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Optimal Unemployment Insurance over the Business Cycle Camille - - PowerPoint PPT Presentation

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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

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SLIDE 1

Optimal Unemployment Insurance

  • ver 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

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SLIDE 2

Literature on Unemployment Insurance

Optimal benefit level:

◮ Baily [’78] ◮ Chetty [’06]

Optimal benefit levels over unemployment spell:

◮ Shavell and Weiss [’79] ◮ Hopenhayn and Nicolini [’97] ◮ Shimer and Werning [’08]

Optimal benefit levels over business cycle: –

Landais, Michaillat, and Saez (08/2011) Optimal Unemployment Insurance 2 / 42

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SLIDE 3

Framework

Model of equilibrium unemployment [Pissarides, ’00] Risk-averse workers, no self-insurance Unobservable job-search efforts [Baily, ’78] Recessions

◮ real wage rigidity [Hall, ’05]

Job rationing [Michaillat, forthcoming]

◮ real wage rigidity & downward-sloping demand for labor Diagram Landais, Michaillat, and Saez (08/2011) Optimal Unemployment Insurance 3 / 42

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SLIDE 4

Framework

Model of equilibrium unemployment [Pissarides, ’00] Risk-averse workers, no self-insurance Unobservable job-search efforts [Baily, ’78] Recessions

◮ real wage rigidity [Hall, ’05]

Job rationing [Michaillat, forthcoming]

◮ real wage rigidity & downward-sloping demand for labor Diagram Landais, Michaillat, and Saez (08/2011) Optimal Unemployment Insurance 3 / 42

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SLIDE 5

Framework

Model of equilibrium unemployment [Pissarides, ’00] Risk-averse workers, no self-insurance Unobservable job-search efforts [Baily, ’78] Recessions

◮ real wage rigidity [Hall, ’05]

Job rationing [Michaillat, forthcoming]

◮ real wage rigidity & downward-sloping demand for labor Diagram Landais, Michaillat, and Saez (08/2011) Optimal Unemployment Insurance 3 / 42

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SLIDE 6

Why Job Rationing in Recessions?

Landais, Michaillat, and Saez (08/2011) Optimal Unemployment Insurance 4 / 42

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SLIDE 7

Why Job Rationing in Recessions?

Landais, Michaillat, and Saez (08/2011) Optimal Unemployment Insurance 4 / 42

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SLIDE 8

Why Job Rationing in Recessions?

Landais, Michaillat, and Saez (08/2011) Optimal Unemployment Insurance 4 / 42

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SLIDE 9

Overview of Results

In recessions, unemployment insurance (UI) should be constant? more generous? less generous?

Landais, Michaillat, and Saez (08/2011) Optimal Unemployment Insurance 5 / 42

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SLIDE 10

Overview of Results

In recessions, unemployment insurance (UI) should be constant more generous: Consumption of unemployed

Consumption of employed ↑

less generous

Landais, Michaillat, and Saez (08/2011) Optimal Unemployment Insurance 5 / 42

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SLIDE 11

What Happens in Recessions?

Unemployment rate ← Rationing unemp. Frictional unemp. 1964 1974 1984 1994 2004 0.02 0.04 0.06 0.08 0.1

Diagram Landais, Michaillat, and Saez (08/2011) Optimal Unemployment Insurance 6 / 42

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SLIDE 12

What Happens in Recessions?

Marginal benefits:

◮ insurance ◮ correction for negative rat-race externality

Marginal cost:

◮ increase of aggregate unemployment

UI

Diagram Landais, Michaillat, and Saez (08/2011) Optimal Unemployment Insurance 6 / 42

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SLIDE 13

What Happens in Recessions?

Marginal benefits:

◮ insurance → ◮ correction for negative rat-race externality ↑

Marginal cost:

◮ increase of aggregate unemployment ↓

UI ↑

Diagram Landais, Michaillat, and Saez (08/2011) Optimal Unemployment Insurance 6 / 42

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SLIDE 14

Outline of the Paper

1 Optimal UI formula: τ = τ(ǫm, ǫM, risk aversion)

◮ τ = cu/ce: replacement rate ◮ in generic model of equilibrium unemployment ◮ formula in sufficient statistics

2 Optimal UI over the business cycle

◮ model of recessions and job rationing [Michaillat,

forthcoming]

◮ charaterize elasticities ǫm, ǫM over business cycle ◮ prove: optimal τ increases in recessions

3 Extension to an infinite-horizon model

◮ verify robustness of theoretical results ◮ extensions: (1) optimal UI with deficit spending; (2)

  • ptimal duration of benefits

Landais, Michaillat, and Saez (08/2011) Optimal Unemployment Insurance 7 / 42

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SLIDE 15

1 Optimal UI Formula: τ = τ(ǫm, ǫM, 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 8 / 42

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SLIDE 16

UI Program

Government gives ce to n employed workers Government gives cu to 1 − n unemployed workers Budget constraint: n · w = n · ce + (1 − n) · cu

Landais, Michaillat, and Saez (08/2011) Optimal Unemployment Insurance 9 / 42

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SLIDE 17

One-Period Model with Matching Frictions

Initial number of unemployed workers: u Job-search effort: e Job openings: o Number of matches: h = m(e · u, o) Labor market tightness: θ ≡ o/(e · u) Vacancy-filling proba.: q(θ) = m (1/θ, 1) Job-finding proba.: e · f (θ) = e · m(1, θ)

Landais, Michaillat, and Saez (08/2011) Optimal Unemployment Insurance 10 / 42

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SLIDE 18

One-Period Model with Matching Frictions

Initial number of unemployed workers: u Job-search effort: e Job openings: o Number of matches: h = m(e · u, o) Labor market tightness: θ ≡ o/(e · u) Vacancy-filling proba.: q(θ) = m (1/θ, 1) Job-finding proba.: e · f (θ) = e · m(1, θ)

