Journal of Monetary Economics 60 (2013) 983–995

Contents lists available at ScienceDirect

Journal of Monetary Economics journal homepage: www.elsevier.com/locate/jme

Intangible investment and Ramsey capital taxation Juan C. Conesa a,n,1, Begoña Domínguez b a b

Department of Economics, Stony Brook University, Stony Brook, NY 11794, USA University of Queensland, Australia

a r t i c l e i n f o

abstract

Article history: Received 13 December 2010 Received in revised form 19 September 2013 Accepted 19 September 2013 Available online 27 September 2013

The standard analysis of optimal fiscal policy aggregates different types of assets into a unique capital good and all types of capital taxes into a unique capital tax. This paper considers a disaggregated framework: an economy with corporate and dividend taxes, where firms invest in both tangible and intangible assets (which can be expensed or sweat). In our setup, firms can always respond to changes in the timing of taxation. We find that the optimal long-run policy features zero corporate taxes and positive dividend taxes, with labor and dividend taxes being identical. Moreover, the initial capital levy is relatively small. & 2013 Elsevier B.V. All rights reserved.

Keywords: Optimal policy Capital taxation Intangible assets Time-consistency

1. Introduction The study of optimal capital taxation stemming from the Ramsey tradition, e.g. Chamley (1986) and Judd (1985), aggregates different types of assets into a unique capital good and all types of capital taxes into a unique capital tax. The main lesson from this literature is that the optimal capital income tax is very high in the short run and zero in the long run and, as shown by Kydland and Prescott (1977), time-inconsistent. This is a robust result and, as such, it has been generalized to a great variety of settings.2 This paper reexamines these standard policy prescriptions in a more disaggregated framework that incorporates many of the issues raised in the public finance literature. Our framework is similar to the one proposed in McGrattan and Prescott (2005, 2010). It is characterized by a corporate sector with perfectly competitive firms that can invest in both tangible and intangible assets. Tangible capital includes equipment, structures, land, and inventories, whereas intangible capital is made of brand names, copyrights, patents, customer lists, reputation or organizational capital. The distinctive feature of intangible capital is that it is unmeasured, and therefore expensed. The accumulation of assets requires both resources and managerial effort (sweat equity). We assume that this effort is necessary to transform resources into productive capital. These firms face corporate income taxes and dividend taxes. Such a theoretical environment incorporates into the analysis of optimal fiscal policy in dynamic general equilibrium models some of the theoretical issues already discussed by Auerbach (2002).

n

Corresponding author. Tel.: þ1 631 6327540. E-mail address: [email protected] (J.C. Conesa). 1 We would like to thank the editor, associate editor and an anonymous referee for very insightful suggestions. We would also like to thank participants at numerous seminars and conferences for their comments. Conesa acknowledges support through the prize “ICREA Academia” for excellence in research funded by the Generalitat de Catalunya, Grant 2009SGR350 from Generalitat de Catalunya, and Grant ECO2012–32392 from Spanish Ministerio de Economía y Competitividad. 2 See Atkeson et al. (1999) for different extensions of this result. Recently, Albanesi and Armenter (2012) identify a general optimality principle behind the elimination of intertemporal distortions in the long run. However, the optimality of zero capital income taxes in the long run is not robust to the introduction of life-cycle features in the analysis, see Erosa and Gervais (2002) and Conesa et al. (2009). 0304-3932/$ - see front matter & 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.jmoneco.2013.09.004

