Trade and Labor Market: Felbermayr, Prat, Schmerer (2011) Davide Suverato 1 1 LMU University of Munich Topics in International Trade, 16 June 2015 Davide Suverato, LMU Trade and Labor Market: Felbermayr, Prat, Schmerer (2011) 1 / 26
Trade with labor market imperfections because of labor market imperfections, lower number of jobs than under perfect labor market: labor demand < labor supply = unemployment every match yields a strictly positive surplus: the wage is a splitting device for the surplus of a match. Davide Suverato, LMU Trade and Labor Market: Felbermayr, Prat, Schmerer (2011) 2 / 26
Trade with labor market imperfections let search and matching frictions be the cause of labor market imperfections search frictions: firms do not hold an infinite number of vacancies because it is costly workers do not have perfect knowledge of all the vacancies in the market matching frictions: probability that a worker finds a job < 1 probability that a vacancy is visited by a worker < 1 every period a match is destroyed with a probability > 0 Davide Suverato, LMU Trade and Labor Market: Felbermayr, Prat, Schmerer (2011) 3 / 26
Trade with labor market imperfections Davidson Martin Matusz (1999), differences in labor market frictions between sectors determine the relative price P X P Y = 2 (ρ + b X ) + 1 2 (ρ + b Y ) + 1 determine the relationship between job finding probability and unemployment / employment ratio at the sector level e l X L sx = b X L ex, e k X K sx = b X K ex e l Y L sy = b Y L ey, e k Y K sy = b Y K ey Davide Suverato, LMU Trade and Labor Market: Felbermayr, Prat, Schmerer (2011) 4 / 26
Trade with labor market imperfections Therefore, differences in labor market frictions between sectors are a source of comparative advantage Assume that b X < b X and b Y = b Y then P X P Y > P X P Y, the domestic economy specializes in the production and export of good X. determine differences in sectoral unemployment Assume that b X > b Y then, sector X is characterized by higher unemployment µ X > µ Y. Davide Suverato, LMU Trade and Labor Market: Felbermayr, Prat, Schmerer (2011) 5 / 26
Trade with labor market imperfections An increase of trade openness determines a loss of jobs, when the domestic economy specializes in the sector that is characterized by relatively higher unemployment. the pattern of specialization depends on across country comparisons of country specific and sector specific labor market frictions which is the sector with relatively higher unemployment depends on comparisons of sector specific labor market frictions within the domestic economy only! Notice: there exists an equilibrium in which the increase in trade openness does not change the job finding probability. Davide Suverato, LMU Trade and Labor Market: Felbermayr, Prat, Schmerer (2011) 6 / 26
Trade with labor market imperfections There is more to say about the effect of trade on the probability of finding a job; in Davidson et al. (1999) it is a function of: domestic relative factor endowment L/K terms of trade P (1 T ) frictions in the domestic labor market {b X, b Y } Felbermayr, Prat, Schmerer (2011) introduce search generated unemployment into a 1 sector Melitz s trade model. Helpman, Itskhoki (2010) introduce search generated unemployment into a 2 sector trade model, with Melitz s monopolistic competition in the tradable sector. They show the relationship between average productivity and probability of finding a job. Davide Suverato, LMU Trade and Labor Market: Felbermayr, Prat, Schmerer (2011) 7 / 26
Felbermayr, Prat, Schmerer (2011) 1 sector = changes in unemployment cannot arise from reallocation of the workforce across sectors, but across firms! C.E.S. love for variety + monopolistic competition + endogenous entry + fixed cost of export = trade induces selection of less productive firms out of the market, which increases sector average productivity labor market frictions + Nash bargaining = wage and job finding probability will be a function of the sector average productivity. Davide Suverato, LMU Trade and Labor Market: Felbermayr, Prat, Schmerer (2011) 8 / 26
