Capacity Constraining Labor Market Frictions in a Global Economy * Christian Holzner † and Mario Larch ‡ May 7, 2013 Abstract Convex vacancy creation costs shape firms’ responses to trade liberalization. They induce capacity constraints by increasing firms’ costs of production. A profit maximizing firm will therefore not fully meet the increased foreign de- mand, but serve only a few export markets. More productive firms will export to more countries and charge higher or similar prices compared to less productive firms. Trade liberalization also affects labor market outcomes. Increased profits by exporting firms trigger firm entry, reduce unemployment and increase wage dispersion in the on-the-job search model with monopolistic competition. Keywords : On-the-job search; capacity constraints; international trade; hetero- geneous firms; monopolistic competition JEL-Codes : F16, F12, J64, L11 * We acknowledge useful comments on earlier drafts of this paper at NOeG, May 2010, in Vienna, EALE/SOLE, June 2010, in London, EEA, August 2010, in Glasgow, at the CESifo Area Conference on Global Economy, February 2011, in Munich and at the Workshop ”Globalization and Labour Market Outcomes”, June 2011, in Geneva. † Ifo Institute, University of Munich, 81679 Munich, Germany. E-mail: [email protected]. ‡ University of Bayreuth, Ifo Institute, CESifo and GEP, 95447 Bayreuth, Germany. E-Mail: [email protected].
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Capacity Constraining Labor Market Frictions in a
Global Economy∗
Christian Holzner†and Mario Larch‡
May 7, 2013
Abstract
Convex vacancy creation costs shape firms’ responses to trade liberalization.
They induce capacity constraints by increasing firms’ costs of production. A
profit maximizing firm will therefore not fully meet the increased foreign de-
mand, but serve only a few export markets. More productive firms will export
to more countries and charge higher or similar prices compared to less productive
firms. Trade liberalization also affects labor market outcomes. Increased profits
by exporting firms trigger firm entry, reduce unemployment and increase wage
dispersion in the on-the-job search model with monopolistic competition.
Keywords: On-the-job search; capacity constraints; international trade; hetero-
geneous firms; monopolistic competition
JEL-Codes: F16, F12, J64, L11
∗We acknowledge useful comments on earlier drafts of this paper at NOeG, May 2010, in Vienna,
EALE/SOLE, June 2010, in London, EEA, August 2010, in Glasgow, at the CESifo Area Conference
on Global Economy, February 2011, in Munich and at the Workshop ”Globalization and Labour
Market Outcomes”, June 2011, in Geneva.†Ifo Institute, University of Munich, 81679 Munich, Germany. E-mail: [email protected].‡University of Bayreuth, Ifo Institute, CESifo and GEP, 95447 Bayreuth, Germany. E-Mail:
Four empirical observations of exporting firm behavior appear in the data:1 i) Only
part of all firms export. ii) Most of the exporting firms sell only to one foreign market
and the frequency of firms that sell to multiple markets declines with the number of
destinations. iii) Firms do not enter markets according to a common hierarchy. iv) The
export strategy of one and the same firm varies widely across countries with similar
characteristics.
The first empirical observation of exporting firm behavior can be explained by in-
troducing firm heterogeneity into the Krugman (1980) trade model based on economies
of scale in production and love-of-variety preferences as done by Melitz (2003). In order
to explain the first three empirical observations Arkolakis (2010) and Eaton, Kortum,
and Kramarz (2011) introduce not only market but also firm-specific heterogeneity in
entry costs and market size. With respect to the fourth observation Eaton, Kortum,
Kramarz (2011) note: “In particular, [our approach] leaves the vastly different perfor-
mance of the same firm in different markets as a residual. Our analysis points to the
need for further research into accounting for this variation.”
We provide an analytically tractable trade model that captures all four empiri-
cal regularities. We introduce capacity constraints into the new trade, monopolistic
competition model with heterogeneous firms by Melitz (2003). As a result the size of
exporting firms does not fully adjust in order to serve all foreign markets. Given the
entry costs to each export market, firms rather react by selling only to a few markets
at a higher price. Thus, even if only symmetric countries trade, exporting firms sell –
depending on their productivity – only to part of the countries. Combined with the
empirical observation of Pareto-distributed firm productivities (see for example Axtell,
2001), our model is able to explain all four empirical observations of exporting firm
1See Dunne, Roberts and Samuelson (1989); Davis and Haltiwanger (1992); Bernard and Jensen
(1995, 1999, 2004); Roberts and Tybout (1997); Clerides, Lach and Tybout (1998); Bartelsman and
Doms (2000); Eaton, Kortum, and Kramarz (2004); Lawless (2009); and Eaton, Kortum, and Kramarz
(2011).
