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Optimal Unemployment Insurance over the Business Cycle Camille Landais, Pascal Michaillat, Emmanuel Saez SIEPR, LSE, UC Berkeley August 2011 Landais, Michaillat, and Saez (08/2011) Optimal Unemployment Insurance 1 / 42 Literature on

  1. Government’s Problem Choose c e , c u to maximize n · v ( c e ) + (1 − n ) · v ( c u ) − u · k ( e ) subject to: ∆ v = v ( c e ) − v ( c u ) budget: n · c e + (1 − n ) · c u = n · w labor market dynamics: n = (1 − u ) + u · e · f ( θ ) optimal job search: e = e ( θ, ∆ v ) labor market clearing: n d ( θ ) = n s ( e ( θ, ∆ v ) , θ ) Landais, Michaillat, and Saez (08/2011) Optimal Unemployment Insurance 14 / 42

  2. Government’s Problem Choose c e , c u to maximize n · v ( c e ) + (1 − n ) · v ( c u ) − u · k ( e ) subject to: ∆ v = v ( c e ) − v ( c u ) budget: n · c e + (1 − n ) · c u = n · w labor market dynamics: n = (1 − u ) + u · e · f ( θ ) optimal job search: e = e ( θ, ∆ v ) labor market clearing: n d ( θ ) = n s ( e ( θ, ∆ v ) , θ ) Landais, Michaillat, and Saez (08/2011) Optimal Unemployment Insurance 14 / 42

  3. Government’s Problem Choose c e , c u to maximize n · v ( c e ) + (1 − n ) · v ( c u ) − u · k ( e ) subject to: ∆ v = v ( c e ) − v ( c u ) budget: n · c e + (1 − n ) · c u = n · w labor market dynamics: n = (1 − u ) + u · e · f ( θ ) optimal job search: e = e ( θ, ∆ v ) labor market clearing: n d ( θ ) = n s ( e ( θ, ∆ v ) , θ ) Landais, Michaillat, and Saez (08/2011) Optimal Unemployment Insurance 14 / 42

  4. Government’s Problem Choose c e , c u to maximize n · v ( c e ) + (1 − n ) · v ( c u ) − u · k ( e ) subject to: ∆ v = v ( c e ) − v ( c u ) budget: n · c e + (1 − n ) · c u = n · w labor market dynamics: n = (1 − u ) + u · e · f ( θ ) optimal job search: e = e ( θ, ∆ v ) labor market clearing: n d ( θ ) = n s ( e ( θ, ∆ v ) , θ ) Landais, Michaillat, and Saez (08/2011) Optimal Unemployment Insurance 14 / 42

  5. Micro-Elasticity ǫ m � � 1 − n · ∂ n s ∆ c · ∂ e ǫ m ≡ � � � � ∂ e ∂ ∆ c � � θ θ Response of individual job-search effort Elasticity used in the literature [Baily, ’78] Interpretation: increase in probability of unemployment when individual UI increases Landais, Michaillat, and Saez (08/2011) Optimal Unemployment Insurance 15 / 42

  6. Macro-Elasticity ǫ M 1 − n · dn ∆ c ǫ M ≡ d ∆ c Response of aggregate unemployment Interpretation: increase in aggregate unemployment when aggregate UI increases Macro-elasticity = micro-elasticity + unemployment change due to equilibrium adjustment of θ � ∂ n s � � ǫ M = ǫ m + ∆ c 1 − n · 1 + κ · d θ � · � κ ∂θ d ∆ c � e Landais, Michaillat, and Saez (08/2011) Optimal Unemployment Insurance 16 / 42

  7. Macro-Elasticity ǫ M 1 − n · dn ∆ c ǫ M ≡ d ∆ c Response of aggregate unemployment Interpretation: increase in aggregate unemployment when aggregate UI increases Macro-elasticity = micro-elasticity + unemployment change due to equilibrium adjustment of θ � ∂ n s � � ǫ M = ǫ m + ∆ c 1 − n · 1 + κ · d θ � · � κ ∂θ d ∆ c � e Landais, Michaillat, and Saez (08/2011) Optimal Unemployment Insurance 16 / 42