Framework 1 sector consists of producers with horizontally differentiated varieties 1 type of agent: workers with one indivisible unit of labor each workers can be employed or unemployed if unemployed, they search for a job. search & matching frictions, wage set through Nash bargaining monopolistic competition with fixed costs that induce increasing returns to scale ex ante investment leads to endogenous entry fixed costs of export induce selection into the export market Davide Suverato, LMU Trade and Labor Market: Felbermayr, Prat, Schmerer (2011) 9 / 26
Preferences, demand and production Consumers value consumption of the aggregate good Y = [ ] σ M 1 σ q (ω) σ 1 σ 1 σ dω ω Ω, σ > 1 let the price of the aggregate good being the numeraire, then Consumers demand q (ω) = Y M p (ω) σ Production, under market clearing q (ω) = ϕ (ω) l (ω) Davide Suverato, LMU Trade and Labor Market: Felbermayr, Prat, Schmerer (2011) 10 / 26
Firm behavior each firm optimally decides to be a monopolist ϕ ω marginal revenue ( in the domestic ) market mr D (ϕ) = 1 p(ϕ) q(ϕ) p D (ϕ) q(ϕ) p(ϕ) marginal revenue ( in the (symmetric) ) export market mr X (ϕ) = 1 p(ϕ) q(ϕ) pd (ϕ) τ for τ > 1. q(ϕ) p(ϕ) segmented markets = it is optimal mr D (ϕ) = mr X (ϕ) p X (ϕ) = τp D (ϕ) q X (ϕ) = τ σ q D (ϕ) Davide Suverato, LMU Trade and Labor Market: Felbermayr, Prat, Schmerer (2011) 11 / 26
Revenue revenue from the domestic market r D (ϕ) = Y M p (ϕ)1 σ revenue from the export market r X (ϕ) = τ 1 σ r D (ϕ) total revenue r (ϕ) = [ 1 + e (ϕ) τ 1 σ] r D (ϕ) where e (ϕ) = 1 if and only if the firm exports. inverse demand: p (ϕ) 1 σ = ( ) 1 σ Y σ M q D (ϕ) σ 1 σ clearing: ϕl (ϕ) = q D (ϕ) + τq X (ϕ) = ( 1 + e (ϕ) τ 1 σ) q D (ϕ) revenue is an increasing, concave, log linear function of employment r (ϕ, l (ϕ)) = [ Y ( 1 + e (ϕ) τ 1 σ )] 1 σ σ 1 (ϕl (ϕ)) σ (1) M Davide Suverato, LMU Trade and Labor Market: Felbermayr, Prat, Schmerer (2011) 12 / 26
Search and matching frictions there are u unemployed workers and v vacancies, define θ = v u the labor market tightness the probability that a firm matches with a worker is decreasing in l.m.t. m (θ), m < 0 the probability that a worker matches with a firm is θm (θ) increasing in l.m.t. holding a vacancy has a cost c > 0 Davide Suverato, LMU Trade and Labor Market: Felbermayr, Prat, Schmerer (2011) 13 / 26
Law of motion for employment firms and workers separate with probability s = δ + χ δχ, that is because of: a firm destruction shock that occurs with probability δ a job destruction shock that occurs with probability χ the next period employment l for a for a firm that employs l workers and holds ϑ vacancies is : l = (1 χ) l + m (θ) ϑ (2) assuming a continuous measure of employees and vacancies. Davide Suverato, LMU Trade and Labor Market: Felbermayr, Prat, Schmerer (2011) 14 / 26
Firm inter temporal problem define the firm profit: π (ϕ, l) = r (ϕ, l) w (ϕ, l) l cϑ (ϕ, l) f D e (ϕ) f x Firms are risk neutral, so they choose the number of vacancies that maximizes the expected discounted lifetime flow of profit: Π (ϕ, l) = max ϑ>0 subject to: the revenue (1) the law of motion for employment (2). 1 { ( π (ϕ, l) + (1 δ) Π ϕ, l )} (3) 1 + r Davide Suverato, LMU Trade and Labor Market: Felbermayr, Prat, Schmerer (2011) 15 / 26
Inter temporal optimality, firm define the value of the marginal job: J (ϕ, l) = Π(ϕ,l) l compute the f.o.c. for the optimality of vacancy posting: c = (1 δ) m (θ) J ( ϕ, l ) (4) A firm will hold vacancies up to the point in which the expected value of hiring the marginal worker is equal to the cost of posting the marginal vacancy. Linear cost = firms can always adjust at the steady state employment l l, therefore: ϑ = χ m (θ) l (5) Davide Suverato, LMU Trade and Labor Market: Felbermayr, Prat, Schmerer (2011) 16 / 26
Inter temporal optimality, firm Solve for the value of a job from the inter temporal problem (3), when posting is optimal c = (1 δ) m (θ) J (ϕ, l ) (1 + r) J (ϕ, l) = r l w l l w c ϑ + c l l m (θ) l where vacancies are optimally chosen ϑ = employment is in steady state l = l J (ϕ, l) = 1 [ r 1 + r l χ m(θ) l such that w (1 χ) c l w + l m (θ) ] (6) Davide Suverato, LMU Trade and Labor Market: Felbermayr, Prat, Schmerer (2011) 17 / 26