Landais, Michaillat, and Saez (08/2011) Optimal Unemployment Insurance 10 / 42

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SLIDE 19

One-Period Model with Matching Frictions

Initial number of unemployed workers: u Job-search effort: e Job openings: o Number of matches: h = m(e · u, o) Labor market tightness: θ ≡ o/(e · u) Vacancy-filling proba.: q(θ) = m (1/θ, 1) Job-finding proba.: e · f (θ) = e · m(1, θ)

Landais, Michaillat, and Saez (08/2011) Optimal Unemployment Insurance 10 / 42

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SLIDE 20

One-Period Model with Matching Frictions

Initial number of unemployed workers: u Job-search effort: e Job openings: o Number of matches: h = m(e · u, o) Labor market tightness: θ ≡ o/(e · u) Vacancy-filling proba.: q(θ) = m (1/θ, 1) Job-finding proba.: e · f (θ) = e · m(1, θ)

Landais, Michaillat, and Saez (08/2011) Optimal Unemployment Insurance 10 / 42

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SLIDE 21

Flows of Workers

Landais, Michaillat, and Saez (08/2011) Optimal Unemployment Insurance 11 / 42

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SLIDE 22

Flows of Workers

Landais, Michaillat, and Saez (08/2011) Optimal Unemployment Insurance 11 / 42

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SLIDE 23

Unemployed Worker’s Problem

Given θ, ∆v = v(ce) − v(cu), choose e to maximize v(cu) + e · f (θ) · ∆v − k(e) Utility-maximizing effort e(θ, ∆v): k′(e) = f (θ) · ∆v Aggregate labor supply: ns(e(θ, ∆v), θ) = (1 − u) + e(θ, ∆v) · f (θ) · u

Landais, Michaillat, and Saez (08/2011) Optimal Unemployment Insurance 12 / 42

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SLIDE 24

Unemployed Worker’s Problem

Given θ, ∆v = v(ce) − v(cu), choose e to maximize v(cu) + e · f (θ) · ∆v − k(e) Utility-maximizing effort e(θ, ∆v): k′(e) = f (θ) · ∆v Aggregate labor supply: ns(e(θ, ∆v), θ) = (1 − u) + e(θ, ∆v) · f (θ) · u

Landais, Michaillat, and Saez (08/2011) Optimal Unemployment Insurance 12 / 42

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SLIDE 25

Unemployed Worker’s Problem

Given θ, ∆v = v(ce) − v(cu), choose e to maximize v(cu) + e · f (θ) · ∆v − k(e) Utility-maximizing effort e(θ, ∆v): k′(e) = f (θ) · ∆v Aggregate labor supply: ns(e(θ, ∆v), θ) = (1 − u) + e(θ, ∆v) · f (θ) · u

Landais, Michaillat, and Saez (08/2011) Optimal Unemployment Insurance 12 / 42

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SLIDE 26

Unemployed Worker’s Problem

Given θ, ∆v = v(ce) − v(cu), choose e to maximize v(cu) + e · f (θ) · ∆v − k(e) Utility-maximizing effort e(θ, ∆v): k′(e) = f (θ) · ∆v Aggregate labor supply: ns(e(θ, ∆v), θ) = (1 − u) + e(θ, ∆v) · f (θ) · u

Landais, Michaillat, and Saez (08/2011) Optimal Unemployment Insurance 12 / 42

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SLIDE 27

Unemployed Worker’s Problem

Given θ, ∆v = v(ce) − v(cu), choose e to maximize v(cu) + e · f (θ) · ∆v − k(e) Utility-maximizing effort e(θ, ∆v): k′(e) = f (θ) · ∆v Aggregate labor supply: ns(e(θ, ∆v), θ) = (1 − u) + e(θ, ∆v) · f (θ) · u

Landais, Michaillat, and Saez (08/2011) Optimal Unemployment Insurance 12 / 42

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SLIDE 28

Unemployed Worker’s Problem

Given θ, ∆v = v(ce) − v(cu), choose e to maximize v(cu) + e · f (θ) · ∆v − k(e) Utility-maximizing effort e(θ, ∆v): k′(e) = f (θ) · ∆v Aggregate labor supply: ns(e(θ, ∆v), θ) = (1 − u) + e(θ, ∆v) · f (θ) · u

Landais, Michaillat, and Saez (08/2011) Optimal Unemployment Insurance 12 / 42

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SLIDE 29

Response of Labor Supply to Lower UI

0.9 0.95 1 0.5 1 1.5 2 Employment n Labor market tightness θ Labor supply (high UI)

Landais, Michaillat, and Saez (08/2011) Optimal Unemployment Insurance 13 / 42

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SLIDE 30

Response of Labor Supply to Lower UI

0.9 0.95 1 0.5 1 1.5 2 Employment n Labor market tightness θ Labor supply (high UI) Labor supply (low UI)

Landais, Michaillat, and Saez (08/2011) Optimal Unemployment Insurance 13 / 42

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SLIDE 31

Government’s Problem

Choose ce, cu to maximize n · v(ce) + (1 − n) · v(cu) − u · k(e) subject to: ∆v = v(ce) − v(cu) budget: n · ce + (1 − n) · cu = n · w labor market dynamics: n = (1 − u) + u · e · f (θ)

  • ptimal job search: e = e(θ, ∆v)

labor market clearing: nd(θ) = ns(e(θ, ∆v), θ)

Landais, Michaillat, and Saez (08/2011) Optimal Unemployment Insurance 14 / 42

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SLIDE 32

Government’s Problem

Choose ce, cu to maximize n · v(ce) + (1 − n) · v(cu) − u · k(e) subject to: ∆v = v(ce) − v(cu) budget: n · ce + (1 − n) · cu = n · w labor market dynamics: n = (1 − u) + u · e · f (θ)

  • ptimal job search: e = e(θ, ∆v)

labor market clearing: nd(θ) = ns(e(θ, ∆v), θ)