1
behavior.
We assume that capacity constraints are caused by convex vacancy creation costs.
While increasing marginal costs could stem for a variety of reasons,2 our predictions
of the labor market effects after trade liberalization are well in line with empirical
findings and anecdotal evidence of “labor shortage”.3 Firm heterogeneity implies that
more productive firms or firms with a higher product quality will despite the convex
costs of production hire more workers in order to be less capacity constrained. Convex
vacancy creation costs make it attractive for firms to hire more workers by offering
higher wages and attracting workers from other employers. In order to capture this
recruiting channel we merge the Melitz (2003) with the on-the-job search model by
Burdett and Mortensen (1998).
Given that our model successfully explains the main empirical facts of firm export-
2Magnier and Toujas-Bernate (1994) and Madden, Savage, and Thong (1994) argue that exporting
firms may not always be able to meet the demands for its goods due to investment constraints. Ruhl
and Willis (2008), Eaton, Eslava, Krizan, Kugler and Tybout (2009), and Fajgelbaum (2011) point
out that firms need time to grow in order to be large enough to export. Redding and Venables (2004)
and Fugazza (2004) find that country specific supply-side conditions can explain part of the differences
in export performance. Manova (2008) isolates the effect of equity market liberalization on export
behavior using panel data for 91 countries. Blum, Claro, and Horstmann (2010) assume that capital
capacity constraints are responsible for fluctuations in export behavior of Chilean firms.3”Labor shortages” are often blamed for reducing firms’ ability to meet their demand. The Man-
powerGroup provides extensive evidence of ”labor shortage”, specifically of highly qualified workers in
the “2011 Talent Shortage Survey” based on nearly 40,000 surveys of employers in 39 countries. There
is also a heavy debate about the effects of ”labor shortage” on the global competitiveness of China.
The New-York-Times wrote on April 3, 2006 that “data from officials suggest that major export in-
dustries are looking for at least one million additional workers, and the real number could be much
higher”. A Chinese supplier survey by Global Sources (2011) reports that “the persistent labor short-
age has nearly driven growth in China’s export industries to a halt”. Lately The National Business
Review wrote about the IT professional shortage in New Zealand (see http://www.nbr.co.nz/article/it-
professional-shortage-continues-survey-118981) and Webmaster Europe, the International-European
labor union for Internet professionals, stated that the IT professional shortage will continue in 2010
in Germany (see http://www.webmasters-europe.org/modules/news/article.php?storyid=95).
2
ing behavior, we investigate the effects of trade liberalization on the size of firms and
the number of firms as well as on labor market outcomes. Trade liberalization leads to
an increase of firms’ expected profits and triggers not only an increase of average firm
size, but in contrast to Melitz (2003) also an increase in the number of firms. This
is well in line with recent empirical findings by Eaton, Kortum, and Kramarz (2004,
2011) that suggest that a large fraction of the adjustment in market shares comes from
changes in the number of firms and not from the adjustments of the amount sold by
existing firms. At the same time, opening up to trade still forces less productive firms
to leave the market like in Melitz (2003).
Additionally, trade liberalization increases wage dispersion since search frictions pin
down the lowest wage at the level of unemployment benefits, while increased profits
of exporting firms increase wages at the top of the distribution.4 Higher profits of
exporting firms also increase job creation (both at the extensive and the intensive
margin) and lead to less unemployment.5
By developing a framework consistent with observed exporting behavior, we con-
tribute to the literature that integrates imperfect labor markets into trade models
and analyzes the effects of trade liberalization on unemployment and wage inequal-
ity. Brecher (1974) was the first to study minimum wages in the Heckscher-Ohlin
model with two countries, two factors, and two goods, and Davis (1998) generalized
this model. Davidson, Martin, and Matusz (1999) and Davidson and Matusz (2004)
introduce search frictions and wage bargaining into multi-sector models of interna-
tional trade governed by comparative advantage. More recently, Cunat and Melitz
(2007, 2010) study the effect of cross-country differences in firing restrictions on the
patterns of comparative advantage in a Ricardian setting. Helpman, Itskhoki, and
Redding (2009, 2010) allow firms to screen workers of different abilities in a Melitz
4Evidence for increasing wage dispersion after trade liberalization is provided by Egger, Egger
and Kreickemeier (2011) based on five European countries and by Helpman, Itskhoki, Muendler and
Redding (2012) using linked employer-employee data for Brazil.5This finding is well in line with recent empirical evidence that trade liberalization lowers unem-
ployment provided by Dutt, Mitra, and Ranjan (2009) and Felbermayr, Prat and Schmerer (2011).
