Offshoring, Firm Heterogeneity and the Labor Market: Some Testable Implications

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Offshoring, Firm Heterogeneity and the Labor
Market Some Testable Implications

• Devashish Mitra (Syracuse University)
• Priya Ranjan (University of California - Irvine)

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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.

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Outline of theory with results

• Mitra and Ranjan (2008). Temporary Shocks, and
  Offshoring The Role of External Economies and
  Firm Heterogeneity, JDE.
• 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(a).
• One unit of a specialized input, y, produces a
  units of the final good (non-numeraire).
• x(a)ay

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• 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(a) wN /a

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• In the South f(0)gt1 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 f(n), where f'(n)lt0
  (captures externalities).
• As long as fwS lt 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.

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• 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) FO

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Figure 1Equilibria with and without firm
heterogeneity
heterogeneous
heterogeneous
homogeneous
heterogeneous
homogeneous
B(n,n)-FO
homogeneous
n1
n2
n1
n
n
Parameters Parameters FO .1,s 3.8, b
1.75,wS .4,wN 1, ß(s-1)/s Heterogeneous
productivity uniform over where
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• 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.

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• 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.

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• 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.

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• Dynamic Implications
• We assume that a firm makes its decision
  regarding offshoring on the basis of foreign
  labor productivity, 1/f, 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.

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Figure 2 Multiple Equilibria Dynamics after a
shock
B(n,n)
FO
n1
n2
n3
n4
n5
n6
n
n
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• 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.

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• 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
• We can allow for search frictions and wage
  bargaining here (i.e., we can introduce
  unemployment).

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• 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.

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• 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.

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• 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.

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• 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.

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• 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.