Frictional Labour Markets, Bargaining Wedges, and Optimal Tax-Rate by ikevantrounk

VIEWS: 12 PAGES: 79

									        FRICTIONAL LABOR MARKETS,
         BARGAINING WEDGES, AND
       OPTIMAL TAX-RATE VOLATILITY

  DAVID M. ARSENEAU           SANJAY K. CHUGH
FEDERAL RESERVE BOARD      UNIVERSITY OF MARYLAND



    INTERNATIONAL RESEARCH FORUM ON MONETARY POLICY
                      JUNE 27, 2008
                                                                            Introduction


TAX SMOOTHING

     Keep labor tax rates across periods (nearly) constant in the face of shocks
                A benchmark result in the theory of optimal fiscal policy



     Basic intuition: deadweight loss of tax collection convex in tax rates




June 27, 2008                      International Research Forum on              2
                                            Monetary Policy
                                                                                      Introduction


TAX SMOOTHING

     Keep labor tax rates across periods (nearly) constant in the face of shocks
                A benchmark result in the theory of optimal fiscal policy



     Basic intuition: deadweight loss of tax collection convex in tax rates
                Barro (1979 JPE): partial equilibrium dynamic model
                Chari, Christiano, and Kehoe (1991 JMCB): partial equilibrium result carries over
                into DSGE representative agent (Ramsey) framework
                Werning (2007 QJE): result carries over into models with consumer heterogeneity
                and nonlinear (Mirrleesian) taxation framework



     An application of standard static Ramsey (1927) taxation principles to
     dynamic macro
                Tax goods with the same price elasticities at the same rate (given some regularity
                assumptions on preferences across goods)




June 27, 2008                      International Research Forum on                         3
                                            Monetary Policy
                                                                      Introduction


TAX SMOOTHING
 P                                                   P


                       MRSt = (1 − τ tn ) MPNt ∀ t


                              Keep tax
                               wedges
                            (roughly) the
                              same size




                       Q                                                Q
           Period t                                      Period t+1



     Result and intuition depend on Walrasian view of labor markets




June 27, 2008          International Research Forum on                      4
                                Monetary Policy
                                                                       Introduction


TAX SMOOTHING
 P                                                    P


                        MRSt = (1 − τ tn ) MPNt ∀ t


                               Keep tax
                                wedges
                             (roughly) the
                               same size




                       Q                                                 Q
           Period t                                       Period t+1



     Result and intuition depend on Walrasian view of labor markets

     Question: Is tax smoothing optimal from the point of view of the
     modern theory of frictional labor markets?




June 27, 2008          International Research Forum on                       5
                                Monetary Policy
                                                                       Introduction


TAX SMOOTHING
 P                                                    P


                        MRSt = (1 − τ tn ) MPNt ∀ t


                               Keep tax
                                wedges
                             (roughly) the
                               same size




                       Q                                                 Q
           Period t                                       Period t+1



     Result and intuition depend on Walrasian view of labor markets

     Question: Is tax smoothing optimal from the point of view of the
     modern theory of frictional labor markets?

     Question: If not, what are the relevant departures from the
     Walrasian view that make it not?
June 27, 2008          International Research Forum on                       6
                                Monetary Policy
                                                                    Introduction


TAX SMOOTHING

                                  In Walrasian view, MPN = MRT
                                  (between labor and consumption)




                     MRSt = (1 − τ tn ) MRTt ∀ t




     Result and intuition depend on Walrasian view of labor markets

     Question: Is tax smoothing optimal from the point of view of the
     modern theory of frictional labor markets?

     Question: If not, what are the relevant departures from the
     Walrasian view that make it not?
June 27, 2008          International Research Forum on                  7
                                Monetary Policy
                                                                          Introduction


LABOR SEARCH AND BARGAINING
     Explosion of DSGE models based on labor search and bargaining
                Walsh (2005 RED), Gertler and Trigari (2006), Krause and Lubik (2007
                JME), many others
                Merz (1995 JME), Andolfatto (1996 AER), denHaan, Ramey, Watson
                (2000 AER) the original DSGE labor search models
                Search and bargaining framework of Pissarides (2000)




June 27, 2008                  International Research Forum on                8
                                        Monetary Policy
                                                                             Introduction


LABOR SEARCH AND BARGAINING
     Explosion of DSGE models based on labor search and bargaining
                Walsh (2005 RED), Gertler and Trigari (2006), Krause and Lubik (2007
                JME), many others
                Merz (1995 JME), Andolfatto (1996 AER), denHaan, Ramey, Watson
                (2000 AER) the original DSGE labor search models
                Search and bargaining framework of Pissarides (2000)


     Framework (arguably?) provides a more realistic description of
     labor markets
                Costly to find a job / costly to find a worker
                “Jobs” are explicitly bilateral long-lived relationships

     Models being used for (monetary…) policy analysis
                Christoffel and Kuester (forthcoming JME), Christoffel et al (2007,
                2008), Blanchard and Gali (2007 JMCB), Faia (2008), Thomas
                (forthcoming JME), many others




June 27, 2008                   International Research Forum on                  9
                                         Monetary Policy
                                                                             Introduction


LABOR SEARCH AND BARGAINING
     Explosion of DSGE models based on labor search and bargaining
                Walsh (2005 RED), Gertler and Trigari (2006), Krause and Lubik (2007
                JME), many others
                Merz (1995 JME), Andolfatto (1996 AER), denHaan, Ramey, Watson
                (2000 AER) the original DSGE labor search models
                Search and bargaining framework of Pissarides (2000)


     Framework (arguably?) provides a more realistic description of
     labor markets
                Costly to find a job / costly to find a worker
                “Jobs” are explicitly bilateral long-lived relationships

     Models being used for (monetary…) policy analysis
                Christoffel and Kuester (forthcoming JME), Christoffel et al (2007,
                2008), Blanchard and Gali (2007 JMCB), Faia (2008), Thomas
                (forthcoming JME), many others


     Our question: optimal fiscal policy in labor search and bargaining
     environment?
June 27, 2008                   International Research Forum on                 10
                                         Monetary Policy
                                                          Introduction


MAIN RESULTS




 1. Tax smoothing not optimal in benchmark DSGE labor search model




June 27, 2008        International Research Forum on         11
                              Monetary Policy
                                                                         Introduction


