EC981 - Topics in Public Economics
Lecture 10: Unemployment Insurance
Miguel Almunia
MSc in Economics - University of Warwick
Thursday, 13th March, 2014
John Bates Clark Medal
“Awarded to that American economist under 40 who has made a
significant contribution to economic thought and knowledge"
"Widely regarded as one of the field’s most prestigious awards, perhaps
second only to the Nobel in economic science." (Wikipedia link)
Year
Winner
Year
Winner
1991
1979
1977
1951
1947
Paul Krugman*
Joseph Stiglitz*
Martin Feldstein
Milton Friedman*
Paul Samuelson*
* Eventual Nobel Prize winners some years later.
John Bates Clark Medal
“Awarded to that American economist under 40 who has made a
significant contribution to economic thought and knowledge"
"Widely regarded as one of the field’s most prestigious awards, perhaps
second only to the Nobel in economic science." (Wikipedia link)
Year
Winner
Year
Winner
2013
2012
2011
2010
2009
Raj Chetty
Amy Finkelstein
Jonathan Levin
Esther Duflo
Emmanuel Saez
1991
1979
1977
1951
1947
Paul Krugman*
Joseph Stiglitz*
Martin Feldstein
Milton Friedman*
Paul Samuelson*
* Eventual Nobel Prize winners some years later.
Social Insurance: Definition
Social insurance: govt intervention providing insurance to
individuals against adverse shocks
Transfers based on events: unemployment, disability, age
Different from welfare programs, which are means-tested
Social insurance is the biggest and most rapidly growing part
of govt expenditure in many countries, both developed and
developing
Social Insurance: Motivation
Why should the government provide insurance?
Market failures
1
2
3
Information asymmetry and adverse selection
(Aggregate) negative shocks suffered by individuals
Myopic decisions leading to suboptimal long-term choices
Key tradeoff: benefits vs. distortions ⇒ Second-best solutions
Insurance Markets with Adverse Selection
Assume individuals are risk averse
Individuals with highest willingness to pay for insurance have,
on average, highest expected costs
Implies a downward-sloping marginal cost (MC) curve
Key distinction between insurance markets and standard
product markets
Insurers can’t charge individuals based on their privately
known marginal cost
Leads to average cost (AC) pricing
Since AC > MC , equilibrium quantity is lower than the
optimum ⇒ Deadweight loss
Insurance Markets with Adverse Selection
Price
B
Demand curve
A
AC curve
C
Peqm
MC curve
D
Qeqm
J
G
E
F
Qmax Quantity
& Finkelstein (Handbook of Public Economics, 2013)
(Source:
8"29+Chetty
92* !"27&.,0&"2
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Government Intervention in Insurance Markets
What policy tools can the government use to solve the
problem of insurance underprovision?
1
Mandates
(+) Helps deal with adverse selection
(−) Implementation details may be tricky
2
Subsidies
(+) Move towards efficient quantity (when Qeff ̸= Qmarket )
(−) Welfare loss from taxation to raise money for subsidy
Unemployment Insurance
Potential benefits
1
2
Smoother path of consumption (Gruber 1997)
Better job matches
Potential distortions
1
2
3
Less job search, higher unemployment rate
Workers’ preferences distorted towards unstable jobs
Shirking on the job
Unemployment Insurance: Vocabulary
Benefit:
b = Amount received when unemployed
Replacement rate:
r=
b
net benefit
=
net-of-tax wage
w
UI reduces effective gain from finding a new job to w (1 − r )
Unemployment duration:
d = weeks until re-employment
Unemployment Insurance: Baily (1978) model
Optimal benefit level can be expressed as a function of a small
set of parameters in a static model
Viewed as having limited practical relevance
Strong assumptions
Chetty (2006)* shows that formula is actually quite general
Parameters identified by Baily are sufficient statistics for
welfare analysis
Baily (1978): Assumptions
1
Fixed wages
No general equilibrium effects
2
No distortions to firm behaviour
Implicitly assume perfect experience rating (contribution to UI
system based on how many employees fired by each firm)
3
No externalities
Such as spillovers to search
Baily (1978): Setup
Static model with two states: high (employed) and low
(unemployed)
Let wh be income in the high state, and wl < wh be income in
low state
Let A denote wealth
Let consumption in high and low states be ch , cl
Agent initially unemployed. Search cost ψ (e), where e is effort
Choose units of e so that probability of being in the high state
is p (e) = e
Baily (1978): Setup
Workers employed with prob e, unemployed with prob (1 − e)
UI system pays constant benefit b to unemployed
Benefits financed by lump sum tax t (b) when employed
Government’s balanced-budget constraint
e · t (b) = (1 − e) · b
Baily (1978): Setup
Individuals maximize expected utility
max eU (A + we − t (b)) + (1 − e) U (A + wu + b) − ψ (e)
U (c) is strictly increasing and concave: Uc > 0, Ucc < 0
A = assets/wealth owned by individual
we = wage when employed
wu = wage when unemployed (usually zero)
ψ (e) = cost of job search
Baily (1978): First Best
No moral hazard problem
Govt chooses b and e jointly to maximize agent’s welfare
max e U (A + we − t (b)) + (1 − e) U (A + wu + b) − ψ (e)
b,e
!