Landais, Michaillat, and Saez (08/2011) Optimal Unemployment Insurance 14 / 42

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SLIDE 33

Government’s Problem

Choose ce, cu to maximize n · v(ce) + (1 − n) · v(cu) − u · k(e) subject to: ∆v = v(ce) − v(cu) budget: n · ce + (1 − n) · cu = n · w labor market dynamics: n = (1 − u) + u · e · f (θ)

  • ptimal job search: e = e(θ, ∆v)

labor market clearing: nd(θ) = ns(e(θ, ∆v), θ)

Landais, Michaillat, and Saez (08/2011) Optimal Unemployment Insurance 14 / 42

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SLIDE 34

Government’s Problem

Choose ce, cu to maximize n · v(ce) + (1 − n) · v(cu) − u · k(e) subject to: ∆v = v(ce) − v(cu) budget: n · ce + (1 − n) · cu = n · w labor market dynamics: n = (1 − u) + u · e · f (θ)

  • ptimal job search: e = e(θ, ∆v)

labor market clearing: nd(θ) = ns(e(θ, ∆v), θ)

Landais, Michaillat, and Saez (08/2011) Optimal Unemployment Insurance 14 / 42

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SLIDE 35

Government’s Problem

Choose ce, cu to maximize n · v(ce) + (1 − n) · v(cu) − u · k(e) subject to: ∆v = v(ce) − v(cu) budget: n · ce + (1 − n) · cu = n · w labor market dynamics: n = (1 − u) + u · e · f (θ)

  • ptimal job search: e = e(θ, ∆v)

labor market clearing: nd(θ) = ns(e(θ, ∆v), θ)

Landais, Michaillat, and Saez (08/2011) Optimal Unemployment Insurance 14 / 42

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SLIDE 36

Micro-Elasticity ǫm

ǫm ≡ ∆c 1 − n · ∂ns ∂e

  • θ

· ∂e ∂∆c

  • 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

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SLIDE 37

Macro-Elasticity ǫM

ǫM ≡ ∆c 1 − n · dn 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 ǫM = ǫm + ∆c 1 − n · 1 + κ κ · ∂ns ∂θ

  • e

· dθ d∆c

  • Landais, Michaillat, and Saez (08/2011)

Optimal Unemployment Insurance 16 / 42

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SLIDE 38

Macro-Elasticity ǫM

ǫM ≡ ∆c 1 − n · dn 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 ǫM = ǫm + ∆c 1 − n · 1 + κ κ · ∂ns ∂θ

  • e

· dθ d∆c

  • Landais, Michaillat, and Saez (08/2011)

Optimal Unemployment Insurance 16 / 42

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SLIDE 39

Macro-Elasticity ǫM

ǫM ≡ ∆c 1 − n · dn 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 ǫM = ǫm + ∆c 1 − n · 1 + κ κ · ∂ns ∂θ

  • e

· dθ d∆c

  • Landais, Michaillat, and Saez (08/2011)

Optimal Unemployment Insurance 16 / 42

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SLIDE 40

Macro-Elasticity ǫM

ǫM ≡ ∆c 1 − n · dn 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 ǫM = ǫm + ∆c 1 − n · 1 + κ κ · ∂ns ∂θ

  • e

· dθ d∆c

  • Landais, Michaillat, and Saez (08/2011)

Optimal Unemployment Insurance 16 / 42

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SLIDE 41

Exact Optimal UI Formula

1 n· τ 1 − τ =

  • n + (1 − n) · v ′(cu)

v ′(ce) −1 · n ǫM · v ′(cu) v ′(ce) − 1

  • +

∆v v ′(ce) · ∆c · κ κ + 1 · ǫm ǫM − 1

  • Landais, Michaillat, and Saez (08/2011)

Optimal Unemployment Insurance 17 / 42

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SLIDE 42

Optimal UI Formula in Sufficient Statistics

τ 1 − τ ≈ ρ ǫM ·(1 − τ)+ κ 1 + κ· ǫm ǫM − 1

  • ·
  • 1 + ρ

2 · (1 − τ)

  • τ: replacement rate cu/ce

ρ: coefficient of relative risk aversion κ: elasticity of marginal disutility of effort ǫM: macro-elasticity of unemployment ǫm: micro-elasticity of unemployment

Landais, Michaillat, and Saez (08/2011) Optimal Unemployment Insurance 18 / 42

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SLIDE 43

Building on the Baily [’78] Formula

τ 1 − τ ≈ ρ ǫm (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: ∂ns ∂θ

  • e

· dθ ∝

  • ǫm − ǫM

Landais, Michaillat, and Saez (08/2011) Optimal Unemployment Insurance 19 / 42

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SLIDE 44

Building on the Baily [’78] Formula

τ 1 − τ ≈ ρ ǫM (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: ∂ns ∂θ

  • e

· dθ ∝

  • ǫm − ǫM

Landais, Michaillat, and Saez (08/2011) Optimal Unemployment Insurance 19 / 42

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SLIDE 45

Building on the Baily [’78] Formula

τ 1 − τ ≈ ρ ǫM (1 − τ) + κ 1 + κ ǫm ǫM − 1 1 + ρ 2(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: ∂ns ∂θ

  • e

· dθ ∝

  • ǫm − ǫM

Landais, Michaillat, and Saez (08/2011) Optimal Unemployment Insurance 19 / 42

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SLIDE 46

1 Optimal UI Formula: τ = τ(ǫm, ǫM, 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

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SLIDE 47

A Model of Recessions and Job Rationing

Given (θ, a), firm chooses n ≥ 1 − u to maximize a · nα

production

− ω · aγ

wage

·n − r · a q(θ)

  • hiring cost

· [n − (1 − u)] Profit-maximizing employment nd(θ, a): α · nα−1 = ω · aγ−1 + r q(θ) Wage rigidity: γ < 1 Diminishing marginal returns to labor: α < 1

