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February 20, 2019 1
LABOR MARKETS – STRUCTURE AND POLICY
Introduction – Motivation
❑ Labor market structure and analysis changing over the years
❑ Secular changes
❑ Cyclical changes
❑ Labor market conditions a prime concern for policy
❑ Search and matching in labor markets
❑ Technological primitives
❑ Costs of posting job openings
❑ Matching function
❑ But many other components of hiring costs
February 20, 2019 2
LABOR MARKETS – STRUCTURE AND POLICY
Introduction – Motivation
❑ Labor market structure and analysis changing over the years
❑ Secular changes
❑ Cyclical changes
❑ Labor market conditions a prime concern for policy
❑ Search and matching in labor markets
❑ Technological primitives
❑ Costs of posting job openings
❑ Matching function
❑ But many other components of hiring costs
❑ Screening/selection in labor markets
❑ Technological primitives
❑ Costs of integrating new workers into production process
❑ Distribution of idiosyncratic “match-quality” shocks for new workers
❑ (Davis, Faberman, & Haltiwanger (2013 QJE): ≈ 60% of hiring costs are vacancy costs)
February 20, 2019 3
LABOR MARKETS – STRUCTURE AND POLICY
Introduction – Questions
❑ Benevolent policy desires efficient labor markets
❑ Characterization of efficient allocations (“first-best”)
❑ Model-consistent efficiency
❑ Model-consistent distortions
❑ Builds on analysis of
❑ GE selection efficiency in Chugh and Merkl (2016 IER)
❑ GE matching efficiency in Arseneau and Chugh (2012 JPE)
February 20, 2019 4
LABOR MARKETS – STRUCTURE AND POLICY
Introduction – Questions
❑ Benevolent policy desires efficient labor markets
❑ Characterization of efficient allocations (“first-best”)
❑ Model-consistent efficiency
❑ Model-consistent distortions
❑ Builds on analysis of
❑ GE selection efficiency in Chugh and Merkl (2016 IER)
❑ GE matching efficiency in Arseneau and Chugh (2012 JPE)
❑ Characterization of optimal policy
❑ Ramsey (1927) (“second-best”)
❑ Lucas and Stokey (1984 JME), CCK (1991 JMCB, 1999 Handbook of Macro), Werning (2007 QJE), many others
❑ Recent summary by Stiglitz (2014 NBER WP)
❑ Pigovian corrective taxation
❑ Ramsey (1927) was response to question posed by Pigou w/o lump-sum T
❑ Pigou (1928, A Study in Public Finance) incorporated Ramsey results w/ T
February 20, 2019 5
LABOR MARKETS – STRUCTURE AND POLICY
Introduction – Methodology
❑ Calibrate exogenous policy economy to hit empirical volatility of
❑ ue, lfp, and η(ε)
❑ Requires distortionary structural parameters
February 20, 2019 6
LABOR MARKETS – STRUCTURE AND POLICY
Introduction – Methodology
❑ Calibrate exogenous policy economy to hit empirical volatility of
❑ ue, lfp, and η(ε)
❑ Requires distortionary structural parameters
❑ Conduct optimal policy given structural parameters
February 20, 2019 7
LABOR MARKETS – STRUCTURE AND POLICY
Introduction – Ramsey Results
❑ Calibrate exogenous policy economy to hit empirical volatility of
❑ ue, lfp, and η(ε)
❑ Requires distortionary structural parameters
❑ Conduct optimal policy given structural parameters
❑ Labor tax rate smoothing not optimal in either selection model…
Labor Selection Walrasian
Relative SD (wrt GDP)
1.0 ≈ 0
(CCK 1999, Werning 2007 QJE, many others)
February 20, 2019 8
LABOR MARKETS – STRUCTURE AND POLICY
Introduction – Ramsey Results
❑ Calibrate exogenous policy economy to hit empirical volatility of
❑ ue, lfp, and η(ε)
❑ Requires distortionary structural parameters
❑ Conduct optimal policy given structural parameters
❑ Labor tax rate smoothing not optimal in either selection model…
❑ …or in matching model
Labor Selection Labor Matching Walrasian
Relative SD (wrt GDP)
1.0 5.6
(Arseneau and Chugh 2012 JPE)
≈ 0
(CCK 1999, Werning 2007 QJE, many others)
February 20, 2019 9
LABOR MARKETS – STRUCTURE AND POLICY
Introduction – Ramsey Results
❑ Calibrate exogenous policy economy to hit empirical volatility of
❑ ue, lfp, and η(ε)
❑ Requires distortionary structural parameters
❑ Conduct optimal policy given structural parameters
❑ Labor tax rate smoothing not optimal in either selection model…
❑ …or in matching model
❑ Hiring subsidies large in long-run –
❑ Hiring subsidies volatile in business cycles
❑ Economic difference vs. Walrasian labor markets?
