Corporate Profit Taxes, Capital Expenditure and Real Wages: The analytics behind a contentious debate

Transcription

1 CDEP CGEG WORKING PAPER SERIES CDEP CGEG WP No. 6 Corporae Profi Taxes, Capial Expendiure and Real Wages: The analyics behind a conenious debae Willem H. Buier and Anne C. Siber May 208

2 Corporae Profi Taxes, Capial Expendiure and Real Wages: The analyics behind a conenious debae 8 May 208 Willem H. Buier Ciigroup Global Markes and Columbia Universiy and Anne C. Siber Birkbeck, Universiy of London and Columbia Universiy The views and opinions expressed are hose of he auhors alone. They canno be aken o represen he views and opinions of Ciigroup or of any oher organizaion he auhors are affiliaed wih. This paper formalizes and furher develops ideas from he Ciigroup publicaion: Corporae Profi Tax Cus, Capial Deepening and Real Wages: Hasse v. Summers - who is righ?", Cii, Cii Research, Muli-Asse, Global, Global Economics View, 22 November 207, hps:// by Willem H. Buier.

3 Absrac The recen reducion in he US corporae profi ax rae from 35 percen o 2 percen has riggered renewed ineres in he impac of a cu in he corporae ax rae on capial accumulaion and real wages. This heoreical conribuion demonsraes ha he familiar proposiion ha a cu in he corporae profi ax rae booss he capial inensiy of producion and he real wage is sensiive o a number of key assumpions. Even when he real ineres rae is exogenously given, full deducibiliy of capial expendiure from he corporae profi ax base will resul in no impac of a corporae profi ax rae cu on he incenive o inves. Adding deducibiliy of ineres can resul in a negaive effec on he capial inensiy of producion of a corporae profi ax rae cu. When he real ineres rae is endogenous, we use he perpeual youh OLG model o demonsrae ha he effecs on consumpion demand of a corporae profi ax cu will reduce he impac on capial inensiy of a corporae profi ax cu if he ax cu is funded by higher lump-sum axes on permanen income households. We have no been able o find examples where he capial inensiy impac is reversed. Alernaive funding rules (e.g. lower public consumpion purchases) and he inroducion of Keynesian consumers could lead o a larger posiive effec on capial inensiy from a cu in he corporae profi ax rae. JEL Classificaion Codes: E2, E22, E62, E63 H2, H3, H25, Key Words: Public economics, public finance, corporae profi ax; deducibiliy of invesmen; capial expendiure, expensing of ineres; endogenous ineres rae; OLG model. Willem H. Buier Ciigroup Global Markes Inc., 388 Greenwich Sree, New York, NY 003, USA Tel.: willem.buier@cii.com Anne C. Siber Birkbeck, Universiy of London, School of Economics, Mahemaics and Saisics Male Sree, London, WCE 7HX, Unied Kingdom Tel.: + 44 (0) asiber@econ.bbk.ac.uk 2

4 . INTRODUCTION The impac of a cu in he corporae profi ax rae on capial accumulaion and hrough ha on real wages has long been he subjec of scholarly and poliical debae. The reducion in he U.S. federal corporae profi ax rae in December 207 for from 35 o 2 percen has riggered renewed ineres in his issue. 2 The debae has been vigorous and even someimes raher ill-empered (see, for example, Hasse (207), Summers (207 a, b, c), Mankiw (207a, b), Mulligan (207 a, b) and Furman (207b)). 3 In his paper we discuss he conrasing views of wo prominen economiss, Kevin Hasse (chairman of he Council of Economic Advisers) and Larry Summers (former Treasury Secreary and former head of he Naional Economic Council) and ry o deermine which is likely o be closer o he ruh. I urns ou ha wo oher feaures of he corporae ax regime are cenral o he deerminaion of he effecs of a cu in he corporae profi ax rae. These are he deducibiliy of capial expendiure and ineres paymens from he corporae profi ax base. The December 207 corporae ax reforms raised, for a period of 5 years, he firs-year bonus depreciaion percenage for capial expendiure from 50% o 00%. Unlimied ineres deducibiliy was changed o ne ineres deducibiliy up o 30% of adjused axable income, wih any excess carried forward up o 5 years. In Secion 2, we exend a simple exogenous consan real ineres rae model proposed by Mankiw (204a, b) and Mulligan (207a, b) o make i applicable o he U.S. corporae ax proposals. In Secion 3 we employ he general equilibrium closed-economy Yaari-Blanchard overlapping-generaions model. For he special case of a zero birh rae his model becomes a convenional infinie-lived represenaive agen model where he seady sae real ineres rae is deermined by he (consan) rae of ime preference. Thus, i subsumes he discussion in Secion 2..A. The Debae In recen publicaions he Council of Economic Advisers (CEA) (207a, b) argues ha reducing he federal corporae ax rae in he US from 35 o 20 percen would increase average household income in he Unied Saes by, very conservaively, 4,000 dollars annually and possibly by as much as 9,000 dollars annually. The idea is ha a lower ax will resul in higher invesmen, and hus a higher capial-labor raio and higher real wages. (See, also, Hasse (207)). Since hen, he corporae ax rae has been reduced o 2 percen. As mos of he debae was based on an assumpion ha he new ax would be 20 percen, ha is he number we focus on in our calculaions in Secion 2. Assume he cu in corporae ax raes from 35 o 20 percen is likely o cos around 200 billion dollars a year in he shor run. This esimae is from he Commiee for a Responsible Federal Budge (207) and is also he number used by Summers (207a) and Furman (207b). Many esimaes are lower ranging from an shorrun one-year revenue loss of 20 billion dollars (Hodge (207)) o 50 billion dollars (Join Commiee on Taxaion (207)) and would make he wage gains relaive o he ax revenue loss look even bigger. There were abou 54 million workers in he U.S. economy in Ocober 207, of whom abou 27 million were full-ime Council of Economic Advisers (207b) is a survey of he empirical research. I is problemaic because of he combinaion of challenges in conrolling for omied variables and difficul idenificaion issues in boh ime series and cross-counry empirical sudies. 2 The corporae ax rae cu permanenly cus he corporae ax rae for profis in excess of $0 million from 35% o 2. 3 Larry Summers (207a) response o Hasse (207) and he Council of Economic Advisers (207a, b) was ha Hasse deserved a failing grade for his analysis. Hasse said of he Tax Policy Foundaion s repor on he Big 6 ax plan, I s inaccurae. I s ficion. Of he negaive public responses o i he said, Tha s wha happens when you behave irresponsibly. Hasse (207, p.).

