optimal fiscal policy with labor selection · february 20, 2019 7 labor markets –structure and...

OPTIMAL FISCAL POLICY WITH

LABOR SELECTION

FEBRUARY 20, 2019

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


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


❑ Costs of posting job openings

❑ Matching function

❑ But many other components of hiring costs

❑ Screening/selection in labor markets


❑ 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


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


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


Introduction – Methodology

❑ Calibrate exogenous policy economy to hit empirical volatility of

❑ ue, lfp, and η(ε)

❑ Requires distortionary structural parameters

February 20, 2019 6


Introduction – Methodology




❑ Conduct optimal policy given structural parameters

February 20, 2019 7


Introduction – Ramsey Results





❑ 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








❑ …or in matching model

Labor Selection Labor Matching Walrasian


1.0 5.6

(Arseneau and Chugh 2012 JPE)

≈ 0


February 20, 2019 9








❑ …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


1.0 5.6

(Arseneau and Chugh 2012 JPE)

≈ 0


81%h =

February 20, 2019 10

LABOR MARKETS – MODEL-CONSISTENT WEDGES

Introduction – Interpretation


❑ 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






❑ Aggregate goods production technology

❑ Aggregate matching technology




❑ 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


LABOR MARKETS – MATCHING VS. SELECTION


❑ Matching and selection two distinct components of recruiting process

“match quality”


LABOR MARKETS – MATCHING VS. SELECTION


❑ Matching and selection two distinct components of recruiting process

❑ Components of recruiting costs

❑ Vacancy posting costs

❑ Screening costs

❑ Training costs

“match quality”


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


CONTRIBUTION TO LABOR & POLICY LITERATURES

Introduction – Contribution

❑ Need to know appropriate “wedges” for designing optimal policy

❑ Fiscal policy

❑ Monetary 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)


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


❑ Implications for Beveridge Curve

❑ Wage determination

❑ Model-consistent wedges and “market tightness”

❑ Conclusion


OUTLINE

Plan







❑ Calibration






❑ Conclusion


LABOR MARKET STRUCTURE

Selection vs. Matching

❑ Matching and selection two distinct concepts of frictional labor markets

“match quality”



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


tv

( ),t tm s v

h

tk


OUTLINE

Plan




❑ Focus on labor selection model



❑ Calibration






❑ 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



❑ Social Planner

Efficient LFP Efficient vacancy creation

Intertemporal Efficiency

… rewrite in terms of

February 20, 2019



( ,)( )

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



❑ Social Planner

Efficient LFP – identical to Arseneau and Chugh 2012 JPE (p. 949, eqn. 21)


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



( ,)( )

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.



( ,)( )

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



❑ Social Planner

❑ zero vacancy posting cost

❑ trivial matching function

February 20, 2019

s.t.


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



❑ Social Planner

Efficient LFP


February 20, 2019


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

+ + =


OUTLINE

Plan







❑ Calibration






❑ Conclusion


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”


FIRMS


❑ 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”


FIRMS


❑ 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 −


HOUSEHOLD OPTIMIZATION


❑ 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




❑ 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




❑ 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


WAGES


❑ Surplus sharing via individualistic Nash bargaining power

❑ Newly-hired employee bargaining power = αE

❑ Incumbent employee bargaining power = αI


WAGES





) )( 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


WAGES





❑ 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


WAGES


❑ Distribution of idiosyncratic hiring costs εi

i

Endogenous selection threshold

better workers worse workers


GOVERNMENT AND RESOURCE FRONTIER


❑ 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 −= − +


PRIVATE-SECTOR EQUILIBRIUM


❑ 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 −= − +


OUTLINE

Plan







❑ Calibration






❑ Conclusion


OUTLINE

Plan






❑ Ramsey equilibrium – optimize on

❑ Calibration






❑ Conclusion

is private-sector decision functions

( ) ( ), n h

t t X X

tX


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


RAMSEY PROBLEM

Ramsey Problem


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


=

− − − = Single Lagrange multiplier μ

PVIC


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

'( '(


t t t

h lfp

u cE w

u c

+

+ + +

+

= − + − − + + −

1 1 1 1 1(1 ( () ) (1 ) 1 ) ( )h h I




RAMSEY PROBLEM

Ramsey Problem


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


=

− − − = Single Lagrange multiplier μ

PVIC

NOT captured in PVIC



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

'( '(


t t t

h lfp

u cE w

u c

+

+ + +

+

= − + − − + + −

1 1 1 1 1(1 ( () ) (1 ) 1 ) ( )h h I


)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

−= + +−



OUTLINE

Plan







❑ Calibration






❑ Conclusion


( ) ( ), n h

t t X X

tX


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)


CALIBRATION


❑ 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 = =


DYNAMIC RESULTS


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


OUTLINE

Plan







❑ Calibration






❑ Conclusion


( ) ( ), n h

t t X X

tX


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


DYNAMIC RESULTS


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


DYNAMIC RESULTS


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


DYNAMIC RESULTS


❑ Impulse response to productivity


OUTLINE

Plan







❑ Calibration






❑ Conclusion


( ) ( ), 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


OUTLINE

Plan







❑ Calibration






❑ Conclusion


( ) ( ), 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


February 20, 2019

1E = =


−=

ts=

(with 1) =

60


Wage Determination


❑ Selection model (no search and matching)

❑ (Trivial matching function)



❑ Search and matching model (no selection)

❑ Matching function (fundamental)


❑ Hosios (1990) condition


February 20, 2019

1E = =


−=

ts=

(with 1) =

1E =


−= (0.3,0.7)

61


Wage Determination


❑ Matching + Selection

❑ No value of can decentralize efficient surplus sharing

❑ Two competing efficiency goals…

❑ …but only ONE wage determination mechanism

February 20, 2019

E


OUTLINE

Plan







❑ Calibration






❑ Conclusion


( ) ( ), n h

t t X X

tX





❑ Aggregate goods resource constraint

❑ Aggregate law of motion of employment




❑ 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

− =


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


( )

( ) 1t

t

t

h lfp

u c

− =


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


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


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


optimal fiscal policy with labor selection · february 20, 2019 7 labor markets –structure and...

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