Helpman, Itskhoki, Redding (2010): Inequality and Unemployment in a Global Economy

Transcription

1 Helpman, Itskhoki, Redding (2010): Inequality and Unemployment in a Global Economy Sybille Lehwald July,

2 Motivation Krugman (1980) importance of intra-industry trade no firm goes out of business no worker loses a job welfare rises for everyone Melitz (2003) importance of firm heterogeneity gains from trade liberalization because aggregate productivity rises full employment and competitive labor market all firms pay the same wages; no wage inequality among workers 2

3 Motivation Helpman, Itskhoki, Redding (2010) framework to examine the impact of trade on wage inequality and unemployment introduction of search and matching frictions on the labor market (Diamond - Mortensen - Pissaridis) into a heterogenous firm model of trade (Melitz (2003)) ex-post worker heterogeneity 3

4 Motivation Main Results more productive firms pay higher wages exporting increases the wage paid by a firm with a given productivity trade opening enhances wage inequality once the economy is open to trade, the relationship between wage inequality and trade openness is at first increasing and later decreasing trade opening can either raise or reduce unemployment 4

5 Sectoral Equilibrium The Model Consumption: [ 1 Q = q(j) dj] β β, 0 < β < 1, (1) j J Revenue: r(j) = p(j)q(j) = Aq(j) β, (2) where A is a demand shifter for the sector and taken as given. product market as in Melitz (2003) firm productivity θ is drawn from Pareto distribution G θ (θ) = 1 (θ min /θ) z, θ θ min > 0. 5

6 Sectoral Equilibrium The Model - continued Production technology: y = θh γ ā, 0 < γ < 1. (3) output of each variety (y) depends on the productivity of the firm (θ), the measure of workers hired (h), and the average ability of these workers (ā) complementarities in worker ability: the productivity of a worker is increasing in the abilities of other workers employed by the firm worker ability is independently distributed and drawn from a Pareto distribution G a(a) = 1 (a min /a) k, a a min > 0. 6

7 Sectoral Equilibrium The Model - continued Labor Market search costs: a firm that pays bn of the numeraire can randomly match with n workers (b is endogenously determined) screening costs: firms can undertake costly investments in worker screening to obtain an imprecise signal of worker ability: by paying ca δ c /δ of the numeraire a firm can identify workers with an ability below a c notice: screening costs are increasing in the ability threshold a c chosen by the firm 7

8 Sectoral Equilibrium The Model - continued Firm s Problem complementarities in production technology provide incentive for firms to screen workers y = θh γ ā, 0 < γ < 1 with a Pareto distribution of worker ability, a firm that chooses screening threshold a c hires a measure h = n(a min /a c) k of workers with average ability ā = ka c/(k 1) production technology can then be written as y = k k 1 aγk min θnγ a 1 γk c, 0 < γk < 1 (4) where 0 < γk < 1 is necessary for a firm to have an incentive to screen 8

9 Sectoral Equilibrium The Model - continued Firm s Problem firm s total revenue: r(θ) r d (θ) + r x(θ) = Υ(θ) 1 β Ay(θ) β (5) Υ(θ) captures the firm s market access 9

10 Sectoral Equilibrium The Model - continued Wage bargaining After having observed its productivity, a firm chooses whether or not to produce, whether or not to export, the measure of workers to sample, and the screening ability threshold and hence the measure of workers to hire wage bargaining with equal weights over division of revenue from production Stole-Zwiebel multilateral bargaining implies that the wage rate is a fraction of the revenue per worker fraction of the firm: 1/(1 + βγ) of revenue (5) fraction for each worker: βγ/(1 + βγ) of average revenue per worker 10

11 Sectoral Equilibrium The Model - continued Firm s problem anticipating the outcome of the bargaining game, the firm maximizes its profits π(θ) FOCs: βγ r(θ) = bn(θ) 1 + βγ (6) β(1 γk) 1 + βγ r(θ) = cac(θ)δ (7) these conditions imply that firms with larger revenue sample more workers and screen to a higher ability threshold under certain assumptions, the measure of workers hired h is increasing in the measure of workers sampled. 11

12 Sectoral Equilibrium The Model - continued Firm s problem wages are given by: w(θ) = βγ r(θ) 1 + βγ h(θ) = b n(θ) [ ] k ac(θ) h(θ) = b (8) a min firms with larger revenue have higher screening ability cutoffs and pay higher wages notice, the expected wage conditional on being sampled is the same across all firms w(θ)h(θ) n(θ) = b risk-neutral workers are indifferent between being matched with a high- or a low-productivity firm, because conditional on being matched, the expected wage is the same in all firms workers have no incentive to direct their search 12

13 Sectoral Equilibrium The Model - continued Solve for 1. labor market tightness x 2. search costs b 3. cutoff-levels ϕ, ϕ, ϕ x, ϕ x 4. sectoral demand shifters A, A and in equilibrium 5. price index 6. consumption index 7. mass of firms 8. size of labor force 13