MAIN RESULTS


     Tax smoothing not optimal in benchmark DSGE labor search model
                Whether using Shimer (2005 AER) calibration…
                     Unemployment benefits 40% of after-tax wages
                …or using Hagedorn and Manovskii (forthcoming AER) calibration
                     Unemployment benefits 95% of after-tax wages




June 27, 2008                   International Research Forum on             12
                                         Monetary Policy
                                                                                    Introduction


MAIN RESULTS


     Tax smoothing not optimal in benchmark DSGE labor search model
                Whether using Shimer (2005 AER) calibration…
                     Unemployment benefits 40% of after-tax wages
                …or using Hagedorn and Manovskii (forthcoming AER) calibration
                     Unemployment benefits 95% of after-tax wages




     Quantitatives of optimal labor tax rate (business cycle shocks)
                SD = 7% (mean = 17%) under Shimer calibration
                SD = 1.7% (mean = 61%) under Hagedorn and Manovskii calibration
                Benchmark Ramsey result: SD = 0.1% (mean = 20%-30%)
                     Shown quantitatively by Chari, Christiano, and Kehoe (1991) and analytically
                     by Werning (2007 QJE)




June 27, 2008                   International Research Forum on                        13
                                         Monetary Policy
                                                             Introduction


MAIN RESULTS
     Reinstating some “Walrasian features” pushes policy prescription
     back towards optimal tax smoothing




June 27, 2008          International Research Forum on          14
                                Monetary Policy
                                                              Introduction


MAIN RESULTS
      Reinstating some “Walrasian features” pushes policy prescription
      back towards optimal tax smoothing


Alter timing of labor market flows

Allow optimal labor force participation decision

Competitive search instead of Nash bargaining




 June 27, 2008          International Research Forum on          15
                                 Monetary Policy
                                                                      Introduction


MAIN RESULTS
      Reinstating some “Walrasian features” pushes policy prescription
      back towards optimal tax smoothing

                                                          (a prerequisite for
Alter timing of labor market flows                        implementing the
                                                          other two)


Allow optimal labor force participation decision          COMBINATION of
                                                          these two reinstates
                                                          tax smoothing
Competitive search instead of Nash bargaining




 June 27, 2008          International Research Forum on                   16
                                 Monetary Policy
                                                          Introduction


MAIN RESULTS




 1. Tax smoothing not optimal in benchmark DSGE labor search model


 2. Tax smoothing IS optimal in competitive search DSGE environment
                with endogenous labor-force participation




June 27, 2008         International Research Forum on        17
                               Monetary Policy
                                                                              Introduction


MAIN RESULTS
      Reinstating some “Walrasian features” pushes policy prescription
      back towards optimal tax smoothing

                                                                  (a prerequisite for
Alter timing of labor market flows                                implementing the
                                                                  other two)


Allow optimal labor force participation decision                  COMBINATION of
                                                                  these two reinstates
                                                                  tax smoothing
Competitive search instead of Nash bargaining

      Full model: tax smoothing is optimal
                 Endogenous labor-force participation                           ala RBC
                 All agents are wage-takers when making search decisions




 June 27, 2008                  International Research Forum on                   18
                                         Monetary Policy
                                                                               Introduction


MAIN RESULTS
      Reinstating some “Walrasian features” pushes policy prescription
      back towards optimal tax smoothing

                                                                  (a prerequisite for
Alter timing of labor market flows                                implementing the
                                                                  other two)


Allow optimal labor force participation decision                  COMBINATION of
                                                                  these two reinstates
                                                                  tax smoothing
Competitive search instead of Nash bargaining

      Full model: tax smoothing is optimal
                 Endogenous labor-force participation                           ala RBC
                 All agents are wage-takers when making search decisions
                 Retains search and matching
                 Results driven by a “usual” static MRS = (1-τ)MRT condition




 June 27, 2008                  International Research Forum on                   19
                                         Monetary Policy
                                                                               Introduction


MAIN RESULTS
      Reinstating some “Walrasian features” pushes policy prescription
      back towards optimal tax smoothing

                                                                  (a prerequisite for
Alter timing of labor market flows                                implementing the
                                                                  other two)


Allow optimal labor force participation decision                  COMBINATION of
                                                                  these two reinstates
                                                                  tax smoothing
Competitive search instead of Nash bargaining

      Full model: tax smoothing is optimal
                 Endogenous labor-force participation                           ala RBC
                 All agents are wage-takers when making search decisions
                 Retains search and matching
                 Results driven by a “usual” static MRS = (1-τ)MRT condition

      Bargaining introduces a “second wedge” between MRS and MRT

 June 27, 2008                  International Research Forum on                   20
                                         Monetary Policy
                                                                                                            Introduction


    BASIC INTUITION

                                          MRSt = (1 − τ tn ) MRTt ∀ t
Walrasian labor market:
Smooth labor taxes




                              Search model: intuition based on model with labor-force participation



Labor market in bargaining

                                        MRSt = (1 − τ tn )Ωt MRTt ∀ t
search equilibrium:
Tax-rate volatility offsets
the bargaining-induced
wedge Ωt
                                                                                            (Expression for MRT in a labor
                                                                                            search model slightly different
                                                                                            than in RBC model)

Labor market in

                                          MRSt = (1 − τ tn ) MRTt ∀ t
competitive search
equilibrium:
Smooth labor taxes




      June 27, 2008                           International Research Forum on                                   21
                                                       Monetary Policy
                                                                                     Introduction


MAIN RESULTS
      Reinstating some “Walrasian features” pushes policy prescription
      back towards optimal tax smoothing

                                                                         (a prerequisite for
Alter timing of labor market flows                                       implementing the
                                                                         other two)


Allow optimal labor force participation decision                         COMBINATION of
                                                                         these two reinstates
                                                                         tax smoothing
Competitive search instead of Nash bargaining



      Market structure in search models critical for policy analysis
                 Nature of wage determination critical
                      Literature’s typical assumption: Nash bargaining
                 Nature of labor supply critical
                      Literature’s typical assumption: fixed




 June 27, 2008                    International Research Forum on                        22
                                           Monetary Policy
                                                                                        Model Sketch


OVERVIEW OF MODEL(S)
     Infinitely-lived representative household
                Employed members               Full consumption insurance – standard in DSGE
                                               labor search models
                Unemployed members


     Exogenous stochastic government spending
                Financed via labor income taxation and one-period real state-contingent
                debt
                Government provides unemployment benefits




June 27, 2008                  International Research Forum on                                 23
                                        Monetary Policy
                                                                                         Model Sketch


