sectoral unemployment rate u
includes both of these components and can be written as one minus the product of the hiring rate
and the tightness of the labor market x:

u=

where

L

H
L

HN
=1
N L

=1

x;

(11)

H=N , H is the measure of hired workers, N is the measure of matched workers, and L

is the measure of workers seeking employment in the sector.
As shown above, equilibrium labor market tightness, x, depends on worker’s outside option,!, which can either remain constant or rise following the opening of trade, depending on how thesector is embedded in general equilibrium (see Helpman, Itskhoki and Redding 2010). In contrast,
the hiring rate, , is unambiguously lower in the open economy than in the closed economy, since
the opening of trade reallocates employment within industries towards more productive exporting…rms, which screen more intensively and hire a smaller fraction of the workers with whom they
are matched. Furthermore, this reduction in the hiring rate can dominate an increase in labormarket tightness, so that the opening of trade not only increases wage inequality but also raises
unemployment.
Although the opening of trade can increase both wage inequality and unemployment, it also
reduces the CES ideal price index for the di¤erentiated sector. Therefore, despite increasing social
disparity, the opening of trade raises the expected welfare of risk neutral workers.

3.6

Multiple Worker Types

Our main results on the impact of trade on wage inequality can be generalized to settings in which
there are multiple types of workers with di¤erent observable characteristics. To illustrate, suppose

14

that there are two types of workers, indexed by ` = 1; 2. There are separate labor markets foreach type of workers, which are modelled as above, where the magnitude of search frictions canvary across worker types. Within each group of workers there is heterogeneity in the match-speci…cability a` , which is not observable. As a result, workers of a given type ` are ex ante homogeneous
but ex post heterogeneous, as for the case of a single type of worker discussed above.
Let the distribution of ability of type-` workers be Pareto with shape parameter k` > 1 for` = 1; 2, and let the production function bey=a1 h1 1{1

a2 h2 2{2;

{1 + {2 = 1:

Then Helpman, Itskhoki and Redding (2010) show that wage inequality is larger within each groupof workers in an open economy in which only a fraction of …rms export than in a closed economy.
Moreover, for k1 < k2 , more productive …rms employ relative more workers of type-1— with thelarger ability dispersion— and pay them relatively lower wages. The relatively larger number oftype-1 workers in higher-productivity …rms weakens these workers’relative bargaining power, whichtranslates into relatively lower wages. As a result, there is less wage dispersion among type-1
workers.
Importantly, while trade raises wage inequality within every group of workers, it may raise or
reduce wage inequality between the two groups. Yet even if trade reduces wage inequality between
the groups, overall wage inequality may still rise as a result of the increase in wage inequality withineach group of workers with similar observable characteristics.

4

Interdependence

Having examined the impact of trade on sectoral inequality and unemployment, we now discussinterdependence between trading countries. Using the results from Helpman and Itskhoki (2010),
we address the following questions: how do labor market frictions impact interdependence acrosscountries? And in particular, what are the impacts of a country’s labor market frictions on its
trade partners?

15

4.1

Analytical Framework

For the purpose of addressing these questions, we consider a two-country world, say countries A
and B, in which every country has the same technology in each one of two sectors. One sector
produces varieties of a di¤erentiated product while the other manufactures a homogeneous good.
Preferences are quasi-linear, given by1
U = q0 + Q ;

<

< 1;

(12)

where q0 is consumption of the homogeneous good, Q is the real consumption index of the di¤erentiated product, and we choose the homogeneous good as the numeraire. As before,elasticity of substitution across varieties, and the new parameter

controls thecontrols the elasticity of substi-

tution between the homogeneous good and the di¤erentiated product. We think of U as the utility
level of a family consisting of a continuum of workers of measure one. There exists a continuum ofsuch families of measure L. As a result, there are L workers in this economy. Each family chooses
the allocation of family members across sectors to maximize family utility. Since the idiosyncraticrisk faced by individual workers as a result of random search and matching is perfectly diversi…ed
across the continuum of workers within each family, each family behaves as if it is risk neutral.
The homogeneous good is produced according to a constant returns to scale technology, with
one unit of labor required to produce one unit of output, and the homogeneous good is costlessly
traded. The technology of the di¤erentiated sector is a simpli…ed version of the technology fromthe previous section, with no worker heterogeneity and no screening. In this case the production
function of every variety is
y = h;
where, as before,

is the …rm’s productivity and h is its employment. Varieties in the di¤erentiatedsector are again subject to iceberg trade costs, where> 1 units must be shipped in order for one

unit to arrive in the other country.
There are labor market frictions in each sector, similar to the labor market frictions described16

in the previous section. In the homogeneous sector the cost of hiring is:b0 =The derived parameter0

0 x0 :is larger the higher the cost of vacancies is and the less e¢ cient is

the matching process in the homogeneous sector. Moreover, in equilibrium w0 = 1= (1 + ) andb0 = = (1 + ), whereis the relative bargaining weight of the employer in the wage bargaining

process (see Appendix).3 As a result,0 x0 =

1+

;

(13)

and equilibrium tightness in the homogeneous sector’s labor market, x0 , is decreasing in the levelof labor market frictions in this sector,

0 . The cost of hiring in the di¤erentiated sector is given by(3). The two countries, A and B, di¤er only in labor market frictions ( 0 ; ). That is, they di¤ereither in the sectoral levels of the e¢ ciency of matching or in the costs of posting vacancies, which
determine the equilibrium levels of the frictions ( 0 ; ).
In equilibrium, workers are indi¤erent between searching for jobs in the homogeneous or thedi¤erentiated sector, which implies that their expected income is the same in each sector, x0 b0 =xb. Together with the search technology, this condition implies the following values of the wage
rate, the cost of hiring, and labor market tightness in the di¤erentiated sector in each country j,
independently of the trade regime:

wj = bj = b0

j

1
1+

;

xj = x0j

0j

j

1
1+

;

j = A; B;

(14)

0j

For simplicity, and without loss of generality, we assume

A = 0A >B = 0B , which implies bA > bB ,i.e., labor market frictions in the di¤erentiated sector are relatively larger in country A.

4.2

Trade and Welfare

Helpman and Itskhoki (2010) show that under these circumstances a larger fraction of di¤erentiatedproduct …rms export in country B, and that country B exports di¤erentiated products on net and3

In Helpman and Itskhoki (2010) the bargaining weights are equal, as a result of which
generalize this result in order to better characterize optimal policies in the next section.

