TAX SMOOTHING IN FRICTIONAL LABOR MARKETS DECEMBER 4, 2014

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1 TAX SMOOTHING IN FRICTIONAL LABOR MARKETS DECEMBER 4, 2014

2 Inroducion TAX SMOOTHING P P MRS = (1 τ n MPN Keep wedges (roughly he same size Period Q Period +1 Q Ramsey wans o keep hese wedges consan Resul and inuiion depend on neoclassical view of labor markes Labor ax is he only wedge à ax-smoohing is wedge-smoohing Quesion: Is ax smoohing opimal from he poin of view of he modern heory of fricional labor markes? December 4,

3 Inroducion TAX SMOOTHING MRS = (1 τ n MPN Ramsey wans o keep hese wedges consan Resul and inuiion depend on neoclassical view of labor markes Labor ax is he only wedge à ax-smoohing is wedge-smoohing Quesion: Is ax smoohing opimal from he poin of view of he modern heory of fricional labor markes? December 4,

4 Inroducion TAX SMOOTHING In neoclassical view, MPN = MRT (beween labor and consumpion MRS n = (1 τ MRT Think in erms of ransformaion fronier in which every objec can be viewed as eiher an inpu o or an oupu of he echnology o which i is associaed Ramsey wans o keep hese wedges consan Resul and inuiion depend on neoclassical view of labor markes Labor ax is he only wedge à ax-smoohing is wedge-smoohing Quesion: Is ax smoohing opimal from he poin of view of he modern heory of fricional labor markes? December 4,

5 Inroducion LABOR FORCE PARTICIPATION Inroduce endogenous labor supply (paricipaion Convenional empirical wisdom Cyclical LFP flucuaions small Basis for ypically absracing from paricipaion in maching models Volailiy of LFP relaive o ha of GDP 0.20 December 4,

6 Model Basics OVERVIEW OF MODEL Infiniely-lived represenaive household, measure one of members Employed members Full consumpion insurance Unemployed members sandard in DSGE labor search models Members ouside he labor force ( leisure Exogenous sochasic governmen spending Financed via labor income axaion and one-period real sae-coningen deb Governmen provides unemploymen benefis Governmen provides vacancy subsidies For compleeness of ax insrumens (Ramsey issue Incompleeness of governmen deb markes NOT driving our resuls (Aiyagari e al (2002 JPE Labor marke wih maching fricions and wage-seing fricions Only an exensive labor margin, no inensive labor margin Timing: insananeous producion December 4,

7 Model Basics OVERVIEW OF MODEL Unemployed are he unsuccessful searchers: ue = (1-p s p = probabiliy an individual finds a job and begins working immediaely December 4,

8 Model HOUSEHOLD OPTIMIZATION Maximize expeced lifeime uiliy max { c,n,s,b } β E 0 =0 ( u(c h (1 p s + n s.. disuiliy of employmen + unsuccessful search c + b = n (1 τ n w + (1 p s χ + R b 1 + (1 τ d d Flow budge consrain measure n earn aferax wage income measure ue = (1-ps receive ue benefi χ (governmen financed Baseline analysis: se τ d = 1 à no profi-axaion issues driving resuls n = (1 ρ n + s p 1 Perceived LOM for employmen ( insananeous producion (exogenous measure of pre-exising employmen relaionships erminae flow of new employmen relaionships = measure of searchers s x probabiliy a searcher successfully lands a job FOCs wih respec c, n, s, b December 4,

9 Model HOUSEHOLDS Household LFP condiion (he labor supply condiion! h'(lfp u'(c = p (1 τ n 1 p w + (1 ρe Ξ p +1 h'(lfp +1 u'(c +1 χ + (1 p χ MRS beween lfp and c = expeced payoff of searching Unemploymen benefi (wih probabiliy 1 p Afer-ax wage + coninuaion value (wih probabiliy p To recover sandard labor supply funcion (e.g., RBC 1. ρ = 1 (all employmen relaionships erminae a end of every period 2. p = 1 (probabiliy a searcher finds a job 3. χ = 0 (no ue benefi because no noion of ue h'(lfp u'(c = (1 τ n w December 4,

10 Model FIRMS Producion Requires a mached job-worker pair: posing cos γ per vacancy Individual job i produces y i = z Aggregae oupu y = n z (symmery across jobs Dynamic profi-maximizaion problem max { n,v } (exogenous measure of pre-exising employmen relaionships erminae Vacancy-creaion condiion =0 Ξ 0 n = n + vq z n w n (1 τ s γ v (1 ρ 1 flow of new employmen relaionships = # job-openings x probabiliy an opening aracs a searching individual γ (1 τ s s γ (1 τ = z q w + (1 ρe Ξ q +1 Ensures compleeness of ax insrumens Firm s perceived LOM for oal employmen ( insananeous hiring cos of posing vacancy (inclusive of subsidy or ax benefi of posing vacancy December 4,