OVERVIEW OF MODEL(S)
     Infinitely-lived representative household
                Employed members               Full consumption insurance – standard in DSGE
                                               labor search models
                Unemployed members
                                                                       Incompleteness of government
                                                                       debt markets NOT driving our
                                                                       results (Aiyagari et al (2002 JPE))
     Exogenous stochastic government spending
                Financed via labor income taxation and one-period real state-contingent
                debt
                Government provides unemployment benefits




June 27, 2008                  International Research Forum on                                 24
                                        Monetary Policy
                                                                                          Model Sketch


OVERVIEW OF MODEL(S)
     Infinitely-lived representative household
                Employed members                Full consumption insurance – standard in DSGE
                                                labor search models
                Unemployed members
                                                                        Incompleteness of government
                                                                        debt markets NOT driving our
                                                                        results (Aiyagari et al (2002 JPE))
     Exogenous stochastic government spending
                Financed via labor income taxation and one-period real state-contingent
                debt
                Government provides unemployment benefits


     Labor market with search and bargaining frictions
                Model 1: Benchmark model
                     Nash bargaining
                     Linear-in-labor production, no capital
                     New jobs become productive with one-period delay
                     No labor-force participation decision




June 27, 2008                   International Research Forum on                                 25
                                         Monetary Policy
                                                                                             Model Sketch


OVERVIEW OF MODEL(S)
     Infinitely-lived representative household
                Employed members                   Full consumption insurance – standard in DSGE
                                                   labor search models
                Unemployed members
                                                                           Incompleteness of government
                                                                           debt markets NOT driving our
                                                                           results (Aiyagari et al (2002 JPE))
     Exogenous stochastic government spending
                Financed via labor income taxation and one-period real state-contingent
                debt
                Government provides unemployment benefits


     Labor market with search and bargaining frictions
                Model 1: Benchmark model
                     Nash bargaining
                     Linear-in-labor production, no capital
                     New jobs become productive with one-period delay
                     No labor-force participation decision
                Model   2:   Model 1, but new jobs become productive immediately
                Model   3:   Model 1, but allow labor force participation decision
                Model   4:   = Model 2 + Model 3
                Model   5:   = Model 4 + competitive wage determination
June 27, 2008                      International Research Forum on                                 26
                                            Monetary Policy
                                                                              Model Sketch


GOVERNMENT AND RESOURCE FRONTIER
     Exogenous government spending financed via
                Labor income tax
                One-period state contingent real debt

                             τ tn wt nt + bt = g t + Rt bt −1 + (1 − nt ) χ
                Government provides unemployment benefits
                     Rather than assuming χ is “home production”




June 27, 2008                   International Research Forum on                   27
                                         Monetary Policy
                                                                              Model Sketch


GOVERNMENT AND RESOURCE FRONTIER
     Exogenous government spending financed via
                Labor income tax
                One-period state contingent real debt

                             τ tn wt nt + bt = g t + Rt bt −1 + (1 − nt ) χ
                Government provides unemployment benefits
                     Rather than assuming χ is “home production”


     Resource constraint
                                   ct + gt + γ vt = zt nt
                = govt budget constraint + hh budget constraint
                Assuming χ is govt-financed allows it to drop out of resource constraint
                     Makes model more comparable to existing Ramsey models than the “home
                     production” interpretation




June 27, 2008                   International Research Forum on                   28
                                         Monetary Policy
                                                                              Model Sketch


GOVERNMENT AND RESOURCE FRONTIER
     Exogenous government spending financed via
                Labor income tax
                One-period state contingent real debt

                             τ tn wt nt + bt = g t + Rt bt −1 + (1 − nt ) χ
                Government provides unemployment benefits
                     Rather than assuming χ is “home production”


     Resource constraint
                                   ct + gt + γ vt = zt nt
                = govt budget constraint + hh budget constraint
                Assuming χ is govt-financed allows it to drop out of resource constraint
                     Makes model more comparable to existing Ramsey models than the “home
                     production” interpretation


     Precise nature of χ (ue benefit? home production?) not typically
     specified in DSGE search models
                Because lump-sum instruments allow it to trivially drop out of resource
                frontier

June 27, 2008                   International Research Forum on                   29
                                         Monetary Policy
                                                                                Model 1: Benchmark Model


PRIVATE SECTOR EQUILIBRIUM
       Stochastic processes {ct , nt +1 , wt , θ t , ut , Rt }t = 0 that satisfy
                                                                    ∞



                  Household’s optimal intertemporal optimality condition

                  Job-creation condition

                  Nash wage outcome

                  Law of motion for employment            nt +1 = (1 − ρ x )(nt + m(ut , vt ))

                  Government budget constraint (key condition in Ramsey models)

                  Resource constraint      ct + gt + γ vt = zt nt

                  Identity limiting size of labor force        nt + ut = 1

                  Given processes   { g , z ,τ }
                                       t    t
                                                 n ∞
                                                t t =0

Standard conditions in basic Ramsey models

  June 27, 2008                    International Research Forum on                               30
                                            Monetary Policy
                                                                            Model Sketch


RAMSEY PROBLEM
     Given { g t , zt }t = 0 , Ramsey planner chooses state-contingent decision
                        ∞

     rules for
                             {c , n         , wt ,τ , θ t , ut , Rt }
                                                    n               ∞
                               t     t +1          t                t =0


     to maximize utility subject to all equilibrium conditions of economy

     Assume commitment
                Government picks state-contingent rules at t = 0 and then follows them


     Focus on asymptotic dynamics
                Ignore any “initial transitional dynamics” induced by different decision
                rules for t = 0 vs. t > 0
                The “timeless” perspective of Woodford (2003)




June 27, 2008                      International Research Forum on              31
                                            Monetary Policy
                                                                            Model Sketch


RAMSEY PROBLEM AND SOLUTION TECHNIQUE
     Given { g t , zt }t = 0 , Ramsey planner chooses state-contingent decision
                        ∞

     rules for
                             {c , n         , wt ,τ , θ t , ut , Rt }
                                                    n               ∞
                               t     t +1          t                t =0


     to maximize utility subject to all equilibrium conditions of economy

     Assume commitment
                Government picks state-contingent rules at t = 0 and then follows them


     Focus on asymptotic dynamics
                Ignore any “initial transitional dynamics” induced by different decision
                rules for t = 0 vs. t > 0
                The “timeless” perspective of Woodford (2003)