3
(2003) model with search and matching labor market frictions. Egger and Kreicke-
meier (2012) explain intra-group wage inequality among ex ante identical workers due
to a fair wage-effort mechanism. Amiti and Davis (2012) also assume a fair wage con-
straint, but focus on output tariffs. Using the Diamond-Mortensen-Pissarides matching
model (see Pissarides, 2000) Felbermayr, Prat, and Schmerer (2011) show within a new
trade theory model that unemployment falls if trade is liberalized. Fajgelbaum (2011)
uses an on-the-job search equilibrium model based on Postel-Vinay and Robin (2002)
to investigate how labor market frictions influence the growth path and export deci-
sion of firms. All of these papers explain part of the empirical findings discussed in the
beginning, but none of them explains all four empirical facts.
The paper is structured as follows. In the next section we present the general
framework that links the new trade model by Melitz (2003) with the on-the-job search
model by Burdett and Mortensen (1998). In section 3 we analyze the equilibrium in
a closed economy. In section 4 we investigate the effects of trade liberalization and
compare the results with the literature focusing particularly on the comparison with
Throughout this section we focus on two scenarios: A world where the country is in
autarky and a world where there are 99 symmetric trading partners.15
In Figure 6 we plot the number of vacancies created (left panel) and the number of
export markets served by a firm with productivity ϕ (right panel). In line with Propo-
sition 1 the number of export markets served is an increasing function of productivity.
We calibrated the model such that no firm is willing to export to all foreign markets.
Firms with the highest productivities enter 57 out of the 99 markets. Like in the model
with fixed vacancies the level of productivity ϕ∗ where firms still make positive profits
is higher in the open economy than in autarky.
With trade the number of vacancies per firm is lower than in autarky for firms with
a low productivity but higher for firms with a high productivity. Additionally, the
number of vacancies are increasing in productivity in both scenarios. More importantly,
the number of vacancies jumps up at each export cutoff because firms increase their
labor input in response to additional demand from abroad.
Figure 7 plots labor inputs (left panel) and outputs (right panel) per firm. The
pattern of vacancies translates into labor input and output pattern. In the open econ-
13Our convergence criterion is
∣∣∣∣∣
(ϕ∫
ϕ∗
Πmax (ϕ) γ (ϕ) dϕ
)− fe
∣∣∣∣∣ < 0.01.
14The grid size is chosen to be 1000. However, results do not depend on the chosen grid size.15The number of (potential) trading partners is not crucial for the basic qualitative results.
30
10 20 30 40 50 60 70 80 90 1000.04
0.045
0.05
0.055
0.06
0.065
0.07
0.075Vacancies as a function of productivity
φ
v(φ)
AutarkyOpen economy
10 20 30 40 50 60 70 80 90 1000
10
20
30
40
50
60Number of countries as a function of productivity
φ
j
AutarkyOpen economy
Figure 6: Vacancies and number of countries served in autarky and in an open economy
with endogenous vacancies
omy labor input and output per firm is lower for firms with low productivities but
higher for firms with high productivities as compared to autarky. High productivity
firms grow at the expense of low productivity firms because the additional revenues
from exporting allow them to create more vacancies. Unlike in Melitz (2003) not all
exporting firms grow because the increased competition in the labor market due to the
increased number of vacancies has a negative effect on employment per firm, similar to
the negative impact that the increased number of active firms M has on labor input
in the basic framework. Hence, the basic results of Proposition 2 for the case of fixed
vacancies survive with the qualification that only less productive firms shrink compared
to autarky.
Let us now investigate domestic prices and quantities under autarky and in an open
economy. Like in Melitz (2003) domestic variety prices are a monotonically falling
function of ϕ under autarky (Figure 8). However, with trade the domestic price profile
of firms looks very different. First, firms that only sell domestically charge a slightly
higher price as firms under autarky because the increased competition in the labor
market reduces their output (see Figure 7). The firm that exports to one trading
partner charges a higher price in the domestic market than the firm selling only locally.
31
10 20 30 40 50 60 70 80 90 1005
5.5
6
6.5
7
7.5
8
8.5
9
9.5
10x 10
−3 Labor input per firm as a function of productivity
φ
l(φ)
AutarkyOpen economy
10 20 30 40 50 60 70 80 90 1000
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1Output per firm as a function of productivity
φ
q(φ)
AutarkyOpen economy
Figure 7: Firm size (labor input and output) in autarky and in an open economy with
endogenous vacancies
The domestic price of the least productive exporter that serves more than one country
is slightly lower than the price charged by the least productive exporter that only serves
one foreign market. However, the price is still higher than the domestic price of the
firm that only serves the local market.16 These results are similar to our results shown
in Figure 4b.