984

J.C. Conesa, B. Domínguez / Journal of Monetary Economics 60 (2013) 983–995

McGrattan and Prescott (2005, 2010) used such a framework in order to understand the implications of changes in corporate income and dividend taxation on the valuation of the stock market. More recently, Gourio and Miao (2010) and Anagnostopoulos et al. (2012) study the impact of capital income taxation in environments with heterogeneous firms and with heterogeneous households, respectively. In contrast to that strand of the literature, our paper is normative and aims to characterize the optimal policy in this environment following the Ramsey approach. As commonly found in the literature, the Ramsey policy features no intertemporal distortions in the long run. In our setup, however, this translates to zero corporate taxes and positive dividend taxes at steady state. Moreover, the optimal level of the dividend tax rate equals that of the labor tax rate in the long run. This in turn implies that labor and effort are equally taxed and therefore the allocation of hours worked across different activities is undistorted. This uniform taxation result follows from the elimination of permanent intertemporal distortions in order to maintain production efficiency.3 Our quantitative exercise shows that the optimal steady-state level of dividend and labor tax rates is roughly equal to their actual levels. The transition phase is characterized by an initial moderate increase in corporate and dividend taxes followed by an immediate drop in corporate taxes and a slow decline of dividend taxes towards their long run level. Along the transition, labor taxes display little variation. These results imply that eliminating corporate income taxes is selffinancing, consistent with efficiency gains and the findings of Strulik and Trimborn (2012), who perform dynamic scoring of capital taxes in the spirit of Trabandt and Uhlig (2011), but use a more disaggregated framework like ours. The ex-ante welfare gains of this policy are equivalent to 2 percent permanent higher consumption. Surprisingly, we find that the initial capital levy is small. In the initial period of our benchmark economy, optimal corporate taxes jump from 35 to 45 percent and dividend taxes from 21 to 29 percent. In addition, our results show that there are very small additional gains from reevaluating the optimal plan, and that, even though optimal taxes are not constant in general, 98 percent of the welfare gains can be attained with constant taxes. These results indicate that the time inconsistency of the optimal plan is not that severe. This is in sharp contrast with the standard aggregated framework where the severity of the time inconsistency problem is large. For example, Chari et al. (1994) find that Ramsey capital tax rates are as high as 796% in the initial period and that these initially high capital taxes result in about 80% of the welfare gains from switching to the Ramsey plan. As a result, the incentives to renege on the promised zero capital taxes are paramount. The size of the initial capital levy is affected by the ability of firms to contemporaneously respond to changes in taxation. There is substantial evidence that corporations do react strongly to changes in the fiscal treatment of corporate income, fiscal deductions or dividends. This empirical evidence is consistent with the mechanism behind our results. Gravelle (1982) and Auerbach (1983) estimate the distortions in the composition of investment caused by corporate taxes. Feldstein et al. (1980) find a very high elasticity of capital gains realizations with respect to tax rates. Poterba (2004) estimates the elasticity of corporate payout policy with respect to the differential between dividend taxes and capital gains taxes. In addition, many papers, see Gravelle and Kotlikoff (1989), Gordon and Hines (2002) and Hines (2001) among others, suggest that corporations do respond to tax incentives when deciding the form of organization, where to locate, invest and report profits. Our results on dividend taxation can be interpreted as an extension to a general equilibrium dynamic framework of several well-known results in the public finance literature. It has been long argued, at least since Hall and Jorgenson (1971), that immediate deductibility of investment together with internal financing renders corporate income taxation nondistortionary (and equivalent to dividend taxes). This result has been recently extended to a dynamic general equilibrium framework by Abel (2007). In his survey of the literature Auerbach (2002) also points out that, under the “new view” of corporate financing, constant dividend taxes are non-distortionary and thus optimally set very high.4 This property does not hold in our environment since the presence of managerial effort makes dividend taxes distortionary. Therefore the optimal level of dividend taxation is not expropriatory, in fact it should be set equal to the tax rate of labor income in the long run so that dividend taxes do not distort the allocation of time across activities. Moreover, our results prescribe that constant dividend taxation is not optimal but desirable in order not to distort the timing of sweat and tangible investments and in turn the timing of dividend payments. There is some theoretical work on heterogeneous capital and its effects on taxation. The general result in Diamond and Mirrlees (1971) is that production efficiency should prevail and all types of capital should be taxed equally. However, there are some conditions, such as those pointed out by Auerbach (1979b) and Feldstein (1990), under which it might be optimal to tax different types of capital differently. These conditions include situations in which the tax on labor is not set optimally or the government cannot move the economy to the golden rule level of capital. In our framework, it is optimal to tax both types of capital equally, but the reason is that intangible investment, sweat and expensed, makes capital income responsive to current changes in taxation. 3 See Diamond and Mirrlees (1971) for the main result and Chari and Kehoe (1999) for clarifying that the uniform commodity taxation result follows from the optimality of zero taxation of intermediate goods. 4 The “new view” (Auerbach, 1979a; Bradford, 1981; King, 1977) assumes that the marginal source of funds for new investment is retained earnings, in contrast to the “traditional view” (Harberger, 1962; Feldstein, 1970; Poterba and Summers, 1985) that assumes that the marginal source of investment is share issuance. The “traditional view” finds dividend taxation to be distortionary, while the new view does not. There is a substantial and long debate about the empirical validity of the “new view” relative to the “traditional view”, going back to the seventies and the eighties. More recently, researchers have used the “natural experiment” of the decrease in dividend taxation instituted by the Jobs and Growth Tax Relief Act (JGTRA) in the U.S. in 2003. The research by Auerbach and Hassett (2006) points out to substantial responses of the price of stock values and very little impact in investment decisions, and they interpret that as evidence in favor of the “new view”. On the other hand, Chetty and Saez (2005) document an unusual increase in dividend payments after the tax cut on dividend income, and they argue that this is evidence that dividend taxes are distortionary.

