Download Offshoring, Firm Heterogeneity and the Labor Market: Some

Offshoring, Firm Heterogeneity and
the Labor Market: Some Testable
Implications
Devashish Mitra (Syracuse University)
Priya Ranjan (University of California - Irvine)
MOTIVATION
• We present certain testable implications that come
out of our theoretical work on offshoring and
heterogeneous firms.
• We do not have the data to test them.
• We are hoping some of you will have such data.
• We will provide a basic outline of our models, and
present our testable results with their intuition.
Outline of theory with results
Mitra and Ranjan (2008). Temporary Shocks, and Offshoring: The
Role of External Economies and Firm Heterogeneity, JDE.




 1
U
ln   d (i ) di   xN ,   1
  1 i

• Utility
• One unit of labor can produce wN units of the
numeraire good in the North. Wage rate there is
fixed at wN in equilibrium.
• Productivity of a firm.
– Distribution function: G(α).
– One unit of a specialized input, y, produces α units of
the final good (non-numeraire).
x(α)=αy
• The final output of any non-numeraire good can only be
produced in the North.
• The specialized input can either be produced domestically
in the North or its production can be outsourced to a
producer in a foreign country called the South.
• One unit of home labor can make one unit of the input
– the cost of producing one unit of the input domestically is wN.
– The unit cost of non-numeraire good, when the input is produced
domestically is
c(α)= wN /α
• In the South φ(0)>1 units of labor are required to produce a
unit of specialized input when no firm has begun
offshoring.
• The labor requirement when a fraction n of firms offshore
is denoted by φ(n), where φ′(n)<0 (captures externalities).
• As long as φwS < wN the South has a comparative advantage
in the production of the specialized inputs. However, all
these inputs are not always imported by the North from
the South due to the presence of the fixed costs of
offshoring and the implicit costs of contract
incompleteness.
• Let us assume that the total fixed cost of offshore
outsourcing for a final goods producer in the
North is FO.
– This consists of search cost, cost of writing a contract
etc.
• We rank the firms in decreasing order of
productivity. B(n) measures the benefit from
offshoring gross of the fixed cost for the marginal
firm when a fraction n of firms offshores.
– In the case of an interior equilibrium, the equilibrium
number of firms that offshore is the solution to B(n)=
Figure 1:Equilibria with and without firm heterogeneity
0.25
heterogeneous
heterogeneous
homogeneous
heterogeneous
0.2
B(n,n)-FO
homogeneous
homogeneous
0.15
0.1
0.05
n*1
n*2
n*1 0.2
-0.05
0.4
0.6
0.8
1
n
n
-0.1
Parameters: Parameters: FO =.1,σ =3.8, b =1.75,wS =.4,wN =1, β=(σ-1)/σ
Heterogeneous productivity: uniform over [0, ] where   (0, )
• Testable Hypothesis 1. When only some firms
in an industry offshore in equilibrium, these
are the most productive firms in the industry.
The most productive completely domestic firm
is less productive than the least productive
offshoring firm.
Testable Hypothesis 2.
• (a) Profits are higher in the case of offshoring firms
except for the marginal firm that is indifferent
between offshoring and not offshoring.
• (b) As we move from autarky to offshoring, profits fall
for the firms that fail to offshore. Profits also fall for
some of the lower productivity offshoring firms, while
they can certainly rise for the most productive
offshoring firms.
• (c) Offshoring firms charge a lower price than other
firms before and after they start offshoring. Upon
offshoring, their prices fall further. Output decreases
and price remains constant for the firms that remain
autarkic.
Intuition:
• Price is a fixed markup over marginal cost that falls
for offshoring firms. Also, MC is lower for the more
productive firms.
• Good with lower price will have higher quantity
demanded and produced and so will have higher
employment (if it is produced domestically).
• Note that the utility function above fixes expenditure
on non-numeraire goods and results in constant
markups, which together ensure that offshoring will
reduce profits of all firms if we had homogeneous
symmetric firms.
Dynamic Implications
• We assume that a firm makes its decision
regarding offshoring on the basis of foreign
labor productivity, 1/φ, in the previous period
which in turn depends on the number of
firms that had outsourced by the end of the
previous period as follows.
Figure 2: Multiple Equilibria & Dynamics after a shock
B(n,n)
FO
n1
n2
n3
n4
n5
n6
n*
n
Testable Hypothesis 3.
• Starting from an equilibrium in which no firms
offshore, a shock (such as a sudden change in
policy) that raises the benefit from offshoring
results in offshoring by the most productive
firms followed by the next most productive
firms and so on until offshoring stops.
Firm-level demand for labor
Mitra and Ranjan (2007). Offshoring & Unemployment
• Let us now modify the model in that labor
now performs two types of tasks: one that can
be offshored and another that has to remain
in the headquarters.
• We also modify the utility function to the


following:





U    d (i )
i
1
1
di 

xN
1
,0    1
• We can allow for search frictions and wage
bargaining here (i.e., we can introduce
unemployment).
• In this model, the reallocation of labor, as a result of
offshoring, can be summarized as follows.
– (1) There is intersectoral reallocation of labor from the
non-numeraire sector (where offshoring takes place) to
the numeraire sector.
– (2) Within the offshoring sector some or all firms move
some of their production activities overseas.
– (3)Within that sector demand for labor shifts to
headquarter-based activities in firms that end up
offshoring their production.
– (4) Finally, since foreign labor is cheaper, offshoring firms
will increase the use of production services (production
input) and depending on the elasticity of substitution and
headquarter intensity of production, decrease or increase
the use of headquarter services.
Testable Hypotheis 4.
• (a) For high enough headquarter intensity and a high enough
wage in the North relative to the South and for a high enough
elasticity of substitution between the various varieties of the
good produced in the non-numeraire offshoring sector, an
offshoring firm, controlling for firm-level characteristics, will
have higher domestic employment relative to that of a firm
which remains fully domestic.
• (b) Similar variables determine, albeit in a much more
complicated manner, whether a firm after offshoring
increases its domestic employment or not.
• (c) Opening an industry to offshoring can reduce the
employment of firms that end up not offshoring in
equilibrium.
Entry, exit and unemployment
• What happens when we introduce the
possibility of offshoring within a Melitz-type
model of firm heterogeneity with entry and
exit?
– Here we have a fixed entry cost that is incurred
before productivity is known to the firm.
– Then after the firm draws its productivity, there is
also a fixed production cost, at which point the
firm may decide to produce or quit.
– Labor performs two activities.
• Testable Hypothesis 5. The threshold productivity at
which firms continue to produce (after entry) goes up
as a result of offshoring.
• Intuition: Firms that are not able to jump the fixed
cost of offshoring face greater competition. They lose
their market to offshoring firms and so they may not
be viable anymore.
• Sectoral Unemployment. Offshoring in any sector/industry
can raise or lower sectoral unemployment depending on many
factors.
– Firstly, if only some of the tasks done by a particular type of labor that
are somewhat complementary to each other are offshored, sectoral
unemployment could actually go down due to offshoring.
• This is driven by the decline in the cost of the input driven by
cheaper labor in the South, which in turn means that more of these
inputs are combined with each unit of labor in the home-based
activities, thereby raising its productivity.
• The presence of alternative employment activities outside the
sector strengthens this result.
• Offshoring is likely to increase entry by making the offshoring
sector more profitable.