1. Offshoring, Firm Heterogeneity and the Labor Market: Some Testable Implications Devashish Mitra (Syracuse University) Priya Ranjan (University of California - Irvine)

2. 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.

3. 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 w N units of the numeraire good in the North. Wage rate there is fixed at w N 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

4. 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 w N. – The unit cost of non-numeraire good, when the input is produced domestically is c(α)= w N /α

5. 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 φw S < w N 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.

6. Let us assume that the total fixed cost of offshore outsourcing for a final goods producer in the North is F O. – 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)= F O

7. Figure 1:Equilibria with and without firm heterogeneity n B(n,n)-F O n*1n*1 n*2n*2 Parameters: Parameters: F O =.1,σ =3.8, b =1.75,w S =.4,w N =1, β=(σ-1)/σ Heterogeneous productivity: uniform over where homogeneous heterogeneous homogeneous heterogeneoushomogeneous heterogeneous n*1n*1 n

8. 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.

9. 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.

10. 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.

11. 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.

12. n1n1 n2n2 n3n3 n4n4 n5n5 Figure 2: Multiple Equilibria & Dynamics after a shock n6n6 n* FOFO n B(n,n)

13. 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.

14. 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).

15. 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.

16. 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.

17. 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.

18. 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.

19. 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.