Labor Selection Labor Matching Walrasian
Relative SD (wrt GDP)
1.0 5.6
(Arseneau and Chugh 2012 JPE)
≈ 0
(CCK 1999, Werning 2007 QJE, many others)
81%h =
February 20, 2019 10
LABOR MARKETS – MODEL-CONSISTENT WEDGES
Introduction – Interpretation
❑ Technological primitives
❑ Develop selection-model consistent transformation function and MRTs
❑ Aggregate goods production technology
❑ Aggregate matching technology
model-consistent decentralized wedges
❑ Tax volatility EFFICIENT fluctuations
❑ Selection model wedge fluctuations EXACTLY = 0
February 20, 2019 11
LABOR MARKETS – MODEL-CONSISTENT WEDGES
Introduction – Interpretation
❑ Technological primitives
❑ Develop selection-model consistent transformation function and MRTs
❑ Aggregate goods production technology
❑ Aggregate matching technology
model-consistent decentralized wedges
❑ Tax volatility EFFICIENT fluctuations
❑ Selection model wedge fluctuations EXACTLY = 0
❑ Analytically characterize source of externalities
❑ Cost gap = marginal hiring cost – avg. hiring cost
❑ “Selection Market Tightness”
❑ Play highly similar role as market tightness externalities in matching model
❑ Compare and contrast with search and matching model
February 20, 2019 12
LABOR MARKETS – MATCHING VS. SELECTION
Introduction – Interpretation
❑ Matching and selection two distinct components of recruiting process
“match quality”
February 20, 2019 13
LABOR MARKETS – MATCHING VS. SELECTION
Introduction – Interpretation
❑ Matching and selection two distinct components of recruiting process
❑ Components of recruiting costs
❑ Vacancy posting costs
❑ Screening costs
❑ Training costs
“match quality”
February 20, 2019 14
CONTRIBUTION TO LABOR & POLICY LITERATURES
Introduction – Contribution
❑ Need to know appropriate “wedges” for designing optimal policy
❑ Fiscal policy
❑ Monetary policy
❑ Regulatory policy
❑ Recent literature on labor selection
❑ Lechthaler, Merkl, and Snower (2010 JECD)
❑ Merkl and van Rens (2012)
❑ Brown, Merkl, and Snower (2015 MD)
❑ Chugh and Merkl (2016 IER)
❑ Faia, Lechthaler, and Merkl (2014 JMCB) (optimal monetary policy)
❑ Baydur (2017 AEJ: Macro) – partial match quality revelation
February 20, 2019 15
CONTRIBUTION TO LABOR & POLICY LITERATURES
Introduction – Contribution
❑ Need to know appropriate “wedges” for designing optimal policy
❑ Fiscal policy
❑ Monetary policy
❑ Regulatory policy
❑ Recent literature on labor selection
❑ Lechthaler, Merkl, and Snower (2010 JECD)
❑ Merkl and van Rens (2012)
❑ Brown, Merkl, and Snower (2015 MD)
❑ Chugh and Merkl (2016 IER)
❑ Faia, Lechthaler, and Merkl (2014 JMCB) (optimal monetary policy)
❑ Baydur (2017 AEJ: Macro) – partial match quality revelation
❑ Previous work
❑ Arseneau, Chahrour, Chugh, Finkelstein Shapiro (2015 JMCB) (customer matching)
❑ Chugh and Ghironi (2015) (endogenous product varieties)
❑ Arseneau and Chugh (2012 JPE)
❑ Aruoba and Chugh (2010 JET) (new monetarist)
❑ Arseneau and Chugh (2008 JME) (nominal wage rigidities in labor matching model)
February 20, 2019 16
OUTLINE
Introduction – Plan
❑ Model – Structure of Labor Markets
❑ GE efficiency – definitions of model-consistent wedges
❑ Extended model (labor search and matching + labor selection)
❑ Focus on labor selection model (this paper)
❑ Positive analysis (non-Ramsey policy)
❑ Ramsey equilibrium
❑ Calibration
❑ Normative analysis (Ramsey policy) – wedge/distortion smoothing
❑ Compare and contrast with search and matching model
❑ Implications for Beveridge Curve
❑ Wage determination
❑ Model-consistent wedges and “market tightness”
❑ Conclusion
February 20, 2019 17
OUTLINE
Plan
❑ Model – Structure of Labor Markets
❑ GE efficiency – definitions of model-consistent wedges
❑ Extended model (labor search and matching + labor selection)
❑ Focus on labor selection model (this paper)
❑ Positive analysis (non-Ramsey policy)
❑ Ramsey equilibrium
❑ Calibration
❑ Normative analysis (Ramsey policy) – wedge/distortion smoothing
❑ Compare and contrast with search and matching model
❑ Implications for Beveridge Curve
❑ Wage determination
❑ Model-consistent wedges and “market tightness”
❑ Conclusion
February 20, 2019 18
LABOR MARKET STRUCTURE
Selection vs. Matching
❑ Matching and selection two distinct concepts of frictional labor markets
“match quality”
February 20, 2019 19
LABOR MARKET STRUCTURE
Definitions
❑ Distribution of idiosyncratic hiring costs εi
better workers worse workers
20
Definitions
❑ endogenous selection threshold
❑ endogenous selection probability
❑ average training cost for all newly-selected employees
❑ cross-sectional SD of training cost distribution
❑ vacancies
❑ matching probability for actively searching individual
❑ vacancy posting cost
❑ aggregate matching function
February 20, 2019
t
( )t
( )
( )
t
t
H
LABOR MARKET STRUCTURE
tv
( ),t tm s v
h
tk
February 20, 2019 21
OUTLINE
Plan
❑ Model – Structure of Labor Markets
❑ GE efficiency – definitions of model-consistent wedges
❑ Extended model (labor search and matching + labor selection)
❑ Focus on labor selection model
❑ Positive analysis (non-Ramsey policy)
❑ Ramsey equilibrium
❑ Calibration
❑ Normative analysis (Ramsey policy) – wedge/distortion smoothing
❑ Compare and contrast with search and matching model
❑ Implications for Beveridge Curve
❑ Wage determination
❑ Model-consistent wedges and “market tightness”
❑ Conclusion
22
MATCHING + SELECTION EFFICIENCY
Matching & Selection: Model-Consistent Wedges
❑ Social Planner
Aggregate LOM for total employment
Goods resource constraint( )( )
( ,)( )
t t t tt
t t tt
t
m s v vc gH
z n
+ + + =
February 20, 2019
( )0
,
, , ,0
max ( )t t tt
t
t tc n
tvs
E u c h lfp
=
−
s.t.