Landais, Michaillat, and Saez (08/2011) Optimal Unemployment Insurance 21 / 42

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SLIDE 48

A Model of Recessions and Job Rationing

Given (θ, a), firm chooses n ≥ 1 − u to maximize a · nα

production

− ω · aγ

wage

·n − r · a q(θ)

  • hiring cost

· [n − (1 − u)] Profit-maximizing employment nd(θ, a): α · nα−1 = ω · aγ−1 + r q(θ) Wage rigidity: γ < 1 Diminishing marginal returns to labor: α < 1

Landais, Michaillat, and Saez (08/2011) Optimal Unemployment Insurance 21 / 42

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SLIDE 49

A Model of Recessions and Job Rationing

Given (θ, a), firm chooses n ≥ 1 − u to maximize a · nα

production

− ω · aγ

wage

·n − r · a q(θ)

  • hiring cost

· [n − (1 − u)] Profit-maximizing employment nd(θ, a): α · nα−1 = ω · aγ−1 + r q(θ) Wage rigidity: γ < 1 Diminishing marginal returns to labor: α < 1

Landais, Michaillat, and Saez (08/2011) Optimal Unemployment Insurance 21 / 42

slide-50
SLIDE 50

A Model of Recessions and Job Rationing

Given (θ, a), firm chooses n ≥ 1 − u to maximize a · nα

production

− ω · aγ

wage

·n − r · a q(θ)

  • hiring cost

· [n − (1 − u)] Profit-maximizing employment nd(θ, a): α · nα−1 = ω · aγ−1 + r q(θ) Wage rigidity: γ < 1 Diminishing marginal returns to labor: α < 1

Landais, Michaillat, and Saez (08/2011) Optimal Unemployment Insurance 21 / 42

slide-51
SLIDE 51

A Model of Recessions and Job Rationing

Given (θ, a), firm chooses n ≥ 1 − u to maximize a · nα

production

− ω · aγ

wage

·n − r · a q(θ)

  • hiring cost

· [n − (1 − u)] Profit-maximizing employment nd(θ, a): α · nα−1 = ω · aγ−1 + r q(θ) Wage rigidity: γ < 1 Diminishing marginal returns to labor: α < 1

Landais, Michaillat, and Saez (08/2011) Optimal Unemployment Insurance 21 / 42

slide-52
SLIDE 52

A Model of Recessions and Job Rationing

Given (θ, a), firm chooses n ≥ 1 − u to maximize a · nα

production

− ω · aγ

wage

·n − r · a q(θ)

  • hiring cost

· [n − (1 − u)] Profit-maximizing employment nd(θ, a): α · nα−1 = ω · aγ−1 + r q(θ) Wage rigidity: γ < 1 Diminishing marginal returns to labor: α < 1

Landais, Michaillat, and Saez (08/2011) Optimal Unemployment Insurance 21 / 42

slide-53
SLIDE 53

A Model of Recessions and Job Rationing

Given (θ, a), firm chooses n ≥ 1 − u to maximize a · nα

production

− ω · aγ

wage

·n − r · a q(θ)

  • hiring cost

· [n − (1 − u)] Profit-maximizing employment nd(θ, a): α · nα−1 = ω · aγ−1 + r q(θ) Wage rigidity: γ < 1 Diminishing marginal returns to labor: α < 1

Landais, Michaillat, and Saez (08/2011) Optimal Unemployment Insurance 21 / 42

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SLIDE 54

Labor Demand over the Business Cycle

0.9 0.95 1 0.5 1 1.5 2 Employment n Labor market tightness θ Labor demand (boom)

Landais, Michaillat, and Saez (08/2011) Optimal Unemployment Insurance 22 / 42

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SLIDE 55

Labor Demand over the Business Cycle

0.9 0.95 1 0.5 1 1.5 2 Employment n Labor market tightness θ Labor demand (boom) Labor demand (recession)

Landais, Michaillat, and Saez (08/2011) Optimal Unemployment Insurance 22 / 42

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SLIDE 56

Baily [’78] Partial-Equilibrium Model

0.9 0.95 1 0.5 1 1.5 2 Employment n Labor market tightness θ Labor supply (high UI) fixed θ

Landais, Michaillat, and Saez (08/2011) Optimal Unemployment Insurance 23 / 42

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SLIDE 57

Baily [’78] Partial-Equilibrium Model

0.9 0.95 1 0.5 1 1.5 2 Employment n Labor market tightness θ Labor supply (high UI) Labor supply (low UI) fixed θ

Landais, Michaillat, and Saez (08/2011) Optimal Unemployment Insurance 23 / 42

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SLIDE 58

Baily [’78] Partial-Equilibrium Model

0.9 0.95 1 0.5 1 1.5 2 Employment n Labor market tightness θ Labor supply (high UI) Labor supply (low UI)

εm

Landais, Michaillat, and Saez (08/2011) Optimal Unemployment Insurance 23 / 42

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SLIDE 59

Our General-Equilibrium Model

0.9 0.95 1 0.5 1 1.5 2 Employment n Labor market tightness θ Labor supply (high UI) Labor demand (boom) Equilibrium (θ , n)

Landais, Michaillat, and Saez (08/2011) Optimal Unemployment Insurance 23 / 42

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SLIDE 60

Our General-Equilibrium Model

0.9 0.95 1 0.5 1 1.5 2 Employment n Labor market tightness θ Labor supply (high UI) Labor supply (low UI) Labor demand (boom) New equilibrium (θ’ , n’)

Landais, Michaillat, and Saez (08/2011) Optimal Unemployment Insurance 23 / 42

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SLIDE 61

Our General-Equilibrium Model

0.9 0.95 1 0.5 1 1.5 2 Employment n Labor market tightness θ Labor supply (high UI) Labor supply (low UI) Labor demand (boom)

εm

Landais, Michaillat, and Saez (08/2011) Optimal Unemployment Insurance 23 / 42

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SLIDE 62

Our General-Equilibrium Model

0.9 0.95 1 0.5 1 1.5 2 Employment n Labor market tightness θ Labor supply (high UI) Labor supply (low UI) Labor demand (boom)