Quantities are just the reverse image of prices charged in the domestic market. The
right panel shows that the domestically sold quantities are much higher under autarky
than in an open economy, specifically for very productive firms. The quantity of the
least productive firm is higher than the quantity of the least productive firm serving in
addition to the domestic market one foreign market. Hence, the results that we derived
in Proposition 3 survive under endogenous vacancy creation.
Figure 9 shows profits as a function of productivity. In both scenarios, autarky and
trade, profits are increasing in productivity. There are no jumps in the profit function,
16We set the number of (potential) trading partners large enough so that even the most productive
firm does not serve all foreign markets. If we would allow a firm to serve all export markets, this firm
could only expand by lowering prices. This would be reflected by a fall of the price line at the right
end.
32
10 20 30 40 50 60 70 80 90 1001
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
1.9Domestic variety prices per firm as a function of productivity
φ
p d(φ)
AutarkyOpen economy
10 20 30 40 50 60 70 80 90 1000
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9Domestic quantities per firm as a function of productivity
φ
q d(φ)
AutarkyOpen economy
Figure 8: Domestic quantities and prices in autarky and in an open economy with
endogenous vacancies
because the extra revenues from exporting are used to pay for the foreign market entry
costs. This is due to the definition of the export cutoff, where the least productive firm
entering j markets has to be indifferent between entering j markets or only serving
j − 1 markets.
If we compare the profits of firms in autarky and in an open economy, we see that
the profit function under trade is much steeper than under autarky. The reason is that
by serving more than one market, a firm can demand higher prices in every market
and therefore can generate higher profits with the same output. Furthermore, like in
Melitz (2003) there are some firms with low productivities that make lower profits in
an open economy compared to autarky, because the increased competition in the labor
market reduces the labor input of low productivity firms and thus the output necessary
to generate higher profits.
In Figure 10 we plot wages as a function of productivity (left panel) and the wage
distribution (right panel). Wages are an increasing function of productivity under
both, autarky and trade. The following three observations are interesting: (i) The
wage distribution starts at a lower productivity values in autarky than in an open
economy. This reflects the fact that only more productive firms can survive in an open
33
10 20 30 40 50 60 70 80 90 1005
10
15
20
25
30
35
40
45
50
55Profits as a function of productivity
φ
Π(φ
)
AutarkyOpen economy
Figure 9: Profits as a function of productivity in autarky and in an open economy with
endogenous vacancy creation.
economy, i.e., the zero cutoff productivity ϕ∗ increases when opening up to trade.17
(ii) Wages are at least as high as unemployment benefits z. (iii) The wage function
is much steeper in an open economy, because exporting generates higher profits and
opens up the opportunity for firms to pay higher wages.
We can also compare the wage distribution in autarky and in an open economy.
The right panel of Figure 10 shows that in both situations the lowest wage is given by
z. Since wages increase at exporting firms, opening up to trade leads to more wage
dispersion as predicted in Proposition 4. Hence, allowing for vacancy creation does not
lead to different conclusions regarding the effects of trade on the wage distribution.
Note, that with endogenous vacancy creation it still holds that in an open economy
the number of firms is higher and the unemployment rate lower compared to autarky.
5.5.3 Convex vacancy costs and concave hiring costs
Convex vacancy costs are crucial for our results. The empirical evidence on the shape
of the vacancy cost function is small. Abowd and Kramarz (2003) and Kramarz and
Michaud (2010) have shown that the shape of the hiring cost function for French firms
17The effect is very small, though. Hence, it can not be seen in the figure.
34
10 20 30 40 50 60 70 80 90 1001
1.5
2
2.5
3
3.5
4
4.5Wages as a function of productivity
φ
wag
e(φ)
AutarkyOpen economy
1 1.5 2 2.5 3 3.5 4 4.50
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1Wage distributions
wage(φ)
G(w
age(
φ))
AutarkyOpen economy
Figure 10: Wages and wage distributions in autarky and in an open economy with
endogenous vacancy creation.
is mildly concave, while Blatter, Muhlemann and Schenker (2009) have shown that the
shape of the hiring cost function for Swiss firms is convex. In this section we show
that a convex vacancy cost function is consistent with a concave and a convex hiring
cost function. Hiring cost functions have the same shape as the vacancy cost functions
if the hiring rate h (v) per vacancy is the same for all firms. However, the hiring rate
per vacancy is increasing in the wage because job offers made by high wage firms are
accepted by more employed workers. This property holds in the Burdett-Mortensen
model like in any monopsony wage model as shown by Manning (2006).18 It can also
be seen by looking at the equation for the hiring rate per vacancy given by,
h (v) = η [u+ (1− u)G (w)] .
