Ljungqvist & Sargent s: The European Unemployment Dilemma

Transcription

1 Ljungqvist & Sargent s: The European Unemployment Dilemma Trevor Gallen Spring, / 34

2 Introduction Fact: European welfare states had similar unemployment levels compared to U.S / 34

3 Introduction Fact: European welfare states had similar unemployment levels compared to U.S Fact: Afterward, unemployment rates diverged. 3 / 34

4 Introduction Fact: European welfare states had similar unemployment levels compared to U.S Fact: Afterward, unemployment rates diverged. Fact: Huge lag between entitlement increases and unemployment increase. 4 / 34

5 Introduction Fact: European welfare states had similar unemployment levels compared to U.S Fact: Afterward, unemployment rates diverged. Fact: Huge lag between entitlement increases and unemployment increase. Q: Can we explain the divergence with unemployment insurance/welfare? 5 / 34

6 Introduction Fact: European welfare states had similar unemployment levels compared to U.S Fact: Afterward, unemployment rates diverged. Fact: Huge lag between entitlement increases and unemployment increase. Q: Can we explain the divergence with unemployment insurance/welfare? A: Yes. The problem agents are solving is dynamic, and our model can explain changes. 6 / 34

7 The Divergence of Unemployment Rates 7 / 34

8 The Divergence of Unemployment Rates 8 / 34

9 Losing Your Job is Bad 9 / 34

10 European Replacement Rates are Generous 10 / 34

11 Some Notation A continuum of workers with geometrically distributed life spans. Balanced number of lives and deaths. Search economy: unemployed worker chooses search intensity s t. Suffers disutility c(s t ) from it. Probability π(s t ) find a job with wage offer F (w). If a job, laid off with probability λ. If alive, probability of dying α. Accumulate skills by working (transitions given by µ). When employed skills increase, unemployed they decrease. 11 / 34

12 Problem Let y t+i be the worker s after-tax income, and the rest is obvious. Worker wants to maximize: E t i=0 β i (1 α) i y t+i Let b(i ) be the unemployment compensation to a worker whose last earnings were I. If worker turns down suitable job offer of I g (I ) or more, then lose unemployment benefits. Want to write out this Bellman. 12 / 34

13 Bellman-I: Employed Worker w is wage. h is skill level, µ e, µ l, µ u is transition probability for employed, laid-off, and unemployed, respectively. 1 α is probability of living, λ is probability of losing job V (w, h) = +(1 α)β [ max {(1 τ)wh +... accept,reject (1 λ) k µ e (h, h )V (w, h ) +... λ k µ l (h, h )V b (wh, h ) ], V 0 (h) } 13 / 34

14 Bellman-I: Employed Worker V (w, h) = +(1 α)β Keep job, or don t [ max {(1 τ)wh +... accept,reject (1 λ) k µ e (h, h )V (w, h ) +... λ k µ l (h, h )V b (wh, h ) ], V 0 (h) } 14 / 34

15 Bellman-I: Employed Worker V (w, h) = +(1 α)β [ max {(1 τ)wh +... accept,reject (1 λ) k µ e (h, h )V (w, h ) +... λ k µ l (h, h )V b (wh, h ) ], V 0 (h) If not, get money, and if you live, you keep your job or lose it. Otherwise, take new job. } 15 / 34

16 Bellman-II: Unemployed Worker V b (I, h) = max { c(s) s +(1 τ)b(i ) + (1 α)β k µ u (h, h ) [ [1 π(s)] V b (I, h ) + π(s) + +(1 α)β w<i g (I )/h +λ h µ l (h, h )V b (wh, h ) [ ( w I g (I )/h V (w, h )df (w) { max (1 τ)wh accept,reject (1 λ) h µ e (h, h )V (w, h ) ], V b (I, h ) } df (w) )]} 16 / 34

17 Bellman-II: Unemployed Worker [ V b (I, h) = max { c(s) s +(1 τ)b(i ) + (1 α)β k ( [1 π(s)] V b (I, h ) + π(s) + +(1 α)β w<i g (I )/h +λ h µ l (h, h )V b (wh, h ) [ µ u (h, h ) w I g (I )/h V (w, h )df (w) { max (1 τ)wh accept,reject (1 λ) h µ e (h, h )V (w, h ) ], V b (I, h ) } df (w) )]} If unemployed, choose how much to search and pay the price / 34