     Local approximation around deterministic steady state of Ramsey
     allocation
                Dynamics described by the t > 0 Ramsey first-order conditions
                Our own implementation of Schmitt-Grohe and Uribe (2004 JEDC)
June 27, 2008                      International Research Forum on              32
                                            Monetary Policy
                                                                                       Model Sketch


PARAMETER VALUES
     Matching technology m(ut , vt ) = ψ ut vt
                                                     ξ 1−ξ

                Set ξ = 0.4 (Blanchard and Diamond (1989))
                                                                  Interpretation: set private gain =
                                                                  social value
     Bargaining power of workers
                Choose bargaining weight η such that (absent proportional taxation)
                labor market outcome is efficient: η = ξ = 0.4
                A non-generic parameter configuration
                     Absent empirical evidence, many DSGE models assume it




June 27, 2008                   International Research Forum on                              33
                                         Monetary Policy
                                                                                       Model Sketch


PARAMETER VALUES
     Matching technology m(ut , vt ) = ψ ut vt
                                                     ξ 1−ξ

                Set ξ = 0.4 (Blanchard and Diamond (1989))
                                                                  Interpretation: set private gain =
                                                                  social value
     Bargaining power of workers
                Choose bargaining weight η such that (absent proportional taxation)
                labor market outcome is efficient: η = ξ = 0.4
                A non-generic parameter configuration
                     Absent empirical evidence, many DSGE models assume it


     Unemployment benefit χ: two main values
                Set so that = 40% of after-tax wages (Shimer (2005 AER))
                Set so that = 95% of after-tax wages (Hagedorn and Manovksii)




June 27, 2008                   International Research Forum on                              34
                                         Monetary Policy
                                                                                       Model Sketch


PARAMETER VALUES
     Matching technology m(ut , vt ) = ψ ut vt
                                                     ξ 1−ξ

                Set ξ = 0.4 (Blanchard and Diamond (1989))
                                                                  Interpretation: set private gain =
                                                                  social value
     Bargaining power of workers
                Choose bargaining weight η such that (absent proportional taxation)
                labor market outcome is efficient: η = ξ = 0.4
                A non-generic parameter configuration
                     Absent empirical evidence, many DSGE models assume it


     Unemployment benefit χ: two main values
                Set so that = 40% of after-tax wages (Shimer (2005 AER))
                Set so that = 95% of after-tax wages (Hagedorn and Manovksii)


     Other parameters “standard”
                Quarterly β = 0.99
                Log utility
                AR(1) processes for TFP and government spending in line with Ramsey
                literature


June 27, 2008                   International Research Forum on                              35
                                         Monetary Policy
                                                                        Model 1: Benchmark Model


      RAMSEY DYNAMICS

                               ue benefits

                              40%     95%

                 Mean         17%     60%
Labor Tax Rate
                 SD            7%     1.4%

Market
tightness (θ)


                Optimal labor tax rate an order of magnitude more volatile than benchmark
                Ramsey result (0.1% around mean of 20%-30%)




        June 27, 2008                 International Research Forum on                   36
                                               Monetary Policy
                                                                                  Model 1: Benchmark Model


      RAMSEY DYNAMICS

                                     ue benefits

                                   40%      95%

                 Mean              17%      60%
Labor Tax Rate
                 SD                 7%      1.4%

Market
                 SD (%)             1.85    2.35
tightness (θ)


                Optimal labor tax rate an order of magnitude more volatile than benchmark
                Ramsey result (0.1% around mean of 20%-30%)
                Ramsey dynamics do not display very high volatility of θ

                GDP volatility: ≈ 1.8 - 2.0 S.D.%
                        Tax volatility not driven by excessive volatility of models
                        True of all models we investigate




        June 27, 2008                       International Research Forum on                       37
                                                     Monetary Policy
                                                                        Model 1: Benchmark Model


      RAMSEY DYNAMICS

                               ue benefits

                              40%     95%

                 Mean         17%     60%
Labor Tax Rate
                 SD            7%     1.4%

Market
                 SD (%)       1.85    2.35
tightness (θ)


                Optimal labor tax rate an order of magnitude more volatile than benchmark
                Ramsey result (0.1% around mean of 20%-30%)
                Ramsey dynamics do not display very high volatility of θ

                Question: What might reinstate optimality of tax smoothing?
                  1. Modifications of the market structure

                  2. Alternative policy instruments



        June 27, 2008                 International Research Forum on                   38
                                               Monetary Policy
                                                                        Model 1: Benchmark Model


      RAMSEY DYNAMICS

                               ue benefits

                              40%     95%

                 Mean         17%     60%
Labor Tax Rate
                 SD            7%     1.4%

Market
                 SD (%)       1.85    2.35
tightness (θ)


                Optimal labor tax rate an order of magnitude more volatile than benchmark
                Ramsey result (0.1% around mean of 20%-30%)
                Ramsey dynamics do not display very high volatility of θ

                Question: What might reinstate optimality of tax smoothing?
                  1. Modifications of the market structure
                          The main path we pursue
                  2. Alternative policy instruments
                          Some conceptual/technical challenges


        June 27, 2008                 International Research Forum on                   39
                                               Monetary Policy
                                                                        Model 1: Benchmark Model


      RAMSEY DYNAMICS
                                Model 1

                               ue benefits

                              40%     95%

                 Mean         17%     60%
Labor Tax Rate
                 SD           7%      1.4%

Market
                 SD (%)       1.85    2.35
tightness (θ)


                Model 1: Tax smoothing not optimal




        June 27, 2008                 International Research Forum on                   40
                                               Monetary Policy
                                                                    Model 2: Instantaneous Hiring


CHANGING THE TIMING OF LABOR FLOWS
     Model 1 (baseline model)
                Period-t law of motion for employment

                             nt +1 = (1 − ρ x )(nt + m(ut , vt ))
                nt used for period-t production
                     nt pre-determined




June 27, 2008                   International Research Forum on                         41
                                         Monetary Policy
                                                                    Model 2: Instantaneous Hiring


CHANGING THE TIMING OF LABOR FLOWS
     Model 1 (baseline model)
                Period-t law of motion for employment

                             nt +1 = (1 − ρ x )(nt + m(ut , vt ))
                nt used for period-t production
                     nt pre-determined


     Walrasian model: “new jobs” produce in the period they are
     “formed”




June 27, 2008                   International Research Forum on                         42
                                         Monetary Policy
                                                                    Model 2: Instantaneous Hiring