5 employees. 4 If oal employmen is wha he average wage income increase applies o, a long run rise in he average wage income of 4,000 dollars he conservaive case means ha aggregae annual wage income would, in he long run, rise by 600 billion dollars, or 3.0 imes he shor-run loss in ax revenue. In he opimisic case where average household income rises by 9,000 dollars, he long-run increase in aggregae annual real wage income would be,350 billion dollars, or 6.75 imes he shor-run annual loss in revenue. Summers (207a) uses he 50 million number in his calculaions. If only he full-ime employed workers benefi from hese increases, aggregae wage income would rise by 508 billion dollars in he case of a 4,000 dollar wage increase per worker (a muliple of 2.54 of he shor-run annual revenue loss) and,43 billion dollars in he case of a 9,000 dollar wage increase per worker (a muliple of 5.72). The CEA/Hasse numbers, however, do no refer o average individual worker income bu o household income. In 206 here were almos 26 million households in he Unied Saes. Working households, hose wih a leas one working adul, numbered close o million. We use he household numbers o calculae he muliples. Wih are 26 million households, his gives a muliple of 2.52 in he case a wage income gain of 4,000 dollars per household and a muliple of 5.67 in he case of 9,000 dollars per household. Wih million households his gives a muliple of 2.22 in he case of 4,000 dollars per household and a muliple of 5.00 in he case of 9000 dollars per household. 5 Table : Raio of Long-Run Annual Labor Income Gains o Shor-Run Revenue Loss from a Cu in he Corporae Tax Rae from 35 o 20 Percen The income gain is applied o: Conservaive Case (wage increase of 4,000 dollars per year) All workers Full-ime workers All households Full-ime households Opimisic Case (wage increase of (9,000 dollars per year) The muliples we have compued are shown in Table and in wha follows we ask, how plausible are hese numbers? We consider only he impac of he proposed corporae profi ax cu rae from 35 o 20 percen and he expensing of invesmen and ineres deducibiliy. There are many oher fiscal measures ha have been proposed by he Whie House, he House of Represenaives and he Senae, ha deal wih oher aspecs of corporae and personal axaion. These oher measures are no considered here. 6.B. Ouline of he Res of he Paper In Secion 2 we show ha if he real ineres rae is exogenous and here is no expensing of invesmen, hen he CEA s proposiion ha a cu in he corporae ax rae increases long-run labor income is qualiaively correc, bu he numbers in Table grealy oversae he magniude of he raio of long-run labor income gains o he 4 Labor Force Saisics, daabase, Bureau of Labor Saisics (hps://bls.gov : accessed 27 April 208), specifically Table A-9 Seleced Employmen Indicaors. We use he average of he numbers from he Curren Populaion Survey and he Curren Employmen Saisics survey. 5 We assume a shor-run revenue loss from he corporae profi ax cu of 200 billion dollars. 6 The complee se of ax reforms can be found in Join Explanaory Saemen of he Commiee of he Conference, 8 December 207, hps://docs.house.gov/billshisweek/20728/join%20explanaory%20saemen.pdf. This documen is 570 pages long. 2

6 shor-run revenue loss of a corporae ax cu. Even he raio of he long-run wage gain o he long-run ax revenue only reaches 2.40 in our benchmark case, beween he Conservaive Case of All households and Full-ime households in Table. If here is parial expensing (ha is, deducibiliy) of capial expendiure from he corporae ax base hen he scenario may be even less rosy. Prior o he December 207 reforms, 50 percen of capial expendiure could be expensed in he firs year. Following he reform ha number is 00 percen (for he nex five years). Wih invesmen expensing, he cos of capial is less sensiive o he corporae ax rae han if here were no expensing. Thus, he capial-labor raio and he real wage are less sensiive, as well. If all capial expendiure can be deduced, hen he cos of capial, he real wage and he capial-labor raio are insensiive o corporae ax rae. For a Cobb-Douglas producion funcion, if here is full expensing of capial expendiures hen here is a greaer proporional response of corporae ax revenue o a cu in he ax rae han here would be wih no expensing. If here is full expensing of capial expendiure and deducibiliy (complee or parial) of ineres from he corporae ax base, and if capial expendiure is a leas in par funded by borrowing, a cu in he corporae profi ax rae reduces he benefi of ineres deducibiliy and, hus, has he perverse effec of increasing he cos of capial. Hence i would lower he capial-labor raio and he real wage as well. In Secion 2 we assume ha he real ineres rae is exogenous and consan. This is consisen wih a represenaive infinie-lived agen model wih a consan subjecive discoun facor. However, in overlappinggeneraions models an increase in he firms demand for capial brough abou by a decrease in he corporae ax rae requires ha he ineres rae adjus o resore equaliy beween he firm s demand for capial and consumers supply. In Secion 3 of he paper we endogenize he real ineres rae using a closed economy, full employmen model wih consumpion deermined by he Perpeual Youh Yaari-Blanchard overlapping generaions model. In our closed economy model (and by exension in a large open economy wih perfec capial mobiliy) 7, a balanced budge cu in he corporae ax rae, wih a lump-sum ax on households balancing he corporae ax cu, will, if here is no full expensing of invesmen, raise boh he capial-labor raio and he real ineres rae. This reduces he long-run US real wage gains relaive o he consan real ineres rae benchmark of Secion 2. The corporae ax cu will no only impac he opimal capial sock hrough he incenive o inves, i will also in general impac household consumpion demand. When he corporae ax cu is funded hrough an increase in lump-sum axes, consumpion demand will, if households are permanenincome-consumers, be boosed a a consan ineres rae and capial-labor raio. A sufficienly large share of Keynesian households wihou access o financial markes can reverse ha resul. When he corporae profi ax cu is funded hrough a cu in public consumpion expendiure, he aggregae demand effec (holding consan he ineres rae and he capial-labor raio) can go eiher way. As noed earlier, if here is full expensing of capial expendiure, a cu in he corporae ax rae has no impac on he incenive o inves and herefore no impac on he capial sock and real wage income if he real ineres rae is exogenous. If he real ineres rae is endogenous, he impac of he corporae profi ax cu on consumpion demand (and possibly also on exhausive public spending) will deermine is effec on he longrun capial-labor raio and real ineres rae. The same condiions ha generae a negaive effec on he longrun capial-labor raio from a balanced budge corporae ax cu/lump sum ax increase when here is no deducibiliy of capial expendiure imply a reducion in he long-run capial-labor raio when here is full 7 The global (large counry) open economy models for which his would hold are he kind analyzed in Siber (985, 990). 3