18 Bellman-II: Unemployed Worker [ V b (I, h) = max { c(s) s +(1 τ)b(i ) + (1 α)β k ( [1 π(s)] V b (I, h ) + π(s) + +(1 α)β w<i g (I )/h +λ h µ l (h, h )V b (wh, h ) [ µ u (h, h ) w I g (I )/h V (w, h )df (w) { max (1 τ)wh accept,reject (1 λ) h µ e (h, h )V (w, h ) ], V b (I, h ) } df (w) )]}...get unemployment benefits, and if live, human capital decays / 34

19 Bellman-II: Unemployed Worker [ V b (I, h) = max { c(s) s +(1 τ)b(i ) + (1 α)β k ( [1 π(s)] V b (I, h ) + π(s) + +(1 α)β max w<i g (I )/h accept,reject +λ h µ l (h, h )V b (wh, h ) [ µ u (h, h ) V (w, h )df (w) w I g (I )/h { (1 τ)wh (1 λ) h µ e (h, h )V (w, h ) ], V b (I, h ) } df (w) )]} Could get no offer, or could get great offer, or could get okay offer, in which case / 34

20 Bellman-II: Unemployed Worker [ V b (I, h) = max { c(s) s +(1 τ)b(i ) + (1 α)β k ( [1 π(s)] V b (I, h ) + π(s) + +(1 α)β w<i g (I )/h +λ h µ l (h, h )V b (wh, h ) [ µ u (h, h ) w I g (I )/h V (w, h )df (w) { max (1 τ)wh accept,reject (1 λ) h µ e (h, h )V (w, h ) ], V b (I, h ) } df (w) )]} For okay offer, if we accept, get wages, if don t die, could be fired again, go on UI (new wages), or could stay. If reject keep UI 20 / 34

21 Bellman-III: unemployed with no UI V 0 (h) = max s { { [1 π(s)] V 0 (h ) + π(s) c(s) + (1 α)β h µ u (h, h ) }} V (w, h )df (w) 21 / 34

22 Bellman-III: unemployed with no UI V 0 (h) = max s { { [1 π(s)] V 0 (h ) + π(s) c(s) + (1 α)β h µ u (h, h ) }} V (w, h )df (w) If unemployed, choose how hard to search, and if live, skills decay, and may not get offer, and may get offer. 22 / 34

23 Period is 2 weeks long. β = , interest rate of 4%. Probability of dying: α = , or 42.7 years of life. Probability laid off: λ = 0.009, or 4.3 years for a job. Calibration: need skill distribution µ, β, F, α, λ, c, π(s), b(i ), I g (I ). Break up skill distribution into 21 parts from 1-2 (skilled make double unskilled). 10% chance of increasing skill if work, otherwise stay same. 20% chance of decreasing skill if no work, otherwise stay same. c(s) = 0.5s π(s) = s 0.3. F (w) N (0.5, 0.1) (truncated, normalized). 23 / 34

24 Steady States 24 / 34

25 Optimal Reservation Wages 25 / 34

26 Optimal Search Intensities 26 / 34

27 With No Benefits, Reservation Wages are Similar 27 / 34

28 Hazard Rates 28 / 34

29 Experiment What if we entered turbulent times? Suddenly fire a bunch of people (raise the fires rate) Those fired lose all skills. Then back to normal. Steady states are similar: responses to shocks are not. Prolonged unemployment in a welfare state: skills depreciate. Unemployment benefits are indexed to previous wage level. When shock comes that makes you obsolete, unemployment far more generous. 29 / 34

30 Hazard Rates 30 / 34

31 Productivity 31 / 34

32 Replicating Jacobson et al. (1993) 32 / 34

33 33 / 34

34 Criticisms Infinitely-lived UI Perfect monitoring (Pavoni 2005) No on-the-job search Firing, hiring independent of age, tenure, skill (Rothstein 2011) Homogeneity in baseline type. No utility, savings. No anticipation of firing (Gallen 2013) Rising evidence that liquidity matters (Chetty 2008). 34 / 34