"
1−e
subj. to t =
b
e
First best solution is full insurance:
U ′ (ce ) = U ′ (cu )
Baily (1978): Second Best
In practice, effort is unobserved by govt, so moral hazard
problem arises
Problem: agents only consider private marginal costs and
benefits when choosing e:
Social marginal product of work is w
Private marginal product is w − b
Agents search too little from social perspective, leading to
efficiency loss
Baily (1978): Second Best
Agents maximize expected utility, taking b and t (b) as given
Don’t internalize that low search has an impact on govt’s
budget constraint
max e U (A + we − t (b)) + (1 − e) U (A + wu + b) − ψ (e)
e
Denote indirect utility by V (b, t)
Govt’s problem (equivalent to Ramsey problem):
max
V (b, t)
s.t.
e (b) t
= [1 − e (b)] b
s.t.
e (b)
= argmaxEU (see above)
b,t
e
Chetty (2006): Sufficient Statistic Formula
At an interior optimum, optimal benefit must satisfy
dV
=0
db (b∗ )
To calculate this derivative, write V (b) as:
V (b) = max e U (A + we − t (b))+(1 − e) U (A + wu + b)−ψ (e)
e
By envelope theorem (agent already optimized):
dV
dt
= (1 − e) U ′ (cl ) − eU ′ (ch )
d (b)
db
Chetty (2006): Sufficient Statistic Formula
Govt’s UI budget constraint t =
dt
db
=
=
# 1−e $
e
b implies:
1−e
b de
− 2
e
e db
ε(1−e),b &
1−e %
1+
e
e
Hence we can rewrite the derivative as:
(
'
%
ε(1−e),b & ′
dV
U (ch )
= (1 − e) U ′ (cl ) − 1 +
db
e
Chetty (2006): Sufficient Statistic Formula
Setting
dV
db
= 0 yields optimality condition:
ε(1−e),b
U ′ (cl ) − U ′ (ch )
=
U ′ (ch )
e
LHS: benefit of transferring $1 from high to low state
RHS: cost of transferring $1 due to behavioural responses
Implementation of this formula requires identification of
U ′ (cl )−U ′ (ch )
U ′ (ch )
Chetty (2006): Consumption-Based Formula
Write marginal utility gap using Taylor expansion
U ′ (cl ) − U ′ (ch ) ≈ U ′′ (ch ) (cl − ch )
Defining coefficient of relative risk aversion γ =
U ′ (cl ) − U ′ (ch )
U ′ (ch )
−U ′′ (c)c
U ′ (c) :
(cl − ch )
ch
∆c
= γ
c
≈ γ
Intuition: gap in marginal utilities is a function of curvature of
utility (risk aversion) and consumption drop from high to low
state
Chetty (2006): Consumption-Based Formula
Optimal unemployment benefit b∗ satisfies:
γ
ε(1−e),b
∆c ∗
(b ) ≈
c
e
where
∆c
c
= consumption drop during unemployment
′′
(ch )ch
γ = −UU ′ (c
= coefficient of relative risk aversion
h)
d log(1−e)
ε(1−e),b =
= elasticity of prob. unemp. w.r.t benefits
d logb
LHS = mgl social benefit of UI; RHS = magl social cost of UI
Gruber (1997): Consumption Smoothing
Brings LHS of Baily-Chetty formula to the data and estimates:
∆c
b
= β1 + β2
c
w
Finds β1 = 0.24 and β2 = −0.28
Without UI, cons drop would be about 24%
Mean drop with current benefit (b = 0.5) is about 10%
Implies a 10 pp increase in UI replace rate cause a 2.8 pp
reduction in the consumption drop
UI provides some (not complete) consumption smoothing
Card, Chetty & Weber (AER-P&P, 2007): Spike at Benefit
Exhaustion
Use Austrian administrative data
Individuals who have worked...
less than 36 months receive up to 20 weeks of UI benefits
more than 36 months receive up to 30 weeks of UI benefits
Important distinction: finding a new job vs. leaving registered
unemployment
CCW (AER-P&P, 2007): Spike at Benefit Exhaustion
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Source: Card, Chetty & Weber (NBER working paper 12893, 2007)
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CCW (AER-P&P, 2007): Spike at Benefit Exhaustion
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Source: Card, Chetty & Weber (NBER working paper 12893, 2007)
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Card, Chetty & Weber (QJE, 2007): Unemployment
Duration
Use discontinuities in Austria’s unemployment benefit system
to estimate liquidity effects
Severance payment is made by firms out of their own funds
Severance Amt.
(months of pay)
ula forfor
sev.
pay amount
for all non-construction wor
Formula
severance
payment:
3
2
0
0
36
60
Job Tenure
Source: Card, Chetty & Weber (QJE, 2007)
Regression Discontinuity Designs
Quasi-experimental variation in severance payments
Allows CCW to study the impact on unemployment duration
Identifying assumption: workers laid off after 36 months are
almost identical as workers laid off after 37 months
Job tenure is called the “running” or “assignment” variable
Main problem: there may be selection around the cutoff
Need to check this empirically
Card, Chetty & Weber (QJE, 2007): Unemployment
Duration
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Source: Card, Chetty & Weber (QJE, 2007)
Card, Chetty & Weber (QJE, 2007): Unemployment
Duration
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Card, Chetty & Weber (QJE, 2007): Unemployment
Duration
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Card, Chetty & Weber (QJE, 2007): Unemployment
Duration
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Card, Chetty & Weber (QJE, 2007): Unemployment
Duration
Receiving severance payments (a form of unemployment
benefit) increases nonemployment duration by about 10 days
(150 vs 160)
Points to the existence of liquidity constraints
If individuals were able to smooth consumption perfectly,
having more cash on hadn would not affect re-employment
probability
Card, Chetty & Weber (QJE, 2007): Other Results
Extended unemployment benefits (30 weeks vs 20) leads to
lower job finding rates in the first 20 weeks
Individuals anticipate longer duration of benefits ans reduce
search effort before the benefit extension takes effect
Neither severance payment nor extended benefits affect the
match quality of subsequent jobs
No evidence of higher wages
No evidence of longer employment duration
Goes against one of the motivations of UI benefits