((1 ))t tt
h
t tslf kp n − +
23
MATCHING + SELECTION EFFICIENCY
Matching & Selection: Model-Consistent Wedges
❑ Social Planner
Efficient LFP Efficient vacancy creation
Intertemporal Efficiency
… rewrite in terms of
February 20, 2019
Aggregate LOM for total employment
Goods resource constraint( )( )
( ,)( )
t t t tt
t t tt
t
m s v vc gH
z n
+ + + =
( )0
,
, , ,0
max ( )t t tt
t
t tc n
tvs
E u c h lfp
=
−
model-consistent wedges …
s.t.
((1 ))t tt
h
t tslf kp n − +
( )1 1 1 11 1
1
( , )(1 ( ) ( ))
( )
( )' s t tt
t
t t
t
t t
t
m s vu c H
u zc
+ + + ++
+
+− −=
−
−
24
MATCHING + SELECTION EFFICIENCY
Matching & Selection: Model-Consistent Wedges
❑ Social Planner
Efficient LFP – identical to Arseneau and Chugh 2012 JPE (p. 949, eqn. 21)
Intertemporal Efficiency
h '(lfpt)
u '(ct)
=g ×m
s(s
t,v
t)
mv(s
t,v
t)
( )1 1 1 11 1
1
( , )(1 ( ) ( ))
( )
( )' s t tt
t
t t
t
t t
t
m s vu c H
u zc
+ + + ++
+
+− −=
−
−
February 20, 2019
Aggregate LOM for total employment
Goods resource constraint( )( )
( ,)( )
t t t tt
t t tt
t
m s v vc gH
z n
+ + + =
( )0
,
, , ,0
max ( )t t tt
t
t tc n
tvs
E u c h lfp
=
−
((1 ))t tt
h
t tslf kp n − +
s.t.
MRT between non-participation and output
IMRT: quantity of ct+1 that can be produced by reducing ct by one unit, all else equal, by accumulating “wealth” in form of employment
25
SELECTION EFFICIENCY
Selection: Model-Consistent Wedges
❑ Social Planner
February 20, 2019
s.t.
Aggregate LOM for total employment
Goods resource constraint( )( )
( ,)( )
t t t tt
t t tt
t
m s v vc gH
z n
+ + + =
( )0
,
, , ,0
max ( )t t tt
t
t tc n
tvs
E u c h lfp
=
−
((1 ))t tt
h
t tslf kp n − +
26
SELECTION EFFICIENCY
Selection: Model-Consistent Wedges
❑ Social Planner
❑ zero vacancy posting cost
❑ trivial matching function
February 20, 2019
s.t.
Aggregate LOM for total employment
Goods resource constraint
( )( )
( )
tt
t
t ttt tc g z nH
s
+ + =
1 ( )(1 )t t ttn n s −= − +
( )
,0
, ,0
max ( )t t t
t
t t
tsc n
E u c h lfp
=
−
( )(1 )t t ttl p sf n − +
0 =
1( , )t t t tm s v s v
−=
if 1 =
( , )t t tm s v s=Crucial obs. #1 for decentralized efficiency
27
SELECTION EFFICIENCY
Selection: Model-Consistent Wedges
❑ Social Planner
Efficient LFP
Intertemporal Efficiency
February 20, 2019
Aggregate LOM for total employment
Goods resource constraint
1 ( )(1 )t tt tn n s −= − +
( )
,0
, ,0
max ( )t t t
t
t t
tsc n
E u c h lfp
=
−
( )(1 )t t ttl p sf n − +
s.t.