7 deducibiliy of capial expendiure. 8 Again, wih enough Keynesian households, he household demand effec can go he oher way. If cus in public spending on consumpion balance he corporae profi ax cus, he impac on aggregae demand and hus on he capial-labor raio is ambiguous. 2. The Case of an Exogenous Real Ineres Rae In his Secion he real ineres rae is assumed o be exogenous and sricly posiive. The analysis of he impac of corporae ax changes on capial formaion, real wages and ax revenues is simple when he real ineres rae is exogenous. Only he opimizaion problem of he represenaive firm has o be analyzed. The household secor and governmen budge consrain play no explici role, alhough he implici assumpion is made ha boh are solven. An exogenous real ineres rae can be jusified for a small open economy wih perfec inernaional capial mobiliy. In a closed economy i can be jusified by assuming ha he represenaive household is an infinie-lived opimizing agen wih a consan rae of erm preference and ha he economy is in a seady-sae equilibrium. There is a single good, which can be used for capial or consumpion. The infinie-lived represenaive compeiive firm uses capial and labor o produce oupu. I issues deb and (non-negaive) equiy and pays ineres o bondholders and (non-negaive) dividends o shareholders. The firm also pays corporae profi axes. Non-negaive shares of ne invesmen, capial depreciaion, he wage bill and ineres paid can be expensed, or deduced from he corporae income ax base. We assume he wage bill can be fully expensed. The ime- budge consrain of he firm is K K B / r + B + Q( E E) = Y wl δ K de T, () where is he capial sock a he beginning of period, is he sock of one-period real discoun bonds ousanding a he beginning of period, is he number of shares of equiy ousanding a he beginning of period, is (one plus) he real ineres rae beween periods - and, is he price of equiy a ime, is oupu a ime, is labor a ime, is he wage rae a ime, is he dividend per share paid a ime on shares ousanding a he beginning of period, is he corporae ax paid a ime and is he capial depreciaion rae. Corporae axes paid by he firm are (2) where is he (consan) corporae ax rae, s is he fracion of ne invesmen and depreciaion ha can be deduced and is he fracion of ineres paymens ha can be deduced. 8 This condiion is ha, ce. par., a higher capial-labor raio booss household demand for consumpion goods by more han i booss he supply of consumpion goods. 4

8 Oupu is produced via a consan reurns o scale producion funcion The funcion is assumed o have sricly posiive and sricly decreasing marginal producs and o saisfy he usual regulariy condiions. 9 The assumpion of consan reurns o scale implies ha where he funcion is oupu per uni of labor and is he ime- capial-labor raio. The corporae ax is he only ax on asse income in his economy. Thus, by consumer arbirage: The period budge ideniy of he represenaive firm, equaion (), can be rewrien as: (3) (4) We impose he sandard no Ponzi scheme erminal condiion: (5) Solving equaion (4) forward and subsiuing equaion (5) ino he resul yields he firm s ineremporal budge consrain: (6) The firm maximizes he value of he ousanding sock of equiy, aking ineres raes, wages, he parameers of he corporae ax regime and he inheried socks of deb, equiy and capial as given. In his Modigliani-Miller world, he opimal capial srucure (deb versus equiy) is indeerminae in he absence of profi axaion and ineres deducibiliy and here are corner soluions when hey are presen. Raher mechanically, we side-sep his issue by assuming ha he firm s deb is a fracion of is capial sock: (7) The firs order condiions for are: r ( r + δ )( θs) λθs ( r ) f '( k) = R θ (8) (9) 9 K 0; L 0; f(0) = 0; lim f '( k) = 0; lim f '( k) = +. k k 0 5

9 Here R is he marginal cos of capial in period. By equaions (8) and (9) he equilibrium capial-labor raio is a funcion solely of he exogenous cos of capial. Differeniaing yields ˆ σ ˆ α k, ˆ ˆ = R w = R, α α (0) where we use he noaional convenion ha proporional raes of change are denoed by a care, so ha, and where α kf '( k)/ f ( k), α (0,) is capial s compeiive share of oupu and f( k) kf '( k)) σ dln k / dln = ( α) f'( k) / ( kf "( k) ) > 0 f '( k ) is he elasiciy of subsiuion beween capial and labor, hereafer referred o as he elasiciy of subsiuion. I is assumed ha aggregae employmen is equal o he exogenous labor supply. I is furher assumed ha his labor supply is consan, and hen wihou loss of generaliy, normalized o one. Then, equaions (8) and (9) can be solved for he capial-labor raio (and hus capial) and he real wage. We now urn o he Hasse- Summers debae. In he remainder of he Secion we assume ha he exogenous ineres rae is a consan r. No expensing of capial expendiure or ineres The social media conribuion o he Hasse-Summers debae focuses on he case where here is no capial expendiure deducibiliy: s = 0. I also ignores he deducibiliy of ineres: s r = 0. We shall refer o his as he Hasse-Mankiw case (see Hasse (207) and Mankiw (207a,b)). In his case he cos of capial and he corporae ax are: R = ( r + δ) / ( θ) () T= θkf'( k). (2) Differeniaing equaion () yields R ˆ = dθ / ( θ). Subsiuing his ino equaion (0) yields kˆ σ dθ α dθ =, wˆ =. α θ α θ (3) Thus, an increase (decrease) in he corporae ax rae increases (decreases) he cos of capial and, hus, decreases (increases) boh he capial-labor raio and he real wage. Differeniaing equaion (2) and using equaion (3) yields ˆ α σθ dθ T =. θ( α ) θ (4) 6