CHANGING THE TIMING OF LABOR FLOWS
     Model 1 (baseline model)
                Period-t law of motion for employment

                             nt +1 = (1 − ρ x )(nt + m(ut , vt ))
                nt used for period-t production
                     nt pre-determined


     Walrasian model: “new jobs” produce in the period they are
     “formed”

     Model 2
                Period-t law of motion for employment

                               nt = (1 − ρ x )nt −1 + m(ut , vt )
                nt used for period-t production
                     nt contemporaneously determined




June 27, 2008                   International Research Forum on                         43
                                         Monetary Policy
                                                                    Model 2: Instantaneous Hiring


CHANGING THE TIMING OF LABOR FLOWS
     Model 1 (baseline model)
                Period-t law of motion for employment

                             nt +1 = (1 − ρ x )(nt + m(ut , vt ))
                nt used for period-t production
                     nt pre-determined


     Walrasian model: “new jobs” produce in the period they are
     “formed”

     Model 2
                Period-t law of motion for employment

                               nt = (1 − ρ x )nt −1 + m(ut , vt )
                nt used for period-t production
                     nt contemporaneously determined


     Slight (straightforward) alterations in timing of job-creation
     condition and Nash wage bargain
June 27, 2008                   International Research Forum on                         44
                                         Monetary Policy
                                                                       Making Labor Market “More Walrasian”


      RAMSEY DYNAMICS
                            Model 1              Model 2

                           ue benefits          ue benefits

                          40%     95%         40%      95%

                 Mean     17%     60%         15%      60%
Labor Tax Rate
                 SD        7%     1.4%        2.5%     0.7%

Market
                 SD (%)   1.85     2.35       0.90      5.80
tightness (θ)


                Model 1: Tax smoothing not optimal
                Model 2: Tax smoothing not optimal…but timing matters




        June 27, 2008                     International Research Forum on                          45
                                                   Monetary Policy
                                                                 Model 3: Labor Force Participation


ENDGENOUS LABOR-FORCE PARTICIPATION
     Model 1 (baseline model)
                Households have no labor-force participation choice
                Size of labor force exogenous: nt + ut = 1




June 27, 2008                  International Research Forum on                            46
                                        Monetary Policy
                                                                                    Model 3: Labor Force Participation


ENDGENOUS LABOR-FORCE PARTICIPATION
     Model 1 (baseline model)
                Households have no labor-force participation choice
                Size of labor force exogenous: nt + ut = 1


     Walrasian model: households choose labor supply

     Model 3
                Endogenize labor-force choice (retain Model 1 timing)
                Household problem ∞
                          max E 0 ∑β t [u (ct ) + g (1 − ut − nt )]
                          {c ,bt , nt +1 ,ut }   t =0
                               ct + bt = nt (1 − τ tn ) wt + ut χ + Rt bt −1 + dt
                                                                                       Household’s perceived law of
                                        nt +1 = (1 − ρ x )(nt + k h (θt ) ut )         motion for total employment
                                                                                       relationships




June 27, 2008                                International Research Forum on                                   47
                                                      Monetary Policy
                                                                                                Model 3: Labor Force Participation


ENDGENOUS LABOR-FORCE PARTICIPATION
     Model 1 (baseline model)
                Households have no labor-force participation choice
                Size of labor force exogenous: nt + ut = 1


     Walrasian model: households choose labor supply

     Model 3
                Endogenize labor-force choice (retain Model 1 timing)
                Household problem ∞
                          max E 0 ∑β t [u (ct ) + g (1 − ut − nt )]
                                  {c ,bt , nt +1 ,ut }   t =0
                                       ct + bt = nt (1 − τ tn ) wt + ut χ + Rt bt −1 + dt
                                                                                                      Household’s perceived law of
                                                nt +1 = (1 − ρ x )(nt + k h (θt ) ut )                motion for total employment
                                                                                                      relationships
     Labor-force-participation condition

                 gt' − u '(ct ) χ                 ⎡                                         gt' +1 − u '(ct +1 ) χ ⎤
                                  = β (1 − ρ ) Et ⎢u '(ct +1 )(1 − τ t +1 ) wt +1 − gt +1 +
                                            x                         n              '
                                                                                                                   ⎥
                     k h (θt )                    ⎣                                               k h (θt +1 )     ⎦

     Wage bargaining outcome same as Model 1
June 27, 2008                                        International Research Forum on                                          48
                                                              Monetary Policy
                                                                        Making Labor Market “More Walrasian”


      RAMSEY DYNAMICS
                             Model 1              Model 2           Model 3

                            ue benefits          ue benefits       ue benefits

                          40%      95%         40%      95%      40%         95%

                 Mean     17%      60%         15%      60%      28%         69%
Labor Tax Rate
                 SD        7%      1.4%        2.5%     0.7%     1.7%        1.1%

Market
                 SD (%)    1.85     2.35       0.90      5.80    3.39        2.59
tightness (θ)


                Model 1: Tax smoothing not optimal
                Model 2: Tax smoothing not optimal…but timing matters
                Model 3: Tax smoothing not optimal…but LF participation choice matters




        June 27, 2008                      International Research Forum on                          49
                                                    Monetary Policy
                                 Model 4: Instantaneous Hiring and Labor Force Participation


TIMING OF FLOWS AND LF PARTICIPATION




                Model 4:      Model 2         +    Model 3

                             instantaneous        endogenous LF
                             hiring               participation




June 27, 2008              International Research Forum on                         50
                                    Monetary Policy
                                                                        Making Labor Market “More Walrasian”


      RAMSEY DYNAMICS
                             Model 1              Model 2           Model 3           Model 4

                            ue benefits          ue benefits       ue benefits       ue benefits

                           40%     95%         40%      95%      40%         95%    40%     95%

                 Mean      17%     60%         15%      60%      28%         69%    36%     73%
Labor Tax Rate
                 SD        7%      1.4%        2.5%     0.7%     1.7%        1.1%   1.2%    1.0%

Market
                 SD (%)    1.85     2.35       0.90      5.80    3.39        2.59   1.00     15.6
tightness (θ)


                Model 1: Tax smoothing not            optimal
                Model 2: Tax smoothing not            optimal…but timing matters
                Model 3: Tax smoothing not            optimal…but LF participation choice matters
                Model 4: Tax smoothing not            optimal…combination of timing and LF
                participation choice matters




        June 27, 2008                      International Research Forum on                          51
                                                    Monetary Policy
                                                           Model 5: Competitive Search Equilibrium


