D ECEMBER 1 3 , 2 0 1 2 Introduction T AX S MOOTHI NG P P = - - PowerPoint PPT Presentation

TAX SMOOTHI NG I N FRI CTI ONAL LABOR MARKETS

DECEMBER 1 3 , 2 0 1 2

December 13, 2012 2

TAX SMOOTHI NG

Introduction

 Ram sey w ants to keep these w edges constant  Result and intuition depend on neoclassical view of labor m arkets

 Labor tax is the only w edge  tax-sm oothing is w edge-sm oothing

 Question: I s tax sm oothing optim al from the point of view of the m odern theory of frictional labor m arkets?

P

Q Period t

(1 )

n t t t

MRS MPN t τ = − ∀

P

Q Period t+ 1 Keep w edges ( roughly) the sam e size

December 13, 2012 4

TAX SMOOTHI NG

Introduction

 Ram sey w ants to keep these w edges constant  Result and intuition depend on neoclassical view of labor m arkets

 Labor tax is the only w edge  tax-sm oothing is w edge-sm oothing

 Question: I s tax sm oothing optim al from the point of view of the m odern theory of frictional labor m arkets?

(1 )

n t t t

MRT MRS t τ = − ∀

I n neoclassical view , MPN = MRT ( betw een labor and consum ption) Think in term s of transform ation frontier in w hich every object can be view ed as either an input to or an

• utput of the technology to w hich it is associated

December 13, 2012 5

LABOR FORCE PARTI CI PATI ON

Introduction

 I ntroduce endogenous labor supply ( participation)  Conventional em pirical w isdom

 Cyclical LFP fluctuations “sm all”  Basis for typically abstracting from participation in m atching m odels  Volatility of LFP relative to that of GDP ≈ 0.20

1 9 6 1 -2 0 0 7

December 13, 2012 7

OVERVI EW OF MODEL

Model Basics

 I nfinitely-lived representative household, m easure one of m em bers

 Em ployed m em bers  Unem ployed m em bers  Mem bers outside the labor force ( “leisure”)

 Exogenous stochastic governm ent spending

 Financed via labor incom e taxation and one-period real state-contingent debt  Governm ent provides unem ploym ent benefits  Governm ent provides vacancy subsidies  For com pleteness of tax instrum ents ( Ram sey issue)

 Labor m arket w ith m atching frictions and w age- setting frictions  Only an extensive labor m argin, no intensive labor m argin  Tim ing: “instantaneous production”

Full consum ption insurance – standard in DSGE labor search m odels I ncom pleteness of governm ent debt m arkets NOT driving our results ( Aiyagari et al ( 2 0 0 2 JPE) )

December 13, 2012 8

OVERVI EW OF MODEL

Model Basics

 Unem ployed are the unsuccessful searchers: ue t = ( 1 -pt) st

 pt = probability an individual finds a job and begins w orking im m ediately

December 13, 2012 11

HOUSEHOLD OPTI MI ZATI ON

Model

 Maxim ize expected lifetim e utility

1

(1 )

t t t t

n n s p ρ

−

= − +

Perceived LOM for em ploym ent ( “instantaneous production”)

s.t.

flow of new em ploym ent relationships = m easure of searchers st x probability a searcher successfully lands a job ( exogenous) m easure of pre-existing em ploym ent relationships term inate FOCs w ith respect ct, nt, st, bt m easure n earn after- tax w age incom e Flow budget constraint m easure ue = ( 1 -p) s receive ue benefit χ ( governm ent financed) disutility of em ploym ent + unsuccessful search Baseline analysis: set τd = 1  no profit-taxation issues driving results

December 13, 2012 13

HOUSEHOLDS

Model

 Household LFP condition ( think of as labor supply condition)

 MRS betw een lfpt and ct = expected payoff of searching  Unem ploym ent benefit ( w ith probability 1 – pt)  After-tax w age + continuation value ( w ith probability pt)

To recover standard labor supply function ( e.g., RBC) 1 . ρ = 1 ( all em ploym ent relationships term inate at end of every period) 2 . p = 1 ( probability a searcher finds a job) 3 . χ = 0 ( no ue benefit because no notion of “ue”)

December 13, 2012 16

FI RMS

Model

 Production

 Requires a m atched job-w orker pair: posting cost γ per vacancy  I ndividual job i produces yit = zt  Aggregate output yt = ntzt ( sym m etry across jobs)

 Dynam ic profit-m axim ization problem  Vacancy-creation condition

( exogenous) m easure of pre-existing em ploym ent relationships term inate flow of new em ploym ent relationships = # job-openings x probability an opening attracts a searching individual

1

(1 )

t t t t

n n v q ρ

−

= − +

cost of posting vacancy ( inclusive of subsidy or tax) benefit of posting vacancy Firm ’s perceived LOM for total em ploym ent ( “instantaneous hiring”) Ensures com pleteness