  8. Macro-Elasticity ǫ M 1 − n · dn ∆ c ǫ M ≡ d ∆ c Response of aggregate unemployment Interpretation: increase in aggregate unemployment when aggregate UI increases Macro-elasticity = micro-elasticity + unemployment change due to equilibrium adjustment of θ � ∂ n s � � ǫ M = ǫ m + ∆ c 1 − n · 1 + κ · d θ � · � κ ∂θ d ∆ c � e Landais, Michaillat, and Saez (08/2011) Optimal Unemployment Insurance 16 / 42

  9. Macro-Elasticity ǫ M 1 − n · dn ∆ c ǫ M ≡ d ∆ c Response of aggregate unemployment Interpretation: increase in aggregate unemployment when aggregate UI increases Macro-elasticity = micro-elasticity + unemployment change due to equilibrium adjustment of θ � ∂ n s � � ǫ M = ǫ m + ∆ c 1 − n · 1 + κ · d θ � · � κ ∂θ d ∆ c � e Landais, Michaillat, and Saez (08/2011) Optimal Unemployment Insurance 16 / 42

  10. Exact Optimal UI Formula � � − 1 n + (1 − n ) · v ′ ( c u ) 1 τ n · 1 − τ = v ′ ( c e ) � n � v ′ ( c u ) � � ǫ m �� ∆ v κ · ǫ M · v ′ ( c e ) − 1 + v ′ ( c e ) · ∆ c · κ + 1 · ǫ M − 1 Landais, Michaillat, and Saez (08/2011) Optimal Unemployment Insurance 17 / 42

  11. Optimal UI Formula in Sufficient Statistics � ǫ m � 1 − τ ≈ ρ τ κ � 1 + ρ � ǫ M · (1 − τ )+ 1 + κ · ǫ M − 1 · 2 · (1 − τ ) τ : replacement rate c u / c e ρ : coefficient of relative risk aversion κ : elasticity of marginal disutility of effort ǫ M : macro-elasticity of unemployment ǫ m : micro-elasticity of unemployment Landais, Michaillat, and Saez (08/2011) Optimal Unemployment Insurance 18 / 42

  12. Building on the Baily [’78] Formula 1 − τ ≈ ρ τ ǫ m (1 − τ ) Public economics: Baily [’78], Chetty [’06] Government budget constraint in general equilibrium Correction for equilibrium adjustment of θ , with first-order welfare effect: � ∂ n s � � ǫ m − ǫ M � · d θ ∝ � ∂θ � e Landais, Michaillat, and Saez (08/2011) Optimal Unemployment Insurance 19 / 42

  13. Building on the Baily [’78] Formula 1 − τ ≈ ρ τ ǫ M (1 − τ ) Public economics: Baily [’78], Chetty [’06] Government budget constraint in general equilibrium Correction for equilibrium adjustment of θ , with first-order welfare effect: � ∂ n s � � ǫ m − ǫ M � · d θ ∝ � ∂θ � e Landais, Michaillat, and Saez (08/2011) Optimal Unemployment Insurance 19 / 42

  14. Building on the Baily [’78] Formula � ǫ m � � � 1 − τ ≈ ρ τ κ 1 + ρ ǫ M (1 − τ ) + ǫ M − 1 2(1 − τ ) 1 + κ Public economics: Baily [’78], Chetty [’06] Government budget constraint in general equilibrium Correction for equilibrium adjustment of θ , with first-order welfare effect: � ∂ n s � ǫ m − ǫ M � � · d θ ∝ � ∂θ � e Landais, Michaillat, and Saez (08/2011) Optimal Unemployment Insurance 19 / 42

  15. 1 Optimal UI Formula: τ = τ ( ǫ m , ǫ M , risk aversion) 2 Optimal UI over the Business Cycle 3 Extension to an Infinite-Horizon Model Landais, Michaillat, and Saez (08/2011) Optimal Unemployment Insurance 20 / 42

  16. A Model of Recessions and Job Rationing Given ( θ, a ), firm chooses n ≥ 1 − u to maximize r · a a · n α − ω · a γ · n − · [ n − (1 − u )] q ( θ ) � �� � � �� � wage production ���� hiring cost Profit-maximizing employment n d ( θ, a ): r α · n α − 1 = ω · a γ − 1 + q ( θ ) Wage rigidity: γ < 1 Diminishing marginal returns to labor: α < 1 Landais, Michaillat, and Saez (08/2011) Optimal Unemployment Insurance 21 / 42