11 Model LABOR MARKET Labor-marke ighness θ = v /u Imporan aggregae variable in maching-based models Maching probabiliies p and q depend only on θ given CRTS maching Key saisic for maching efficiency December 4,

12 Model LABOR MARKET Labor-marke ighness θ = v /u Imporan aggregae variable in maching-based models Maching probabiliies p and q depend only on θ given CRTS maching Key saisic for maching efficiency Maching funcion LOM for aggregae employmen 1 ms (, v sv ξ = ψ ξ n = (1 ρ n + m( s, v 1 Nash bargaining over wage paymen solves max w ( η J 1 η W U W U = η n 1 τ 1 η J Gain o household of successfully forming anoher employmen relaionship Value o firm of hiring anoher worker χ w = ηz + (1 η 1 τ + η(1 ρe Ξ n +1 1 (1 p +1 1 τ n +1 n γ (1 τ s +1 1 τ q +1 December 4,

13 Model GOVERNMENT AND RESOURCE FRONTIER Exogenous governmen spending financed via Labor income ax One-period sae coningen real deb τ n w n + b + τ d d = g + R b 1 + (1 p s χ + τ s γ v Governmen provides unemploymen benefis Raher han assuming χ is home producion December 4,

14 Model GOVERNMENT AND RESOURCE FRONTIER Exogenous governmen spending financed via Labor income ax One-period sae coningen real deb τ n w n + b + τ d d = g + R b 1 + (1 p s χ + τ s γ v Governmen provides unemploymen benefis Raher han assuming χ is home producion Resource consrain c + g + γ v = zn = gov budge consrain + hh budge consrain Assuming χ is gov-financed allows i o drop ou of resource consrain Makes model more comparable o exising Ramsey models Precise naure of χ (ue benefi? home producion? value of leisure? no ypically specified in DSGE maching models Our model ariculaes boh ue benefi and value of leisure December 4,

15 Model PRIVATE-SECTOR EQUILIBRIUM { c, n, s, w, θ, R, b} = 0 Sochasic processes ha saisfy Household s bond Euler equaion Vacancy-creaion condiion Labor force paricipaion condiion Nash wage oucome Law of moion for employmen n = (1 ρ n + m( s, v 1 Governmen budge consrain (key condiion in Ramsey models Resource consrain c + g + γ v = zn Given processes {,, n s g z τ, τ } = 0 Sandard condiions in basic Ramsey models December 4,

16 Efficiency MATCHING EFFICIENCY Social Planner s.. max { c,n,s,v } E 0 β =0 u(c h lfp c + g + γ v = zn ( Resource consrain n = (1 ρ n + m( s, v 1 Aggregae LOM for oal employmen December 4,

17 Efficiency MATCHING EFFICIENCY Social Planner s.. max { c,n,s,v } E 0 β =0 c + g + γ v = zn ( u(c h lfp Resource consrain n = (1 ρ n + m( s, v 1 Aggregae LOM for oal employmen FOCs (consider deerminisic case h'(lfp u'(c = γ m (s,v s m v (s,v = γθ ξ 1 ξ Saic Efficiency Condiion. Efficien Paricipaion Condiion Can insead derive direcly off ransformaion fronier of model. u' ( c βu'( c + 1 γ (1 ρ 1 s( + 1, + 1 mv( s+ 1, v+ 1 = γ z m ( s, v v Ineremporal Efficiency Condiion. Efficien Vacancies Condiion ( m s v Can insead derive direcly off ransformaion fronier of model. December 4,

18 Efficiency TRANSFORMATION FRONTIER Generalize he PPF c + γ v = z n n = + (1 ρ n 1 m s, v ( à, hen inser ino LOM for n à v n zn c = γ n (1 1 s, z ρ n m c = 0 γ December 4,

19 Efficiency TRANSFORMATION FRONTIER Generalize he PPF c + γ v = z n n = + (1 ρ n 1 m s, v ( à, hen inser ino LOM for n à v n zn c = γ n (1 1 s, z ρ n m c = 0 γ Use lfp = (1-ρn -1 + s o consruc ransformaion fronier Γ ( c, lfp, n; n ρ n 1 m lfp 1 ρ n 1 Use IFT o obain MRT c, lfp zn c ( 1 (, = 0 γ Γlfp m (, s s v = = γ Γ m ( s, v c v STATIC MRT beween consumpion and labor SUPPLY December 4,

