A Macroeconomic Approach to Optimal Unemployment Insurance: Theory and Applications

Transcription

1 A Macroeconomic Approach to Optimal Unemployment Insurance: Theory and Applications Landais (LSE), Michaillat (LSE), and Saez (Berkeley) December / 55

2 Baily-Chetty theory of optimal UI insurance-incentive tradeoff: UI provides a safety net but UI reduces job search and raises unemployment two aspects of the debate are missing: sometimes jobs are unavailable UI affects job creation problem: partial-equilibrium model labor supply fixed labor market tightness 2 / 55

3 In this paper: general-equilibrium model of optimal UI labor supply and labor demand equilibrium labor market tightness macroeconomic model captures three effects of UI: UI may reduce job-search effort UI may alleviate rat race for jobs in bad times UI may raise wages and deter job creation application: optimal UI over the business cycle 3 / 55

4 A matching model of UI 4 / 55

5 UI program moral hazard: search effort is unobservable employed workers receive c e unemployed workers receive c u replacement rate R measures generosity of UI: R 1 (c e c u )/w R = tax rate + benefit rate workers keep fraction 1 R of earnings 5 / 55

6 Labor market measure 1 of identical workers, initially unemployed search for jobs with effort e measure 1 of identical firms post v vacancies to hire workers CRS matching function: l = m(e, v ) + + labor market tightness: θ v/e 6 / 55

7 Matching probabilities vacancy-filling probability: q(θ) l ( ) 1 v = m θ,1 job-finding rate per unit of effort: f (θ) l + e = m(1,θ) job-finding probability: e f (θ) < / 55

8 Matching cost: ρ recruiters per vacancy [ ] employees = 1 + τ(θ ) producers + proof: l }{{} employees = }{{} n + ρ v }{{} producers recruiters l = n + ρ q(θ) [ ] ρ = 1 + n q(θ) ρ } {{ } 1+τ(θ) 8 / 55

9 Representative worker consumption utility U(c), search disutility ψ(e) utility gain from work: U U(c e ) U(c u ) solves max e {U(c u ) + e f (θ) U ψ(e)} effort supply e s (θ, U) gives optimal effort: + + ψ (e s (θ, U)) = f (θ) U labor supply l s (θ +, U + ) gives employment rate: l s (θ, U) = e s (θ, U) f (θ) 9 / 55

10 Labor supply labor market tightness labor supply: l s (, U) employment 10 / 55

11 Representative firm hires l employees n = l/(1 + τ(θ)) producers l n recruiters production function: y(n) solves max l {y(l/(1 + τ(θ))) w l} labor demand l d (θ,w) gives optimal employment: ( l y d ) = (1 + τ(θ)) w 1 + τ(θ) 11 / 55

12 Labor demand labor market tightness labor demand: l d (,w) l s (, U) employment 12 / 55

13 Labor-market equilibrium as in any matching model, need a price mechanism general wage schedule: w = w(θ, U) in equilibrium, θ is such that supply = demand: l s (θ, U) = l d (θ,w(θ, U)) equilibrium tightness: θ( U) 13 / 55

14 Labor-market equilibrium labor market tightness l d (,w(, U)) l s (, U) ( U) unemployment 0 0 l 1 employment 14 / 55

15 Sufficient-statistics formula for optimal UI 15 / 55

16 Government s problem choose U to maximize welfare SW = l U(c e ) + (1 l) U(c u ) ψ(e) subject to the following constraints: budget constraint: ( ) l y = l c e + (1 l) c u 1 + τ(θ) workers response: e = e s (θ, U), l = l s (θ, U) equilibrium constraint: θ = θ( U) 16 / 55

17 Condition for optimal UI express all the variables as a function of (θ, U) express social welfare as SW = SW(θ, U) government solves max U SW(θ( U), U) first-order condition: 0 = SW U + SW } {{ θ θ } U Baily-Chetty formula dθ d U } {{ } correction term 17 / 55

18 Optimal UI versus Baily-Chetty Baily-Chetty formula is valid if UI has no effect on θ or θ is efficient (that is, SW/ θ U = 0) optimal UI departs from Baily-Chetty if UI affects θ and θ is inefficient (that is, SW/ θ U 0) optimal UI > Baily-Chetty iff UI brings θ closer to its efficient level government UI beneficial when Baily-Chetty invalid 18 / 55