  17. A Model of Recessions and Job Rationing Given ( θ, a ), firm chooses n ≥ 1 − u to maximize r · a a · n α − ω · a γ · n − · [ n − (1 − u )] q ( θ ) � �� � � �� � wage production ���� hiring cost Profit-maximizing employment n d ( θ, a ): r α · n α − 1 = ω · a γ − 1 + q ( θ ) Wage rigidity: γ < 1 Diminishing marginal returns to labor: α < 1 Landais, Michaillat, and Saez (08/2011) Optimal Unemployment Insurance 21 / 42

  18. A Model of Recessions and Job Rationing Given ( θ, a ), firm chooses n ≥ 1 − u to maximize r · a a · n α − ω · a γ · n − · [ n − (1 − u )] q ( θ ) � �� � � �� � wage production ���� hiring cost Profit-maximizing employment n d ( θ, a ): r α · n α − 1 = ω · a γ − 1 + q ( θ ) Wage rigidity: γ < 1 Diminishing marginal returns to labor: α < 1 Landais, Michaillat, and Saez (08/2011) Optimal Unemployment Insurance 21 / 42

  19. A Model of Recessions and Job Rationing Given ( θ, a ), firm chooses n ≥ 1 − u to maximize r · a a · n α − ω · a γ · n − · [ n − (1 − u )] q ( θ ) � �� � � �� � wage production ���� hiring cost Profit-maximizing employment n d ( θ, a ): r α · n α − 1 = ω · a γ − 1 + q ( θ ) Wage rigidity: γ < 1 Diminishing marginal returns to labor: α < 1 Landais, Michaillat, and Saez (08/2011) Optimal Unemployment Insurance 21 / 42

  20. A Model of Recessions and Job Rationing Given ( θ, a ), firm chooses n ≥ 1 − u to maximize r · a a · n α − ω · a γ · n − · [ n − (1 − u )] q ( θ ) � �� � � �� � wage production ���� hiring cost Profit-maximizing employment n d ( θ, a ): r α · n α − 1 = ω · a γ − 1 + q ( θ ) Wage rigidity: γ < 1 Diminishing marginal returns to labor: α < 1 Landais, Michaillat, and Saez (08/2011) Optimal Unemployment Insurance 21 / 42

  21. A Model of Recessions and Job Rationing Given ( θ, a ), firm chooses n ≥ 1 − u to maximize r · a a · n α − ω · a γ · n − · [ n − (1 − u )] q ( θ ) � �� � � �� � wage production ���� hiring cost Profit-maximizing employment n d ( θ, a ): r α · n α − 1 = ω · a γ − 1 + q ( θ ) Wage rigidity: γ < 1 Diminishing marginal returns to labor: α < 1 Landais, Michaillat, and Saez (08/2011) Optimal Unemployment Insurance 21 / 42

  22. A Model of Recessions and Job Rationing Given ( θ, a ), firm chooses n ≥ 1 − u to maximize r · a a · n α − ω · a γ · n − · [ n − (1 − u )] q ( θ ) � �� � � �� � wage production ���� hiring cost Profit-maximizing employment n d ( θ, a ): r α · n α − 1 = ω · a γ − 1 + q ( θ ) Wage rigidity: γ < 1 Diminishing marginal returns to labor: α < 1 Landais, Michaillat, and Saez (08/2011) Optimal Unemployment Insurance 21 / 42

  23. Labor Demand over the Business Cycle 2 Labor demand (boom) Labor market tightness θ 1.5 1 0.5 0 0.9 0.95 1 Employment n Landais, Michaillat, and Saez (08/2011) Optimal Unemployment Insurance 22 / 42

  24. Labor Demand over the Business Cycle 2 Labor demand (boom) Labor demand (recession) Labor market tightness θ 1.5 1 0.5 0 0.9 0.95 1 Employment n Landais, Michaillat, and Saez (08/2011) Optimal Unemployment Insurance 22 / 42

  25. Baily [’78] Partial-Equilibrium Model 2 Labor supply (high UI) Labor market tightness θ 1.5 fixed θ 1 0.5 0 0.9 0.95 1 Employment n Landais, Michaillat, and Saez (08/2011) Optimal Unemployment Insurance 23 / 42

  26. Baily [’78] Partial-Equilibrium Model 2 Labor supply (high UI) Labor supply (low UI) Labor market tightness θ 1.5 fixed θ 1 0.5 0 0.9 0.95 1 Employment n Landais, Michaillat, and Saez (08/2011) Optimal Unemployment Insurance 23 / 42

