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

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

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and perfect competition in the final good market results in unit-cost pricing:p Y=p γ 1d p1−γ 2dγ γ . (2)(1 − γ) 1−γThe production of intermediate goods takes place in bilateral matches between workers andfirms who randomly meet in a labor market subject to search frictions. At each point in time, aworker is characterized by her labor market status and a vector h = (h 1 , h 2 ) ∈ H of sector-specifichuman capital stocks in sector 1 and 2 respectively. A match between a sector-i firm and a workerwith human capital h produces output according toq i (z, h) = A i zh i , (3)where A i is sectoral aggregate productivity, and z is a productivity level idiosyncratic to the match.Relative productivity across sectors, A 1 / A 2 > 1, is the only source of comparative advantage inthe model. I assume that A 1 is sufficiently large that the country is a net exporter of good 1 anda net importer of good 2 in equilibrium.Labor MarketsUnemployed workers search for jobs in an undirected fashion and are randomlymatched with a vacant firm, taking the match probability φ w as given. On the other sideof the market, idle firms draw a pair of vacancy creation costs (c 1 , c 2 ) in terms of the final goodindependently from a distribution F c (c) with support [0, ∞). They then decide whether to createvacancies, and if so, which sector to enter. The economy-wide measure of new matches ism(U, V ) =U · V(U λ + V λ , (4)) 1/λwhere U is the measure of unemployed workers, and V is the measure of total vacancies. 10 Matchingprobabilities for workers and firms are thus defined as φ w = m(U, V )/U and φ f= m(U, V )/V10 This constant-returns-to-scale functional form, proposed by Den Haan et al. (2000), has the desirable featurethat it generates matching probabilities bounded between 0 and 1.8

espectively. Defining market tightness as θ = V/U, these probabilities are given by:φ w = (θ −λ + 1) −1/λ , (5)φ f = (θ λ + 1) −1/λ . (6)Conditional on locating a vacancy, the probability of the match being in sector i is given by µ i ,an endogenous object to be characterized later. The probability that an unemployed worker willmatch with a sector-i vacancy isφ wi = φ w µ i .Not all matches in this economy are transformed into jobs. A newly formed worker-firm pairdraws a match-specific productivity level z from the distribution F z (z) with support [0, z] and densityf z (z). The pair decides whether it is optimal to produce output, taking into consideration theiroutside options. Since some matches do not result in production, job filling and job finding probabilitiesdiffer from matching probabilities. If a pairing generates positive rents, the parties produceoutput and split the associated surplus through Nash bargaining, with the worker’s share beingσ ∈ (0, 1). Match specific productivity is fixed thereafter. Firm-worker pairings are exogenouslydestroyed with probability (δ y JD , δo JD) for young and old respectively, or endogenously terminatedwhen the surplus falls below zero because of on-the-job learning. More details on the latter sourceof separation will be given below.tt + 1timeDraw (c 1 , c 2 )Pay c 1 and postvacancy in sector 1Pay c 2 and postvacancy in sector 2φ f1 − φ fMatch, draw zNo match,draw (c 1 , c 2 )AcceptReject,draw (c 1 , c 2 )Post no vacancyDraw (c 1 , c 2 )Figure 1 – Timing of Events for Idle FirmsFigure 1 summarizes the sequence of events for idle firms. All such firms are ex-ante homogeneousand cost draws are independent across time. In other words, firms do not carry these costs asa state variable and the outside option has the same value for all matched firms. There is free entry9

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