SLIDE 1
beveridgean unemployment gap
Pascal Michaillat (Brown) Emmanuel Saez (Berkeley)
SLIDE 2 unemployment gap: key for macro policies
- US government mandate is to achieve “full employment”
– Humphrey–Hawkins Full Employment Act of 1978 – unemployment gap = distance from “full employment”
- optimal macro policies depend on distance from efficiency
– monetary policy, fiscal policy, labor subsidies/taxes – unemployment gap = distance from efficiency
SLIDE 3 challenges in measuring unemployment gap
- 1. statistical approach (CBO)
– trend unemployment generally not efficient
- 2. Phillips-curve approach
– based on inflation dynamics but not welfare
- 3. our approach: based on welfare in matching model
– same welfare concept as Hosios (1990) – but applicable to any matching model – and implementable with observable statistics
SLIDE 4
- verview of the method: 2009–2019
2% 4% 6% 8% 10%
Unemployment rate
1% 2% 3% 4% 5%
Vacancy rate 2010:Q1 2019:Q3
SLIDE 5
- verview of the method: 2009–2019
2% 4% 6% 8% 10%
Unemployment rate
1% 2% 3% 4% 5%
Vacancy rate Beveridge curve
SLIDE 6
- verview of the method: 2009–2019
2% 4% 6% 8% 10%
Unemployment rate
1% 2% 3% 4% 5%
Vacancy rate Beveridge curve Iso-welfare curve
SLIDE 7
- verview of the method: 2009–2019
2% 4% 6% 8% 10%
Unemployment rate
1% 2% 3% 4% 5%
Vacancy rate Beveridge curve Iso-welfare curve u* = 3.7%
SLIDE 8
theory
SLIDE 9 beveridge curve
– v: vacancy rate – u: unemployment rate – decreasing, convex
- present in many countries (Elbsy, Michaels, Ratner 2015)
- present in many models
– matching (Diamond-Mortensen-Pissarides + variants) – mismatch (Shimer 2007) – stock-flow matching (Ebrahimy, Shimer 2010)
SLIDE 10 social welfare
- recruiting cost: ρ workers / vacancy
- social value of unemployment / employment: z
- social welfare (Hosios 1990):
(1 − u) + u · z − ρ · v(u)
- first-order condition wrt u to maximize welfare:
−1 + z − ρ · v′(u) = 0
v′(u) = −1 − z
ρ
SLIDE 11
efficient unemployment & business cycles
u* Unemployment rate Vacancy rate Beveridge curve: v(u) Iso-welfare curve: slope = -(1 - z)/ρ
SLIDE 12
efficient unemployment & business cycles
Slump Unemployment rate Vacancy rate Beveridge Iso-welfare u > u*
SLIDE 13
efficient unemployment & business cycles
Unemployment rate Vacancy rate Beveridge Boom Iso-welfare u < u*
SLIDE 14
costlier recruiting
u* Unemployment rate Vacancy rate Beveridge Iso-welfare
SLIDE 15
costlier unemployment
u* Unemployment rate Vacancy rate Beveridge Iso-welfare
SLIDE 16
worse mismatch
u* Unemployment rate Vacancy rate Beveridge Iso-welfare
SLIDE 17
measurement
SLIDE 18 sufficient-statistic formula
- labor market tightness: θ = v/u
- Beveridge elasticity: ǫ = −d ln(v)/d ln(u) = −v′(u)/θ
- efficient labor market tightness: θ∗
v′(u) = −1 − z
ρ −v′(u) θ · θ = 1 − z ρ θ∗= 1 − z ρǫ
- u − u∗ obtained from θ − θ∗ through Beveridge curve
SLIDE 19 log beveridge curve: 1951–1959
Log unemployment rate
Log vacancy rate
SLIDE 20 log beveridge curve: 1959–1971
Log unemployment rate
Log vacancy rate
SLIDE 21 log beveridge curve: 1971–1975
Log unemployment rate
Log vacancy rate
SLIDE 22 log beveridge curve: 1975–1987
Log unemployment rate
Log vacancy rate
SLIDE 23 log beveridge curve: 1990–1999
Log unemployment rate
Log vacancy rate
SLIDE 24 log beveridge curve: 2001–2009
Log unemployment rate
Log vacancy rate
SLIDE 25 log beveridge curve: 2010–2019
Log unemployment rate
Log vacancy rate
SLIDE 26 log beveridge curve: 2010–2019
Log unemployment rate
Log vacancy rate
SLIDE 27
beveridge elasticity: 1951–2019
1951 1970 1985 2000 2019 0.3 0.6 0.9 1.2 1.5
SLIDE 28 recruiting cost & value of unemployment
- recruiting cost: 1997 National Employer Survey (Villena 2010)
– 4,500 establishments – firms spend 2.5% of labor costs on recruiting
ρ = 0.72
- value of unemployment: military administrative data for
1993–2004 (Borgschulte, Martorell 2018) – 420,000 veterans – during unemployment: 13%–35% of earnings loss is offset by leisure and home production
z = 0.24
SLIDE 29
efficient unemployment & unemployment gap
1951 1970 1985 2000 2019 0% 3% 6% 9% 12%
Efficient unemployment Actual unemployment
SLIDE 30
alternative calibrations of z
SLIDE 31
baseline efficient unemployment rate
1951 1970 1985 2000 2019 0% 3% 6% 9% 12%
u* u
SLIDE 32
lower bound: z = 0
1951 1970 1985 2000 2019 0% 3% 6% 9% 12%
u* with z = 0.24 u* with z = 0 u
SLIDE 33
chodorow-reich, karabarbounis (2016): z = 0.4
1951 1970 1985 2000 2019 0% 3% 6% 9% 12%
u* with z = 0.4 u u* with z = 0.24
SLIDE 34
hagedorn, manovskii (2008): z = 0.96
1951 1970 1985 2000 2019 0% 5% 10% 15% 20% 25%
u* with z = 0.96 u u* with z = 0.24
SLIDE 35 minnesota z: no unemployment gap
1951 1970 1985 2000 2019
0.25 0.5 0.75 1