  27. Baily [’78] Partial-Equilibrium Model 2 Labor supply (high UI) Labor supply (low UI) Labor market tightness θ 1.5 1 ε m 0.5 0 0.9 0.95 1 Employment n Landais, Michaillat, and Saez (08/2011) Optimal Unemployment Insurance 23 / 42

  28. Our General-Equilibrium Model 2 Labor supply (high UI) Labor demand (boom) Labor market tightness θ 1.5 1 Equilibrium ( θ , n) 0.5 0 0.9 0.95 1 Employment n Landais, Michaillat, and Saez (08/2011) Optimal Unemployment Insurance 23 / 42

  29. Our General-Equilibrium Model 2 Labor supply (high UI) Labor supply (low UI) Labor market tightness θ Labor demand (boom) 1.5 New equilibrium ( θ ’ , n’) 1 0.5 0 0.9 0.95 1 Employment n Landais, Michaillat, and Saez (08/2011) Optimal Unemployment Insurance 23 / 42

  30. Our General-Equilibrium Model 2 Labor supply (high UI) Labor supply (low UI) Labor market tightness θ Labor demand (boom) 1.5 1 ε m 0.5 0 0.9 0.95 1 Employment n Landais, Michaillat, and Saez (08/2011) Optimal Unemployment Insurance 23 / 42

  31. Our General-Equilibrium Model 2 Labor supply (high UI) Labor supply (low UI) Labor market tightness θ Labor demand (boom) 1.5 1 ε M 0.5 0 0.9 0.95 1 Employment n Landais, Michaillat, and Saez (08/2011) Optimal Unemployment Insurance 23 / 42

  32. Our General-Equilibrium Model 2 Labor supply (high UI) Labor supply (low UI) Labor market tightness θ Labor demand (boom) 1.5 1 0.5 ε m − ε M 0 0.9 0.95 1 Employment n Landais, Michaillat, and Saez (08/2011) Optimal Unemployment Insurance 23 / 42

  33. Micro-Elasticity ǫ m > Macro-Elasticity ǫ M Positive wedge between ǫ m and ǫ M : ǫ m > ǫ M Estimable statistic: ∝ ∆ c θ · d θ ǫ m − ǫ M � � d ∆ c Testable implication: ◮ model with Nash bargaining [Pissarides, ’00]: ǫ m < ǫ M ◮ model with rigid wages [Hall, ’05]: ǫ m = ǫ M Landais, Michaillat, and Saez (08/2011) Optimal Unemployment Insurance 24 / 42

  34. Micro-Elasticity ǫ m > Macro-Elasticity ǫ M Positive wedge between ǫ m and ǫ M : ǫ m > ǫ M Estimable statistic: ∝ ∆ c θ · d θ ǫ m − ǫ M � � d ∆ c Testable implication: ◮ model with Nash bargaining [Pissarides, ’00]: ǫ m < ǫ M ◮ model with rigid wages [Hall, ’05]: ǫ m = ǫ M Landais, Michaillat, and Saez (08/2011) Optimal Unemployment Insurance 24 / 42

  35. Micro-Elasticity ǫ m > Macro-Elasticity ǫ M Positive wedge between ǫ m and ǫ M : ǫ m > ǫ M Estimable statistic: ∝ ∆ c θ · d θ ǫ m − ǫ M � � d ∆ c Testable implication: ◮ model with Nash bargaining [Pissarides, ’00]: ǫ m < ǫ M ◮ model with rigid wages [Hall, ’05]: ǫ m = ǫ M Landais, Michaillat, and Saez (08/2011) Optimal Unemployment Insurance 24 / 42

  36. Micro-Elasticity ǫ m > Macro-Elasticity ǫ M Positive wedge between ǫ m and ǫ M : ǫ m > ǫ M Estimable statistic: ∝ ∆ c θ · d θ ǫ m − ǫ M � � d ∆ c Testable implication: ◮ model with Nash bargaining [Pissarides, ’00]: ǫ m < ǫ M ◮ model with rigid wages [Hall, ’05]: ǫ m = ǫ M Landais, Michaillat, and Saez (08/2011) Optimal Unemployment Insurance 24 / 42