17= 1 and b0 = 1=2. We

imports homogeneous goods. Since the only di¤erence between the two countries is in their labormarket frictions, it follows that this pattern of trade is determined by di¤erences in labor market
frictions across countries; the country that has the relatively lower level of labor market frictionsin the di¤erentiated sector exports di¤erentiated goods on net. Moreover, in this world economy
the share of intra-industry trade is smaller the larger the gap in relative hiring costs bA =bB is.
Another interesting result is that both countries gain from trade, in the sense that a representative family’s utility level U is higher in the trade equilibrium than in autarky. Since the idiosyncraticrisk faced by individual workers is perfectly diversi…ed within families, the expected utility of every
worker is higher in the open economy than in autarky.

4.3

Interdependence in Labor Market Frictions

A reduction in labor market frictions in the di¤erentiated sector of country j,

j , reduces thecost of hiring bj , raises country j’s welfare and reduces its trade partner’s welfare. In this eventa country loses from the lowering of labor market frictions in its trade partner. The intuition
for this negative welfare e¤ect is that indirect utility equals income plus consumer surplus in thedi¤erentiated sector. Lower labor market frictions in the di¤erentiated sector in country j makethis sector more competitive relative to that in its trade partner, which induces an expansion in
the di¤erentiated sector in country j and a contraction in this sector in its trade partner. Thesechanges in the size of the di¤erentiated sector raise consumer surplus and welfare in country j andreduce consumer surplus and welfare in its trade partner.
A simultaneous proportional reduction of

A and

B raises welfare in both countries, because it

expands the size of the di¤erentiated sector in each one of them. On the other hand, a reduction inj and

0j at a common rate (which does not change the hiring cost bj ) raises country j’s welfare

and does not a¤ect the welfare level of its trade partner. This results from the fact that this type of
reduction in labor market frictions does not impact competitiveness, yet it leads to higher aggregate
utilization of resources in country j; see the discussion of unemployment below.

4.4

Trade Liberalization

Reductions of trade impediments, , raise welfare in both countries, because they also expand thesize of the di¤erentiated sector in each country. Unlike the welfare consequences of lower trade18

frictions, however, the e¤ects on unemployment can di¤er across countries. A country’s rate ofunemployment equals a weighted average of its sectoral rates of unemployment— (1homogeneous sector and (1x0j ) in thexj ) in the di¤erentiated sector— with weights equal to the shares ofworkers seeking employment in these sectors. In other words, country j’s rate of unemployment is

uj =

N0j
(1
Lj

x0j ) +Nj(1
Ljxj ) ;

where N0j is the measure of workers seeking employment in the homogeneous sector and Nj is themeasure of workers seeking employment in the di¤erentiated sector, with N0j +Nj = Lj . Since trade
impediments do not impact sectoral rates of unemployment, because tightness in labor markets does
not depend on trade frictions, the only channel through which reductions in

can in‡uence therate of unemployment is through worker reallocation across industries. Therefore, if the rate ofunemployment is higher in the di¤erentiated sector than in the homogeneous sector, aggregate
unemployment rises as a result of the expansion of the di¤erentiated sector induced by lower trade
frictions. And if unemployment is higher in the homogenous sector than in the di¤erentiated sector,
aggregate unemployment declines as a result of the expansion of the di¤erentiated sector induced
by lower trade frictions. Moreover, (14) implies that the rate of unemployment is higher in thedi¤erentiated sector if and only if it has higher labor market frictions than the homogeneous sector,
i.e.,

j >

0j .

Helpman and Itskhoki (2010) show that lower trade frictions may impact the rates of unemployment in the two countries in the same direction or in opposite directions. Moreover, the rate ofunemployment can be higher in country A for some levels of trade frictions and higher in country
B for other levels of trade frictions. As a result, di¤erences in aggregate levels of unemployment do
not necessarily re‡ect di¤erences in labor market frictions; a country with more rigid labor markets
may have a higher or lower rate of unemployment. Finally, since lower trade frictions raise welfare
in both countries, but may raise the rate of unemployment in both or only in one of them, it isevident that the impact of lower trade frictions on unemployment provides no information on its
impact on welfare; welfare goes up in both countries even when their rates of employment increase.

19

4.5

Unemployment and Labor Market Frictions

Of special interest is the relationship between labor market frictions and rates of unemployment.
This relationship is sharpest in the case of symmetric countries, which have the same levels of labormarket frictions ( 0 ; ). In this case, Helpman and Itskhoki (2010) show that raising the common
level of labor market frictions in the di¤erentiated sector raises the rate of unemployment in bothcountries if and only if = 0 is smaller than a threshold that exceeds one. It follows that whenever<0 , i.e., labor market frictions are lower in the di¤erentiated sector, this condition is satis…edand raising

increases the rate of unemployment. This increase in the rate of unemployment occurs

for two di¤erent reasons: …rst, the sectoral rate of unemployment rises in the di¤erentiated sector;
second, workers move from the di¤erentiated sector to the homogeneous sector and the latter hasa higher sectoral rate of unemployment. Alternatively, when

>

0 but

= 0 is smaller than

the threshold, higher frictions in the di¤erentiated sector raise the sectoral rate of unemployment
which raises in turn the aggregate rate of unemployment. But now the movement of workers
from the di¤erentiated to the homogenous sector reduces aggregate unemployment, because thehomogeneous sector has a lower rate of unemployment than the di¤erentiated sector. The formere¤ect dominates, however, as long as = 0 is below the threshold. Above the threshold higher
frictions in the di¤erentiated sector’s labor market reduce aggregate unemployment, because inthis case the negative impact of worker reallocation across industries outweighs the positive impactof the rise in the rate of unemployment in the di¤erentiated sector.4
When countries are not symmetric, the sectoral unemployment rate and labor force composition e¤ects interact in complex ways. For example, starting with>

0 and raising labor market

frictions in country A’s di¤erentiated sector can initially raise the rate of unemployment in bothcountries but eventually reduce it in country A, whereas it continues to raise the rate of unemployment in country B. As a result, A may have a higher rate of unemployment for low values ofbut a lower rate of unemployment for high values ofA >A , or it may have lower unemployment for all. Again, we encounter a case in which knowledge of relative rates of unemployment acrosscountries is not su¢ cient to draw inferences about their relative levels of labor market frictions.
4

A

When

0 and

increase proportionately, aggregate unemployment rises.