εM

Landais, Michaillat, and Saez (08/2011) Optimal Unemployment Insurance 23 / 42

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SLIDE 63

Our General-Equilibrium Model

0.9 0.95 1 0.5 1 1.5 2 Employment n Labor market tightness θ Labor supply (high UI) Labor supply (low UI) Labor demand (boom)

εm − εM

Landais, Michaillat, and Saez (08/2011) Optimal Unemployment Insurance 23 / 42

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SLIDE 64

Micro-Elasticity ǫm > Macro-Elasticity ǫM

Positive wedge between ǫm and ǫM: ǫm > ǫM Estimable statistic:

  • ǫm − ǫM

∝ ∆c θ · dθ d∆c Testable implication:

◮ model with Nash bargaining [Pissarides, ’00]:

ǫm < ǫM

◮ model with rigid wages [Hall, ’05]:

ǫm = ǫM

Landais, Michaillat, and Saez (08/2011) Optimal Unemployment Insurance 24 / 42

slide-65
SLIDE 65

Micro-Elasticity ǫm > Macro-Elasticity ǫM

Positive wedge between ǫm and ǫM: ǫm > ǫM Estimable statistic:

  • ǫm − ǫM

∝ ∆c θ · dθ d∆c Testable implication:

◮ model with Nash bargaining [Pissarides, ’00]:

ǫm < ǫM

◮ model with rigid wages [Hall, ’05]:

ǫm = ǫM

Landais, Michaillat, and Saez (08/2011) Optimal Unemployment Insurance 24 / 42

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SLIDE 66

Micro-Elasticity ǫm > Macro-Elasticity ǫM

Positive wedge between ǫm and ǫM: ǫm > ǫM Estimable statistic:

  • ǫm − ǫM

∝ ∆c θ · dθ d∆c Testable implication:

◮ model with Nash bargaining [Pissarides, ’00]:

ǫm < ǫM

◮ model with rigid wages [Hall, ’05]:

ǫm = ǫM

Landais, Michaillat, and Saez (08/2011) Optimal Unemployment Insurance 24 / 42

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SLIDE 67

Micro-Elasticity ǫm > Macro-Elasticity ǫM

Positive wedge between ǫm and ǫM: ǫm > ǫM Estimable statistic:

  • ǫm − ǫM

∝ ∆c θ · dθ d∆c Testable implication:

◮ model with Nash bargaining [Pissarides, ’00]:

ǫm < ǫM

◮ model with rigid wages [Hall, ’05]:

ǫm = ǫM

Landais, Michaillat, and Saez (08/2011) Optimal Unemployment Insurance 24 / 42

slide-68
SLIDE 68

Effect of Lower UI in Expansion

0.9 0.95 1 0.5 1 1.5 2 Employment n Labor market tightness θ Labor supply (high UI) Labor supply (low UI) Labor demand (boom)

εm

Landais, Michaillat, and Saez (08/2011) Optimal Unemployment Insurance 25 / 42

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SLIDE 69

Effect of Lower UI in Expansion

0.9 0.95 1 0.5 1 1.5 2 Employment n Labor market tightness θ Labor supply (high UI) Labor supply (low UI) Labor demand (boom)

εM

Landais, Michaillat, and Saez (08/2011) Optimal Unemployment Insurance 25 / 42

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SLIDE 70

Effect of Lower UI in Expansion

0.9 0.95 1 0.5 1 1.5 2 Employment n Labor market tightness θ Labor supply (high UI) Labor supply (low UI) Labor demand (boom)

εm − εM

Landais, Michaillat, and Saez (08/2011) Optimal Unemployment Insurance 25 / 42

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SLIDE 71

Effect of Lower UI in Recession

0.9 0.95 1 0.5 1 1.5 2 Employment n Labor market tightness θ Labor supply (high UI) Labor supply (low UI)

Landais, Michaillat, and Saez (08/2011) Optimal Unemployment Insurance 25 / 42

slide-72
SLIDE 72

Effect of Lower UI in Recession

0.9 0.95 1 0.5 1 1.5 2 Employment n Labor market tightness θ Labor supply (high UI) Labor supply (low UI) Labor demand (recession)

Landais, Michaillat, and Saez (08/2011) Optimal Unemployment Insurance 25 / 42

slide-73
SLIDE 73

Effect of Lower UI in Recession

0.9 0.95 1 0.5 1 1.5 2 Employment n Labor market tightness θ Labor supply (high UI) Labor supply (low UI) Labor demand (recession)

εm

Landais, Michaillat, and Saez (08/2011) Optimal Unemployment Insurance 25 / 42

slide-74
SLIDE 74

Effect of Lower UI in Recession

0.9 0.95 1 0.5 1 1.5 2 Employment n Labor market tightness θ Labor supply (high UI) Labor supply (low UI) Labor demand (recession)

εM

Landais, Michaillat, and Saez (08/2011) Optimal Unemployment Insurance 25 / 42

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SLIDE 75

Effect of Lower UI in Recession

0.9 0.95 1 0.5 1 1.5 2 Employment n Labor market tightness θ Labor supply (high UI) Labor supply (low UI) Labor demand (recession)

εm − εM

Landais, Michaillat, and Saez (08/2011) Optimal Unemployment Insurance 25 / 42

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SLIDE 76

Cyclicality of Elasticities

Assume: isoelastic utility functions, Cobb-Douglas matching function Wedge ǫm/ǫM > 1 is countercyclical : ∂

  • ǫm/ǫM

∂a

  • τ

< 0 Macro-elasticity ǫM is procyclical: ∂ǫM ∂a

  • τ

> 0

Landais, Michaillat, and Saez (08/2011) Optimal Unemployment Insurance 26 / 42

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SLIDE 77

Intuition for Optimal UI in Recession

τ 1 − τ ≈ ρ ǫM · (1 − τ)+ κ 1 + κ· ǫm ǫM − 1

  • ·
  • 1 + ρ

2 · (1 − τ)