COMPETITIVE SEARCH EQUILIBRIUM
     Wages determined before search, not after search (Moen 1997 JPE)
                All parties direct search according to “posted” wages
                An alternative to bargaining – little explored in DSGE models




June 27, 2008                   International Research Forum on                          52
                                         Monetary Policy
                                                           Model 5: Competitive Search Equilibrium


COMPETITIVE SEARCH EQUILIBRIUM
     Wages determined before search, not after search (Moen 1997 JPE)
                All parties direct search according to “posted” wages
                An alternative to bargaining – little explored in DSGE models

     Several ways to implement
                Perfectly-competitive “market-maker” sector
                Individuals announce wages before firms search for workers
                Firms announce wages before individuals search for jobs




June 27, 2008                   International Research Forum on                          53
                                         Monetary Policy
                                                           Model 5: Competitive Search Equilibrium


COMPETITIVE SEARCH EQUILIBRIUM
     Wages determined before search, not after search (Moen 1997 JPE)
                All parties direct search according to “posted” wages
                An alternative to bargaining – little explored in DSGE models

     Several ways to implement
                Perfectly-competitive “market-maker” sector
                Individuals announce wages before firms search for workers
                Firms announce wages before individuals search for jobs
                     The implementation we use
                     The mathematics: maximize the asset value of a filled job taking as given
                     reaction function u(w) (defined by LF participation condition)




June 27, 2008                   International Research Forum on                          54
                                         Monetary Policy
                                                                           Model 5: Competitive Search Equilibrium


COMPETITIVE SEARCH EQUILIBRIUM
     Wages determined before search, not after search (Moen 1997 JPE)
                All parties direct search according to “posted” wages
                An alternative to bargaining – little explored in DSGE models

     Several ways to implement
                Perfectly-competitive “market-maker” sector
                Individuals announce wages before firms search for workers
                Firms announce wages before individuals search for jobs
                     The implementation we use
                     The mathematics: maximize the asset value of a filled job taking as given
                     reaction function u(w) (defined by LF participation condition)



     Wage defined (implicitly) by

                          g '(1 − ut − nt ) − u '(ct ) χ                  ⎛ ξ ⎞
                                                         = (1 − τ tn )γθt ⎜ u ⎟
                                     u '(ct )                             ⎝ 1 − ξu ⎠




June 27, 2008                        International Research Forum on                                     55
                                              Monetary Policy
                                                                           Model 5: Competitive Search Equilibrium


COMPETITIVE SEARCH EQUILIBRIUM
     Wages determined before search, not after search (Moen 1997 JPE)
                All parties direct search according to “posted” wages
                An alternative to bargaining – little explored in DSGE models

     Several ways to implement
                Perfectly-competitive “market-maker” sector
                Individuals announce wages before firms search for workers
                Firms announce wages before individuals search for jobs
                     The implementation we use
                     The mathematics: maximize the asset value of a filled job taking as given
                     reaction function u(w) (defined by LF participation condition)



     Wage defined (implicitly) by

                          g '(1 − ut − nt ) − u '(ct ) χ                  ⎛ ξ ⎞
                                                         = (1 − τ tn )γθt ⎜ u ⎟
                                     u '(ct )                             ⎝ 1 − ξu ⎠
                          MRS (consumption-leisure)            MRT (consumption-search)




June 27, 2008                        International Research Forum on                                     56
                                              Monetary Policy
                                                                           Model 5: Competitive Search Equilibrium


COMPETITIVE SEARCH EQUILIBRIUM
     Wages determined before search, not after search (Moen 1997 JPE)
                All parties direct search according to “posted” wages
                An alternative to bargaining – little explored in DSGE models

     Several ways to implement
                Perfectly-competitive “market-maker” sector
                Individuals announce wages before firms search for workers
                Firms announce wages before individuals search for jobs
                     The implementation we use
                     The mathematics: maximize the asset value of a filled job taking as given
                     reaction function u(w) (defined by LF participation condition)



     Wage defined (implicitly) by

                          g '(1 − ut − nt ) − u '(ct ) χ                  ⎛ ξ ⎞           Tax creates static wedge
                                                         = (1 − τ tn )γθt ⎜ u ⎟           between MRS and MRT
                                     u '(ct )                             ⎝ 1 − ξu ⎠      Conjecture: tax smoothing
                                                                                          optimal
                          MRS (consumption-leisure)            MRT (consumption-search)




June 27, 2008                        International Research Forum on                                       57
                                              Monetary Policy
                                                                        Making Labor Market “More Walrasian”


      RAMSEY DYNAMICS
                             Model 1              Model 2           Model 3           Model 4          Model 5

                            ue benefits          ue benefits       ue benefits       ue benefits     ue benefits

                           40%     95%         40%      95%      40%         95%    40%     95%     40%      95%

                 Mean      17%     60%         15%      60%      28%         69%    36%     73%     26%      65%
Labor Tax Rate
                 SD        7%      1.4%        2.5%     0.7%     1.7%        1.1%   1.2%    1.0%    0.26%    0.91%

Market
                 SD (%)    1.85     2.35       0.90      5.80    3.39        2.59   1.00     15.6   2.67     2.56
tightness (θ)


                Model 1: Tax smoothing not            optimal
                Model 2: Tax smoothing not            optimal…but timing matters
                Model 3: Tax smoothing not            optimal…but LF participation choice matters
                Model 4: Tax smoothing not            optimal…combination of timing and LF
                participation choice matters




        June 27, 2008                      International Research Forum on                              58
                                                    Monetary Policy
                                                                            Making Labor Market “More Walrasian”


      RAMSEY DYNAMICS
                                 Model 1              Model 2           Model 3             Model 4              Model 5

                                ue benefits          ue benefits       ue benefits        ue benefits        ue benefits

                              40%      95%         40%      95%      40%         95%     40%      95%      40%         95%

                 Mean         17%      60%         15%      60%      28%         69%     36%      73%      26%         65%
Labor Tax Rate
                 SD            7%      1.4%        2.5%     0.7%     1.7%        1.1%   1.2%      1.0%    0.26%        0.91%

Market
                 SD (%)        1.85     2.35       0.90      5.80    3.39        2.59    1.00     15.6     2.67        2.56
tightness (θ)


