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Adjusting to Trade Liberalization: Reallocation and Labor Market ...

Adjusting to Trade Liberalization: Reallocation and Labor Market ...

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to vacancy posting. 11 If an idle firm finds its cost draws for both sectors prohibitively expensive, itremains inactive and redraws next period. If it creates a vacancy, matching uncertainty is resolvedat the beginning of next period. Vacancy creation costs are sunk before the matching uncertaintyis resolved. 12Human Capital Accumulation Human capital is sector-specific and accumulated throughon-the-job learning. Each newborn worker starts her life with an initial endowment h = (h 1 , h 2 )normalized to h 1 = h 2 = 1. The law of motion for h depends on the labor market state of theworker:h ′ i =⎧⎪⎨h α i H1−α if employed in sector i,⎪⎩ max{1 , (1 − δ h )h i }otherwise,(7)with α ∈ (0, 1). This expression implies that human capital is an element in the closed and boundedset H = [1, H] × [1, H]. Over time, a worker’s sector-i human capital continues to accumulate aslong as she is employed in that sector, approaching H asymptotically.Also, if a worker is notemployed in sector i, her human capital for that sector depreciates at the rate δ h ∈ [0, 1) per periodbut never falls below the initial level.The age-earnings profile implied by this functional form is consistent with the micro-estimatesof life-cycle earnings growth. Murphy and Welch (1990) document the concave earning profileswith rapid initial earnings growth and a leveling off after mid-career in the US data. Menezes-Filhoet al. (2008) provide a similar picture for Brazil. Note that unlike Mincer (1974) and Ben-Porath(1967), skill formation is simply a by-product of market work. Heckman (1971) and Shaw (1989)use similar models of learning-by-doing to analyze labor supply over the life-cycle.State SpaceAt any point in time, a worker is either employed in a sector with match specificproductivity z, or unemployed. Denote these states byl ∈ L = {l 1 (z), l 2 (z), l u }.11 The measure of potential entrants, however, is bounded by one.12 In order to pay the sunk cost c i, an idle firm needs to have access to credit markets. The entry process can bedecentralized with the following ownership structure. Suppose that there is a mutual fund whose shares are equallyowned by workers. It can borrow funds from the market at a rate 1 + r = 1/β which makes young agents indifferentbetween lending or not. Borrowed funds are used to finance vacancy creation costs. The mutual funds holds adiversified portfolio and owns productive matches until the debt on them is paid back. Since firms constitute a fixedfactor, the fund earns positive profits which is distributed to its owners as dividend.10

The state space for a worker is a collection of terms indicating her labor market state, humancapital stock and generation:s w ∈ S w = L × H × G.A firm is either idle, or it is producing with a worker (h, g) in sector i and has productivity z. Thisdefines the state space for firms:s m ∈ S m = {m 1 (z, h, g), m 2 (z, h, g), m u }.Next, I describe the job acceptance and vacancy creation problems.2.2 Job Acceptance ProblemA firm-worker pair jointly decides to continue or terminate the match, depending on the valueof the job and their outside options. Using time subscripts, let Π it (z, h t , g) denote the value at timet of a sector-i job with productivity z and a worker (h t , g). For an old worker (g = o),Π it (z, h t , o) = p idt · q i (z, h t ) + β(1 − δ o JD)(1 − δ m )Π it+1 (z, h t+1 , o) (8)where human capital level h t+1 evolves according to the law of motion (7). For a young worker(g = y), the same sector-i match has value:]Π it (z, h t , y) = p idt · q i (z, h t ) + β(1 − δ y JD[δ ) a Π it+1 (z, h t+1 , o) + (1 − δ a )Π it+1 (z, h t+1 , y) . (9)The continuation values in equations (8) and (9) reflect the different life-cycle shocks faced byyoung and old agents. An old worker survives the period with probability (1−δ m ). A young workerhas a probability of δ a of becoming old. Otherwise, she remains young. As a result, old agentshave a higher effective discounting rate which leads to generational differences in unemploymentand inter-sectoral mobility over and above of the level of human capital.The worker’s outside option is to go back to the unemployment pool, and that of the firm isto become idle and redraw a new pair of costs within the same period. Let the values of theiroutside options be W t (l u , h t , g) and J t (m u ) respectively (see Appendix B for the derivation of11

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