  • Small impact of UI on unemployment: ǫM ↓

Strong rat-race externality: ǫm/ǫM ↑ τ ↑: UI should be more generous

Landais, Michaillat, and Saez (08/2011) Optimal Unemployment Insurance 27 / 42

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SLIDE 78

Intuition for Optimal UI in Recession

τ 1 − τ ≈ ρ ǫM · (1 − τ)+ κ 1 + κ· ǫm ǫM − 1

  • ·
  • 1 + ρ

2 · (1 − τ)

  • Small impact of UI on unemployment: ǫM ↓

Strong rat-race externality: ǫm/ǫM ↑ τ ↑: UI should be more generous

Landais, Michaillat, and Saez (08/2011) Optimal Unemployment Insurance 27 / 42

slide-79
SLIDE 79

Intuition for Optimal UI in Recession

τ 1 − τ ≈ ρ ǫM · (1 − τ)+ κ 1 + κ· ǫm ǫM − 1

  • ·
  • 1 + ρ

2 · (1 − τ)

  • Small impact of UI on unemployment: ǫM ↓

Strong rat-race externality: ǫm/ǫM ↑ τ ↑: UI should be more generous

Landais, Michaillat, and Saez (08/2011) Optimal Unemployment Insurance 27 / 42

slide-80
SLIDE 80

Intuition for Optimal UI in Recession

τ 1 − τ ≈ ρ ǫM · (1 − τ)+ κ 1 + κ· ǫm ǫM − 1

  • ·
  • 1 + ρ

2 · (1 − τ)

  • Small impact of UI on unemployment: ǫM ↓

Strong rat-race externality: ǫm/ǫM ↑ τ ↑: UI should be more generous

Landais, Michaillat, and Saez (08/2011) Optimal Unemployment Insurance 27 / 42

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SLIDE 81

Optimal Replacement Rate τ is Countercyclical

τ = cu/ce captures generosity of UI Use exact optimal UI formula Prove: optimal UI is more generous in recessions: dτ da < 0

Landais, Michaillat, and Saez (08/2011) Optimal Unemployment Insurance 28 / 42

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SLIDE 82

1 Optimal UI Formula: τ = τ(ǫm, ǫM, 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

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SLIDE 83

Flows of Workers

Landais, Michaillat, and Saez (08/2011) Optimal Unemployment Insurance 30 / 42

slide-84
SLIDE 84

Flows of Workers

Landais, Michaillat, and Saez (08/2011) Optimal Unemployment Insurance 30 / 42

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SLIDE 85

Stochastic Environment

Fluctuations are driven by technology {at}∞

t=0.

All workers receive the same ce

t (if employed) and

cu

t (if unemployed) at time t

Firm’s, worker’s, and government’s decisions at time t are measurable wrt at = (a0, a1, . . . , at). Government can commit to policy.

Landais, Michaillat, and Saez (08/2011) Optimal Unemployment Insurance 31 / 42

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SLIDE 86

Worker’s Problem (Labor Supply)

Given {at, θt, ce

t , cu t }∞ t=0,

Choose job-search effort {et}∞

t=0

To maximize expected utility: E0

+∞

  • t=0

δt (1 − ns

t)v(cu t ) + ns tv(ce t ) −

  • 1 − (1 − s)ns

t−1

  • k(et)
  • Subject to

ns

t =

  • 1 − (1 − s) · ns

t−1

  • · et · f (θt) + (1 − s) · ns

t−1.

Landais, Michaillat, and Saez (08/2011) Optimal Unemployment Insurance 32 / 42

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SLIDE 87

Firm’s Problem (Labor Demand)

Given {at, θt, wt}∞

t=0

Choose hiring {ht}∞

t=0

To maximize expected profits: E0

+∞

  • t=0

δt

  • at ·
  • nd

t

α − wt · nd

t − r · at

q(θt) · ht

  • Subject to:

nd

t = (1 − s) · nd t−1 + ht.

Landais, Michaillat, and Saez (08/2011) Optimal Unemployment Insurance 33 / 42

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SLIDE 88

Equilibrium on the Labor Market

Wage is indeterminate wt = ω · aγ

t , γ < 1

Tightness θ equalizes labor supply and labor demand nt ≡ ns

t = nd t

Landais, Michaillat, and Saez (08/2011) Optimal Unemployment Insurance 34 / 42

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SLIDE 89

Government’s Problem

Given {at}∞

t=0

Choose consumptions {ce

t , cu t }∞ t=0

To maximize worker’s expected utility E0

+∞

  • t=0

δt {(1 − nt)v(cu

t ) + ntv(ce t ) − [1 − (1 − s)nt−1] k(et)}

Subject to worker’s and firm’s optimality conditions, equilibrium conditions, and budget constraints nt · wt = nt · ce

t + (1 − nt) · cu t .

Landais, Michaillat, and Saez (08/2011) Optimal Unemployment Insurance 35 / 42

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SLIDE 90

Calibration: US, weekly frequency

Interpretation Value Source ρ Relative risk aversion 1 Chetty [’06] γ Real wage rigidity 0.5 Haefke et al. [’08], Pissarides [’09] η Effort-elasticity of matching 0.7 Petrongolo & Pissarides [’01] s Separation rate 0.95% JOLTS, 2000–2010 ωm Effectiveness of matching 0.23 JOLTS, 2000–2010 r Recruiting cost 0.21 Barron et al. [’97], Silva & Toledo [’09] α Marginal returns to labor 0.67 Matches labor share= 0.66 ω Steady-state real wage 0.67 Matches unemployment= 5.9% κ Curvature of disutility of effort 2.1 Matches Meyer [’90] ωk 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

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SLIDE 91

Steady State: Optimal Replacement Rate

0.04 0.05 0.06 0.07 0.08 0.09 0.1 0.6 0.65 0.7 0.75 0.8 0.85 Unemployment rate Replacement rate τ