14 Firm-Specific Variables r(θ) = Υ(θ) (1 β)/γ r d ( θ θ d ) β/γ (9) h(θ) = Υ(θ) (1 β)(1 k/δ)/γ h d ( θ θ d ) β(1 k/δ)/γ (10) w(θ) = Υ(θ) k(1 β)/(δγ) w d ( θ θ d ) βk/(δγ) (11) 14

15 Firm-Specific Variables r(θ) = Υ(θ) (1 β)/γ r d ( θ θ d ) β/γ (9) h(θ) = Υ(θ) (1 β)(1 k/δ)/γ h d ( θ θ d ) β(1 k/δ)/γ (10) w(θ) = Υ(θ) k(1 β)/(δγ) w d ( θ θ d ) βk/(δγ) (11) more productive firms not only have higher revenue, and employment, but also pay higher wages 14

16 Firm-Specific Variables r(θ) = Υ(θ) (1 β)/γ r d ( θ θ d ) β/γ (9) h(θ) = Υ(θ) (1 β)(1 k/δ)/γ h d ( θ θ d ) β(1 k/δ)/γ (10) w(θ) = Υ(θ) k(1 β)/(δγ) w d ( θ θ d ) βk/(δγ) (11) more productive firms not only have higher revenue, and employment, but also pay higher wages more productive firms have workforces of higher average ability, which are more costly to replace in bargaining game, and therefore they pay higher wages 14

17 Firm-Specific Variables r(θ) = Υ(θ) (1 β)/γ r d ( θ θ d ) β/γ (9) h(θ) = Υ(θ) (1 β)(1 k/δ)/γ h d ( θ θ d ) β(1 k/δ)/γ (10) w(θ) = Υ(θ) k(1 β)/(δγ) w d ( θ θ d ) βk/(δγ) (11) more productive firms not only have higher revenue, and employment, but also pay higher wages more productive firms have workforces of higher average ability, which are more costly to replace in bargaining game, and therefore they pay higher wages the reason more productive firms have workforces of higher average ability is that they screen more intensively 14

18 Sectoral Wage Inequality 15

19 Sectoral Wage Inequality ex ante: workers are identical and have the same expected income ex post: wage inequality because workers receive different wages depending on the employer with whom they are matched 15

20 Sectoral Wage Inequality ex ante: workers are identical and have the same expected income ex post: wage inequality because workers receive different wages depending on the employer with whom they are matched Closed Economy sectoral wage distribution is an untruncated Pareto distribution with lower limit w d and shape parameter 1 + 1/µ: G w,d (w) = 1 ( wd ) 1+1/µ βk/δ, µ = w zγ β shape parameter is sufficient statistic for wage inequality 15

21 Sectoral Wage Inequality Closed Economy Proposition In the closed economy, inequality in the sectoral distribution of wages is increasing in firm productivity dispersion (lower z) and increasing in worker ability dispersion (lower k) iff z 1 + δ 1 γ > β 1. While greater firm productivity dispersion is one potential source of increased wage inequality, another potential source is international trade. 16

22 Sectoral Wage Inequality Open Economy in the open economy, wage distribution is a mix of Truncated Pareto (1 + 1/µ) (non-exporting firms) Pareto (1 + 1/µ) (exporting firms) Two limiting cases: trade costs are sufficiently high: no firm exports trade costs are sufficiently low: all firms export the open economy wage distribution is an untruncated Pareto distribution with shape parameter 1 + 1/µ. the same level of wage inequality as in the closed economy. 17

23 Sectoral Wage Inequality Open Economy Only some firms export: It is shown that sectoral wage inequality is strictly greater than in the closed economy Intuition: some but not all workers are employed by exporters who pay higher wages 18

24 Theil Index, T w μ ln(1+μ) Trade Openness, ρ=θ d /θ x FIGURE 3. Trade openness and sectoral wage inequality. 19

25 Sectoral Wage Inequality Open Economy since wage inequality when all firms export is the same as in the closed economy, but sectoral wage inequality when only some firms export is higher than in the closed economy, the relationship between sectoral wage inequality and the fraction of exporters is at first increasing and later decreasing important implication: the initial level of trade openness is a relevant control for empirical studies examining the relationship between wage inequality and trade. 20

26 Sectoral Unemployment sectoral unemployment rate: u = 1 σx where σ is the hiring rate and x is the labor market tightness opening to trade affects sectoral unemployment rate through different channels Overall, the opening of the closed economy to trade has an ambiguous overall effect on the sectoral unemployment rate and depends on general equilibrium effects. 21

27 Sectoral Distribution of Income depends on both the sectoral distribution of wages and the unemployment rate As the opening of trade raises wage inequality and has ambiguous effect on unemployment, income and wage inequality can move in opposite directions 22