10 In he empirically reasonable case where he elasiciy of subsiuion exceeds labor s share of oupu,, corporae ax revenue is subjec o a Laffer curve. An increase in he corporae ax rae increases corporae ax revenue up unil and hen causes i o decrease. If he elasiciy of subsiuion is less han labor s share of oupu, hen here is no Laffer curve and corporae ax revenue is monoonically increasing in he corporae ax rae. For he special case of he Cobb-Douglas producion funcion, capial and labor s shares of oupu are consan and he elasiciy of subsiuion is equal o one; hence, corporae ax revenue follows a Laffer curve. If we suppose ha capial s share of oupu is abou 40 percen, hen increasing he corporae ax rae causes corporae ax revenue o go up unil a corporae ax rae of abou 60 percen and afer ha revenue begins o fall. 0 The numbers in Table are raios of he change in wage income wih respec o a change in he corporae ax o (minus one imes) he change in corporae ax revenue wih respec o he corporae ax. In using his model o check how reasonable hey are, we migh begin by using equaions (3) and (4) o compue dd ρ : = ( w/ θ)/( T / θ). Boh he effec of he ax rae change on he real wage and he effec on ax revenues are dynamic or long-run effecs. The capial sock is endogenous and responds fully o he ax change. Noe ha wih a consan ineres rae, consan fiscal policy rules and no adjusmen coss, he long run or seady-sae adjusmen is achieved in a single period. Mankiw and Mulligan are also ineresed in he shor-run impac on ax revenues. This can be inerpreed as he impac of he unexpeced announcemen in period (afer he period capial sock has been chosen) of a cu in he corporae profi ax rae in period and s T aferwards, on period corporae ax receips. This shor run effec on revenue, denoed is of course given θ s T s s s by = k f '( k ) since he capial sock is, by assumpion, held consan a k = k. The dynamic-saic θ ds s Furman raio can now be defined as ρ ( w/ θ)/( T / θ). By equaions (3) and (4), he dynamicdynamic and dynamic-saic Furman raios are herefore given by: ρ dd α = (5) α σθ ρ α f( k ) k f '( k ) s = / ( θ) if k k s s = = θ α k f '( k ) ds (6) ds Noe ha he simple version of he dynamic-saic Furman raio, ρ = / ( θ) requires ha he capiallabor raios in he dynamic and saic calculaions are he same. This will only be exacly correc for infiniesimal changes in he ax rae, no he change from 35 percen o 2 percen ha was acually enaced. 0 Labor s share of oupu declined from abou wo-hirds a he sar of he 960s o 56 percen in 20Q4. I had increased o 58.4 percen by 206Q4. See Esimaing he U.S. Labor Share, Bureau of Labor Saisics, Feb. 207, online aricle, (hps:// : accessed 5 Apr. 208). There is no agreemen on he size of he elasiciy of subsiuion. Young (203), Lawrence (205), Herrendorf e al. (207) and Chirinko and Mallinck (forhcoming) find i o be below one; Karabarbounis and Neiman (204) esimae i o be abou.25; Pikey (204) also esimaes i o be greaer han one. 7

11 The heoreical values of he raios given in Table are herefore.54 when equaion (6) is evaluaed a θ = 0.35 and.25 when equaion (6) is evaluaed a θ = Boh numbers are well below 2.22, he lowes number in Table he Conservaive Case for Full-ime households. For he special case of he Cobb-Douglas producion funcion where capial s share of oupu is equal o 40 percen, he dynamic-dynamic Furman raio is equal o abou 2.40 when he corporae ax is equal o 35 percen and o abou.5 when he corporae ax is equal o abou 20 percen. A decrease in he corporae ax rae from 35 o 20 percen is associaed wih a raio of he increase in wage income o he decrease in corporae ax revenue of beween abou.5 and Independen of facor shares and he elasiciy of subsiuion, he dynamicsaic Furman raio is equal o abou.54 when he corporae ax is equal o 35 percen and o.25 when he corporae ax rae is 20 percen. Thus, an unanicipaed decrease in he corporae ax rae from 35 o 20 percen is associaed wih a raio of an increase in (long-run) wage income o he decrease in shor-run ax revenue beween abou.25 and.54. Clearly hese numbers are lower han all bu he mos conservaive in Table and far lower han he ones of he opimisic scenario. The dynamic-dynamic numbers are sensiive o he value of he elasiciy of subsiuion, paricularly for high ax raes. Even if he elasiciy of subsiuion were as high as.25 and capial s share of oupu were abou 40 percen, he dynamic-dynamic Furman raio ranges from 2.4 o 3.69, sill much lower han he even he lowes figure suppored by he Opimisic Case Expensing of Capial Expendiure In wha follows we only consider he dynamic dynamic (capial-labor raio endogenous) case. We now add he expensing of capial o he model. We assume ha he shares of ne invesmen and depreciaion ha can be expensed are consan and equal o s. Then by equaion (2) corporae ax revenue is ( ) T= θ[ Kf'( K/ L) sk K sδk], (7) + We now consider an unexpeced permanen cu in he corporae profi ax rae in period By equaion (8), he cos of capial is R ( r + δ)( θs) = θ (8) Differeniaing yields: dr d s r s r 2 / θ = ( )( + δ) / ( θ) > 0 if < and + δ > 0 = 0 if s = (9) The impac of a corporae ax change on he cos of capial, and hence on he real wage and capial-labor raio, is smaller when capial expendiure can be deduced from he corporae profi ax base han when i canno. If 8

