Involuntary (Unlucky) Unemployment and the Business Cycle
Lawrence Christiano
Mathias Trabandt Karl Walentin
Background
• New Keynesian (NK) models receive lots of attention in central banks.
tt ti i
t lb k
• People use these models to place structure on discussions about monetary policy. – Recent: Curdia‐Woodford, Gertler‐Kiyotaki.
• In recent years, push to introduce labor market variables like unemployment. Why Unemployment?
• Viewed by some as a direct observation on the efficiency with which resources are used (output gap).
– With a theory of unemployment, can investigate this in a structured way
in a structured way.
• Because
Because of imperfect labor market insurance, of imperfect labor market insurance
unemployment viewed as an indicator of welfare cost of business cycles.
– Can assess general presumption that Lucas cost of business cycles conclusion not robust to assumption of imperfect labor market insurance
of imperfect labor market insurance.
What We Do:
• Investigate a particular approach to modeling p y
unemployment.
– Hopenhayn‐Nicolini (1997), Shavell‐Weiss (1979).
• Explore the implications for monetary equilibrium (DSGE) models
equilibrium (DSGE) models.
– Simple NK model without capital (CGG)
– Standard empirical NK model (e.g., CEE, ACEL, SW)
• Estimate the model.
• Does well reproducing response of unemployment and labor force to three identified shocks.
Unemployment
• To be ‘unemployed’ in US data, must
– be ‘willing and able’ to work. – recently, made concrete efforts to find a job.
recently made concrete efforts to find a job
• Our presumption: a person has lower utility when unemployed than when employed
unemployed than when employed.
– Some indicators of utility (health, suicide, subjective sense of well being, kids’ well being) deteriorate when people experience unemployment – Brenner (1979), Ruhm (2000), Oreopoulos, et al (2008), Schimmack et al (2008), Sullivan and von Wachter (2009)
• Current monetary DSGE models with ‘unemployment’:
C
t
t DSGE
d l ith ‘
l
t’
– Unemployed are the lucky ones.
– Finding a job requires no effort.
– US Census Bureau employee dropped into current monetary DSGE US C
B
l
d
di t
t
t
DSGE
models would find zero unemployment.
Miracle to Malaise: What’s next for Japan, Cox and Koo, Economic letter, Dallas Fed, Jan. 2006.
Unemployment
• To be ‘unemployed’ in US data, must
– be ‘willing and able’ to work. – recently, made concrete efforts to find a job.
recently made concrete efforts to find a job
• Our presumption: a person has lower utility when unemployed than when employed
unemployed than when employed.
– Some indicators of utility (health, suicide, subjective sense of well being, kids’ well being) deteriorate when people experience unemployment – Brenner (1979), Ruhm (2000), Oreopoulos, et al (2008), Schimmack et al (2008), Sullivan and von Wachter (2009)
• Current monetary DSGE models with ‘unemployment’:
C
t
t DSGE
d l ith ‘
l
t’
– Unemployed are the lucky ones.
– Finding a job requires no effort.
– US Census Bureau employee dropped into current monetary DSGE US C
B
l
d
di t
t
t
DSGE
models would find zero unemployment.
What we do:
• We explore a simple prototype model of unemployment, which has two key features.
• Probability, p(e), of securing a job is increasing in effort, e. e.
– Essential component of empirical measure of unemployment
• Unemployed worse off than employed. – assume household search effort, e, is not publicly observable.
observable
– full insurance against household labor market outcomes is not possible
outcomes is not possible.
• under perfect consumption insurance, no one would make an effort to secure a job.
Outline
• Simple Clarida‐Gali‐Gertler (CGG) NK model
p
(
)
– Information in unemployment on the output gap.
– Welfare cost of business cycles.
• CEE model
– Evaluate model’s ability to match US macroeconomic data, including unemployment and labor force
– No loss on standard macro variables.
No loss on standard macro variables
– Do fine on unemployment rate and labor force.
Clarida‐Gali‐Gertler Model
• Goods Production:
Yt 
1
1
f
 0 Yi,t di
f
, 1 ≤  f  .
• Monopolists produce intermediate goods
– Technology:
gy Yi,ti t  A t h i,ti t
– Calvo sticky prices:
P i,t 
P i,t−1
with prob.  p
chosen optimally with prob. 1 −  p
– Enter competitive markets to hire labor.
• Policy: R̂ t   R R̂ t−1  1 −  R r  ̂ t  r y x̂ t    t
Households
• This is where the new stuff is...
This is where the new stuff is
Typical Household During Period
Typical Household During Period
l
Draw privately observed, idiosyncratic shock, , from Uniform, 0, 1, that determines utility cost
from Uniform, , that determines utility cost of work:
F   t 1   L l  L .
After observing l decide whether to join
After observing , decide whether to join Household that stays out Household
that stays out
of labor market does not work and has utility out of labor force
logc t
the labor force or stay out. t
Household that joins labor force tries to find a job by choosing effort, e, and receiving ex ante utility ex post utility in case household finds a job
pe t  logc wt  − F −  t 1   L l  L − 1 e 2t
2
pe t     ae t
ex post utility in case of unemployment
 1 − pe t 
logc ut  − 1 e 2t
2
t+1
Typical Household During Period
Typical Household During Period
l
Draw privately observed, idiosyncratic shock, , from Uniform, 0, 1, that determines utility cost
from Uniform, , that determines utility cost of work:
F   t 1   L l  L .