  37. Effect of Lower UI in Expansion 2 Labor supply (high UI) Labor supply (low UI) Labor market tightness θ Labor demand (boom) 1.5 1 ε m 0.5 0 0.9 0.95 1 Employment n Landais, Michaillat, and Saez (08/2011) Optimal Unemployment Insurance 25 / 42

  38. Effect of Lower UI in Expansion 2 Labor supply (high UI) Labor supply (low UI) Labor market tightness θ Labor demand (boom) 1.5 1 ε M 0.5 0 0.9 0.95 1 Employment n Landais, Michaillat, and Saez (08/2011) Optimal Unemployment Insurance 25 / 42

  39. Effect of Lower UI in Expansion 2 Labor supply (high UI) Labor supply (low UI) Labor market tightness θ Labor demand (boom) 1.5 1 0.5 ε m − ε M 0 0.9 0.95 1 Employment n Landais, Michaillat, and Saez (08/2011) Optimal Unemployment Insurance 25 / 42

  40. Effect of Lower UI in Recession 2 Labor supply (high UI) Labor supply (low UI) Labor market tightness θ 1.5 1 0.5 0 0.9 0.95 1 Employment n Landais, Michaillat, and Saez (08/2011) Optimal Unemployment Insurance 25 / 42

  41. Effect of Lower UI in Recession 2 Labor supply (high UI) Labor supply (low UI) Labor market tightness θ Labor demand (recession) 1.5 1 0.5 0 0.9 0.95 1 Employment n Landais, Michaillat, and Saez (08/2011) Optimal Unemployment Insurance 25 / 42

  42. Effect of Lower UI in Recession 2 Labor supply (high UI) Labor supply (low UI) Labor market tightness θ Labor demand (recession) 1.5 1 ε m 0.5 0 0.9 0.95 1 Employment n Landais, Michaillat, and Saez (08/2011) Optimal Unemployment Insurance 25 / 42

  43. Effect of Lower UI in Recession 2 Labor supply (high UI) Labor supply (low UI) Labor market tightness θ Labor demand (recession) 1.5 1 ε M 0.5 0 0.9 0.95 1 Employment n Landais, Michaillat, and Saez (08/2011) Optimal Unemployment Insurance 25 / 42

  44. Effect of Lower UI in Recession 2 Labor supply (high UI) Labor supply (low UI) Labor market tightness θ Labor demand (recession) 1.5 1 ε m − ε M 0.5 0 0.9 0.95 1 Employment n Landais, Michaillat, and Saez (08/2011) Optimal Unemployment Insurance 25 / 42

  45. Cyclicality of Elasticities Assume: isoelastic utility functions, Cobb-Douglas matching function Wedge ǫ m /ǫ M > 1 is countercyclical : � ǫ m /ǫ M � � ∂ � < 0 � ∂ a � τ Macro-elasticity ǫ M is procyclical: � ∂ǫ M � > 0 � ∂ a � τ Landais, Michaillat, and Saez (08/2011) Optimal Unemployment Insurance 26 / 42

  46. Intuition for Optimal UI in Recession � ǫ m � � � 1 − τ ≈ ρ τ κ 1 + ρ ǫ M · (1 − τ )+ 1 + κ · ǫ M − 1 · 2 · (1 − τ ) Small impact of UI on unemployment: ǫ M ↓ Strong rat-race externality: ǫ m /ǫ M ↑ τ ↑ : UI should be more generous Landais, Michaillat, and Saez (08/2011) Optimal Unemployment Insurance 27 / 42

  47. Intuition for Optimal UI in Recession � ǫ m � � � 1 − τ ≈ ρ τ κ 1 + ρ ǫ M · (1 − τ )+ 1 + κ · ǫ M − 1 · 2 · (1 − τ ) Small impact of UI on unemployment: ǫ M ↓ Strong rat-race externality: ǫ m /ǫ M ↑ τ ↑ : UI should be more generous Landais, Michaillat, and Saez (08/2011) Optimal Unemployment Insurance 27 / 42

  48. Intuition for Optimal UI in Recession � ǫ m � � � 1 − τ ≈ ρ τ κ 1 + ρ ǫ M · (1 − τ )+ 1 + κ · ǫ M − 1 · 2 · (1 − τ ) Small impact of UI on unemployment: ǫ M ↓ Strong rat-race externality: ǫ m /ǫ M ↑ τ ↑ : UI should be more generous Landais, Michaillat, and Saez (08/2011) Optimal Unemployment Insurance 27 / 42