12 capial expendiure can be fully expensed ( ), hen a change in he corporae ax has no effec on he cos of capial. In his case, he effec on long-run ax revenue is. Comparing his wih equaion (4) i is seen ha if capial expendiure can be fully expensed and here is a Cobb-Douglas producion funcion corporae ax revenue is more sensiive o he corporae ax rae when capial expendiure is fully expensed han here is no expensing. Noe ha if here is more han 00% expensing of capial expendiure ( s > ) a lower corporae profi ax rae will resul in capial shallowing. This is currenly he case for cerain kinds of capial expendiure in Ialy. A higher capial expendiure expensing share lowers he cos of capial and increases he capial-labor raio if boh he cos of capial and he corporae profi ax rae are posiive: dr / ds = ( r + δθ ) / ( θ) (20) The impac effec of an unanicipaed increase in he invesmen expensing share on ax revenues is obviously negaive if he corporae profi ax rae is posiive. 2 In he long run, he negaive effec on corporae ax receips of he higher deducion is a leas parly offse by capial deepening (and may be urned ino a posiive effec if we are on he wrong side of he Laffer curve). For insance, if here is a Cobb-Douglas producion funcion, hen differeniaing equaion (2) wih respec o he expensing share and using equaions (0) and (9) yields: (2) Expensing of Ineres We now consider he case of ineres deducibiliy when here is also expensing of capial expendiure he empirically relevan case for he USA, boh before and afer he ax reforms. Ineres deducibiliy is of ineres for capial expendiure only if borrowing and capial expendiure are linked. We achieve his by he ad-hoc requiremen ha λ, he raio of he sock of corporae deb o he sock of capial is a posiive consan. Assuming he firs-order condiion for he opimal capial sock now is: rb ( r + δ )( θs) λθs ( r ) R =. θ (22) If s =, hen equaion (22) becomes rb λθs ( r ) R= r + δ. θ (23) If here were no borrowing ( λ = 0 ), a cu in he corporae profi ax rae would have no effec on he capiallabor raio. If capial expendiure has o be financed a leas in par by borrowing, hen he cos of capial is See hp://axsummaries.pwc.com/id/ialy-corporae-deducions. T / s = θk ( α θσ s ) / ( α). 2 s + 9

13 sricly decreasing in he corporae ax. A higher corporae ax rae increases he benefi o he firm of he ineres deducibiliy and hus reduces he cos of capial. Thus, a cu in he corporae ax rae increases he cos of capial and decreases boh he capial labor raio and he real wage. Even if here is only parial expensing of capial expendiure, a cu in he corporae ax rae can have a negaive effec on he capial-labor raio and he real wage if he allowed expensing shares are sufficienly large. 3. Corporae Tax Cus in a Closed Economy wih an Endogenous Ineres Rae The model is a discree-ime version of he Yaari-Blanchard OLG model or perpeual youh model. 3 In period zero here is a uni inerval of consumers. Each period a consan fracion q (0,] of he consumers die and a fracion - q are born. Thus, he populaion size remains consan a one. 4 When q =, he model becomes a represenaive agen model and is hus he model of Secion 2. Consumers consume he single capial-consumpion good and supply labor inelasically. Thus, he labor supply is equal o he populaion. A consumer born a ime s and alive a ime s, has expeced uiliy a ime represened by: ( q/ π ) ln c s, + u, (24) u= 0 where is he consumpion in period of a household born in period born in period s, s 0 if i is sill alive in ha period and is consan subjecive rae of ime preference. I is assumed ha here is a compeiive annuiies marke. In period all consumers born before or in period - receive a (gross) reurn on heir savings if hey are alive in period and heir savings accrue o he life insurance company if hey die. Thus, life insurance companies make zero profis and he consumer s wihinperiod budge consrain is: (25) where is his financial wealh a he beginning of period + u and is a lump-sum ime-+u ax on consumers. Iniial financial wealh is given and assumed o be zero: a, = 0. Consumers maximize (24) subjec o (25) and he no-ponzi finance erminal condiion: 3 See Yaari (965), Blanchard (985), Weil (985), Frenkel and Razin (987) and Buier (990)). 4 An earlier version of he paper allowed for populaion growh. This is sraighforward bu added o he noaion and had lile impac on our resuls. 0

14 (26) Necessary and sufficien condiions for an opimum are equaions (25), (26) wih equaliy and (27) Solving equaion (25) forward and subsiuing in (26) (wih equaliy) and (27) (solved backwards) yields (28) A ime here are ( qq ) s consumers alive ha were born a ime s. Thus, aggregae consumpion and savings are given by: c =, a =. ( q) q c if q< ( q) q a if q< + u + u + u s + u s s, + u s, + u s= 0 s= 0 c0, + u if q= a0, + u if q= (29) By equaions (25) and (29), (30) 5 By equaions (28) and (29), c ( π q)( a + h) =, (3) π h q ( w τ ) u H H + u + u = w τ + u= u r s= + s (32) From he definiion in equaion (32), h = ( r / q)( h w + τ ). (33) H Noe ha a = QE + B

15 We assume a balanced-budge rule so ha he governmen s budge consrain is (34) where g is exogenous (consan) governmen spending a ime. Goods marke clearing is given by (35) In wha follows we assume ha labor coss are fully deducible and we consider wo cases of he profi ax. The firs case has no deducibiliy/expensing of capial expendiure and depreciaion. The corporae profi ax funcion is herefore given by: (36) The second case has full expensing of gross capial formaion. The corporae profi ax funcion for his case is given by: (37) Equaions, (30), (3) and (33) permi us o derive he following firs-order difference equaion for aggregae consumpion: π q π q H c+ = r+ q c + ( q ) r+ ( a + w τ ). π πq (.38) When q = (he represenaive agen special case), his simplifies o: c r c π = + (.39) + In his case we have he familiar resul ha in he seady sae he real ineres rae equals he rae of ime preference: r = π. Wihou expensing of capial formaion, he saionary equilibrium is given by: (40) r + δ f '( k) = R θ (4) 2