20 Efficiency TRANSFORMATION FRONTIER Generalize he PPF c + γ v = z n n = (1 ρ n 1 + m( s, v à, hen inser ino LOM for n à v n zn c = γ n (1 ρ n 1 m s, z c = 0 γ Use lfp = (1-ρn -1 + s o consruc ransformaion fronier Γ ( c, lfp, n; n ρ n 1 m lfp 1 ρ n 1 Use IFT o obain MRT c, lfp zn c ( 1 (, = 0 γ Γlfp m (, s s v = = γ Γ m ( s, v c v n Γ c m (, v s v = = c Γ γ zm ( s, v n v STATIC MRT beween consumpion and labor SUPPLY Marginal effec on n of a change in c which has ineremporal consequences December 4,

21 Efficiency TRANSFORMATION FRONTIER Transformaion fronier Gc n n n (,, c, n (1 ρ n m lfp 1 ρ, ; ( = 0 Use IFT o obain z n c γ IMRT c, c + 1 γ (1 ρ 1 s( 1, 1 G + + c m ( 1, 1 v s+ v+ = = G γ c + 1 z m ( s, v v ( m s v INTERTEMPORAL MRT beween c and c +1 MRT c, lfp Γlfp m (, s s v = = γ Γ m ( s, v c v STATIC MRT beween consumpion and labor SUPPLY December 4,

22 Efficiency MATCHING EFFICIENCY Efficiency characerized by h'(lfp u'(c = γ m (s,v s m v (s,v = γθ ξ 1 ξ u'( c βu'( c + 1 = γ (1 ρ 1 s( + 1, + 1 mv( s+ 1, v+ 1 γ z m ( s, v v ( m s v = Saic MRT = Ineremporal MRT Saic Efficiency Condiion. Can insead derive direcly off ransformaion fronier of model. Ineremporal Efficiency Condiion. Can insead derive direcly off ransformaion fronier of model. December 4,

23 Efficiency MATCHING EFFICIENCY Efficiency characerized by h'(lfp u'(c = γ m (s,v s m v (s,v = γθ ξ 1 ξ u'( c βu'( c + 1 = γ (1 ρ 1 s( + 1, + 1 mv( s+ 1, v+ 1 γ z m ( s, v v ( m s v = Saic MRT = Ineremporal MRT Saic Efficiency Condiion. Can insead derive direcly off ransformaion fronier of model. Ineremporal Efficiency Condiion. Can insead derive direcly off ransformaion fronier of model. Hypohesis based on Ramsey heory: sabilizing or closing any wedges in THESE efficiency condiions is opimal Conribuion o undersanding efficiency in DGE models wih enry margins IMRT in search-heoreic moneary models: Aruoba and Chugh (2010 JET IMRT in endogenous produc variey framework: Chugh and Ghironi (2012 December 4,

24 Exogenous-Policy Analysis CALIBRATION Baseline calibraion So ha exogenous policy (non-ramsey equilibrium broadly maches U.S. labor marke flucuaions Preferences and key parameers κ u(c h(lfp = lnc 1+1/ ι lfp 1+1/ι Paricipaion (labor supply elasiciy (ι = 0.18 Low worker bargaining power (η = 0.05 High unemploymen benefi (98% of real wage The wo key parameers of HM calibraion Res of parameers, maching-relaed and oherwise, sandard β = 0.99 ρ = 0.10 ξ = 0.40 AR(1 parameers for LOMs for TFP and governmen spending Ec. December 4,

25 Resuls DYNAMICS Ramsey Exogenous Policy Benchmark Daa Calibraion HM 0% and Hosios Calibraion HM Gerler and Trigari (2009 JPE Labor Tax Rae Marke ighness (θ Mean 11% 22% 22% Rel SD Rel SD Vacancies Rel SD Unemploymen LFP Rel SD Rel SD Real wage Rel SD 0.52 Saic wedge SD (% Ineremporal wedge SD (% December 4,

26 Resuls DYNAMICS Ramsey Exogenous Policy Benchmark Daa Calibraion HM 0% and Hosios Calibraion HM Gerler and Trigari (2009 JPE Labor Tax Rae Marke ighness (θ Mean 11% 22% 22% Rel SD Rel SD Vacancies Rel SD Unemploymen LFP Rel SD Rel SD Real wage Rel SD Saic wedge SD (% Ineremporal wedge SD (% December 4,