• f tax instrum ents

December 13, 2012 19

LABOR MARKET

Model

 Labor-m arket tightness θt = vt/ ut  I m portant aggregate variable in m atching-based m odels  Matching probabilities p and q depend only on θ given CRTS m atching  Key statistic for m atching efficiency  Matching function  LOM for aggregate em ploym ent  Nash bargaining over w age paym ent solves

Value to firm of hiring another w orker Gain to household

• f successfully

form ing another em ploym ent relationship

1

( , )

t t t t

m s v s v

ξ ξ

ψ

−

=

1

(1 ) ( , )

t t t t

n n m s v ρ

−

= − +

Although m ain results also hold if w e discard Nash bargaining and assum e ad-hoc real w age rigidity: w t = w bar in every period t

December 13, 2012 22

GOVERNMENT AND RESOURCE FRONTI ER

Model

 Exogenous governm ent spending financed via

 Labor incom e tax  One-period state contingent real debt  Governm ent provides unem ploym ent benefits

 Rather than assum ing χ is “hom e production”

 Resource constraint

 = govt budget constraint + hh budget constraint  Assum ing χ is govt-financed allow s it to drop out of resource constraint

 Makes m odel m ore com parable to existing Ram sey m odels

 Precise nature of χ ( ue benefit? hom e production? value of leisure?) not typically specified in DSGE m atching m odels

 Our m odel articulates both ue benefit and value of leisure

t t t t t

c g v z n γ + + =

December 13, 2012 23

PRI VATE-SECTOR EQUI LI BRI UM

Model

 Stochastic processes that satisfy

 Household’s bond Euler equation  Vacancy-creation condition  Labor force participation condition  Nash w age outcom e  Law of m otion for em ploym ent  Governm ent budget constraint ( key condition in Ram sey m odels)  Resource constraint  Given processes

{ }

, , , , , ,

t t t t t t t t

c n s w R b θ

∞ =

{ }

, , ,

n s t t t t t

g z τ τ

∞ =

Standard conditions in basic Ram sey m odels

1

(1 ) ( , )

t t t t

n n m s v ρ

−

= − +

t t t t t

c g v z n γ + + =

December 13, 2012 26

MATCHI NG EFFI CI ENCY

E fficiency

 Social Planner

Static Efficiency Condition. “Efficient Participation Condition” Can instead derive directly off transform ation frontier of m odel. I ntertem poral Efficiency Condition. “Efficient Vacancies Condition” Can instead derive directly off transform ation frontier of m odel. Resource constraint

t t t t t

v c g z n γ + + =

Aggregate LOM for total em ploym ent

1

(1 , ) ) (

t t t t

n n m v s ρ

−

= − +

FOCs ( consider determ inistic case)

s.t.

December 13, 2012 28

MATCHI NG EFFI CI ENCY

E fficiency

 Efficiency characterized by  Hypothesis based on Ram sey theory: stabilizing or closing any w edges in THESE efficiency conditions is optim al  Contribution to understanding efficiency in DGE m odels w ith “entry” m argins

 I MRT in search-theoretic m onetary m odels: Aruoba and Chugh ( 2 0 1 0 JET)  I MRT in endogenous product variety fram ew ork: Chugh and Ghironi ( 2 0 1 2 )

Static Efficiency Condition. Can instead derive directly off transform ation frontier of m odel. I ntertem poral Efficiency Condition. Can instead derive directly off transform ation frontier of m odel.

= Static MRTt = I ntertem poral MRTt

December 13, 2012 30

CALI BRATI ON

E xogenous-Policy Analysis

 Baseline calibration

 So that exogenous policy ( non-Ram sey) equilibrium broadly m atches U.S. labor m arket fluctuations

 Preferences and key param eters

 Participation ( labor supply) elasticity ( ι = 0 .1 8 )  Low w orker bargaining pow er ( η = 0 .0 5 )  High unem ploym ent benefit ( 9 8 % of real w age)

 Rest of param eters, m atching-related and otherw ise, standard

 β = 0 .9 9  ρ = 0 .1 0  ξ = 0 .4 0  AR( 1 ) param eters for LOMs for TFP and governm ent spending  Etc.

The tw o key param eters of Hagedorn and Manovskii ( 2 0 0 8 AER) calibration

December 13, 2012 33

DYNAMI CS

Results

Calibration Calibration HM 0 % and Hosios HM Labor Tax Rate Mean 1 1 % 2 2 % 2 2 % Rel SD 5 .6 1 .4 1 .4 Market tightness ( θ) Rel SD 1 .1 1 .1 1 0 .9 1 1 .3 Vacancies Rel SD 1 .3 1 .3 6 .9 6 .3 Unem ploym ent LFP Rel SD 1 .4 1 .4 5 .4 5 .2 Rel SD 0 .1 3 0 .1 3 0 .2 0 0 .2 0 Real w age Rel SD 0 .5 0 0 .2 8 0 .5 2 Static w edge SD ( % ) 0 .0 8 2 2 .9 I ntertem poral w edge SD ( % ) 1 2 .3 Ram sey Exogenous Policy Benchm ark Data Gertler and Trigari ( 2 0 0 9 JPE)