16 (42) π q c= ( a+ h) π r H a = ( w c τ ) r r H h= ( w τ ) r q (43) (44) (45) (46) (47) From equaions (40) o (47), we obain he following wo equaions which deermine he seady-sae value of he capial-labor raio and he ineres rae for q < : ( θ ) ( ) π q r q ( q) kf ' k f( k) δk g = f( k) g δk + π q q r q r (48) r = ( θ) f '( k) δ + (49) Noe ha, if g =0, here always is an exincion equilibrium in his model, ha is an equilibrium in which k = 0. 6 When q = equaions (48) and (49) are replaced by and ( θ) f '( k) + δ = π (50) r = π (5) Subsiuing equaion (49) ino equaion (48) and oally differeniaing, he effec of a change in he corporae profi ax rae on he seady-sae capial-labor raio is for q < given by: dk dθ α α = (52) 2 6 P H The full exincion equilibrium is characerized by: k = a = h= w= τ = τ = 0; r = +. 3

17 α 2 f '( k) = ( π q) f( k) g δk α = f '( k) ( ) 2 ( ) 2 π q + q r q r q θ q r kf k r q k ( ) ( ) ( )( ) 2 ( )( )( ) '( ) ( ) 2 2 q q r r q q r r δ ( f( k) g) δ k 2 2 ( q r ) q ( r ) ( θ ) f "( k) π q ( q )( θ ) kf '( k) ( q r ) π q ( q r ) q ( r ) + + ( ) ( ) ( ) ( ) f '( k) δ ( q )( θ ) f '( k) + kf ''( k) r q r q r q r q r (53) (54) (55) When q =, dk f '( k) = < 0 dθ ( θ) f "( k) (56) Furher assumpions The assumpions ha follow are saisfied in he numerical examples we provide below. The condiion for dynamic efficiency is f '( k) > δ. We assume i holds. r > is he condiion ruling ou viable Ponzi finance. We assume i holds. Noe ha, since q, r > implies 2 f '( k) δ q r > 0. The erm becomes ( f '( k) δ ) > 0 q r q ( r ) r q r > 0 and when q = and he f '( k) δ condiions for dynamic efficiency and no viable Ponzi finance hold. We assume > 0 in q r q ( r ) ( f( k) g) δ wha follows. The erm k 2 2 ( q r ) q ( r ) becomes 2 2 ( ( ) ) 0 r f k g k δ = r c ( f( k) g) δ k < ( q r ) q ( r ) when q =. We assume in wha follows. The erm f '( k) + kf ''( k) is in general ambiguous in 4

18 α sign. In he Cobb-Douglas case, wih f ( k) = Ak, A > 0; 0 < α <, we have We assume f '( k) + kf ''( k) > 0 in wha follows. 7 f k + kf k = k α >. '( ) ''( ) 0 Given hese assumpions, he sum of he firs hree erms of α is posiive. These can be viewed as reflecing he incenive effecs of a change in he corporae profi ax rae on he capial sock, working hrough he aferax rae of reurn on capial. The las erm of α is negaive. This las erm represens he aggregae demand effec of a higher corporae ax rae, funded hrough a cu in lump-sum axes on households. We discuss his below. Wih no expensing of capial expendiure, all numerical examples we considered have α > 0. This is obviously he case when q = and he las erm of α vanishes. Even a high depreciaion rae like δ = 0.20 or public spending equal o half of GDP ( g = 0.5 f( k) ) does no reverse he sign of α. Wha abou he sign of α 2? Decompose α 2 as follows: α 2 = Sk ( ) Dk ( ), where Sk ( ) f'( k) δ and ( f( k) g) δ k 2 2 ( q r ) q ( r ) ( θ ) f "( k) π q ( q )( θ ) kf '( k) 2 Dk ( ) 2 2 ( q r ). π q ( q r ) q ( r ) f '( k) δ ( q )( θ ) ( f '( k) + kf ''( k) ) + r + q r q ( r ) ( q r ) q ( r ) Given dynamic efficiency, Sk ( ) > 0. Given he furher assumpions we made, Dk ( ) > 0. The erm Sk ( ) measures he effec of a small increase in he capial-labor raio on he seady-sae per capia supply of consumer goods. The erm Dk ( ) measures he effec of a small increase in he capial-labor raio on he seady-sae per capia demand for consumer goods. We consider i inuiively plausible ha Dk ( ) > Sk ( ), in par because he supply effec of a higher capial sock is subjec o diminishing reurns. If we make his assumpion, α 2 < 0 dk and 0 dθ < : a higher corporae profi ax rae reduces he seady-sae capial-labor raio. Alhough we canno claim ha here exis no reasonable funcional forms and parameer values for he producion funcion and uiliy funcion ha would suppor he opposie resul, all our numerical soluions for he model have suppored dk < 0 when here is no expensing of capial expendiure. dθ Consider, for insance, a numerical example wih he following parameer values and producion funcion α specificaion: y = Ak ; A =.00; α = 0.33; q =.02; δ = 0.05; π =.04; g = 0. We compue seady sae equilibria for he following hree values of he corporae profi ax rae: θ = 0; θ 2 = 0.2; θ 3 = This yields he following resuls for he capial-labor raio and he real ineres rae: 7 From he definiion of he elasiciy of subsiuion i follows ha f '( k σ ) + "( ) 0 α kf k = 5.

19 θ = 0; k 6.39; r θ = 0.2; k 4.58; r θ = 0.35; k 3.47; r As expeced, a lower corporae profi ax rae (absen full expensing of invesmen) resuls in a higher seadysae capial-labor raio. A lower profi ax rae also raises he real ineres rae ineres rae: he lower corporae ax rae is no fully offse by he lower marginal produc of capial associaed wih a higher capial inensiy of producion.. Raising he depreciaion rae o 0% ( δ = 0.0 ) and keeping he oher parameer values unchanged yields he following resuls for he capial-labor raio and he real ineres rae: θ = 0; k 3.46; r θ = 0.2; k 2.46; r θ = 0.35; k.85; r Raising he share of labor in GDP o 75% ( α = 0.25) and keeping he oher parameer values he same as in he firs numerical example yields he following resuls for he capial-labor raio and he real ineres rae: θ = 0; k 3.57; r θ = 0.2; k 2.75; r θ = 0.35; k 2.45; r Because in our numerical examples he real ineres rises when he corporae profi ax rae is cu, he impac of a lower ax rae on he capial-labor raio, while sill posiive, is less han ha obained in he consan ineres rae model of Secion 2. The represenaive agen special case Equaion (50) characerizes he seady-sae capial-labor raio in he represenaive agen special case ( q = ) and equaion (56) gives he negaive effec of a change in he corporae profi ax rae on he seady-sae capial labor raio for his case. Seady-sae consumpion when q = is hen derived from wih ( ( ) δ ) c= f( k) g δ k (57) dc f ' k f '( k) = < 0 iff f '( k) δ > 0 dθ ( θ) f "( k) (58) Even hough all profi axes are refunded o he represenaive household as lump-sum ransfer paymens, a higher profi ax rae lowers he seady-sae capial-labor raio and hus, if he economy is dynamically efficien, reduces seady-sae per capia consumpion, hrough he familiar supply side incenive effecs. All resuls from Secion 2 of his paper abou he model wih he exogenous real ineres rae go hrough for his represenaive agen model. Wih full expensing of capial expendiure, a cu in he corporae profi ax rae will have no long-run effec on he capial-labor raio and he real wage. Wih full expensing of capial expendiure and 6