205

Policy Implications

We now use the previous section’s analytical framework to study economic policies. One resultof interest from that section is that a reduction in a country’s cost of hiring in the di¤erentiatedsector raises its competitiveness relative to its trade partner and thereby hurts the trade partner.
In the previous section, the change in the cost of hiring was induced by a reduction in labor market
frictions in the form of lower costs of vacancies or more e¢ cient matching. In this section we
examine instead how unemployment bene…ts— a prevalent labor market policy— in‡uence the costof hiring. The results from the previous section imply that if higher unemployment bene…ts raisea country’s cost of hiring then this policy bene…ts the trade partner, and if higher unemployment
bene…ts reduce a country’s cost of hiring then this policy hurts the trade partner.
We have also seen that a country bene…ts from lower costs of hiring in its di¤erentiated sector
when this reduction is achieved through labor market frictions. If, alternatively, a similar reductionin the cost of hiring is attained with unemployment bene…ts, does this too raise welfare? Onedi¤erence between this policy-induced reduction in the cost of hiring and a decline in labor market
frictions is that unemployment bene…ts require …nancing in the form of taxes while the decline inlabor market frictions does not. For this reason unemployment bene…ts that reduce the cost of hiring
might be advantageous up to a point, while large unemployment bene…ts might be detrimental.
After discussing unemployment bene…ts in Sections 5.1 and 5.2, and the nature of the economy’s
distortions in Section 5.3, we examine in Section 5.4 policies that implement a constrained Pareto
optimum. The focus on a constrained rather than an unconstrained optimal allocation stems fromour desire to treat search and matching in the labor market as a constraint on economic activity
that a social planner cannot remove, and she therefore cannot costlessly allocate workers to …rms.
We show that there exists a simple set of policies in labor and product markets that support sucha constrained Pareto optimal allocation. This set of policies is not unique, because there exist
alternative combinations of labor market and product market policies that can achieve the sameend. One conclusion from this analysis is that there are cases in which unemployment bene…ts canplay a useful role in the optimal policy design, but that there are also cases in which unemployment
bene…ts are not congruent with e¢ ciency. Another conclusion is that optimal policies do notdiscriminate between …rms by export status; the same policies should be applied to exporters and21

nonexporters alike.

5.1

Unemployment Bene…ts

Unemployment bene…ts impact wages and the cost of hiring. Wages are a¤ected directly when
workers bargain with employers, because in the presence of unemployment bene…ts bu — measured
in units of the homogeneous numeraire good— the outside option of a worker in the bargaining
game is bu instead of zero (we drop the country index in what follows). In addition, unemployment
bene…ts a¤ect tightness in labor markets and thereby the incentives of workers to search for jobs
in the homogenous versus di¤erentiated sectors.
In the homogenous sector the wage rate is now

w0 = bu +11+

b0 = (1bu )(1bu ) ;(15)

the cost of hiring is
1+;

and tightness in the labor market satis…es (see Appendix for details)

0 x0 = (1

bu )

1+

;

(16)

which is the same as (13) when the unemployment bene…ts are equal to zero. Evidently, in thiscase higher unemployment bene…ts reduce x0 and raise the sectoral rate of unemployment. And, as
before, higher frictions in the labor market reduce x0 . From (15) and (16) we obtain the expected
income of a worker searching for employment in the homogeneous sector, ! = w0 x0 + bu (1x0 ),

as a function of unemployment bene…ts. Moreover, ! is the outside option of workers searching for
employment in the di¤erentiated sector. Therefore, in an equilibrium with positive employment inboth sectors, ! also equals the expected income of a worker searching for a job in the di¤erentiatedsector, and therefore ! = wx + bu (1x).

In the di¤erentiated sector bargaining over wages yields a wage rate equal to the fraction= ( + ) of revenue per worker plus bu = ( + ) (in the absence of unemployment bene…ts thesecond component equals zero). Accounting for the …rm’s pro…t-maximizing choice of employment
22and the requirement that the expected income of workers be the same in both sectors, we obtain:0x = x0

1
1+

:

(17)

As a result, there is a proportional relationship between labor market tightness in the two sectors,
and a change in unemployment bene…ts has the same proportional e¤ect on labor market tightness
in each sector. In particular, higher unemployment bene…ts reduce tightness in both labor markets.
We also show in the Appendix thatb= x +

1+

bu :

(18)

Therefore unemployment bene…ts, bu , directly a¤ect the cost of hiring in the di¤erentiated sector
and also have indirect e¤ects through labor market tightness, x. Higher unemployment bene…ts
raise b directly because they increase workers’ outside option in wage bargaining. But higher
unemployment bene…ts reduce b indirectly because they reduce tightness in the labor market, x.
Equations (16)-(18) imply that higher unemployment bene…ts raise the cost of hiring b on net if
and only if labor market frictions are higher in the homogeneous sector; that is, if and only if
0 >.5 When labor market frictions are higher in the di¤erentiated sector, the di¤erentiatedsector has a higher sectoral rate of unemployment than the homogenous sector. Under thesecircumstances higher unemployment bene…ts reduce the hiring cost in the di¤erentiated sector
and lead to its expansion, as more workers choose to search for jobs in this industry. In otherwords, unemployment bene…ts have an uneven e¤ect on sectoral employment, favoring the sector
with higher unemployment. As a result, by raising unemployment bene…ts a country makes its
di¤erentiated sector more competitive on world markets if this sector has the higher sectoral rateof unemployment, in which case this policy hurts the country’s trade partner. Alternatively, by
raising unemployment bene…ts a country bene…ts its trade partner when the country’s labor market
frictions are higher in the homogenous sector.
5

Equations (16)-(18) can be used to derive a closed form solution for the hiring rate:"#
1=(1+ )b=1+

bu + (1

bu )

;

0

from which this result is transparent.

23

1

0.5

0

-0.5

-1

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

Figure 2: Welfare gains and losses from unemployment bene…ts

5.2

Unemployment Bene…ts and Welfare

The next question is whether a country gains from raising its unemployment bene…ts. Figure 2
shows that the answer depends on structural features of the labor market. The …gure depicts
percentage changes in welfare, measured on the vertical axis, in response to changes in the levelof unemployment bene…ts, measured as a replacement ratio of the homogenous sector’s wage rate,
bu =w0 . It describes simulations of a closed economy in which labor market frictions are higher in thedi¤erentiated sector.6 In this case higher unemployment bene…ts always reduce the equilibrium costof hiring in both sectors. Yet for high values of
eventually declines, while for low values of
It follows that when

welfare …rst rises in unemployment bene…ts andwelfare always declines in unemployment bene…ts.

is large welfare is maximized at a positive level of unemployment bene…ts,

while the optimal level of unemployment bene…ts equals zero whenis small.