                Model 1: Tax smoothing not                optimal
                Model 2: Tax smoothing not                optimal…but timing matters
                Model 3: Tax smoothing not                optimal…but LF participation choice matters
                Model 4: Tax smoothing not                optimal…combination of timing and LF
                participation choice matters
                Model 5
                        Tax smoothing optimal for Shimer calibration, but not for HM calibration


                                                                                   due to constant term in MRS
                                                                                   (same effect would arise in RBC model)

        June 27, 2008                          International Research Forum on                                    59
                                                        Monetary Policy
                                                                          Some Economics


MRT IN A SEARCH MODEL
     Examine MRT between search and consumption

     Resource constraint               “Usual” notion of MRT goes through
                                       production technology (leads to MRT = MPN)



                       ct + gt + γ vt = zt nt




June 27, 2008         International Research Forum on                               60
                               Monetary Policy
                                                                          Some Economics


MRT IN A SEARCH MODEL
     Examine MRT between search and consumption

     Resource constraint               “Usual” notion of MRT goes through
                                       production technology (leads to MRT = MPN)



                       ct + gt + γ vt = zt nt
                              Search model: can define MRT through
                              matching technology




June 27, 2008         International Research Forum on                               61
                               Monetary Policy
                                                                                  Some Economics


MRT IN A SEARCH MODEL
     Examine MRT between search and consumption

     Resource constraint                       “Usual” notion of MRT goes through
                                               production technology (leads to MRT = MPN)



                               ct + gt + γ vt = zt nt
                                      Search model: can define MRT through
                                      matching technology


     Holding all else (including n) constant, one unit of u
                Can be converted to θ(ξ/(1-ξ)) units of v
                The MRTS implied by the Cobb-Douglas matching technology




June 27, 2008                 International Research Forum on                               62
                                       Monetary Policy
                                                                                   Some Economics


MRT IN A SEARCH MODEL
     Examine MRT between search and consumption

     Resource constraint                        “Usual” notion of MRT goes through
                                                production technology (leads to MRT = MPN)



                                ct + gt + γ vt = zt nt
                                       Search model: can define MRT through
                                       matching technology


     Holding all else (including n) constant, one unit of u
                Can be converted to θ(ξ/(1-ξ)) units of v
                The MRTS implied by the Cobb-Douglas matching technology

     Holding all else constant, one unit of v
                Can be converted to γ units of c
                The MRT implied by the resource constraint




June 27, 2008                  International Research Forum on                               63
                                        Monetary Policy
                                                                                   Some Economics


MRT IN A SEARCH MODEL
     Examine MRT between search and consumption

     Resource constraint                        “Usual” notion of MRT goes through
                                                production technology (leads to MRT = MPN)



                                ct + gt + γ vt = zt nt
                                       Search model: can define MRT through
                                       matching technology


     Holding all else (including n) constant, one unit of u
                Can be converted to θ(ξ/(1-ξ)) units of v
                The MRTS implied by the Cobb-Douglas matching technology

     Holding all else constant, one unit of v
                Can be converted to γ units of c
                The MRT implied by the resource constraint
                                             ⎛ ξ ⎞
         MRT between u and c is γθ ⎜                ⎟
                                             ⎝ 1− ξ ⎠
June 27, 2008                  International Research Forum on                               64
                                        Monetary Policy
                                                                                    Some Economics


MRT IN A SEARCH MODEL
     Examine MRT between search and consumption

     Resource constraint                        “Usual” notion of MRT goes through
                                                production technology (leads to MRT = MPN)



                                ct + gt + γ vt = zt nt
                                       Search model: can define MRT through
                                       matching technology


     Holding all else (including n) constant, one unit of u
                Can be converted to θ(ξ/(1-ξ)) units of v
                The MRTS implied by the Cobb-Douglas matching technology

     Holding all else constant, one unit of v
                Can be converted to γ units of c
                The MRT implied by the resource constraint            A novel (interesting?...) notion of
                                             ⎛ ξ ⎞                    MRT in a search model
         MRT between u and c is γθ ⎜                ⎟
                                             ⎝ 1− ξ ⎠
June 27, 2008                  International Research Forum on                                65
                                        Monetary Policy
                                                            Some Intuition


    THE BARGAINING WEDGE
Labor market in

                      MRSt = (1 − τ tn ) MRTt ∀ t
competitive search
                                                          MODEL 5
equilibrium:
Smooth labor taxes




      June 27, 2008     International Research Forum on             66
                                 Monetary Policy
                                                                   Some Intuition


    THE BARGAINING WEDGE
Labor market in

                           MRSt = (1 − τ tn ) MRTt ∀ t
competitive search
                                                                MODEL 5
equilibrium:
Smooth labor taxes


Labor market bargaining

                          MRSt = (1 − τ tn )Ωt MRTt ∀ t
search equilibrium                                              MODEL 4 (for most
                                                                direct comparison)




      June 27, 2008           International Research Forum on             67
                                       Monetary Policy
                                                                                                  Some Intuition


    THE BARGAINING WEDGE
Labor market in

                                     MRSt = (1 − τ tn ) MRTt ∀ t
competitive search
                                                                                              MODEL 5
equilibrium:
Smooth labor taxes


Labor market bargaining

                                  MRSt = (1 − τ tn )Ωt MRTt ∀ t
search equilibrium                                                                            MODEL 4 (for most
                                                                                              direct comparison)


            Wedge Ωt reflects gap between ex-ante search value and ex-post
            bargaining value
                                                                                              Ex-ante search value
      MRSt                       gt'              ⎡       MRSt +1 ⎤                           (i.e., LF participation
                = (1 − τ t ) wt − ' + (1 − ρ ) Et ⎢Ξt +1|t h
                          n                 x
                                                                     ⎥                        condition)
      k h (θt )                  ut               ⎣       k (θt +1 ) ⎦
                                                                                              Ex-post bargaining
      Wt − U t = (1 − τ ) wt − χ + (1 − ρ ) Et ⎡Ξt +1|t (1 − k h (θt +1 ))(Wt+1 − U t+1 ) ⎤
                          t
                           n                 x
                                               ⎣                                          ⎦
                                                                                              value




            Tax-rate volatility offsets cyclical fluctuations in Ωt


      June 27, 2008                      International Research Forum on                                  68
                                                  Monetary Policy
                                                          Some Interpretations


INCOMPLETE CONTRACTS
     Cannot contract with a party you have not yet met

     Labor tax rate “partially directs search”




June 27, 2008           International Research Forum on              69
                                 Monetary Policy
                                                                  Some Interpretations


INCOMPLETE CONTRACTS
     Cannot contract with a party you have not yet met

     Labor tax rate “partially directs search”

     Ωt possibly reflects Caballero’s (2007) “fundamental
     transformation”
                Change from an ex-ante competitive situation to an ex-post monopoly
                situation

     A holdup problem?
                Not from the point of view of private-sector agents…
                …but rather from point of view of the Ramsey government

     Ramsey government a third agent in this “bilateral” game
     Ramsey government internalizes effects of (all) private-sector
     agents
     Ramsey government can “strategically” alter choices to
     “manipulate” bargaining sets
June 27, 2008                  International Research Forum on               70
                                        Monetary Policy
                                                              Ramsey Theory


ALTERNATIVE TAX INSTRUMENTS
     Is volatility in labor tax rate proxying for another (unallowed)
     instrument?