19 Baily-Chetty formula ( R = R ε m, U (c u ) ) U (c e ) ε m > 0: microelasticity of unemployment wrt UI measures disincentive from search U (c u )/U (c e ) > 1: ratio of marginal utilities measures need for insurance R is decreasing in ε m R is increasing in U (c u )/U (c e ) 19 / 55

20 Microelasticity of unemployment LS, low UI labor market tightness θ employment 20 / 55

21 Microelasticity of unemployment LS, high UI LS, low UI labor market tightness θ ε m employment 20 / 55

22 Efficiency term SW/ θ U depends on several estimable statistics τ(θ): recruiter-producer ratio u: unemployment rate 1 η: elasticity of the job-finding rate f (θ) U: the utility gain from work indicates the state of the labor market 21 / 55

23 Efficiency term and efficient tightness social welfare SW(, U) efficiency term = 0 ( U) labor market tightness 22 / 55

24 Efficiency term and efficient tightness social welfare SW(, U) efficiency term < 0 ( U) > labor market tightness 22 / 55

25 Efficiency term and efficient tightness social welfare SW(, U) efficiency term > 0 < ( U) labor market tightness 22 / 55

26 Macroelasticity of unemployment LD LS labor market tightness θ employment 23 / 55

27 Macroelasticity of unemployment LD LS labor market tightness θ ε m employment 23 / 55

28 Macroelasticity of unemployment LD LS labor market tightness θ ε m ε M employment 23 / 55

29 1 ε M /ε m gives effect of UI on θ labor market tightness LD dθ > 0 LS ε m ε M employment 24 / 55

30 1 ε M /ε m gives effect of UI on θ labor market tightness LD dθ = 0 LS ε m ε M employment 24 / 55

31 1 ε M /ε m gives effect of UI on θ LS labor market tightness LD dθ < 0 ε M ε m employment 24 / 55

32 Optimal UI formula in sufficient statistics ( R = R ε m, U (c u ) ) ) U (c e + (1 εm ) ε m efficiency term R R ( ε M,U (c u )/U (c e ) ) ε M alone is not useful for optimal UI efficiency term fluctuates with θ optimal UI over the business cycle importance of 1 ε M /ε m 25 / 55

33 Optimal UI over the business cycle: theory 26 / 55

34 Three matching models model standard rigid-wage job-rationing prod. function linear linear concave wage bargaining rigid rigid reference Pissarides [2000] Hall [2005] Michaillat [2012] 27 / 55

35 Standard model: 1 ε M /ε m < 0 LS labor market tightness LD employment 28 / 55

36 Standard model: 1 ε M /ε m < 0 labor market tightness LD LS moral hazard ε m employment 28 / 55

37 Standard model: 1 ε M /ε m < 0 LS moral hazard labor market tightness LD job creation ε m ε M employment 28 / 55

38 Rigid-wage model: 1 ε M /ε m = 0 LS labor market tightness LD employment 29 / 55

39 Rigid-wage model: 1 ε M /ε m = 0 labor market tightness LD LS moral hazard ε m employment 29 / 55

40 Rigid-wage model: 1 ε M /ε m = 0 labor market tightness LD LS moral hazard ε m = ε M employment 29 / 55

41 Job-rationing model: 1 ε M /ε m > 0 LD LS labor market tightness employment 30 / 55

42 Job-rationing model: 1 ε M /ε m > 0 LD LS labor market tightness ε m moral hazard employment 30 / 55

43 Job-rationing model: 1 ε M /ε m > 0 LD LS labor market tightness rat race ε m ε M moral hazard employment 30 / 55

44 Cyclicality of optimal UI: theory standard model: procyclical UI bargaining shocks inefficient fluctuations job-creation mechanism 1 ε M /ε m < 0 rigid-wage model: acyclical UI no mechanism 1 ε M /ε m = 0 job-rationing model: countercyclical UI productivity shocks inefficient fluctuations rat-race mechanism 1 ε M /ε m > 0 31 / 55