27 Resuls DYNAMICS Ramsey flucuaions IDENTICAL o efficien flucuaions for ANY (η, χ pair In erms of flucuaions around a given seady sae Seady-sae levels of (τ n, τ s depend on (η, χ pair December 4,

28 0 lfp 0 s 10 (1-ps Efficien HM Ramsey Efficien HM Ramsey Efficien HM Ramsey n Efficien HM Ramsey θ Efficien HM Ramsey v Efficien HM Ramsey

29 Resuls DYNAMICS Ramsey flucuaions IDENTICAL o efficien flucuaions for ANY (η, χ pair In erms of flucuaions around a given seady sae Seady-sae levels of (τ n, τ s depend on (η, χ pair Inerpreaion: Ramsey governmen always ensures efficien labormarke flucuaions (v, s, θ By appropriaely adjusing (τ n, τ s over he business cycle December 4,

30 Resuls DYNAMICS Ramsey Exogenous Policy Benchmark Daa Calibraion HM 0% and Hosios Calibraion HM Gerler and Trigari (2009 JPE Labor Tax Rae Marke ighness (θ Mean 11% 15% 22% 22% Rel SD Rel SD Vacancies Rel SD Unemploymen LFP Rel SD Rel SD Real wage Rel SD Saic wedge SD (% Ineremporal wedge SD (% December 4,

31 Resuls DYNAMICS Ramsey flucuaions IDENTICAL o efficien flucuaions for ANY (η, χ pair In erms of flucuaions around a given seady sae Seady-sae levels of (τ n, τ s depend on (η, χ pair Inerpreaion: Ramsey governmen always ensures efficien labormarke flucuaions (v, s, θ By appropriaely adjusing (τ n, τ s over he business cycle Wedge dynamics? Ramsey smoohs boh saic wedge. and ineremporal wedge December 4,

32 Resuls DYNAMICS Ramsey Exogenous Policy Benchmark Daa Calibraion HM 0% and Hosios Calibraion HM 0% and Hosios Gerler and Trigari (2009 JPE Labor Tax Rae Marke ighness (θ Mean 11% 15% 22% 22% Rel SD Rel SD Vacancies Rel SD Unemploymen LFP Rel SD Rel SD Real wage Rel SD Saic wedge SD (% Ineremporal wedge SD (% December 4,

33 Wedges STATIC AND INTERTEMPORAL CONDITIONS Saic Condiion Efficiency characerized by h'(lfp u'(c = γ m (s,v s m v (s,v = γθ ξ 1 ξ u'(c βu'(c +1 = Ineremporal Condiion γ (1 ρ m v (s +1,v +1 1 m (s,v s γ m v (s,v z ( Decenralized equilibrium condiions characerized by h'(lfp u'(c χ(1 ξ η(1 ξ ξ = + (1 τ n γ ξ θ (1 τ s γθ ξ(1 η 1 ξ (Too complicaed o gain any immediae inuiion see Secion 6 and Appendix D = wedge beween saic MRS and saic MRT December 4,

34 Wedges STATIC AND INTERTEMPORAL CONDITIONS Saic Condiion Efficiency characerized by h'(lfp u'(c = γ m (s,v s m v (s,v = γθ ξ 1 ξ u'(c βu'(c +1 = Ineremporal Condiion γ (1 ρ m v (s +1,v +1 1 m (s,v s γ m v (s,v z ( Decenralized equilibrium condiions characerized by h'(lfp u'(c χ(1 ξ η(1 ξ ξ = + (1 τ n γ ξ θ (1 τ s γθ ξ(1 η 1 ξ (Too complicaed o gain any immediae inuiion see Secion 6 and Appendix D = wedge beween saic MRS and saic MRT To obain zero saic wedge in every period, need τ n = τ s = 0 in every period, η = ξ, χ = 0 To obain zero ineremporal wedge in every period, need τ n = τ s = 0 in every period, η = ξ, χ = 0 December 4,

35 Summary CONCLUSIONS Labor ax smoohing no opimal in DSGE search and maching model Calibraed o mach key labor marke dynamics under exogenous ax policy Rigid real wage (delivered hrough Nash-Hosios bargaining as benchmark he imporan feaure of he model Bu wedge smoohing IS opimal Basic Ramsey heory Ramsey flucuaions in allocaions efficien regardless of calibraion Welfare-relevan noions of wedges Developing maching-model conceps of efficiency and MRTs for use in virually any maching applicaion Could hink of labor wedge as feauring boh saic and ineremporal dimensions Use as framework o empirically measure labor wedges? December 4,

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