Inter temporal optimality, worker Worker are risk neutral, so they search for a job to maximize the expected discounted lifetime flow of income: value of being employed (and working) re (ϕ, l) = w (ϕ, l) + s [ U E ( ϕ, l )] value of being unemployed (and searching) steady state l l ru = b w + θm (θ) [ E ( ϕ, l ) U ] E (ϕ, l) U = w (ϕ, l) ru r + s (7) Davide Suverato, LMU Trade and Labor Market: Felbermayr, Prat, Schmerer (2011) 18 / 26
Wage determination within the period, the wage is the outcome of a Nash bargaining, in which the firm bargains with every worker on how to split the surplus of the marginal job: βj (ϕ, l) = (1 β) [E (ϕ, l) U] which together with the worker s surplus (7) yields (r + s) J (ϕ, l) = 1 β β (w (ϕ, l) ru) (8) Davide Suverato, LMU Trade and Labor Market: Felbermayr, Prat, Schmerer (2011) 19 / 26
Wage equation The system of value of a job (6) and optimality in vacancy posting (4) yields the job creation condition, [ ] r (ϕ, l) w (ϕ, l) (r + s) J (ϕ, l) = l w (ϕ, l) (9) l l which in conjunction with the bargaining equation (8) yields the wage equation: ( ) r (ϕ, l) w (ϕ, l) w (ϕ, l) = β l + (1 β) ru (10) l l Davide Suverato, LMU Trade and Labor Market: Felbermayr, Prat, Schmerer (2011) 20 / 26
One wage! The wage equation (10) is an( O.D.E. ) in w (l) with a particular solution w = (1 β) ru + β σ r σ β l, which I refer to as ( ). Solving for the revenue (1), allows [ to ( compute ) ] the monopsony component of wages w l l = 1 σ β σ r σ β l < 0. Inserting this result in the job creation ( ) condition ( (9), ) where c J (ϕ, l) = (1 δ)m(θ) yields w = σ r σ β l r+s c 1 δ m(θ), which I refer to as ( ). The system with the solution of the wage equation ( ) yields: w (ϕ, l) = ru + ( β 1 β ) ( r + s 1 δ ) c m (θ) ϕ, l (11) Davide Suverato, LMU Trade and Labor Market: Felbermayr, Prat, Schmerer (2011) 21 / 26
The Wage curve Since there is one wage, w w, which allows to solve for the outside option of the unemployed ru = bw + β cθ 1 β 1 δ. Inserting this result in the (11) yields the first equilibrium condition the Wage Curve: w = β [ ] c r + s 1 β (1 b) (1 δ) m (θ) + θ (12) The wage curve describes an increasing and convex relationship between wage and labor market tightness. Davide Suverato, LMU Trade and Labor Market: Felbermayr, Prat, Schmerer (2011) 22 / 26
The Labor Demand curve Look at ( ), and use the definition of marginal revenue to substitute for r l = ( ) σ 1 σ p (ϕ) ϕ. As in Melitz (2003) define ϕ the productivity of the firm with average revenue. Then p ( ϕ) coincides with the C.E.S. consumption based price index of the aggregate good, which is the numeraire, so p ( ϕ) = 1. This allows to write the wage ( ) as ( ) σ w = ϕ σ β ( r + s 1 δ ) c m (θ) (13) an increasing function of the measure of average productivity ϕ, and a decreasing function of labor market tightness θ. Davide Suverato, LMU Trade and Labor Market: Felbermayr, Prat, Schmerer (2011) 23 / 26
Equilibrium Davide Suverato, LMU Trade and Labor Market: Felbermayr, Prat, Schmerer (2011) 24 / 26
The effect of trade on the average wage Notice that from now on the solution of the model follows Melitz (2003). A trade liberalization, τ or f X, that determines an increase in the average productivity will lead to: higher wage w, both in nominal and in real terms. higher labor market tightness θ Davide Suverato, LMU Trade and Labor Market: Felbermayr, Prat, Schmerer (2011) 25 / 26
The effect of trade on unemployment The job finding probability is increasing in labor market tightness θm (θ) The steady state unemployment rate has to satisfy the Beveridge curve. Let 1 u be the number of workers unemployed, then s (1 u) = θm (θ) u implies: u = s s + θm (θ) A trade liberalization, τ or f X, that determines an increase in the average productivity leads to a lower unemployment. (14) Davide Suverato, LMU Trade and Labor Market: Felbermayr, Prat, Schmerer (2011) 26 / 26