To gain further insight into these results, Figure 3 decomposes the changes in welfare that
result from unemployment bene…ts for the case

= 1:2. The North-Western panel describes

the contribution of the di¤erentiated sector to welfare, Q , and the contribution of income netof taxes, E = !LT , as well as the total welfare level, W . As the cost of hiring declines with

unemployment bene…ts, the contribution of the di¤erentiated sector rises throughout. But net
6
The following parameters were used in the simulations described in Figures 2 and 3: = 1:2, = 1,
= 1=2, 0 = 0:6, = 0:66, fd = 1, L = 1:5. In addition, fe , min and z were chosen to yield d = 1.

24

= 2=3,

4

0.3

2

0.2

0
0.1
-2
0

0.1

0.2

0.3

0
0

0.4

1

0.2

0.3

0.4

0.1

0.2

0.3

0.4

1

0.4
0

0.1

0.1

0.2

0.3

0.6
0

0.4

Figure 3: Changes resulting from unemployment bene…ts:= 1:2

income rises initially as long as the rise in !L is larger than the rise in taxes T needed to …nancethe unemployment bene…ts, and declines eventually. As a result, the welfare curve W has a humpshape. The North-East panel shows that not only do taxes rise with unemployment bene…ts, theyalso rise as a fraction of net income, T =E. In addition, the fraction of workers searching for jobs
in the di¤erentiated sector, N=L, rises. Finally, rising unemployment bene…ts reduce tightness inboth sectors’ labor markets, as shown in the South-West panel of the …gure (which also shows
the rise in !).7 As a result, higher unemployment bene…ts raise sectoral rates of unemployment.
Since workers also move from the homogeneous to the di¤erentiated sector, which is the higher
unemployment rate sector, aggregate unemployment rises with unemployment bene…ts.

5.3

Product and Labor Market Distortions

An interesting implication of the example depicted in Figure 3 is that unemployment bene…ts arebene…cial up to a point despite the fact that they raise unemployment. Yet if we were to reducein this example to a su¢ ciently low level, we would …nd that unemployment bene…ts raise
unemployment and reduce welfare. The question is "Why?" To understand the answer, …rst note
7

Our numerical example illustrates more general patterns. It can be shown analytically that wages and expected
wages rise in both sectors with bu while the levels of tightness in both sectors’ labor markets decline with bu . In
addition, the hiring cost b decreases in bu if and only if > 0 , as we show in footnote 5. The only analyticalambiguity in the derivation of the optimal unemployment bene…ts stems from the response of E = !L T .

25

that in this type of economy there are multiple distortions. To begin with, the di¤erentiated sector
is too small, because it prices goods with a markup above marginal cost and there is too little
entry into the industry. For this reason unemployment bene…ts that reduce the cost of hiringin the di¤erentiated sector and induce a reallocation of workers from the homogeneous to thedi¤erentiated sector, bene…t the economy. On the other side, in this example tightness in the labormarket is too high initially and unemployment bene…ts bring it down. This is illustrated in theSouth-East panel of Figure 3 for the homogenous sector, in which the horizontal dashed line xH0describes the optimal level of tightness, and the vertical dashed line shows the welfare-maximizing
unemployment bene…ts policy. For low levels of unemployment bene…ts x0 is too high, while forhigh levels of unemployment bene…ts it is too low. For this reason raising unemployment bene…ts
from an initially low level reduces distortions in labor markets by reducing labor market tightness,and this raises welfare. But when initial unemployment bene…ts are high, the levels of tightness in
the labor markets are too low and further increases in unemployment bene…ts aggravate the labormarket distortions, which may reduce welfare.
There are no distortions in the labor market when the Hosios (1990) condition is satis…ed, whichin our case is= 1 (i.e., the elasticity of the matching function with respect to the number ofvacancies equals the weight of employers in the bargaining game). While the Hosios condition had
been derived in models with linear revenue and single-job …rms, we extend this condition to a modelwith monopolistic competition, multiple-job …rms, and Sole and Zwiebel (1996) style multilateralbargaining. When the Hosios condition holds, or

1, unemployment bene…ts always magnify

the distortions in the labor markets, which reduces welfare. But because they reduce the distortionin the intersectoral allocation of labor (when they increase N ), unemployment bene…ts may initiallyraise welfare on net. Whenis very low, however, the distortions in the labor markets are sohigh that even small unemployment bene…ts reduce welfare on net.
To understand the link between the Hosios condition and labor market distortions in this model,
consider the following experiment. Suppose we want to employ H workers in the di¤erentiatedsector, but we cannot allocate them directly to …rms; all we can do is instruct N workers to searchfor jobs in the di¤erentiated sector and the remaining L

N workers to search for jobs in thehomogeneous sector. How many vacancies do we need to open in each sector in order to secure theemployment of H workers in the di¤erentiated sector at minimum cost to the economy?
26

Instead of working directly with vacancies we can instead choose levels of tightness in the
sectoral labor markets, x0 and x. Naturally, in this case we need to send N = H=x workers tosearch for jobs in the di¤erentiated sector, which leaves L

H=x workers searching for jobs in thehomogeneous sector. However, only a fraction x0 of the latter workers …nd employment in thehomogeneous sector, producing (L(L

H=x) x0 units of the homogenous good. The cost of …lling up

H=x) x0 vacancies in the homogenous sector is (LH=x) x0 0 x0 , because the cost of hiring is0 x0 per worker. And the cost of …lling up H vacancies in the di¤erentiated sector is H

x , because

the cost of hiring is x per worker in the di¤erentiated sector. Consequently, the net output ofhomogenous goods— which can be used for consumption or for entry of …rms in the di¤erentiatedsector— equals:8(LH=x) x0 (10 x0 )H x :Given H, the optimal levels of x and x0 maximize this measure of net output. The solution to thisproblem does not depend on H, however, and it can be characterized by:

0 x0 =1
1+(19)

and (17). When these conditions are satis…ed, the ratio x=x0 is at the optimal level independentlyof H or the level of unemployment bene…ts. Comparing (16) with (19), we see that levels oflabor market tightness are optimal in the absence of unemployment bene…ts if and only if
Moreover, if= 1.