MRT between non-participation and output
'(
'( )( )
)( )t
t
t t t
h lfp
u cH −=
( )( )
1
1 11 1( ) ( )))
(
1'
)
(( tt
t
t t t
t t
u c
zc
H
u
++ +
+
+ −
−
−−=
Derivation in Appendix D based on transformation frontier
IMRT: quantity of ct+1 that can be produced by reducing ct by one unit, all else equal, by accumulating “wealth” in form of employment
( )( )
( )
tt
t
t tt ttc g s z nH
+ + =
February 20, 2019 28
OUTLINE
Plan
❑ Model – Structure of Labor Markets
❑ GE efficiency – definitions of model-consistent wedges
❑ Extended model (labor search and matching + labor selection)
❑ Focus on labor selection model (this paper)
❑ Positive analysis (non-Ramsey policy)
❑ Ramsey equilibrium
❑ Calibration
❑ Normative analysis (Ramsey policy) – wedge/distortion smoothing
❑ Compare and contrast with search and matching model
❑ Implications for Beveridge Curve
❑ Wage determination
❑ Model-consistent wedges and “market tightness”
❑ Conclusion
February 20, 2019 29
OVERVIEW
Decentralized Economy
❑ Infinitely-lived representative household, measure one of members
❑ Full consumption insurance amongst – i.e., risk-sharing
❑ Employed members
❑ Unemployed members
❑ Members outside the labor force (“leisure”)
❑ Labor income taxation
❑ Government-provided hiring subsidies
❑ Government-provided unemployment benefits
❑ Individual-specific Nash bargaining for newly-hired worker with εi
❑ Only an extensive labor margin, no intensive labor margin
❑ Long-lasting labor-market relationships – exogenous separation rate ρ
Guarantees completeness of tax instruments (Ramsey issue)
New hiresAvg.
hiring costs
Avg. wage for new workers
Marg. wage for threshold new
worker
Wage for incumbent
worker“Tightness”
February 20, 2019 30
FIRMS
Decentralized Economy
❑ Production
❑ New job i produces yit = zt – εit (output – hiring cost)
❑ Hiring costs subsidized at rate τh
❑ (Each incumbent job produces yt = zt)
( )
( )
t
t
H
( )
NEW
t t tn s =( )
( )
e t
t
)( tw I
tw ( ) ( )t t tH −
New hiresAvg.
hiring costs
Avg. wage for new workers
Marg. wage for threshold new
worker
Wage for incumbent
worker“Tightness”
February 20, 2019 31
FIRMS
Decentralized Economy
❑ Production
❑ New job i produces yit = zt – εit (output – hiring cost)
❑ Hiring costs subsidized at rate τh
❑ (Each incumbent job produces yt = zt)
❑ Selection condition (aka labor demand) condition
❑ Given individualistic wage setting, holds for every new worker
( )
( )
t
t
H
( )
NEW
t t tn s =( )
( )
e t
t
)( tw I
tw
Cost of hiring = expected payoff of hiring
1 1 1 1 1(1 ( () ) (1 ) 1 ) ( )h h I
t t t t t t t t t tw Ez w w + + + + + + − = − − + − −
1 1 1 1 1(1 ( () ) (1 )) ()1h h I
t it t it t t t t t tEz w w w + + + + + − = − − + − + −
( ) ( )t t tH −
February 20, 2019 32
HOUSEHOLD OPTIMIZATION
Decentralized Economy
❑ Maximize expected lifetime utility
s.t.disutility of participation
aggregate flow dividends received
lump sum
1 1) ) )1
(1 (1 (1 (1 (1) )j n I n pret
t t t t t t t t t t
j
t tj
t t
c b w sR
n s b
+ −
+ = − − + − + − + −
+
( )0
,, ,0
max ( ) (1 )itt t
t
tc n b
t
t t ts
sE u c h n
=
− − +
wages for measure of incumbent employees
wages for measure of newly-hired employees
ue benefits for unemployed
View χ as fixed institutional parameter, not a cyclical policy choice
February 20, 2019 33
HOUSEHOLD OPTIMIZATION
Decentralized Economy
❑ Maximize expected lifetime utility
1(1 )t t t tn n s −= − + Perceived LOM for employment (“instantaneous production”)
s.t.