  49. Intuition for Optimal UI in Recession � ǫ m � � � 1 − τ ≈ ρ τ κ 1 + ρ ǫ M · (1 − τ )+ 1 + κ · ǫ M − 1 · 2 · (1 − τ ) Small impact of UI on unemployment: ǫ M ↓ Strong rat-race externality: ǫ m /ǫ M ↑ τ ↑ : UI should be more generous Landais, Michaillat, and Saez (08/2011) Optimal Unemployment Insurance 27 / 42

  50. Optimal Replacement Rate τ is Countercyclical τ = c u / c e captures generosity of UI Use exact optimal UI formula Prove: optimal UI is more generous in recessions: d τ da < 0 Landais, Michaillat, and Saez (08/2011) Optimal Unemployment Insurance 28 / 42

  51. 1 Optimal UI Formula: τ = τ ( ǫ m , ǫ M , risk aversion) 2 Optimal UI over the Business Cycle 3 Extension to an Infinite-Horizon Model Landais, Michaillat, and Saez (08/2011) Optimal Unemployment Insurance 29 / 42

  52. Flows of Workers Landais, Michaillat, and Saez (08/2011) Optimal Unemployment Insurance 30 / 42

  53. Flows of Workers Landais, Michaillat, and Saez (08/2011) Optimal Unemployment Insurance 30 / 42

  54. Stochastic Environment Fluctuations are driven by technology { a t } ∞ t =0 . All workers receive the same c e t (if employed) and c u t (if unemployed) at time t Firm’s, worker’s, and government’s decisions at time t are measurable wrt a t = ( a 0 , a 1 , . . . , a t ). Government can commit to policy. Landais, Michaillat, and Saez (08/2011) Optimal Unemployment Insurance 31 / 42

  55. Worker’s Problem (Labor Supply) Given { a t , θ t , c e t , c u t } ∞ t =0 , Choose job-search effort { e t } ∞ t =0 To maximize expected utility: + ∞ � δ t � � � � (1 − n s t ) v ( c u t ) + n s t v ( c e 1 − (1 − s ) n s t ) − k ( e t ) E 0 t − 1 t =0 Subject to � � n s 1 − (1 − s ) · n s · e t · f ( θ t ) + (1 − s ) · n s t = t − 1 . t − 1 Landais, Michaillat, and Saez (08/2011) Optimal Unemployment Insurance 32 / 42

  56. Firm’s Problem (Labor Demand) Given { a t , θ t , w t } ∞ t =0 Choose hiring { h t } ∞ t =0 To maximize expected profits: + ∞ � � t − r · a t � α − w t · n d � � δ t n d a t · q ( θ t ) · h t E 0 t t =0 Subject to: n d t = (1 − s ) · n d t − 1 + h t . Landais, Michaillat, and Saez (08/2011) Optimal Unemployment Insurance 33 / 42

  57. Equilibrium on the Labor Market Wage is indeterminate w t = ω · a γ t , γ < 1 Tightness θ equalizes labor supply and labor demand n t ≡ n s t = n d t Landais, Michaillat, and Saez (08/2011) Optimal Unemployment Insurance 34 / 42

  58. Government’s Problem Given { a t } ∞ t =0 Choose consumptions { c e t , c u t } ∞ t =0 To maximize worker’s expected utility + ∞ � δ t { (1 − n t ) v ( c u t ) + n t v ( c e t ) − [1 − (1 − s ) n t − 1 ] k ( e t ) } E 0 t =0 Subject to worker’s and firm’s optimality conditions, equilibrium conditions, and budget constraints n t · w t = n t · c e t + (1 − n t ) · c u t . Landais, Michaillat, and Saez (08/2011) Optimal Unemployment Insurance 35 / 42

  59. Calibration: US, weekly frequency Interpretation Value Source Relative risk aversion 1 Chetty [’06] ρ Real wage rigidity 0.5 Haefke et al. [’08], Pissarides [’09] γ η Effort-elasticity of matching 0.7 Petrongolo & Pissarides [’01] s Separation rate 0.95% JOLTS, 2000–2010 ω m Effectiveness of matching 0.23 JOLTS, 2000–2010 Recruiting cost 0.21 Barron et al. [’97], Silva & Toledo r [’09] Marginal returns to labor 0.67 Matches labor share= 0 . 66 α Steady-state real wage 0.67 Matches unemployment= 5 . 9% ω Curvature of disutility of effort 2.1 Matches Meyer [’90] κ ω k Disutility of effort 0.58 Matches effort = 1 for t = 7 . 65%, b = 60% Landais, Michaillat, and Saez (08/2011) Optimal Unemployment Insurance 36 / 42