45 Optimal UI over the business cycle: empirics 32 / 55

46 Direct evidence: 1 ε M /ε m > 0 Levine [1993]: 1 ε M /ε m = 1 > 0 UI extensions in the US in 1980s Marinescu [2014]: 1 ε M /ε m = 0.3 > 0 UI extensions in the US during Great Recession Johnston & Mas [2015]: 1 ε M /ε m = 0 UI reduction in Missouri in 2011 Lalive et al. [2015]: 1 ε M /ε m = 0.2 > 0 reform of UI system in Austria in the 1990s 33 / 55

47 Indirect evidence: 1 ε M /ε m > 0 convincing evidence of rat-race mechanism negative spillover of higher job search Crepon et al. [2013], Burgess & Profit [2001] no evidence of job-creation mechanism re-employment wages unaffected by UI Card et al. [2007], Schmieder et al. [2015] only exception is Hagedorn et al. [2013] 34 / 55

48 Recruiter-producer ratio τ(θ) 4% CES data on recruiting industry 3% JOLTS data on vacancy-filling rate 2% 1% CPS data on job-finding rate 0% / 55

49 Elasticity of matching function η ln(f(t + 1)) ln(f(t)) = ln(θ(t + 1)) ln(θ(t)) 36 / 55

50 Utility gain from work U extended empirical model: U = log(c e /c h ) + Z consumption drop upon unemployment: 19% consumption drop for food: 7% income elasticity of food consumption: 0.36 nonpecuniary cost of unemployment: Z = 45% well-being surveys: 45% of yearly income career choices [Borgschulte & Martorell 2015] standard macro assumption: Z < 0 37 / 55

51 Efficiency term = 0: UI = Baily-Chetty / 55

52 Efficiency term = 0: UI = Baily-Chetty / 55

53 Efficiency term < 0: UI < Baily-Chetty / 55

54 Efficiency term > 0: UI > Baily-Chetty / 55

55 Nonpecuniary cost of unemployment Z is critical Z= Z= / 55

56 Optimal UI over the business cycle: simulations of the job-rationing model 42 / 55

57 First simulation: constant UI, R = 50% 80% Replacement rate 70% 60% 50% 40% slump boom 30% Technology 43 / 55

58 Large fluctuations in unemployment Unemployment rate 13% 11% 9% 7% 5.9% 5% slump boom 3% Technology 44 / 55

59 Large fluctuations in tightness Labor market tightness boom slump Technology 45 / 55

60 The microelasticity ε m is stable Microelasticity slump boom Technology 46 / 55

61 The elasticity wedge 1 ε M /ε m is positive 1 Elasticity wedge Technology 47 / 55

62 The rat race is stronger in slumps Elasticity wedge slump: strong rat race Technology boom: weak rat race 48 / 55

63 The rat race is stronger in slumps LD, slump LS, high UI LS, low UI Labor market tightness ε m ε M θ Employment 48 / 55

64 The rat race is stronger in slumps LS, high UI LS, low UI Labor market tightness θ ε M ε m LD, boom Employment 48 / 55

65 The efficiency term changes sign Efficiency term slump: inefficiently low tightness efficient tightness boom: inefficiently high tightness Technology 49 / 55

66 The optimal UI is countercyclical Replacement rate 80% 70% 60% 50% 40% slump Optimal UI Constant UI boom 30% Technology 50 / 55

67 The optimal UI is countercyclical 30% boom Consumption drop 20% 19% 10% Optimal UI Constant UI 0% slump Technology 50 / 55

68 Despite large disincentive to search Job-search effort slump boom Optimal UI Constant UI Technology 51 / 55

69 Higher UI slightly higher unemployment Macroelasticity Optimal UI Constant UI boom slump Technology 52 / 55

70 Higher UI slightly higher unemployment Unemployment rate 13% 11% 9% 7% 5% slump Optimal UI Constant UI boom 3% Technology 52 / 55

71 Conclusion 53 / 55

72 Theoretical approach is broadly applicable formula for optimal policy τ is 0 = public-finance term + dθ dτ public-finance term = SW/ τ θ efficiency term = SW/ θ τ efficiency term Michaillat & Saez [2014]: monetary and debt policy Michaillat & Saez [2015]: government purchases 54 / 55

73 Empirical applications would benefit from better estimates of many statistics determinants of the efficiency term, and thus of the natural rate of unemployment nonpecuniary cost of unemployment (z) recruiter-producer ratio (τ) matching elasticity with endogenous search (η) elasticity wedge (1 ε M /ε m ) 55 / 55