flow of new employment relationships = measure of searchers st x probability a searcher successfully lands a job
(exogenous) measure of pre-existing employment relationships terminate
FOCs
disutility of participation
aggregate flow dividends received
lump sum
1 1) ) )1
(1 (1 (1 (1 (1) )j n I n pret
t t t t t t t t t t
j
t tj
t t
c b w sR
n s b
+ −
+ = − − + − + − + −
+
( )0
,, ,0
max ( ) (1 )itt t
t
tc n b
t
t t ts
sE u c h n
=
− − +
wages for measure of incumbent employees
wages for measure of newly-hired employees
ue benefits for unemployed
View χ as fixed institutional parameter, not a cyclical policy choice
February 20, 2019 34
HOUSEHOLD OPTIMIZATION
Decentralized Economy
❑ Optimal labor force participation (aka labor supply) condition
❑ Equates MRS cost with expected payoff of participation
Envelope condition of period t+1 hh-level problem
11| 1 1
1
)) ) ) )
) )
'((1 (1 (1 (1
'( '(
n n It et htt t t t t t t t
t t t
h lfp
u cE w
u c
+
+ + +
+
= − + − − + + −
'( )(1 )
'( )
ntt et
t
h lfp
u c = −
ρ = 1
χ = 1
η = 1
Nests RBC labor supply function
February 20, 2019 35
WAGES
Decentralized Economy
❑ Surplus sharing via individualistic Nash bargaining power
❑ Newly-hired employee bargaining power = αE
❑ Incumbent employee bargaining power = αI
February 20, 2019 36
WAGES
Decentralized Economy
❑ Surplus sharing via individualistic Nash bargaining power
❑ Newly-hired employee bargaining power = αE
❑ Incumbent employee bargaining power = αI
) )( P( D)11
V(E h
it t t itn t
t
w
− −= + +−
)1
PDV( t n
t
tw
= +−
Wage for marginal new worker
Wage for infra-marginal new worker εit
February 20, 2019 37
WAGES
Decentralized Economy
❑ Surplus sharing via individualistic Nash bargaining power
❑ Newly-hired employee bargaining power = αE
❑ Incumbent employee bargaining power = αI
❑ Endogenous wage dispersion
❑ Within newly-hired employees
❑ Across newly-hired employees and incumbent employees
) )( P( D)11
V(E h
it t t itn t
t
w
− −= + +−
)1
PDV( t n
t
tw
= +−
( )PDV
(
(
1( )
))
)(1
he Et
n
t
t
t
tt t
t
H
= +
−
− +
−
Wage for marginal new worker
Wage for infra-marginal new worker εit
Conditional average wage for all new workers
“Tightness”
(1 PD)1
VI I h
t t tn
t
tw
−= + +−
Wage for incumbent worker
February 20, 2019 38
WAGES
Decentralized Economy
❑ Distribution of idiosyncratic hiring costs εi
i
Endogenous selection threshold
better workers worse workers
February 20, 2019 39
GOVERNMENT AND RESOURCE FRONTIER
Decentralized Economy
❑ Government
❑ Government spending
❑ Labor income tax
❑ Hiring subsidies
❑ Provision of ue benefits
❑ One-period state contingent real debt
❑ Aggregate goods resource constraint
❑ Aggregate LOM for labor
)(
()
)(t t t t
tt t
t
Hc g s z n
+ + =
1) ( )(1 t t tt nn s −= − +
February 20, 2019 40
PRIVATE-SECTOR EQUILIBRIUM
Decentralized Economy
❑ State-contingent stochastic processes that satisfy
❑ Household’s bond Euler equations
❑ LFP condition
❑ Selective hiring condition
❑ Nash wage outcomes
❑ Law of motion for employment
❑ Government budget constraint (key condition in Ramsey models)
❑ Goods resource constraint
❑ Given processes
0
, , , , , ( ), ( ),I
t t e
j
t t tt t tc n s w w R
=
0
, , ,n
t
h
t t t tg z
=
)(
()
)(t t t t
tt t
t
Hc g s z n
+ + =
1 ((1 ) )t tt tn n s −= − +
February 20, 2019 41
OUTLINE
Plan
❑ Model – Structure of Labor Markets
❑ GE efficiency – definitions of model-consistent wedges
❑ Extended model (labor search and matching + labor selection)
❑ Focus on labor selection model
❑ Positive analysis (non-Ramsey policy)
❑ Ramsey equilibrium
❑ Calibration
❑ Normative analysis (Ramsey policy) – wedge/distortion smoothing
❑ Compare and contrast with search and matching model
❑ Implications for Beveridge Curve
❑ Wage determination
❑ Model-consistent wedges and “market tightness”
❑ Conclusion
February 20, 2019 42
OUTLINE
Plan
❑ Model – Structure of Labor Markets
❑ GE efficiency – definitions of model-consistent wedges
❑ Extended model (labor search and matching + labor selection)
❑ Focus on labor selection model
❑ Positive analysis (non-Ramsey policy)
❑ Ramsey equilibrium – optimize on
❑ Calibration
❑ Normative analysis (Ramsey policy) – wedge/distortion smoothing
❑ Compare and contrast with search and matching model
❑ Implications for Beveridge Curve
❑ Wage determination
❑ Model-consistent wedges and “market tightness”
❑ Conclusion
is private-sector decision functions
( ) ( ), n h
t t X X
tX
February 20, 2019 43
RAMSEY PROBLEM
Ramsey Problem
❑ Ramsey problem – “Hybrid” Formulation
0
, ,,0
max )( ) (t t t t
t
t tc n
ts
E u c h lfp
=
−s.t.