< 1, x0 is too small without unemployment bene…ts and it moves further away fromthe optimal level the larger the unemployment bene…ts are. If, on the other hand,> 1, there

exists a positive level of unemployment bene…ts at which the levels of tightness in the labor markets
are optimal. In the South-East panel of Figure 3 this happens at the intersection point with thehorizontal dashed line, where x0 = xH
0 . However, the level of unemployment bene…ts that securesthe optimal levels of labor market tightness does not maximize welfare, because it leaves distortionsin the allocation of labor across sectors (the optimal levels of unemployment bene…ts are depictedin this …gure by the dashed vertical lines). If, for example, the di¤erentiated sector has a higher
rate of unemployment than the homogeneous sector, then it is optimal to raise bu above the levelthat maximizes the net output of homogeneous goods, because this would attract more workers to
8

See the Appendix for more details.

27the di¤erentiated sector and thereby partially o¤set the monopolistic distortion that reduces thesize of the di¤erentiated sector9 . Evidently, since this economy has multiple distortions, multiple
instruments are needed to attain e¢ ciency. These instruments are discussed in the next section.

5.4

Optimal Policies

We now consider policies that implement a constrained Pareto optimal allocation. The objective is
to maximize the joint welfare of countries A and B, which— in view of the utility function (12)— is
given by:X

1
q0j + Qj:

j=A;BThe constraint is that the planner can allocate workers to industries but not to …rms. However,the planner can post vacancies for every …rm and thereby determine the probability with which
vacancies are …lled in every industry.
The Appendix contains an explicit formulation and solution to the planner’s problem. Thissolution satis…es the labor market tightness conditions (17) and (19) in every country, for thereasons explained in the previous section. Therefore, if= 1, no intervention is required in

the labor markets, despite the fact that the frictions

di¤er across countries. If, however,0 and

6= 1, then it is necessary to design labor market policies in the country in which the Hosios
condition is not satis…ed in order to implement the optimal allocation. Importantly, a country’s
optimal labor market policies depend only on its labor market parametersand.10 A direct

policy that eliminates the labor market distortions is a subsidy or tax to the hiring cost, which isequivalent to a subsidy or tax to the cost of posting vacancies.11 When the subsidy rate to hiringin the homogeneous sector is sb0 (possibly negative), the resulting tightness in this labor market
9

The impact of unemployment bene…ts on the relative size of sectors is similar in our case to Acemoglu andShimer’s (1999) analysis of policies that maximize output, except that in their case the distortion results from thereluctance of risk averse workers to search for jobs in high unemployment sectors. In their case aggregate output is
too small without policy intervention, while unemployment bene…ts encourage workers to take the risk of searchingfor jobs and thereby raises output.
10
In the main text we assume that the relative bargaining weight is the same in both sectors, although it mayvary across countries. In the Appendix we allow to also vary across sectors.
11
Note that a correction of this distortion requires a labor market policy that encourages job creation through lower
costs of matching. For example, it cannot be a direct employment subsidy, because this policy does not reduce thematching costs to …rms. Moreover, an employment subsidy is equivalent to a subsidy to the …rms’revenues.

28

satis…es(1sb0 ) 0 x0 =1+:

Comparing this condition to (19) we see that x0 is optimal if and only if

sb0 =

1
1+

:

Evidently, hiring has to be subsidized in the homogeneous sector when> 1. For< 1 and taxed when

< 1, …rms post too few vacancies and labor market tightness is too low. The

required hiring subsidy is decreasing in the relative weight of job-seekers in the matching technology,, and in the relative weight of the employer in wage bargaining, . For> 1, …rms post too

many vacancies and labor market tightness is too high, which implies that a hiring tax is required.
In this latter case, optimal labor market tightness can be also achieved with unemployment bene…ts,
but unemployment bene…ts cannot correct the labor market distortion when< 1.12 A similarlabor market policy is required in the di¤erentiated sector, with the rate of subsidy the same in thetwo sectors: sb = sb0 .
With the optimal labor market subsidies in place, there are no remaining distortions in labormarkets. But the relative size of the two sectors is not optimal. To correct the distortions in therelative size of the two sectors the planner can subsidize sales of the di¤erentiated product. A
subsidy of sr per unit of sales in terms of the numeraire raises the revenue of every manufacturer,
and the optimal subsidy issr =The …rst term on the right had side, (1

1
1+

:

) = , represents the subsidy that o¤sets the distortion

that results from the markup of price over the marginal cost (the monopolistic distortion), while
the second term, = (1 + ), represents the subsidy that o¤sets the distortion that results from wage
bargaining. The total subsidy is increasing in the relative weight of employers in wage bargaining( ) and decreasing in the elasticity of substitution between varieties of the di¤erentiated product( ). A higher elasticity of substitution reduces the manufacturers’market power and thereby theirmarkups above marginal costs, which leads to expansion of output and employment and implies that
12

In this case bu < 0 is required, which means taxing the unemployed.

29

a lower subsidy to sales is required. The relative weight of employers in wage bargaining a¤ects thevalue of the subsidy, because in the Stole-Zwiebel bargaining game …rms have an incentive to hire
more workers than is socially optimal in order to reduce the wage paid to infra-marginal workers,
i.e., this bargaining mechanism leads to overemployment. This overemployment distortion partiallyo¤sets the e¤ect of monopolistic pricing that makes the di¤erentiated sector too small. The subsidy
increases with the relative weight of employers in wage bargaining, because a larger value for thisweight reduces the over-hiring distortion, and hence reduces the size of the di¤erentiated sector,
which implies that a larger subsidy is required to restore the size of the di¤erentiated sector to its
socially optimal level.
In addition to the subsidy to sales in the di¤erentiated sector the …xed costs of production,
export and entry have to be subsidized at a common rate, equal to

sf =

1
:
1+

This subsidy is decreasing in the relative weight of employers in wage bargaining ( ), because of theoverhiring distortion in the Stole-Zwiebel bargaining game discussed above. Note that this subsidy
does not depend on , because the markup does not distort entry.
Importantly, the same optimal policies in the di¤erentiated sector apply to all …rms. In otherwords, they equally apply to low- and high-productivity …rms, and to exporters and nonexporters
alike. This means that the optimal policies do not discriminate between …rms based on productivity,
size, or export status.
We show in the Appendix that the optimal policies in product markets depend on whether
subsidies or unemployment bene…ts are used in the labor market. If the social planner uses unemployment bene…ts in the labor market, which are feasible when

> 1, then the subsidies to sales

and to …xed plus entry costs in the di¤erentiated sector depend not only on
the frictions in the labor markets,

0 and

and

but also on. For this reason, the optimal policies based on subsidies

discussed above require less information than policies that rely on unemployment bene…ts.