Landais, Michaillat, and Saez (08/2011) Optimal Unemployment Insurance 37 / 42

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SLIDE 92

Steady State: Optimal Benefit Rate

0.04 0.05 0.06 0.07 0.08 0.09 0.1 0.6 0.65 0.7 0.75 0.8 0.85 Unemployment rate Benefit rate

Landais, Michaillat, and Saez (08/2011) Optimal Unemployment Insurance 37 / 42

slide-93
SLIDE 93

Steady State: Optimal Labor Tax Rate

0.04 0.05 0.06 0.07 0.08 0.09 0.1 0.02 0.04 0.06 0.08 0.1 Unemployment rate Labor tax rate

Landais, Michaillat, and Saez (08/2011) Optimal Unemployment Insurance 37 / 42

slide-94
SLIDE 94

Comparison with Baily [’78] Formula

0.04 0.05 0.06 0.07 0.08 0.09 0.1 0.1 0.2 0.3 0.4 0.5 Unemployment rate Elasticity of (1−n) wrt ∆ C Micro

Optimal UI formula in infinite-horizon model Landais, Michaillat, and Saez (08/2011) Optimal Unemployment Insurance 38 / 42

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SLIDE 95

Comparison with Baily [’78] Formula

0.04 0.05 0.06 0.07 0.08 0.09 0.1 0.4 0.5 0.6 0.7 0.8 0.9 1 Unemployment rate Replacement rate τ Baily with micro−elasticity

Optimal UI formula in infinite-horizon model Landais, Michaillat, and Saez (08/2011) Optimal Unemployment Insurance 38 / 42

slide-96
SLIDE 96

Comparison with Baily [’78] Formula

0.04 0.05 0.06 0.07 0.08 0.09 0.1 0.1 0.2 0.3 0.4 0.5 Unemployment rate Elasticity of (1−n) wrt ∆ C Micro Macro

Optimal UI formula in infinite-horizon model Landais, Michaillat, and Saez (08/2011) Optimal Unemployment Insurance 38 / 42

slide-97
SLIDE 97

Comparison with Baily [’78] Formula

0.04 0.05 0.06 0.07 0.08 0.09 0.1 0.4 0.5 0.6 0.7 0.8 0.9 1 Unemployment rate Replacement rate τ Baily with micro−elasticity Baily with macro−elasticity

Optimal UI formula in infinite-horizon model Landais, Michaillat, and Saez (08/2011) Optimal Unemployment Insurance 38 / 42

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SLIDE 98

Comparison with Baily [’78] Formula

0.04 0.05 0.06 0.07 0.08 0.09 0.1 0.1 0.2 0.3 0.4 0.5 Unemployment rate

εm/εM − 1 > 0

Elasticity of (1−n) wrt ∆ C Micro Macro

Optimal UI formula in infinite-horizon model Landais, Michaillat, and Saez (08/2011) Optimal Unemployment Insurance 38 / 42

slide-99
SLIDE 99

Comparison with Baily [’78] Formula

0.04 0.05 0.06 0.07 0.08 0.09 0.1 0.4 0.5 0.6 0.7 0.8 0.9 1 Unemployment rate Replacement rate τ Baily with micro−elasticity Baily with macro−elasticity Approximated formula

Optimal UI formula in infinite-horizon model Landais, Michaillat, and Saez (08/2011) Optimal Unemployment Insurance 38 / 42

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SLIDE 100

Comparison with Baily [’78] Formula

0.04 0.05 0.06 0.07 0.08 0.09 0.1 0.4 0.5 0.6 0.7 0.8 0.9 1 Unemployment rate Replacement rate τ Baily with micro−elasticity Baily with macro−elasticity Approximated formula Optimum

Optimal UI formula in infinite-horizon model Landais, Michaillat, and Saez (08/2011) Optimal Unemployment Insurance 38 / 42

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SLIDE 101

Dynamics: Government Cannot Borrow

−1% −0.5% 0% Technology 0% 2% 4% 6% Unemployment 0% 0.5% 1% Replacement rate τ 0% 0.5% 1% Deficit 50 100 150 200 250 300 −1% −0.5% 0% 0.5% 1% Consumption (employed) Weeks after shock 50 100 150 200 250 300 −1% −0.5% 0% 0.5% 1% Consumption (unemployed) Weeks after shock

Landais, Michaillat, and Saez (08/2011) Optimal Unemployment Insurance 39 / 42

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SLIDE 102

Dynamics: Government Can Borrow

−1% −0.5% 0% Technology No deficit spending Deficit spending 0% 2% 4% 6% Unemployment 0% 0.5% 1% Replacement rate τ 0% 0.5% 1% Deficit 50 100 150 200 250 300 −1% −0.5% 0% 0.5% 1% Consumption (employed) Weeks after shock 50 100 150 200 250 300 −1% −0.5% 0% 0.5% 1% Consumption (unemployed) Weeks after shock

Landais, Michaillat, and Saez (08/2011) Optimal Unemployment Insurance 39 / 42

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SLIDE 103

Flows of Workers: Finite-Duration Model

Landais, Michaillat, and Saez (08/2011) Optimal Unemployment Insurance 40 / 42

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SLIDE 104

Flows of Workers: Finite-Duration Model

Landais, Michaillat, and Saez (08/2011) Optimal Unemployment Insurance 40 / 42

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SLIDE 105

Flows of Workers: Finite-Duration Model

Landais, Michaillat, and Saez (08/2011) Optimal Unemployment Insurance 40 / 42

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SLIDE 106

Optimal Composition of Unemployment

0.98 1 1.02 1.04 0.02 0.04 0.06 0.08 0.1 Technology Unemployment rate Total Eligible Ineligible

Landais, Michaillat, and Saez (08/2011) Optimal Unemployment Insurance 41 / 42

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SLIDE 107

Optimal Job-Search Effort

0.04 0.05 0.06 0.07 0.08 0.09 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 Unemployment rate Search effort Eligible Ineligible