20 some degree of expensing of ineres paymens, a cu in he corporae profi ax rae will lower he long-run capial-labor raio and real wage, if capial expendiure is financed a leas in par by borrowing. Full expensing of capial expendiure Wih full expensing of capial expendiure all seady sae equilibrium condiions excep for equaion (4) remain he same. Equaion (4) is replaced by: The seady-sae capial-labor raio and ineres rae are deermined by: r = f '( k) + δ (59) ( θ ) ( ) ( ) π q f( k) g δk q ( q) kf ' k f( k) δ k g = r qπ q r + q ( r ) q r q r (60) r = f '( k) δ + (6) Noe ha he corporae profi ax rae only eners equaions (60) and (6) hrough he aggregae demand effec of he redisribuion beween owners of capial and all households/workers currenly alive. I is easily checked ha: where dk dθ α α = (62) 2 π q ( q) kf '( k) α = r (63) π q ( q r )( r ) α = α (64) 2 2 Making he same assumpions as before, α < 0. This means ha, if α 2 < 0, as our earlier assumpions imply, he impac on he capial-labor raio of a higher corporae ax rae wih full expensing of invesmen is posiive. This reflecs he absence of any incenive effecs and he presence of a paricular kind of demand effec, as discussed below. Our numerical examples suppor his proposiion. Using some of he same parameer values ha we used before, le A=.0; α = 0.33; q =.02; δ = 0.05; π =.04; g = 0. We obain he following resuls for he hree ax raes: θ = 0; k 6.39; r θ = 0.2; k 6.63; r θ = 0.35; k 6.8; r

21 When we raise he depreciaion rae o 0 percen ( δ = 0.0 ) keeping all oher parameer values consan we ge: θ = 0; k 3.46; r θ = 0.2; k 3.56; r θ = 0.35; k 3.63; r Lowering capial s share o 25% ( α = 0.25), wih all oher parameer values he same as in our firs numerical exercise yields: θ = 0; k 3.57; r θ = 0.2; k 3.68; r θ = 0.35; k 3.75; r In he consan ineres rae model of Secion 2, here was no impac of a cu in he corporae profi ax rae on he capial inensiy of producion if here is also full expensing of capial expendiure. When he ineres rae is endogenous, a cu in he corporae profi ax rae lowers he capial-labor raio and raises he ineres rae. The reason for his is ha, alhough, wih full expensing of capial expendiure he corporae profi ax rae does no affec he incenive o inves, he ax cu will impac household demand when g is exogenous and he corporae profi ax receips are used o lower (lump sum) axes on labor income; i would impac governmen demand if he governmen were o spend he proceeds of he corporae profi ax on purchases of real goods and services. The demand effec of a corporae ax cu Because of he OLG naure of he model (when q < ) a cu in corporae axes wih higher lump-sum axes on workers ensuring coninued budge balance (exogenous g ) will boos household consumpion a a given ineres rae and real wage. Consider a permanen corporae ax cu and assume, counerfacually, ha neiher he real ineres rae nor he capial-labor raio change. The corporae profi ax cu raises he value of hese r P households per capia financial asses by he capialized value of his ax cu: τ > 0 (see equaion (44) r ). All fuure corporae ax cus are (in PDV erms) owned by hose alive oday. The impac on household per π q r P capia consumpion demand is τ > 0. π r By our balanced budge assumpion, per capia (lump-sum) axes on hose households alive a he ime of he corporae profi ax cu and subsequenly increase each period by he same amoun ha he corporae profi ax H P falls: τ = τ > 0. These lump-sum axes are born equally by all hose alive a he ime he axes are paid. Tha means ha he share of hese fuure axes ha will be paid by fuure generaions ha are no ye born (if q < ), does no reduce he human capial of hose currenly alive. These are he only households ha spend he unborn don consume or pay axes. The PDV of he increase in fuure lump-sum axes ha will 8

22 r fall on hose currenly alive is H 0 r q τ < (see equaion (45)).. The impac on per capia consumpion π q r H q r P is π τ = τ < 0 if r > q. π r q π r q The ne impac on household consumpion demand of a permanen profi ax cu and a maching increase in lump-sum axes on households, a a given real ineres rae and real wage is herefore: π q rq ( ) P c = τ π ( r )( rq ) (65) p This is posiive (for negaive τ ) if viable Ponzi finance is ruled ou ( r >, which implies r > q ). Thus, when q < a balanced budge corporae ax cu will, ceeris paribus, boos household consumpion demand. π q The marginal propensiy o consume ou of comprehensive wealh,, is independen of he real ineres π rae. If Dk ( ) > Sk ( ) he seady-sae capial-labor raio will have o fall and he real ineres will have o rise o resore equilibrium following a corporae profi ax rae cu. The conclusion ha ce. par. a cu in he corporae profi ax rae booss demand when ax receips are refunded o workers as lump-sum ransfers/ax cus is dependen on he assumpions ha all surviving households, π q regardless of age, have he same marginal propensiy o consume,, ou of heir comprehensive wealh π q (because hey all have he same life expecancy, q capial markes. ),and ha hey have access on he same erms o perfec I clearly makes empirical sense o assume ha he beneficiaries of he cu in he profi ax (in a more realisic model ha would be he old and he rich) have a lower marginal propensiy o consume ou of curren disposable income ha hose who pay he lump-sum ax on labor income. In he model under consideraion, his feaure could be inroduced by assuming ha some fracion φ,0< φ < of all surviving households and H fuure households ye o be born always spends is enire disposable income, w τ while he remaining fracion φ follows he comprehensive wealh or permanen-income-driven consumpion behavior characerisic of all consumers in our formal model. The Keynesian, curren-disposable-income-consrained households never accumulae any financial wealh and herefore don benefi from he corporae profi ax cu. They do, however, pay he lump-sum ax on labor income. The resuling seady-sae consumpion equaion becomes now: π q r P P c= ( φ) a+ ( w+ τ ) + φ( w+ τ ) π r q (66) 9

