- Text
- Workers,
- Unemployment,
- Sector,
- Employment,
- Reallocation,
- Economy,
- Productivity,
- Initial,
- Transition,
- Aggregate,
- Adjusting

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

The last term represents the case in which the firm does not enter at all.CTransition Function for the DistributionDefine a probability function Γ t : S w × S w → [0, 1] such that Γ t (s w , s ′ w) is the probability of aworker in state s w **to** be in state s ′ w next period. Note that the state variable s w is a vec**to**r (l, h, g)which summarizes the labor market state, human capital s**to**ck **and** the generation of a worker.If the worker is matched in sec**to**r i with productivity z, it has the form (l i (z), h, g). A genericelement for an unemployed worker is (l u , h, g).Some transitions are infeasible in this environment. For example, an old worker with (l, h) cannot become a young worker with h ′ ≥ h. On the other h**and**, old workers are replaced by youngworkers when they die, so a transition from (l, h, o) **to** (l u , h, y) is feasible. In order **to** characterizefeasible transitions, let h ′ (h) denote human capital s**to**ck attained from h according **to** the law ofmotion (7). Noting that F z (·) is the distribution function for match specific productivity drawswith the density f z (z), Γ t is defined as follows:⎧(1 − δ { m) (1 − φ wt) + ∑ i φw it Fz[˜zit(h′ (h), o)] } if s w = (l u, h, o) **and** s ′ w = (l u, h ′ (h), o),(1 − δ m)φ wit f z(z)Iit+1(z, a h ′ (h), o) if s w = (l u, h, o) **and** s ′ w = (l i(z), h ′ (h), o),δ mif s w = (l, h, o) **and** s ′ w = (l u, h, y),(1 − δ m)(1 − δ o JD)I a it+1(z, h ′ (h), o) if s w = (l i(z), h, o)) **and** s ′ w = (l i(z), h ′ (h), o),(1 − δ m)δ o JD if s w = (l i(z), h, o) **and** s ′ w = (l u, h ′ (h), o),(1 − δ a)(1 − δ y JD )Ia it+1(z, h ′ (h), y) if s w = (l i(z), h, y) **and** s ′ w = (l i(z), h ′ (h), y),Γ t(s w, s ′ w) =⎪⎨ δ a(1 − δ y JD )Ia it+1(z, h ′ (h), o)if s w = (l i(z), h, y) **and** s ′ w = (l i(z), h ′ (h), o),(1 − δ a)δ y JDif s w = (l i(z), h, y) **and** s ′ w = (l u, h ′ (h), y),δ aδ y JDif s w = (l i(z), h, y) **and** s ′ w = (l u, h ′ (h), o),(1 − δ { a) (1 − φ wt) + ∑ i φw it Fz[˜zit(h′ (h), y)] } if s w = (l u, h, y) **and** s ′ w = (l u, h ′ (h), y),{δ a (1 − φwt) + ∑ i φw it Fz[˜zit(h′ (h), o)] }if s w = (l u, h, y) **and** s ′ w = (l u, h ′ (h), o),(1 − δ a)φ wit f z(z)Iit+1(z, a h ′ (h), y) if s w = (l u, h, y) **and** s ′ w = (l i(z), h ′ (h), y),δ aφ wit f z(z)I a it+1(z, h ′ (h), o)if s w = (l u, h, y) **and** s ′ w = (l i(z), h ′ (h), o),⎪⎩ 0 otherwise.42

DNumerical Implementation **and** Solution AlgorithmThis section describes the numerical solution **to** the model, **and** the algorithms used **to** compute the steady stateequilibrium **and** the transition path. The software used in computations is 32-bit Matlab R2009a.D.1 The State SpaceI use a discrete state space for match-specific productivity z **and** human capital level h i. For z, I use 40 equallydistanced grid points between [0, 1]. I use 200 grid points for h i. For the case with positive depreciation of skills,I use equally distanced grid points between [1, H] **and** evaluate out-of-grid points through interpolation.For thebenchmark case with no depreciation, I construct the grid points in line with the increments implied by the learningfunction (7).D.2 Steady State AlgorithmStep 1.Step 2.Start iteration j with a pair of values for entrants’ expected values of matching (EJ j 1 , EJ j 2 ) in the two sec**to**rs.Calculate (J(m u), φ f , φ w, ˜µ 1, ˜µ 2) by simulating a large number of cost draws for firms from the distributionF c(c), **and** using expressions (5), (6), (15), (16), (25) **and** the fact that market tightness θ is equal **to** ˜µ 1 + ˜µ 2.Step 3.Solve for the job acceptance cu**to**ffs ˜z it(h, g), **and** the value functions (11) **and** (12) using the following subroutine:i. Start with old workers. Assume initial set of values for unemployment W (l u, ·, o) **and** matches Π i(z, ·, o)for both sec**to**rs. Use (10) **to** find the job acceptance cu**to**ffs, **and** update Π i(z, ·, o) using equation (8).ii.To update W (l u, ·, o), use the job acceptance cu**to**ffs in (22). Iterate until convergence.iii. Repeat the same steps for young workers, using equation (9).Step 4.Simulate the economy with a large number of workers drawing demographic shocks, labor market shocks(matching **and** separating), **and** match-specific productivity terms. Aggregate the cross-sections of workers **to**find the distribution of workers Ψ.Step 5. Use the distributions **to** update (EJ j+11 , EJ j+12 ) using equation (14), iterate until the distances |EJ j+11 −EJ j 1 |,**and** |EJ j+12 − EJ j 2 | are sufficiently small.D.3 Transition AlgorithmThe algorithm used **to** solve for the transition between two steady states is similar **to** Costantini **and** Melitz(2009). The basic idea is **to** start with an initial path of aggregate variables, **to** solve the decision functions backward**and** **to** simulate agents’ behavior forward according **to** these decision rules **and** r**and**om shocks. The simulation allowsus **to** update the aggregate variables which are iterated upon until convergence. Importantly, I fix the length of thetransition at N = 400 periods (equivalent **to** 100 years) such that at period t = N + 1, the terminal steady state is43

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- Page 31 and 32: ReferencesJ.M. Abowd and F. Kramarz
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