Landais, Michaillat, and Saez (08/2011) Optimal Unemployment Insurance 41 / 42

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SLIDE 108

Optimal Weekly Arrival Rate of Ineligibility

0.04 0.05 0.06 0.07 0.08 0.09 0.05 0.1 Unemployment rate Arrival rate of ineligibility

Landais, Michaillat, and Saez (08/2011) Optimal Unemployment Insurance 41 / 42

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SLIDE 109

Optimal Expected Duration of Benefits

0.04 0.05 0.06 0.07 0.08 0.09 100 200 300 400 500 Unemployment rate Benefit duration (weeks)

Landais, Michaillat, and Saez (08/2011) Optimal Unemployment Insurance 41 / 42

slide-110
SLIDE 110

Next Step: Estimation of ǫm and ǫM

Estimation of ǫm:

◮ evidence for Germany: Schmieder et al. [’11] ◮ our data: Continuous Wage & Benefit History (CWBH) ◮ UI data for 7 US states, 1978–1983 ◮ regression kink design: use kink in schedule of UI benefits ◮ details: Micro-elasticity

Direct estimation of ǫM:

◮ preliminary evidence: Notowidigdo & Kroft [’11] ◮ but, very difficult

Indirect estimation of ǫM: estimation of ǫm/ǫM

◮ our data: Regional Extended Benefit Program (REBP) ◮ Austria, 1988–1995 ◮ difference-in-difference: compare job-finding probability

  • f non-treated in treated vs. non-treated regions

◮ details: Macro-elasticity Landais, Michaillat, and Saez (08/2011) Optimal Unemployment Insurance 42 / 42

slide-111
SLIDE 111

BACK-UP SLIDES

Landais, Michaillat, and Saez (08/2011) Optimal Unemployment Insurance 43 / 42

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SLIDE 112

Equilibrium: Pissarides [’00] Model

0.85 0.9 0.95 1 0.05 0.1 0.15 0.2 Employment Canonical model Gross marginal profit Marginal recruiting expenses

Return Landais, Michaillat, and Saez (08/2011) Optimal Unemployment Insurance 44 / 42

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SLIDE 113

Equilibrium: Pissarides [’00] Model

0.85 0.9 0.95 1 0.05 0.1 0.15 0.2 Employment Canonical model Gross marginal profit Marginal recruiting expenses

Return Landais, Michaillat, and Saez (08/2011) Optimal Unemployment Insurance 44 / 42

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SLIDE 114

Equilibrium: Hall [’05] Model

0.85 0.9 0.95 1 0.01 0.02 0.03 0.04 0.05 Employment Model with wage rigidity Gross marginal profit Marginal recruiting expenses

Return Landais, Michaillat, and Saez (08/2011) Optimal Unemployment Insurance 44 / 42

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SLIDE 115

Equilibrium: with Job Rationing

0.85 0.9 0.95 1 0.01 0.02 0.03 0.04 0.05 Employment Model with job rationing Gross marginal profit Marginal recruiting expenses Rationing unemp. Frictional unemp.

Return Landais, Michaillat, and Saez (08/2011) Optimal Unemployment Insurance 44 / 42

slide-116
SLIDE 116

Equilibrium: with Job Rationing

0.85 0.9 0.95 1 0.01 0.02 0.03 0.04 0.05 Employment Model with job rationing Gross marginal profit Marginal recruiting expenses Frictional unemp. Rationing unemp.

Return Landais, Michaillat, and Saez (08/2011) Optimal Unemployment Insurance 44 / 42

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SLIDE 117

Optimal UI Formula in Infinite-Horizon Model

τ 1 − τ ≈ ρ ǫM ·(1 − τ)+1 + κ κ · ǫm ǫM − 1

  • ·
  • 1 + ρ

2 · (1 − τ)

  • Return

Landais, Michaillat, and Saez (08/2011) Optimal Unemployment Insurance 45 / 42

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SLIDE 118

Unemployment Rates in CWBH

4 6 8 10 12 14 U rate (CPS) 1978m1 1980m1 1982m1 1984m1 GA ID LA MO NM PA WA

Return Landais, Michaillat, and Saez (08/2011) Optimal Unemployment Insurance 46 / 42

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SLIDE 119

Weekly UI Benefits Schedule: Missouri

25 50 75 100 125 150 wba 2000 4000 6000 Highest Quarter Earnings 1978−1980 1980−1983

Return Landais, Michaillat, and Saez (08/2011) Optimal Unemployment Insurance 47 / 42

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SLIDE 120

RKD Design

75 150 wba 5 10 15 duration 2500 5000 Highest Quarter Earnings duration wba

MO 1980−84

Return Landais, Michaillat, and Saez (08/2011) Optimal Unemployment Insurance 48 / 42

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SLIDE 121

Micro-Elasticity over the Business Cycle

SC 80 SC 82 SC 83 GA 78 GA 80 GA 83 NM 80 NM 81 NM 82 NM 83 MO 78 MO 80 MO 82 MO 83 ID 78 ID 80 ID 80 ID 81 ID 82

−.5 .5 1 Elasticity 4 6 8 10 12 Unemployment rate

Return Landais, Michaillat, and Saez (08/2011) Optimal Unemployment Insurance 49 / 42

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SLIDE 122

Regional Distribution of REBP

Return Landais, Michaillat, and Saez (08/2011) Optimal Unemployment Insurance 50 / 42

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SLIDE 123

Difference in Non-Employment Duration: Age 50-53

−10 10 20 30 40 weeks 1980 1985 1990 1995 2000 Year of entry into unemployment Return Landais, Michaillat, and Saez (08/2011) Optimal Unemployment Insurance 51 / 42

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SLIDE 124

Difference in Non-Employment Duration: Age 46-49

−4 −2 2 weeks 1980 1985 1990 1995 2000 Year of entry into unemployment Return Landais, Michaillat, and Saez (08/2011) Optimal Unemployment Insurance 51 / 42