June 27, 2008           International Research Forum on            71
                                 Monetary Policy
                                                                                 Ramsey Theory


ALTERNATIVE TAX INSTRUMENTS
     Is volatility in labor tax rate proxying for another (unallowed)
     instrument?

     Some natural candidates
                Time-varying hiring subsidy:     γ (1 − τ ts )
                     Conceptual challenge: optimal hiring subsidy allows Ramsey government to
                     engineer socially-efficient labor-market outcome      an effective lump-sum
                     instrument
                     Technical challenge: zeros out Ramsey multipliers       numerical
                     approximations are just of the fully-efficient equilibrium
                     Circumvents content of Ramsey problem




June 27, 2008                   International Research Forum on                        72
                                         Monetary Policy
                                                                                  Ramsey Theory


ALTERNATIVE TAX INSTRUMENTS
     Is volatility in labor tax rate proxying for another (unallowed)
     instrument?

     Some natural candidates
                Time-varying hiring subsidy:      γ (1 − τ ts )
                     Conceptual challenge: optimal hiring subsidy allows Ramsey government to
                     engineer socially-efficient labor-market outcome      an effective lump-sum
                     instrument
                     Technical challenge: zeros out Ramsey multipliers       numerical
                     approximations are just of the fully-efficient equilibrium
                     Circumvents content of Ramsey problem


                Time-varying unemployment benefit:                χt
                     Conceptual challenge: steady-state Ramsey optimal χ = 0 (in ss, labor tax
                     only distorts economy by changing after-tax outside option)     makes labor
                     tax an effective lump-sum instrument
                     Technical challenge: zeros out Ramsey multipliers       numerical
                     approximations are just of the fully-efficient equilibrium
                     Circumvents content of Ramsey problem




June 27, 2008                    International Research Forum on                        73
                                          Monetary Policy
                                                                                  Ramsey Theory


ALTERNATIVE TAX INSTRUMENTS
     Is volatility in labor tax rate proxying for another (unallowed)
     instrument?

     Some natural candidates
                Time-varying hiring subsidy:      γ (1 − τ ts )
                     Conceptual challenge: optimal hiring subsidy allows Ramsey government to
                     engineer socially-efficient labor-market outcome      an effective lump-sum
                     instrument
                     Technical challenge: zeros out Ramsey multipliers       numerical
                     approximations are just of the fully-efficient equilibrium
                     Circumvents content of Ramsey problem


                Time-varying unemployment benefit:                χt
                     Conceptual challenge: steady-state Ramsey optimal χ = 0 (in ss, labor tax
                     only distorts economy by changing after-tax outside option)     makes labor
                     tax an effective lump-sum instrument
                     Technical challenge: zeros out Ramsey multipliers       numerical
                     approximations are just of the fully-efficient equilibrium
                     Circumvents content of Ramsey problem


     Standard criticism of Ramsey taxation models

June 27, 2008                    International Research Forum on                        74
                                          Monetary Policy
                                                                                         Summary


TAXONOMY OF MODELS AND RESULTS

                       Walrasian    Model 1      Model 2       Model 3    Model 4   Model 5


Search friction
(i.e., probability <
1 of finding a
match)


Work as soon as a
job is found?



Labor-force
participation
decision?



Competitive wage-
setting?


Tax Smoothing?           YES           NO           NO               NO     NO       YES



 June 27, 2008                     International Research Forum on                         75
                                            Monetary Policy
                                                                                       Summary


CONCLUSIONS
     Labor-tax smoothing not optimal in benchmark DSGE search and bargaining
     model
                Ex-post bargaining creates cyclically-varying wedges


     Labor-tax smoothing optimal if LF-margin AND competitive search
                Labor tax the only wedge between MRS and MRT – conceptually standard




June 27, 2008                     International Research Forum on                      76
                                           Monetary Policy
                                                                                       Summary


CONCLUSIONS
     Labor-tax smoothing not optimal in benchmark DSGE search and bargaining
     model
                Ex-post bargaining creates cyclically-varying wedges


     Labor-tax smoothing optimal if LF-margin AND competitive search
                Labor tax the only wedge between MRS and MRT – conceptually standard


     What model of wage determination is empirically relevant?
                Bargaining?
                Competitive search?




June 27, 2008                     International Research Forum on                      77
                                           Monetary Policy
                                                                                       Summary


CONCLUSIONS
     Labor-tax smoothing not optimal in benchmark DSGE search and bargaining
     model
                Ex-post bargaining creates cyclically-varying wedges


     Labor-tax smoothing optimal if LF-margin AND competitive search
                Labor tax the only wedge between MRS and MRT – conceptually standard


     What model of wage determination is empirically relevant?
                Bargaining?
                Competitive search?
                Don’t know…
                …but has potentially important implications for policy advice




June 27, 2008                     International Research Forum on                      78
                                           Monetary Policy
                                                                                       Summary


CONCLUSIONS
     Labor-tax smoothing not optimal in benchmark DSGE search and bargaining
     model
                Ex-post bargaining creates cyclically-varying wedges


     Labor-tax smoothing optimal if LF-margin AND competitive search
                Labor tax the only wedge between MRS and MRT – conceptually standard


     What model of wage determination is empirically relevant?
                Bargaining?
                Competitive search?
                Don’t know…
                …but has potentially important implications for policy advice



     Simple MRT interpretation of search environment – first in the literature?

     Future work
                Other models of bargaining
                      Any that do not create a wedge?
                Monetary policy in competitive search framework
                      Existing monetary labor search models invariably use Nash bargaining

June 27, 2008                     International Research Forum on                      79
                                           Monetary Policy

								
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