0 0
0
) ) ) (1 )'( '( '(t d
t t t t t t
t
c lE u c h lfp u c Afp d
=
− − − =
Lagrange multiplier for each t
Single Lagrange multiplier μ
PVIC
) / ( )(( ( ))t t t tt t ttc g H s z n + + =
lfpt ≡ (1-ηt)st + nt
February 20, 2019 44
RAMSEY PROBLEM
Ramsey Problem
❑ Ramsey problem – “Hybrid” Formulation
0
, ,0
, , ( ), , ,
ma ( ) )(xI n
t t t t t t t th
t
t tc n
ts w w
E u c h lfp
=
−
0 0
0
) ) ) (1 )'( '( '(t d
t t t t t t
t
c lE u c h lfp u c Afp d
=
− − − = Single Lagrange multiplier μ
PVIC
Lagrange multiplier for each t
s.t. ) / ( )(( ( ))t t t tt t ttc g H s z n + + =
1 ((1 ) )t tt tn n s −= − +
11| 1 1
1
)) ) ) )
) )
'((1 (1 (1 (1
'( '(
n n It et htt t t t t t t t
t t t
h lfp
u cE w
u c
+
+ + +
+
= − + − − + + −
1 1 1 1 1(1 ( () ) (1 ) 1 ) ( )h h I
t t t t t t t t t tw Ez w w + + + + + + − = − − + − −
lfpt ≡ (1-ηt)st + nt
February 20, 2019 45
RAMSEY PROBLEM
Ramsey Problem
❑ Ramsey problem – “Hybrid” Formulation
0
, ,0
, , ( ), , ,
ma ( ) )(xI n
t t t t t t t th
t
t tc n
ts w w
E u c h lfp
=
−
0 0
0
) ) ) (1 )'( '( '(t d
t t t t t t
t
c lE u c h lfp u c Afp d
=
− − − = Single Lagrange multiplier μ
PVIC
NOT captured in PVIC
Lagrange multiplier for each t
Lagrange multiplier for each t
s.t. ) / ( )(( ( ))t t t tt t ttc g H s z n + + =
1 ((1 ) )t tt tn n s −= − +
11| 1 1
1
)) ) ) )
) )
'((1 (1 (1 (1
'( '(
n n It et htt t t t t t t t
t t t
h lfp
u cE w
u c
+
+ + +
+
= − + − − + + −
1 1 1 1 1(1 ( () ) (1 ) 1 ) ( )h h I
t t t t t t t t t tw Ez w w + + + + + + − = − − + − −
)1
PDV( t n
t
tw
= +−
( )PDV
(
(
1( )
))
)(1
he Et
n
t
t
t
tt t
t
H
= +
−
− +
−(1 PD)
1V
I I h
t t tn
t
tw
−= + +−
lfpt ≡ (1-ηt)st + nt
February 20, 2019 46
OUTLINE
Plan
❑ Model – Structure of Labor Markets
❑ GE efficiency – definitions of model-consistent wedges
❑ Extended model (labor search and matching + labor selection)
❑ Focus on labor selection model
❑ Positive analysis (non-Ramsey policy)
❑ Ramsey equilibrium – optimize on
❑ Calibration
❑ Normative analysis (Ramsey policy) – wedge/distortion smoothing
❑ Compare and contrast with search and matching model
❑ Implications for Beveridge Curve
❑ Wage determination
❑ Model-consistent wedges and “market tightness”
❑ Conclusion
is private-sector decision functions
( ) ( ), n h
t t X X
tX
February 20, 2019 47
CALIBRATION
Quantitative – Positive Analysis
❑ Parameterize so non-Ramsey economy generates empirically reasonable labor market fluctuations in ue, lfp, and hiring rate η(ε)
❑ Conditional on exogenous fluctuations in
❑ Labor tax rate
❑ Productivity
❑ Government purchases
❑ Crucial parameters – Part I
❑ Distributional form – logistic (also have used normal distribution)
❑ Mean με = 0.30
❑ Cross-sectional standard deviation σε = 0.19
❑ Value of σε disciplined by micro-level evidence
❑ SD σε across new hires of training costs = 207 hours ( = 40% of MPN)
❑ Barron, Black, and Loewenstein (1989 JLE)
❑ Firm-level costs of interviewing/hiring/training new workers
❑ Based on 1982 EOPP (Employment Opportunities Pilot Project)
February 20, 2019 48
CALIBRATION
Quantitative – Positive Analysis
❑ Parameterize so non-Ramsey economy generates empirically reasonable labor market fluctuations in ue, lfp, and hiring rate η(ε)
❑ Conditional on exogenous fluctuations in
❑ Labor tax rate
❑ Productivity
❑ Government purchases
❑ Crucial parameters – Part I
❑ Distributional form – logistic (also have used normal distribution)
❑ Mean με = 0.30
❑ Cross-sectional standard deviation σε = 0.19
❑ Crucial parameters – Part II
❑ Unemployment benefits = 0.70
❑ Worker Nash bargaining power
❑ For both new hires and incumbents
❑ Other parameters “standard” (Table 3)
Crucial obs. #2 for decentralized efficiency
0.50E I = =
February 20, 2019 49
DYNAMIC RESULTS
Quantitative – Positive Analysis
Non-Ramsey Policy
(positive)
Data
Labor Tax RateMean 20% 20%
Rel. SD 0.98 1.8
“Tightness”
( εη(ε) – H(ε) )Rel. SD 5.58
Hiring rate η(ε) Rel. SD 3.5 3.7
Unemployment
LFP
Rel. SD 8.6 5.2
Rel. SD 0.22 0.20
February 20, 2019 50
OUTLINE