30

6Conclusion

The impact of trade liberalization on wage inequality and unemployment and the role of labormarket institutions in shaping the e¤ects of trade liberalization are areas of intense policy debate.
Until recently, the ability of research in international trade to engage with this policy debate has
been hampered by the widespread assumption of ‡exible labor markets and the associated predictionof full employment at a common wage.
In this paper, we have reviewed a new framework that combines …rm heterogeneity in the
product market with search and matching frictions in the labor market to examine the economy’s
response to trade. The resulting framework highlights a new mechanism for international trade
to a¤ect wage inequality: when only some …rms export, the increase in wages that occurs at the
productivity threshold for exporting raises wage inequality across …rms. This mechanism accounts
for empirical …ndings of rising wage inequality in both developed and developing countries following
trade liberalization and rationalizes rising wage inequality among groups of workers with the sameobserved characteristics. While the opening of trade can raise social disparity through both higher
wage inequality and higher unemployment, expected welfare necessarily rises.
The introduction of labor market frictions into a general equilibrium model of trade permits
the study of interdependence in labor market institutions across countries and the analysis ofinteractions between labor market institutions and trade liberalization. While labor market reforms
that reduce search and matching frictions in the di¤erentiated sector increase a country’s own
welfare, they reduce welfare in its trade partners. The aggregate unemployment rate depends
on both the unemployment rate within each sector and the composition of the labor force acrosssectors. In consequence, policies that reduce the unemployment rate within the di¤erentiated sector
need not reduce aggregate unemployment if they also change the composition of the labor force
across sectors. One important implication is that relative aggregate unemployment rates acrosscountries are not, in general, fully informative about relative levels of labor market frictions.
In our setting with multiple product and labor market distortions, the market allocation is notconstrained e¢ cient. Only if the Hosios condition is satis…ed, which requires the relative bargaining
weight of employers to equal their relative weight in the matching technology, is the e¢ cient levelof labor market tightness attained. More generally, if the Hosios condition is not satis…ed, subsidies31to hiring costs or the costs of posting vacancies or unemployment bene…ts can be used to achieve
the e¢ cient level of labor market tightness. However, with several distortions in product andlabor markets, unemployment bene…ts alone cannot achieve the constrained e¢ cient allocation andtheir introduction can either raise or reduce welfare. To achieve the constrained e¢ cient allocation
requires a combination of these interventions in the labor market and subsidies to revenue and …xed
costs in the product market. Notably, the e¢ cient subsidies in the product market take the samevalue for both exporters and non-exporters. Finally, the use of direct subsidies or taxes to hiring
requires less information than unemployment bene…ts and avoids the limitation that unemployment
bene…ts have to be non-negative.

32

Appendix
This appendix sets up the model for Sections 4 and 5 and derives the results reported in thetext; the model is based on Helpman and Itskhoki (2010), with the addition of policy instruments.
We start by describing the decentralized equilibrium. We then set up the planner’s problem andcompare its solution with the decentralized allocation.

A

Decentralized Equilibrium

We consider a decentralized equilibrium of the Helpman and Itskhoki (2010) model, allowing fornonsymmetric bargaining power of …rms and workers, unemployment bene…ts, subsidies and taxes
to hiring costs, entry costs, …xed production costs, and …rm revenues in the di¤erentiated sector.

A.1

Labor market equilibrium

In Helpman and Itskhoki (2010) we showed how a Cobb-Douglas matching function results in thefollowing hiring cost function in the homogenous-good sector:

b0 =

where

0 x0 ;

0 is the ratio of vacancy costs to the productivity of the matching technology, x0 is theendogenous labor market tightness (equal to the probability of a worker …nding a job), andisthe ratio of the Cobb-Douglas parameters on unemployment and vacancies. In words, b0 is the(expected) cost for a homogenous-good producer of matching with (hiring) one worker. Similarly,
the cost of matching in the di¤erentiated sector is x , where we allow

to di¤er from0.

Consider the homogenous-good sector. Upon matching, the …rm and the worker produce one
unit of the homogenous good, which is our numeraire. They split this surplus via Nash bargaining.
The outside option is zero for the …rm and it equals unemployment bene…ts, bu < 1, for the worker.
In the process of bargaining, the surplus (1bu ) is divided between the …rm and the worker

according to their relative bargaining power, which we denote by33

0.

This results an operating

pro…t level

0 and a wage rate w0 :

0 =

0

1+

(1

bu )

and

w0 = bu +

0

1
(1
1+ 0

bu ):

With free entry, equilibrium pro…ts equal zero, and therefore the operating pro…ts equal hiringcosts. That is,
0 = (1sb0 )b0 ;where sb0 is the hiring cost subsidy. Combining this with the previous expressions, we obtain:(1sb0 ) 0 x0 =which reduces to (16) when sb0 = bu = 0 and

0

(1

bu );

(20)

1+

0

=

Finally, the expected income of workers in0.

the homogenous good sector is given by!0

x0 w0 + (1= bu + x0= bu +

1x0 )bu

1
(1
1+ 0
(1

0

bu )

:
sb0 ) 0 x1+
0

Next consider the di¤erentiated sector. We show below that the equilibrium wage in this sectorisw = bu +
where

1

(1

sb ) x ;is the relative bargaining power of …rms in this sector, sb is the sector-speci…c hiring-cost

subsidy to …rms,

is the sectoral labor market friction parameter (i.e., the ratio of vacancy costs

to the productivity level of the matching technology), and x is the sector’s labor market tightness(equal to the matching probability for workers). Therefore, a worker’s expected income in thedi¤erentiated sector is!

xw + (1x)bu = bu +1(1sb ) x1+ :In equilibrium workers have to be indi¤erent between searching for jobs in the homogeneous or34

di¤erentiated sectors, which requires ! 0 = !. The latter implies:
1

(1

0

sb0 ) 0 x1+=
01sb ) x1+ :(1

Naturally, (17) is a special case of this conditions, for

0 =

(21)

and no hiring subsidies. Also notethat as long as unemployment bene…ts are common to the unemployed in both sectors, they do nota¤ect relative labor market tightness in the two sectors. Conditions (20) and (21) pin down labormarket tightness in the two sectors.