December 13, 2012 34

DYNAMI CS

Results

 Ram sey fluctuations I DENTI CAL to efficient fluctuations for ANY ( η, χ) pair

 I n term s of fluctuations around a given steady state  Steady-state levels of ( τn, τs) depend on ( η, χ) pair

20 40

• 0.7
• 0.6
• 0.5
• 0.4
• 0.3
• 0.2
• 0.1

lfp

20 40

• 20
• 15
• 10
• 5

s

20 40

• 50
• 40
• 30
• 20
• 10

10

(1-p)s

20 40 0.5 1 1.5 2 2.5 3

n

20 40 10 20 30 40



20 40 5 10 15 20 25 30 35

v

Efficient HM Ramsey Efficient HM Ramsey Efficient HM Ramsey Efficient HM Ramsey Efficient HM Ramsey Efficient HM Ramsey

December 13, 2012 36

DYNAMI CS

Results

 Ram sey fluctuations I DENTI CAL to efficient fluctuations for ANY ( η, χ) pair

 I n term s of fluctuations around a given steady state  Steady-state levels of ( τn, τs) depend on ( η, χ) pair

 I nterpretation: Ram sey governm ent alw ays ensures efficient labor- m arket fluctuations ( vt, st, θt)

 By appropriately adjusting ( τn, τs) over the business cycle

December 13, 2012 37

DYNAMI CS

Results

Calibration Calibration HM 0 % and Hosios HM Labor Tax Rate Mean 1 1 % 1 5 % 2 2 % 2 2 % Rel SD 5 .6 1 .4 1 .4 Market tightness ( θ) Rel SD 1 .1 1 .1 1 0 .9 1 1 .3 Vacancies Rel SD 1 .3 1 .3 6 .9 6 .3 Unem ploym ent LFP Rel SD 1 .4 1 .4 5 .4 5 .2 Rel SD 0 .1 3 0 .1 3 0 .2 0 0 .2 0 Real w age Rel SD 0 .5 0 1 .1 0 .2 8 0 .5 2 Static w edge SD ( % ) 0 .0 8 2 2 .9 I ntertem poral w edge SD ( % ) 1 2 .3 Ram sey Exogenous Policy Benchm ark Data Gertler and Trigari ( 2 0 0 9 JPE)

December 13, 2012 38

DYNAMI CS

Results

 Ram sey fluctuations I DENTI CAL to efficient fluctuations for ANY ( η, χ) pair

 I n term s of fluctuations around a given steady state  Steady-state levels of ( τn, τs) depend on ( η, χ) pair

 I nterpretation: Ram sey governm ent alw ays ensures efficient labor- m arket fluctuations ( vt, st, θt)

 By appropriately adjusting ( τn, τs) over the business cycle

 W edge dynam ics?

 Ram sey sm ooths both static w edge….  …and intertem poral w edge

December 13, 2012 39

DYNAMI CS

Results

Calibration Calibration HM 0 % and Hosios HM 0 % and Hosios Labor Tax Rate Mean 1 1 % 1 5 % 2 2 % 2 2 % Rel SD 5 .6 1 .4 1 .4 Market tightness ( θ) Rel SD 1 .1 1 .1 1 0 .9 1 1 .3 Vacancies Rel SD 1 .3 1 .3 6 .9 6 .3 Unem ploym ent LFP Rel SD 1 .4 1 .4 5 .4 5 .2 Rel SD 0 .1 3 0 .1 3 0 .2 0 0 .2 0 Real w age Rel SD 0 .5 0 1 .1 0 .2 8 0 .5 2 Static w edge SD ( % ) 0 .0 8 2 2 .9 0 .6 6 I ntertem poral w edge SD ( % ) 1 2 .3 0 .6 3 Ram sey Exogenous Policy Benchm ark Data Gertler and Trigari ( 2 0 0 9 JPE)

December 13, 2012 43

STATI C AND I NTERTEMPORAL CONDI TI ONS

Wedges

 Efficiency characterized by  Decentralized equilibrium conditions characterized by

Static Condition I ntertem poral Condition

= w edge betw een static MRSt and static MRTt ( Too com plicated to gain any im m ediate intuition – see Section 6 and Appendix D) To obtain zero static w edge in every period, need τn = τs = 0 in every period, η = ξ, χ = 0 To obtain zero intertem poral w edge in every period, need τn = τs = 0 in every period, η = ξ, χ = 0

December 13, 2012 45

CONCLUSI ONS

Summary

 Labor tax sm oothing not optim al in DSGE search and m atching m odel

 Calibrated to m atch key labor m arket dynam ics under exogenous tax policy  Rigid real w age ( delivered through Nash-Hosios bargaining as benchm ark) the im portant feature of the m odel

 But w edge sm oothing I S optim al

 Basic Ram sey theory

 Ram sey fluctuations in allocations efficient regardless of calibration  W elfare-relevant notions of w edges

 Developing m atching-m odel concepts of efficiency and MRTs for use in virtually any m atching application  Could think of “labor w edge” as featuring both static and intertem poral dim ensions  Use as fram ew ork to em pirically m easure labor w edges?