After observing l decide whether to join
After observing , decide whether to join Household that stays out Household
that stays out
of labor market does not work and has utility out of labor force
logc t
the labor force or stay out. t
Household that joins labor force tries to find a job by choosing effort, e, and receiving ex ante utility ex post utility in case household finds a job
pe t  logc wt  − F −  t 1   L l  L − 1 e 2t
2
pe t     ae t
ex post utility in case of unemployment
 1 − pe t 
logc ut  − 1 e 2t
2
t+1
Typical Household During Period
Typical Household During Period
l
Draw privately observed, idiosyncratic shock, , from Uniform, 0, 1, that determines utility cost
from Uniform, , that determines utility cost of work:
F   t 1   L l  L .
After observing l decide whether to join
After observing , decide whether to join Household that stays out Household
that stays out
of labor market does not work and has utility out of labor force
logc t
the labor force or stay out. t
Household that joins labor force tries to find a job by choosing effort, e, and receiving ex ante utility ex post utility in case household finds a job
pe t  logc wt  − F −  t 1   L l  L − 1 e 2t
2
pe t     ae t
ex post utility in case of unemployment
 1 − pe t 
logc ut  − 1 e 2t
2
t+1
Typical Household During Period
Typical Household During Period
l
Draw privately observed, idiosyncratic shock, , from Uniform, 0, 1, that determines utility cost
from Uniform, , that determines utility cost of work:
F   t 1   L l  L .
After observing , decide whether to join After
observing l decide whether to join
the labor force or stay out. t
Household that stays out Household
that stays out
of labor market does not work and has utility outt off labor
l b force
f
logc t
Household that joins labor force tries to find a job by choosing effort, e, and receiving ex ante utility ex post utility in case household finds a job
pe t  logc wt  − F −  t 1   L l  L − 1 e 2t
2
pe t     ae t
ex post utility in case of unemployment
 1 − pe t 
logc ut  − 1 e 2t
2
t+1
Typical Household During Period
Typical Household During Period
l
Draw privately observed, idiosyncratic shock, , from Uniform, 0, 1, that determines utility cost
from Uniform, , that determines utility cost of work:
F   t 1   L l  L .
After observing , decide whether to join After
observing l decide whether to join
the labor force or stay out. t
Household that stays out Household
that stays out
of labor market does not work and has utility outt off labor
l b force
f
logc t
Household that joins labor force tries to find a job by choosing effort, e, and receiving ex ante utility ex post utility in case household finds a job
pe t  logc wt  − F −  t 1   L l  L − 1 e 2t
2
t+1
ex post utility in case of unemployment
 1 − pe t 
pe t     ae t
logc ut  − 1 e 2t
2
Typical Household During Period
Typical Household During Period
l
Draw privately observed, idiosyncratic shock, , from Uniform, 0, 1, that determines utility cost
from Uniform, , that determines utility cost of work:
F   t 1   L l  L .
After observing , decide whether to join After
observing l decide whether to join
the labor force or stay out. t
Household that stays out Household
that stays out
of labor market does not work and has utility outt off labor
l b force
f
logc t
Household that joins labor force tries to find a job by choosing effort, e, and receiving ex ante utility ex post utility in case household finds a job
pe t  logc wt  − F −  t 1   L l  L − 1 e 2t
2
t+1
ex post utility in case of unemployment
 1 − pe t 
pe t     ae t
logc ut  − 1 e 2t
2
Household Insurance
• They need it:
They need it:
– Idiosyncratic work aversion.
– Job‐finding effort, e, may or may not produce a job.
• Assume households gather into large families, like in Merz and Andolfatto
– With complete information:
• Households with low work aversion told to make big effort to find work.
work
• All households given same consumption.
• Not feasible with private information.
– With private information:
• To give households incentive to look for work, must make them better off in case they find work.
• Trade‐off between incentives and insurance.
Optimal Insurance
• Relation of family to household: standard principal/agent relationship.
principal/agent relationship.
– family receives wage from working households
– family observes current period employment status of household.
• For family with given C, h:
– allocates consumption: c wt , c nw
t
– c wt /c
bi
h i
i i h
/ nw
t big enough to incentivize h.
– must satisfy family resource constraint:
h t c wt  1 − h t c nw
 Ct .
t
Family Indirect Utility Function
• Utility:
uC
g t  − zh
 t , h t ,  t   logC
 t, t 
• Where
zh t ,  t   logh t e
F t 1 L fh t , t   L
− 1  1
a 2  2t 1   L  2L
−
fh t ,  t  2 L 1 −  t  L fh t ,  t   L 1 .
2 L  1
• Clarida‐Gali‐Gertler utility function: uC t , h t ,  t   logC t  −
11 L
tht
Family Indirect Utility Function
• Utility:
uC
g t  − zh
 t , h t ,  t   logC
 t, t 
• Where
zh t ,  t   logh t e
F t 1 L fh t , t   L
− 1  1
a 2  2t 1   L  2L
−
fh t ,  t  2 L 1 −  t  L fh t ,  t   L 1 .
2 L  1
• Clarida‐Gali‐Gertler utility function: uC t , h t ,  t   logC t  −
11 L
tht
Family Indirect Utility Function
• Utility:
uC
g t  − zh
 t , h t ,  t   logC
 t, t 
• Where
zh t ,  t   logh t e
F t 1 L fh t , t   L
− 1  1
a 2  2t 1   L  2L
−
fh t ,  t  2 L 1 −  t  L fh t ,  t   L 1 .
2 L  1
• Clarida‐Gali‐Gertler utility function: uC t , h t ,  t   logC t  −
11 L
tht
Family Problem
Family Problem