Plan
❑ Model – Structure of Labor Markets
❑ GE efficiency – definitions of model-consistent wedges
❑ Extended model (labor search and matching + labor selection)
❑ Focus on labor selection model
❑ Positive analysis (non-Ramsey policy)
❑ Ramsey equilibrium – optimize on
❑ Calibration
❑ Normative analysis (Ramsey policy) – wedge/distortion smoothing
❑ Compare and contrast with search and matching model
❑ Implications for Beveridge Curve
❑ Wage determination
❑ Model-consistent wedges and “market tightness”
❑ Conclusion
is private-sector decision functions
( ) ( ), n h
t t X X
tX
February 20, 2019 51
DYNAMIC RESULTS
Quantitative – Normative Analysis
❑ Ramsey simulations: shocks to z, g conditional on structural parameters
❑ Observations
1. Labor income tax rate smoothing NOT optimal
2. Volatility of η(ε) much smaller than in data
Ramsey
Non-Ramsey Policy
(positive)
Data
Labor Tax RateMean 22% 20% 20%
Rel. SD 0.98 0.98 1.8
“Tightness”
( εη(ε) – H(ε) )Rel. SD 1.09 5.58
Hiring rate η(ε) Rel. SD 0.03 3.5 3.7
Unemployment
LFP
Rel. SD 5.3 8.6 5.2
Rel. SD 0.23 0.22 0.20
February 20, 2019 52
DYNAMIC RESULTS
Quantitative – Normative Analysis
Ramsey Policy
Baseline parameters
Social Planner
Labor Tax Rate
Mean 22% 0%
Rel. SD 0.99 0
“Tightness”
( εη(ε) – H(ε) )Rel. SD 1.09 1.09
Hiring rate η(ε) Rel. SD 0.03 0.03
Unemployment
LFP
Rel. SD 5.39 5.39
Rel. SD 0.04 0.04
❑ Social Planner simulations: shocks to z
❑ Ramsey simulations: Inefficient structural parameters DO appear in problem
❑ Efficient surplus sharing
February 20, 2019 53
DYNAMIC RESULTS
Quantitative – Normative Analysis
Ramsey Policy
Baseline parameters
For ANY (α,χ) pair
Social Planner
Labor Tax Rate
Mean 22% --- 0%
Rel. SD 0.99 --- 0
“Tightness”
( εη(ε) – H(ε) )Rel. SD 1.09 1.09 1.09
Hiring rate η(ε) Rel. SD 0.03 0.04 0.03
Unemployment
LFP
Rel. SD 5.39 5.39 5.39
Rel. SD 0.04 0.04 0.04
❑ Social Planner simulations: shocks to z
❑ Ramsey simulations: Inefficient structural parameters DO appear in problem
❑ Efficient surplus sharing for ANY (α, χ) pair
February 20, 2019 54
DYNAMIC RESULTS
Quantitative – Normative Analysis
❑ Impulse response to productivity
February 20, 2019 55
OUTLINE
Plan
❑ Model – Structure of Labor Markets
❑ GE efficiency – definitions of model-consistent wedges
❑ Extended model (labor search and matching + labor selection)
❑ Focus on labor selection model
❑ Positive analysis (non-Ramsey policy)
❑ Ramsey equilibrium – optimize on
❑ Calibration
❑ Normative analysis (Ramsey policy) – wedge/distortion smoothing
❑ Compare and contrast with search and matching model
❑ Implications for Beveridge Curve
❑ Wage determination
❑ Model-consistent wedges and “market tightness”
❑ Conclusion
is private-sector decision functions
( ) ( ), n h
t t X X
tX
56
BEVERIDGE CURVE
Matching & Selection
❑ Outwards shift of Beveridge Curve during Great Recession
❑ Elsby, Michaels, and Ratner (2015 JEL)
❑ Diamond and Sahin (2014 NY Fed Staff Report)
❑ Reduced-form interpretation: “matching efficiency” Ω has declined
❑ Cheremukhin and Restrepo-Echavarria (2014 EER)
❑ Pescatori and Tasci (2011)
❑ Chahrour, Chugh, and Potter (2018)
❑ Proposal: increase in primitive cross-sectional SD σε
❑ Gets inside black-box Ω
❑ (Distributional explanation at heart of Lester (2010 JET))
February 20, 2019
( , )t tm s v
57
BEVERIDGE CURVE
Matching & Selection
❑ Outwards shift of Beveridge Curve during Great Recession
February 20, 2019
February 20, 2019 58
OUTLINE
Plan
❑ Model – Structure of Labor Markets
❑ GE efficiency – definitions of model-consistent wedges
❑ Extended model (labor search and matching + labor selection)
❑ Focus on labor selection model
❑ Positive analysis (non-Ramsey policy)
❑ Ramsey equilibrium – optimize on
❑ Calibration
❑ Normative analysis (Ramsey policy) – wedge/distortion smoothing
❑ Compare and contrast with search and matching model
❑ Implications for Beveridge Curve
❑ Wage determination
❑ Model-consistent wedges and “market tightness”
❑ Conclusion
