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

T AX S MOOTHI NG I N F RI CTI ONAL L ABOR M ARKETS D ECEMBER 1 3 , 2 0 1 2

Introduction T AX S MOOTHI NG P P = − τ ∀ n MRS (1 ) MPN t t t t Keep w edges ( roughly) the sam e size Q Q Period t Period t + 1  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? December 13, 2012 2

Introduction T AX S MOOTHI NG I n neoclassical view , MPN = MRT ( betw een labor and consum ption) = − τ ∀ n MRS (1 ) MRT t t t t Think in term s of transform ation frontier in w hich every object can be view ed as either an input to or an output of the technology to w hich it is associated  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? December 13, 2012 4

Introduction L ABOR F ORCE P ARTI CI PATI ON  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 5

Model Basics O VERVI EW OF M ODEL  I nfinitely-lived representative household, m easure one of m em bers  Em ployed m em bers Full consum ption insurance –  standard in DSGE labor search Unem ployed m em bers m odels  Mem bers outside the labor force ( “leisure”) I ncom pleteness of governm ent debt m arkets NOT driving our results ( Aiyagari et al ( 2 0 0 2 JPE ) )  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” December 13, 2012 7

Model Basics O VERVI EW OF M ODEL  Unem ployed are the unsuccessful searchers: ue t = ( 1 - p t ) s t  p t = probability an individual finds a job and begins w orking im m ediately December 13, 2012 8

Model H OUSEHOLD O PTI MI ZATI ON  Maxim ize expected lifetim e utility disutility of em ploym ent + s.t . unsuccessful search Flow budget constraint Baseline analysis: set τ d = 1  no m easure n earn after- m easure ue = ( 1 - p ) s receive ue benefit χ tax w age incom e profit- taxation issues driving results ( governm ent financed) = − ρ + Perceived LOM for n (1 ) n s p − em ploym ent ( “instantaneous t t 1 t t production”) ( exogenous) m easure of flow of new em ploym ent relationships = pre-existing em ploym ent m easure of searchers s t x probability a relationships term inate searcher successfully lands a job FOCs w ith respect c t , n t , s t , b t December 13, 2012 11

Model H OUSEHOLDS  Household LFP condition ( think of as labor supply condition)  MRS betw een lfp t and c t = expected payoff of searching  Unem ploym ent benefit ( w ith probability 1 – p t )  After-tax w age + continuation value ( w ith probability p t ) 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 13

Model F I RMS  Production Requires a m atched job-w orker pair: posting cost γ per vacancy   I ndividual job i produces y it = z t  Aggregate output y t = n t z t ( sym m etry across jobs)  Dynam ic profit-m axim ization problem Ensures com pleteness of tax instrum ents = − ρ + Firm ’s perceived LOM for total n (1 ) n v q − t t 1 t t em ploym ent ( “instantaneous hiring”) ( exogenous) m easure of flow of new em ploym ent relationships = pre-existing em ploym ent # job-openings x probability an opening relationships term inate attracts a searching individual  Vacancy-creation condition cost of posting vacancy benefit of posting vacancy ( inclusive of subsidy or tax) December 13, 2012 16

Model L ABOR M ARKET Labor-m arket tightness θ t = v t / u t   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 = ψ ξ − ξ 1 m s v ( , ) s v  Matching function t t t t = − ρ + n (1 ) n m s v ( , )  LOM for aggregate em ploym ent − t t 1 t t  Nash bargaining over w age paym ent solves Although m ain results also hold if w e discard Nash bargaining and assum e ad-hoc real w age rigidity: Gain to household Value to firm of of successfully hiring another form ing another w orker em ploym ent w t = w bar in every period t relationship December 13, 2012 19

Model G OVERNMENT AND R ESOURCE F RONTI ER  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 + + γ = c g v z n t t t t t  = 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 December 13, 2012 22

Model P RI VATE- S ECTOR E QUI LI BRI UM { } ∞ θ c n s w , , , , , R b ,  Stochastic processes that satisfy = t t t t t t t t 0  Household’s bond Euler equation  Vacancy-creation condition  Labor force participation condition  Nash w age outcom e = − ρ + n (1 ) n m s v ( , )  Law of m otion for em ploym ent − t t 1 t t  Governm ent budget constraint ( key condition in Ram sey m odels) + + γ = c g v z n  Resource constraint t t t t t { } ∞ g z τ τ n s , , ,  Given processes t t t t = 0 t Standard conditions in basic Ram sey m odels December 13, 2012 23

E fficiency M ATCHI NG E FFI CI ENCY  Social Planner s.t. + + γ = c g v z n Resource constraint t t t t t = − ρ + Aggregate LOM for n (1 ) n m ( s , v ) − t t 1 t t total em ploym ent FOCs ( consider determ inistic case) I ntertem poral Efficiency Condition. Static Efficiency Condition. “Efficient Vacancies Condition” “Efficient Participation Condition” Can instead derive directly off transform ation frontier of Can instead derive directly off transform ation m odel. frontier of m odel. December 13, 2012 26

E fficiency M ATCHI NG E FFI CI ENCY  Efficiency characterized by = Static MRT t = I ntertem poral MRT t Static Efficiency Condition. I ntertem poral Efficiency Condition. Can instead derive directly off transform ation Can instead derive directly off transform ation frontier of frontier of m odel. m odel.  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 ) December 13, 2012 28

E xogenous-Policy Analysis C ALI BRATI ON  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 )  The tw o key param eters of Hagedorn and Manovskii  High unem ploym ent benefit ( 9 8 % of real w age) ( 2 0 0 8 AER ) calibration  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. December 13, 2012 30

Results D YNAMI CS Exogenous Policy Ram sey Data Benchm ark Gertler and Trigari Calibration Calibration ( 2 0 0 9 JPE ) 0 % HM and HM Hosios Mean 1 1 % 2 2 % 2 2 % Labor Tax Rate Rel SD 5 .6 0 1 .4 1 .4 Market Rel SD 1 .1 1 .1 1 0 .9 1 1 .3 tightness ( θ ) Vacancies Rel SD 1 .3 1 .3 6 .9 6 .3 Unem ploym ent Rel SD 1 .4 1 .4 5 .4 5 .2 LFP 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 0 2 2 .9 I ntertem poral SD ( % ) 0 0 1 2 .3 w edge December 13, 2012 33