  60. Steady State: Optimal Replacement Rate 0.85 Replacement rate τ 0.8 0.75 0.7 0.65 0.6 0.04 0.05 0.06 0.07 0.08 0.09 0.1 Unemployment rate Landais, Michaillat, and Saez (08/2011) Optimal Unemployment Insurance 37 / 42

  61. Steady State: Optimal Benefit Rate 0.85 0.8 Benefit rate 0.75 0.7 0.65 0.6 0.04 0.05 0.06 0.07 0.08 0.09 0.1 Unemployment rate Landais, Michaillat, and Saez (08/2011) Optimal Unemployment Insurance 37 / 42

  62. Steady State: Optimal Labor Tax Rate 0.1 0.08 Labor tax rate 0.06 0.04 0.02 0 0.04 0.05 0.06 0.07 0.08 0.09 0.1 Unemployment rate Landais, Michaillat, and Saez (08/2011) Optimal Unemployment Insurance 37 / 42

  63. Comparison with Baily [’78] Formula Elasticity of (1−n) wrt ∆ C 0.5 0.4 0.3 0.2 0.1 Micro 0 0.04 0.05 0.06 0.07 0.08 0.09 0.1 Unemployment rate Optimal UI formula in infinite-horizon model Landais, Michaillat, and Saez (08/2011) Optimal Unemployment Insurance 38 / 42

  64. Comparison with Baily [’78] Formula Baily with micro−elasticity 1 0.9 Replacement rate τ 0.8 0.7 0.6 0.5 0.4 0.04 0.05 0.06 0.07 0.08 0.09 0.1 Unemployment rate Optimal UI formula in infinite-horizon model Landais, Michaillat, and Saez (08/2011) Optimal Unemployment Insurance 38 / 42

  65. Comparison with Baily [’78] Formula Elasticity of (1−n) wrt ∆ C 0.5 0.4 0.3 0.2 0.1 Micro Macro 0 0.04 0.05 0.06 0.07 0.08 0.09 0.1 Unemployment rate Optimal UI formula in infinite-horizon model Landais, Michaillat, and Saez (08/2011) Optimal Unemployment Insurance 38 / 42

  66. Comparison with Baily [’78] Formula Baily with micro−elasticity 1 Baily with macro−elasticity 0.9 Replacement rate τ 0.8 0.7 0.6 0.5 0.4 0.04 0.05 0.06 0.07 0.08 0.09 0.1 Unemployment rate Optimal UI formula in infinite-horizon model Landais, Michaillat, and Saez (08/2011) Optimal Unemployment Insurance 38 / 42

  67. Comparison with Baily [’78] Formula Elasticity of (1−n) wrt ∆ C 0.5 0.4 0.3 ε m / ε M − 1 > 0 0.2 0.1 Micro Macro 0 0.04 0.05 0.06 0.07 0.08 0.09 0.1 Unemployment rate Optimal UI formula in infinite-horizon model Landais, Michaillat, and Saez (08/2011) Optimal Unemployment Insurance 38 / 42

  68. Comparison with Baily [’78] Formula Baily with micro−elasticity 1 Baily with macro−elasticity Approximated formula 0.9 Replacement rate τ 0.8 0.7 0.6 0.5 0.4 0.04 0.05 0.06 0.07 0.08 0.09 0.1 Unemployment rate Optimal UI formula in infinite-horizon model Landais, Michaillat, and Saez (08/2011) Optimal Unemployment Insurance 38 / 42

  69. Comparison with Baily [’78] Formula Baily with micro−elasticity 1 Baily with macro−elasticity Approximated formula 0.9 Replacement rate τ Optimum 0.8 0.7 0.6 0.5 0.4 0.04 0.05 0.06 0.07 0.08 0.09 0.1 Unemployment rate Optimal UI formula in infinite-horizon model Landais, Michaillat, and Saez (08/2011) Optimal Unemployment Insurance 38 / 42

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