is private-sector decision functions
( ) ( ), n h
t t X X
tX
59
NASH BARGAINING & EFFICIENCY
Wage Determination
❑ Suppose zero taxes in decentralized economy
❑ Selection model (no search and matching)
❑ (Trivial matching function)
❑ Nash bargaining parameter achieves efficient allocations
❑ Efficient surplus sharing
February 20, 2019
1E = =
1( , )t t t tm s v s v
−=
ts=
(with 1) =
60
NASH BARGAINING & EFFICIENCY
Wage Determination
❑ Suppose zero taxes in decentralized economy
❑ Selection model (no search and matching)
❑ (Trivial matching function)
❑ Nash bargaining parameter achieves efficient allocations
❑ Efficient surplus sharing
❑ Search and matching model (no selection)
❑ Matching function (fundamental)
❑ Nash bargaining parameter achieves efficient allocations
❑ Hosios (1990) condition
❑ Efficient surplus sharing
February 20, 2019
1E = =
1( , )t t t tm s v s v
−=
ts=
(with 1) =
1E =
1( , )t t t tm s v s v
−= (0.3,0.7)
61
NASH BARGAINING & EFFICIENCY
Wage Determination
❑ Suppose zero taxes in decentralized economy
❑ Matching + Selection
❑ No value of can decentralize efficient surplus sharing
❑ Two competing efficiency goals…
❑ …but only ONE wage determination mechanism
February 20, 2019
E
February 20, 2019 62
OUTLINE
Plan
❑ Model – Structure of Labor Markets
❑ GE efficiency – definitions of model-consistent wedges
❑ Extended model (labor search and matching + labor selection)
❑ Focus on labor selection model
❑ Positive analysis (non-Ramsey policy)
❑ Ramsey equilibrium – optimize on
❑ Calibration
❑ Normative analysis (Ramsey policy) – wedge/distortion smoothing
❑ Compare and contrast with search and matching model
❑ Implications for Beveridge Curve
❑ Wage determination
❑ Model-consistent wedges and “market tightness”
❑ Conclusion
is private-sector decision functions
( ) ( ), n h
t t X X
tX
February 20, 2019 63
LABOR MARKETS – MODEL-CONSISTENT WEDGES
Introduction – Interpretation
❑ Develop selection-model consistent transformation function and MRTs
❑ Aggregate goods resource constraint
❑ Aggregate law of motion of employment
model-consistent decentralized wedges
❑ Tax volatility EFFICIENT fluctuations
❑ Selection model wedge fluctuations EXACTLY = 0
❑ Analytically characterize source of externalities
❑ Cost gap = marginal hiring cost – avg. hiring cost
❑ “Selection Market Tightness”
❑ Play highly similar role as market tightness externalities in matching model
,1t tc tnMRS
− = , ( ) ( )
t t tc t tnMRS H −=Efficient labor
supply from Chugh and Merkl
2016 IER
Efficient labor supply in matching model (Arseneauand Chugh 2012 JPE)
64
LABOR MARKETS
Matching vs. Selection: Wedges
( )
( ) 1t
t
t
h lfp
u c
− =
Efficient labor supply in matching model (Arseneauand Chugh 2012 JPE)
Within-period MRT
1
1
1
(1 )
(
(1 )'( ) 1
)
1
'(
)
t
t
t
t
tt
u c
u cz
+
+
−
+
−
− −
−
−
=
−
−
Intertemporal MRT
February 20, 2019
65
LABOR MARKETS
Matching vs. Selection: Wedges
( )
( ) 1t
t
t
h lfp
u c
− =
Efficient labor supply in matching model (Arseneauand Chugh 2012 JPE)
Within-period MRTWithin-period MRT
1
1
1
(1 )
(
(1 )'( ) 1
)
1
'(
)
t
t
t
t
tt
u c
u cz
+
+
−
+
−
− −
−
−
=
−
−
Intertemporal MRTIntertemporal MRT
Substitute intratemporal conditions into intertemporal conditions
Efficient labor supply in
selection model (Chugh and
Merkl 2016 IER)
February 20, 2019
66
LABOR MARKETS
Matching vs. Selection: Wedges
1
1
1
1
( )
( )(1 )
'( )
'( )
(1 )
(1 )
t
tt
t
t
t
t
h l
u c
u cz
fp
u c
−
+
−
+
+
+
− −
=
−
−
−
Marginal cost of hiring a new employee
Marginal cost of hiring a new employee
February 20, 2019
February 20, 2019 67
CONCLUSIONS
Summary
❑ Selective hiring framework realistic
❑ Selective hiring costs are distinct from vacancy posting costs
❑ Davis, Faberman, and Haltiwanger (2013 QJE): ≈ 40% of hiring costs are NOT vacancy posting costs
❑ Smoothing (model-consistent) wedges the goal for optimal policy
❑ Not smoothing policy instruments
❑ Model-consistent wedges apply to
❑ Fiscal policy
❑ Monetary policy
❑ Regulatory policy