23 A sufficienly high value of φ will ensure ha a corporae ax cu will depress aggregae consumpion, ce. par., ha is, for a given real ineres rae, wage rae and capial-labor raio. Noe ha if changes in corporae profi ax receips are refleced one-for-one in changes in public spending on real goods and services, here sill are, in general, demand effecs from a cu in he corporae profi ax rae, even wih full expensing of capial expendiure. For simpliciy assume here are no lump-sum axes paid by H households a all, so τ = 0 and g = θkf '( k). Wih he corporae profi ax rae exogenous, real public spending now is endogenous. Equaion (60) becomes: π q ( q ) kf '( k) f ( k) δk θkf '( k) f ( k) δk θkf '( k) = r + + π q q ( r )( q r ) q r q ( r ) (67) The neuraliy proposiion, ha wih full expensing of capial expendiure, a cu in he corporae profi ax rae does no affec he capial-inensiy of producion, requires ha here be no demand effec from he corporae ax rae cu. When q < here always is a posiive demand effec if he corporae ax cu is funded by an increase in lump-sum axes on households. When he corporae profi ax cu is funded by a cu in public secor π q r purchases, equaion (67) ells us ha his will be neural if = : he household s marginal π ( r ) propensiy o consume ou of a permanen cu in profi axes equals one. This condiion is auomaically saisfied when q =. π q A sufficienly high value of will resul in oal (privae plus public) demand for consumpion goods π being higher, ce. par, a a lower corporae ax rae. In his case, he permanen cu in he profi ax rae booss household consumpion by more han he full amoun of he cu in profi ax paymens by firms, a he predeermined capial-labor raio. Public spending, however falls by he same amoun as he cu in profi ax receips of he governmen; a he inheried capial-labor raio, he change in public spending is given by: dg = kf '( k) dθ. Thus aggregae demand is boosed and, given our earlier assumpions, a lower capial-labor raio resuls - again for reasons ha have nohing o do wih he marginal incenive effecs on capial expendiure of a cu in he corporae profi ax rae. (4) Conclusion The familiar proposiion ha a cu in he corporae profi ax rae booss he capial inensiy of producion and he real wage is sensiive o a number of key assumpions. Even when he real ineres rae is exogenously given, full deducibiliy of capial expendiure from he corporae profi ax base will resul in no impac of a corporae profi ax rae cu on he incenive o inves. Adding deducibiliy of ineres can resul in a negaive effec on he capial inensiy of producion of a corporae profi ax rae cu. When he real ineres rae is endogenous, a simple OLG model demonsraes ha he effecs on consumpion demand of a corporae profi ax cu will reduce he impac on capial inensiy of a corporae profi ax cu if he ax cu is funded by higher lump-sum axes on permanen income households. Alernaive funding rules 20

24 (e.g. lower public consumpion purchases) and he inroducion of Keynesian consumers could lead o a larger posiive effec on capial inensiy from a cu in he corporae profi ax rae. References Auerbach, Alan (983), The Taxaion of Capial Income, Harvard Universiy Press, 983. Auerbach, Alan, Michael Devereux and Helen Simpson, Taxing Corporae Income, in J. Mirrlees e al., eds. Dimensions of Tax Design, Oxford: Oxford Universiy Press, 200). Blanchard, Olivier (985), Blanchard, 0. J. [985] "Deb, Deficis and Finie Horizons." Journal of Poliical Economy, 93, April, pp Buier, Willem H. (988), "Deah, birh, produciviy growh and deb neuraliy," Economic Journal 98, Jun Buier, Willem H. (989), "Deb neuraliy, Professor Vickrey and Henry George's `single ax'," Economics Leers 29, 989, Buier, Willem H. (99), "Deb neuraliy, redisribuion and consumer heerogeneiy: A survey and some exensions," in W.C. Brainard e al, eds., Money, Macroeconomics and Economic Policy; Essays in Honor of James Tobin, MIT Press. Buier, Willem H. (207), Corporae Profi Tax Cus, Capial Deepening and Real Wages: Hasse v. Summers - who is righ?", Cii, Cii Research, Muli-Asse, Global, Global Economics View, 22 November 207, hps:// Chamley, Chrisophe Opimal Taxaion of Capial Income in General Equilibrium wih Infinie Lives. Economerica 54 (3): Chirinko, R.S. and D. Mallinck, The Subsiuion Elasiciy, Facor Shares, and he Low-Frequency Panel Model, American Economic Journal: Macroeconomics, forhcoming. Commiee for a Responsible Federal Budge (207), How much will Trump s Tax Plan Cos? April hp:// Council of Economic Advisers (207a), Corporae Tax Reform and Wages; Theory and Evidence, Ocober, hps:// Council on Economic Advisers (207b), The Growh Effecs of Corporae Tax Reform and Implicaions for Wages, Ocober, hps:// owh%20final.pdf Desai, M. A., Foley, C. F. and Hines, J. R. (2007). Labor and Capial Shares of he Corporae Tax Burden: Inernaional Evidence. Inernaional Tax Policy Forum and Urban-Brookings Tax Policy Cener Conference. Felix, R.A. (2009). Do Sae Corporae Income Taxes Reduce Wages? Federal Reserve Bank of Kansas Ciy Economic Review, Second Quarer. 2

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