max
C t ,h t ,B t1 
E 0 ∑  t logC t  − zh t ,  t 
t0
– Subject to:
Subject to:
P t C t  B t1 ≤ B t R t−1  Wt h t  Transfers
f and pprofits
f t.
• Family takes market wage rate as given and tunes incentives so that marginal cost of extra work equals marginal benefit:
C t z h h t ,  t  
Wt
Pt
.
Family Problem
Family Problem

max
C t ,h t ,B t1 
E 0 ∑  t logC t  − zh t ,  t 
t0
– Subject to:
Subject to:
P t C t  B t1 ≤ B t R t−1  Wt h t  Transfers
f and pprofits
f t.
• Family takes market wage rate as given and tunes incentives so that marginal cost of extra work equals marginal benefit:
C t z h h t ,  t  
Wt
Pt
.
Reduced Form Properties
p
• Model is observationally equivalent to standard NK model when represented in terms of output
model, when represented in terms of output, interest rate, inflation:
̂ t  E t ̂ t1 
1−
1
1  p 
 p 1−
p
1   z x̂ t
x̂ t  E t x̂ t1 − R̂ t − ̂ t1 − R̂ ∗t .
R̂ t   R R̂ t−1  1
 −  R r
  ̂ t  r y x̂ t    t ,
Reduced Form Properties
p
• Model is observationally equivalent to standard NK model when represented in terms of output
model, when represented in terms of output, interest rate, inflation:
̂ t  E t ̂ t1 
1− p 1− p 
p
1   z x̂ t
x̂ t  E t x̂ t1 − R̂ t − ̂ t1 − R̂ ∗t .
R̂ t   R R̂ t−1  1 −  R r  ̂ t  r y x̂ t    t ,
Reduced Form Properties
p
z function: disutility of labor for family
• Model is observationally equivalent
to standard NK model when represented in terms of output
model, when represented in terms of output, z hh h
‘curvature
of
disutility
of
labor’:

≡
z
zh
interest rate, inflation:
̂ t  E t ̂ t1 
1− p 1− p 
p
1   z x̂ t
x̂ t  E t x̂ t1 − R̂ t − ̂ t1 − R̂ ∗t .
R̂ t   R R̂ t−1  1 −  R r  ̂ t  r y x̂ t    t ,
Unemployment Gap
• Can express everything in terms of unemployment gap:
unemployment gap:
 − okun x̂ t .
g
ut
 okun
natural rate of unemployment
actual unemployment
g
ut


ut
a 2  2L m  L 1 − u

 0.
2 L
2
1 − u  a  L m
−

u ∗t
Unemployment Gap
• Can express everything in terms of unemployment gap:
unemployment gap:
g
ut
 − okun x̂ t .
 okun
efficient level of unemployment
actual rate of unemployment
g
ut


ut
a 2  2L m  L 1 − u

 0.
2 L
2
1 − u  a  L m
−

u ∗t
Unemployment Gap
• Can express everything in terms of unemployment gap:
unemployment gap:
g
ut
 − okun x̂ t .
 okun
efficient level of unemployment
actual rate of unemployment
g
ut


ut
a 2  2L m  L 1 − u

 0.
2 L
2
1 − u  a  L m
−

u ∗t
Non‐accelerating rate of inflation level of unemployment, NAIRU
Properties of the Model
Properties of the Model
• Calibrated model first... Calibrated model first
Calibration of the Model
T bl 1:
Table
1 Structural
S
l Parameters
P
off Small
S ll Model
M d l Held
H ld Fixed
Fi d Across
A
N
Numerical
i l Experiments
E
i
Parameter
Value
Description

1.03
.03 −.25
Discount
scou t factor
acto
gA
1.0047
Technology growth
p
0.75
Price stickiness
f
1.2
Price markup
R
0.8
Taylor rule: interest smoothing
r
1.5
Taylor rule: inflation
ry
0.2
Taylor rule: output gap
g
0.2
Government consumption share on GDP