A.2

Product market equilibrium

In the di¤erentiated sector …rms solve the following maximization problem:

( )=

max

h 0;Ix 2f0;1gn(1 + sr )R(h; )w(h; )h(1sb ) x h(1sd )fd=(1where h is employment, Ix is the …rm’s export status indicator,

)

Ix (1

o
sx )fx ;is a measure of its

productivity, sr is the revenue subsidy rate, x is the hiring (matching) cost per worker, sb is thesubsidy rate to hiring costs, fd is the …xed cost of production, fx is the …xed cost of exporting, sd
is the subsidy rate to the …xed cost of production, and sx is the subsidy rate to the …xed cost ofexporting. As show in Helpman and Itskhoki (2010), the revenue function of a …rm in country j is1

R(h; ) = Q

1

+ Ix

1

Q( 1j)

1h ;where ( j) denotes the foreign country and we drop the subscript j from country j’s variables.
Importantly, revenue is a power function of employment.
Wages are set via bargaining over revenue between the …rm and its workers. At the bargaining
stage, entry costs, the export status, the …xed costs of production and export, and the hiring costs,
are all sunk. We adopt Stole and Zweibel’s (1996) bargaining game, which implies that the wage
function satisfy the following di¤erential equation:@ h(1 + sr )R(h; )@hiw(h; )h =35w(h; )bu :In words, the incremental surplus of the …rm from an additional worker equals the surplus of
the worker, weighted by the …rm’s relative bargaining power. This di¤erential equation has thefollowing solution:w(h; ) =+(1 + sr )R(h; )
+
bu :
h
1+

Anticipating this bargaining outcome, the …rm’s pro…t maximization problem becomes:

( )=

max

+

h 0;Ix 2f0;1g(1 + sr )R(h; )bh(1sd )fdIx (1sx )fx ;where its e¤ective hiring cost isb = (1sb ) x +bu :1+

The solution of the …rm’s problem can now be characterized in the following way. Optimal
employment can be expressed as h( ) = hd ( ) + Ix ( )hx ( ), where:111

hd ( ) =(1 + sr ) 1

+

1

1

(1

sb ) x +

1+

Q

bu

1

(1 + sr ) 1

+

;

(22)

1

1

hx ( ) =

1

1

1

(1

sb ) x +1+bu

Q( 1j)

1:(23)

Here hd ( ) represents employment needed to supply the home market while hx ( ) represents
employment needed to supply the foreign market. The pro…t level can be similarly decomposed
into pro…ts from domestic sales and pro…ts from export sales, ( ) =

d(

)=

x(

)=

1
+
1
+

(1 + sr )Q ()(1 + sr )

(

Q( j)

1

hd ( ))

1hx ( )(1d() + Ix ( ) x ( ), where:sd )fd ;(1sx )fx :See Helpman and Itskhoki (2010) for more detail. An immediate implication of (22)-(23) is that36

the solution to the wage bargaining problem yields the equilibrium wage
1

w =

b+

bu
1+
1
= bu + (1 sb ) x ;the same for all …rms, independently of export status or productivity.
A …rm’s decisions as to whether to stay in the industry and whether to export can be characterized by two cuto¤ productivity levels
x(

d and

x , which are implicitly de…ned byx ) = 0. That is, …rms with productivity below

d exit, …rms with productivity

serve the domestic market only, and …rms with productivity above
market and export. The two conditionsd(d(d ) = 0 andx(d ) = 0 and

2[

d;

x)

x serve both the domesticx ) = 0 can be expressed as:

1

1

1

+

(1 + sr )1(1sb ) x +

bu

1+

Q

1

d = (1sd )fd ;(24)

x = (1sx )fx :

(25)

1

1

1

+

1

(1

(1 + sr )sb ) x +1+bu

Q( 1j)

1

Finally, free entry requires the entry cost net of the entry subsidy to equal expected pro…ts fromdomestic and export sales:Z 1d()dG( ) +Z 1x()dG( ) = (1se )fe :xdUsing the expressions for optimal pro…ts and cuto¤s, this condition can be expressed as :(1sd )fdZ 1
d1 dG( ) + (1sx )fxdZ 1d1 dG( ) = (1se )fe :(26)

xConditions (24)-(26) characterize product market equilibrium in the home country. Speci…cally,
given x and Q( j) , they allow us to solve for (d;x ; Q) for country j (recall that we have dropped

the index j from the home country’s variables). Similar conditions describe the foreign country’s
product market equilibrium. Jointly, the two countries’ equilibrium conditions allow us to solve
the cuto¤s and real consumption indexes (dj ;xj ; Qj ) and (d( j) ;

x( j) ; Q( j) ).

Finally, conditions (20)-(26) together with the parallel conditions for the foreign country, de-37

scribe the decentralized equilibrium allocation for the world economy, given labor and productmarket policies in the two countries. In this equilibrium the governments are assumed to have access to lump-sum taxes and transfers in order to …nance their policies. Under the circumstances weneed not worry about the government’s budget constraint as long as there is positive consumptionof the homogenous good, which is assured when L is large enough.

B

Optimal Policies

The world planner’s problem— constrained by search frictions— can be formulated as follows:

fx0j ;xj ;

dj ;

max

xj ;Mj ;hdj ( );hxj ( )gj=A;BX

1
q0j + Qj

;

j=A;B

where

Qj = MjZ 1

1

hdj ( ) dG( ) + M( j)dj

q0j = x0j (Lj

Hj =xj )(1
H j = Mj

Z 1

1hx( j) ( ) dG( );x( j)0j x0j )Z 1

j xj Hj

Mj fe + fd 1

hdj ( )dG( ) + Mj

Z 1

G(

dj )

+ fx 1

G(

xj )

;

hxj ( )dG( );xjdjwhere Mj denotes the measure of di¤erentiated product …rms that enter in country j and the othervariables have been previously de…ned. The equation for Qj comes from the CES aggregator once
we notice that1hdj ( ) = qdj ( ) , where qdj ( ) is consumption of a home variety producedin country j by a …rm with productivity, and similarly for imported varieties. The last term on

the right hand side of the expression for q0j represents total entry, production, and export …xed
costs in terms of the homogenous good, where 1
1

G(

G(

dj ) is the fraction of surviving …rms andxj ) is the fraction of exporting …rms out of all entrants.