In addition the number of vacancies are an increasing function of the wage paid by
firms, i.e.,∂v (w)
∂w> 0.
18Using firm level data from the Labour Turnover Survey in the UK, Manning (2006) shows that
there are increasing marginal costs of recruitment, i.e., that the vacancy cost function is convex.
35
Thus, the total number of workers hired H = h (v) v increase with the wage for two
reasons: (i) the number of vacancies created increase with the wage and (ii) the hiring
rate per vacancy increases with the wage.
Now consider the shape of the hiring cost function K (H) given any convex vacancy
cost function c (v) with c′v (v) > 0 and c′′vv (v) > 0. Using the inverse function of
H = h (v) v and v (w), the first derivative of the hiring cost function is given by,
∂K (H)
∂H= c′v (v)
∂v
∂H= c′v (v)
1
h (v) + v∂h (v)
∂w
∂w (v)
∂v
> 0,
where the inequality follows from,
∂h (v)
∂w= (1− u) g (w) > 0 and
∂w (v)
∂v> 0.
The second derivative that determines the shape of the hiring cost function is given by,
∂2K (H)
∂H2= c′′vv (v)
(∂v
∂H
)2
−c′v (v)
2∂h (v)
∂w
∂w (v)
∂v+ v
∂2h (v)
∂w2
(∂w (v)
∂v
)2
+ v∂h (v)
∂w
∂2w (v)
∂v2(h (v) + v
∂h (v)
∂w
∂w (v)
∂v
)2
∂v
∂H,
where∂2h (v)
∂w2= (1− u) g′w (w) ≷ 0 and
∂2w (v)
∂v2≷ 0.
Thus, a convex vacancy cost function implies a concave hiring cost function, if and
only if
c′′vv (v) < c′v (v)
(2∂h (v)
∂w
∂w (v)
∂v+ v
∂2h (v)
∂w2
(∂w (v)
∂v
)2
+ v∂h (v)
∂w
∂2w (v)
∂v2
)∂v
∂H,
which is feasible since ∂h (v) /∂w > 0 and ∂w (v) /∂v > 0. Thus, a convex vacancy
cost function is consistent with a concave hiring cost function as found by Abowd and
Kramarz (2003) and Kramarz and Michaud (2010) for French firms as well as a convex
hiring cost function as found by Blatter, Muhlemann and Schenker (2009) for Swiss
firms. Our simulations also provide an example that a convex vacancy cost function
36
30 40 50 60 70 80 90 1000
0.5
1
1.5
2
2.5
3x 10
−3 Vacancies as a function of productivity
φ
v(φ)
0 0.5 1 1.5 2 2.5 3
x 10−3
0
0.2
0.4
0.6
0.8
1
1.2
1.4Hiring cost function
Number of workers hired
Hiri
ng c
osts
Figure 11: Concave hiring cost function for a convex vacancy cost function
leads to a concave hiring cost function as shown in the following Figure.19
6 Conclusions
The implications of trade liberalization on firms’ behavior is one of the most heavily
discussed consequences of increasing globalization. We show that capacity constraints
change firms’ responses to trade liberalization compared to models with perfect labor
markets or with imperfect labor markets without capacity constraining effects. With
capacity constraining labor market frictions not all firms will serve all export markets,
even when export markets are similar. Rather the number of export markets served by a
firm is increasing in its productivity or product quality. Given the capacity constraints
that firms face if they want to recruit more workers in their domestic country, an
obvious extension of our model is to allow for foreign direct investment. This would
allow firms to relax their capacity constraints by recruiting and producing in a foreign
country.
19The parametrization is as follows: χ = 0.02, η = 0.9, δ = 0.02, φ = 0.02, ρ = 0.75, c = 500,
α = 1.01, f = 0.0001, fe = 5, γ = 3.2, ϕ = 30, ϕ = 100 and z = 1. We only focus on the case of
autarky here.
37
Concerning trade liberalization and labor market outcomes we find that unemploy-
ment falls and wage dispersion increases with trade liberalization. Opening up to trade
increases expected profits, triggers firm entry and reduces unemployment. Increased
profits of exporting firms also increases wages at the upper end of the wage distribu-
tion. Wages at the lower end of the wage distribution are pinned down by workers’
reservation wage which equals unemployment benefits.
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