0.001 Diffusion speed of technology into government consumption
To parameterize preference and search function, set:
g
0.8
AR(1) government consumption
 g A labor force participation rate: m=0.67
08
l b f 0.8
tiAR(1)
i ti technology
t
0 67
  employment rate: h=0.63
0.8
AR(1) disutility of labor
unemployment rate: u=0.056
0.05489 a Standard deviation government consumption shock
g
Properties
• Replacement ratio
Replacement ratio
c nw  0. 18
cw
– Very
Very low! In model with habit persistence in low! In model with habit persistence in
preferences, replacement ratio = 0.80.
• Cost of business cycles (in % of consumption)…
fb i
l (i % f
i )
Limited Information Model Full Information Model
Technology Shock Only
0.52%
0.57%
Government Spending Shock Only
0.11%
0.13%
Monetary Policy Shock Only
0.07
0.10
Properties
• Replacement ratio
Replacement ratio
c nw  0. 18
cw
– Very
Very low! In model with habit persistence in low! In model with habit persistence in
preferences, replacement ratio = 0.80.
• Cost of business cycles (in % of consumption)
fb i
l (i % f
i )
Limited Information Model Full Information Model
Technology Shock Only
0.52%
0.57%
Government Spending Shock Only
0.11%
0.13%
Monetary Policy Shock Only
0.07
0.10
Properties
• Replacement ratio
Replacement ratio
c nw  0. 18
cw
– Very
Very low! In model with habit persistence in low! In model with habit persistence in
preferences, replacement ratio = 0.80.
• Cost of business cycles (in % of consumption)
fb i
l (i % f
i )
Limited Information Model Full Information Model
Technology Shock Only
0.52%
0.57%
Government Spending Shock Only
0.11%
0.13%
Monetary Policy Shock Only
0 07
0.07
0 10
0.10
• Ongoing: analysis in simple RBC model
Properties
• Replacement ratio
Replacement ratio
c nw  0. 18
cw
– Very
Very low! In model with habit persistence in low! In model with habit persistence in
preferences, replacement ratio = 0.80.
• Cost of business cycles (in % of consumption)
fb i
l (i % f
i )
Limited Information Model Full Information Model
Technology Shock Only
0.52%
0.57%
Government Spending Shock Only
0.11%
0.13%
Monetary Policy Shock Only
0 07
0.07
0 10
0.10
Using Unemployment to Estimate the Output Gap
Output Gap
• CTW, ‘Handbook chapter’
CTW ‘H db k h t ’
• Estimated Simple CGG model:
p
– 2 observables: real GDP per capita growth, unemployment rate
– 4 shocks: technology, labor supply, Phillips curve, monetary policy
– Calibrate economic parameters
Calibrate economic parameters
– Estimate parameters of exogenous processes using: i) Bayesian moment matching estimation and ii) Bayesian full information estimation
Using Unemployment to Estimate the Output Gap
Output Gap
•
What is the information content of the Wh
t i th i f
ti
t t f th
unemployment rate for the output gap? •
Experiment:
– Examine impact of including unemployment on estimate of the output gap for the US economy. Put our theory of unemployment into a medium‐sized DSGE Model
di
i d
d l
• Habit persistence in preferences.
Habit persistence in preferences
• Variable capital utilization.
p
• Investment adjustment costs.
• Wage setting frictions as in Erceg‐Henderson‐Levin.
• Impulse‐response matching by Bayesian methods: – prices reoptimized on average every 2.7 quarters.
i
ti i d
27
t
– wages reoptimized on average every 4 quarters.
Finding
• Estimate VAR impulse responses of macro variables to two technology shocks and monetary i bl t t t h l
h k
d
t
policy shock (following Fisher and ACEL).
• Results:
– Performance on standard macro variables same as CEE and ACEL.
– Performance on unemployment and the labor force is fine.
Micro Implications of Model
• Model: consumption premium higher in booms.
– Have time series evidence on cross‐household variance, V, of log consumption. – Heathcote, Perri and Violante (2010) show V
(
)
ggoes down in three of past 5 recessions.
c wt
V t  1 − h t h t log nw
ct
2
.
• Model: search intensity lower in recessions
– Consistent with evidence on Consistent with evidence on ‘discouraged
discouraged workers
workers’
Conclusion
• Integrated a model of involuntary (unlucky) unemployment into monetary DSGE model.
• Results:
– Obtained
Obtained a theory of Okun
a theory of Okun’ss gap, NAIRU.
gap NAIRU
– Able to match responses of unemployment and labor force to macro shocks.
– Raises several further empirical questions.
R i
l f th
ii l
ti
• Why introduce unemployment?
– A policy variable of direct interest.
– Useful for estimating output gap (CTW, ‘handbook p )
chapter’).
– By bringing in more data, get a better read on unobserved shocks and may improve forecasts.