The second term on the righthand side is the total hiring cost paid in the di¤erentiated sector, where Hj is the total number ofmatches (employment) in this sector andj xj

is the search cost per match. Finally, the …rst termis the output of homogenous goods less search costs in the homogenous good sector (see the main
text for a detailed discussion of the …rst two terms on the right hand side of the equation for q0j ).
Consider the planner’s optimal allocation in a world of two symmetric countries (most of the38

following results generalize to a world of asymmetric countries). In this case we need to consider
the optimality conditions for x0 ; x; hd ( ); hx ( );

d;

x; M

, which are common to both countries.

The …rst order conditions for this problem yield:13

0 x0 =

1
;
1+

x1+ =

(20P )

1+
0 x0(21P )

;
1
1+

1
1

hd ( ) =Q(22P )

;

1

0
1
1+

1
1

hx ( ) =Q

1(23P )

;

1

0
1
1+

1

1

Q

(24P )

d = fd

1

0
1
1+

1

1

Q

1

fd

Z 1
d

(25P )

x = fx10Z 1

1 dG( ) + fxd

1 dG( ) = fe :(26P )xd

Equations (20P )-(26P ) characterizes the planner’s allocation, and they are a direct counterpart tothe decentralized equilibrium system (20)-(26). In order to characterize optimal policies, we simply
need to …nd policy parameters (bu ; sb0 ; sb ; sr ; sd ; sx ; se ) which implement the planner’s allocation(x0 ; x; hd ( ); hx ( );d;x ; Q) as a decentralized equilibrium, i.e., policies with which the solution of

13
Equation (20P ) is obtained from the …rst order condition with respect to x0 ; (21P ) is obtained from the …rst
order condition with respect to x, combined with (20P ). Equations (22P )-(23P ) obtain from the …rst order conditions
with respect to hd ( ) and hx ( ) after substituting in

x + (1
P

0 x0 )

1
1+

x0
=
x

0

P

which is implied by (20 )-(21 ). We can use the above equation in similar fashion to derive the other conditions.
Equations (24P )-(25P ) obtain from the …rst order conditions with respect to d and x after substituting in theexpressions for hd ( d ) and hx ( x ) from (22P )-(23P ). Equation (26P ) is obtained through manipulation of the …rst
order conditions with respect to M , which can be written as
1

1
1+

H = M fe + fd 1

Q

G(

d)

+ fx 1

G(

x)

:

0

Next substitute (22P )-(23P ) into the de…nition of Q and H which implies:
1
1+

Q =

1
1+

H=M
0

1

Q

1

0

Z 1

dG( ) +dFinally, combine the above two expressions with (24P )-(25P ) to obtain (26P ).

39

1

Z 1
x

dG( ) :

(20)-(26) coincides with the solution of (20P )-(26P ).14

B.1

Optimal policy with hiring-cost subsidies

We …rst consider the case without unemployment bene…ts (bu = 0), but with hiring-cost subsidies(sb0 ; sb ) used to o¤set distortions in the labor market. Comparing (20)-(26) with (20P )-(26P ), we
obtain the following characterization of the optimal policy:

sb0 =

sr =

1
1+

1

0

;

sb =

0

= 0
1

0

1+

1
1+

1+
(
1+ 0

0

;

sd = sx = se =

0

0

0)

1
:
1+ 0

The policies simplify when the …rm’s relative bargaining power is the same in the two sectors. In
this case, we have:

sb0 = sb =

1
1+

;

sr =

1
1+

;

sd = sx = sx =1:
1+This corresponds to the expression in Section 5.4 where we provide interpretation.

B.2

Optimal policy with unemployment bene…ts

We now consider the case when hiring cost subsidies are unavailable, and the government uses unemployment bene…ts in order to o¤set labor market distortions. As long as unemployment bene…ts
are common in the two sectors, it would be impossible to decentralize the planner’s allocation when
6=0 . We therefore consider the case with

0 =. In this case the comparison of (20)-(26) and(20P )-(26P ) yields the following optimal policies:

bu =
sr =

1
;
(1 + )
11
sd = sx = se =
1+
14

1+

1
(1 + )"+
1(1 + )"
1
1(1 + )(1 + )

1
1+

0

1
1+

#

0

#

;

:

We replace M with Q in the …nal equations, because it is simpler to discuss allocations in these terms.

40

In comparison to direct hiring subsidies, unemployment bene…ts attract more workers to the sector
with the higher labor market frictions and therefore with the higher rate of unemployment. Thise¤ect needs then to be neutralized by the adjustment of the optimal product market policies, as
the above equations demonstrate.

B.3

Single instrument: unemployment bene…ts

From the above discussion it is clear that the constrained e¢ cient allocation is no feasible when the
countries can use unemployment bene…ts as the only policy instruments. Therefore, the above usedmethod to characterizing optimal policies no longer applies. For this reason we directly search forthe level of unemployment bene…ts that maximizes world welfare in a decentralized equilibrium.
Consider again a world of symmetric countries. The indirect utility function for a country isgiven by
V=E+

1

Q ;

where E is disposable household income (for details see Helpman and Itskhoki, 2010). Unemployment bene…ts are …nanced by a lump-sum tax T on households, so that disposable incomeis
E = !0L

T;

where ! 0 = x0 b0 is expected income in the economy. Finally, the government budget constraint
can be written as lump-sum taxes equal total spending on unemployment bene…ts, or:T = bu (1x0 )(LN ) + (1

x)N :

(27)

Therefore, we numerically maximize welfare V with respect to bu ,max x0 b0 L
bu

T+

1

Q

;

subject to the government budget constraint (27), and with (b0 ; x0 ; x; Q; N ) determined as functions41

of bu from the equilibrium system (20)-(26).15

15

Note that N = H=x and
1

H=

+

x +

1+

bu

Q :

1

To see this, note from (22)-(23) that h( ) = +x + 1+ bu
R( ) when sr = sb = 0. Furthermore, aggregateRRrevenue equals Q = M R( )dG( ) and aggregate employment equals H = M h( )dG( ). For more details see
Helpman and Itskhoki (2010).

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