J.C. Conesa, B. Domínguez / Journal of Monetary Economics 60 (2013) 983–995

985

Few papers contemplate intangible investment and its effect on taxation. To our knowledge, one of the first is that of Summers (1987), which criticizes the “level the playing field” doctrine because, among other things, it ignores the inherent non-neutralities of the tax system, such as the one between tangible and intangible investments. In the same spirit Fullerton and Lyon (1988) estimate the efficiency cost of taxation in a model that incorporates intangible capital. More recently, Grubert and Slemrod (1998) and Hanlon et al. (2007) find that firms with more intangible assets have greater opportunities for tax planning, consistent with the mechanism behind our results. The rest of the paper is organized as follows. Section 2 describes the model, Section 3 sets up the Ramsey problem and characterizes analytically the optimal policy at steady state, Section 4 provides a numerical characterization of the optimal policy and explains the role of expensed and sweat intangibles in our results, and Section 5 concludes. 2. The model economy In order to have the minimal departure from Chamley's (1986) framework, we maintain the representative agent structure. Therefore, our households will be at the same time price-taking workers and investors, and owner-managers of firms. 2.1. Technology The corporate sector is composed of a continuum (measure 1) of identical firms operating in a competitive environment. Each one of them produces output with a constant returns to scale production technology yt ¼f(km,t,ku,t,nt). The inputs in the production function are hours worked, nt, physical (or tangible) capital, km,t, and intangible capital, ku,t. These assets depreciate respectively at the rates δm and δu, both positive and smaller than one. Following McGrattan and Prescott (2010), managerial effort (sometimes referred to as sweat equity) is incorporated in the model. They study the changes in hours and productivity in the 1990s and show the importance of intangible investment in expensed and sweat equity. According to their environment, expensed investment in intangible assets increases future profits but is treated as an operating expense, and sweat equity is financed by workers–owners of the firm who spend hours in their business building equity. Our version of McGrattan–Prescott's model incorporates both expensed and sweat investment.5 Therefore, we assume that management time is necessary in order to ensure the transformation of resources into new productive capital. In other words, the production of both tangible and intangible capital requires physical investment (measured in units of the final good), xm,t and xu,t, and managerial effort, em,t and eu,t, that is: I m ðxm;t ; em;t Þ ¼ km;t þ 1  ð1 δm Þkm;t ;

ð1Þ

I u ðxu;t ; eu;t Þ ¼ ku;t þ 1  ð1 δu Þku;t :

ð2Þ

j

The functions I , j¼m,u, are strictly increasing, homogeneous of degree 1, continuously differentiable and concave. A specification without effort is nested if I j(xj,t,.) ¼xj,t is assumed for any ej,t. 2.2. Corporate income and dividend payments Corporate income Πt is defined as the value added net of depreciation of tangible assets, δmkm,t, labor income,wtnt, and investment in intangible assets, xu,t, that is: Π t ¼ f ðkm;t ; ku;t ; nt Þ  xu;t  wt nt  δm km;t :

ð3Þ

τct .

If positive, corporate income is taxed at a rate We believe Eq. (3) captures some important aspects of the corporate tax law in the U. S.6 While there are differences at the state and local level, Federal corporate taxes are paid on corporate gross receipts less the cost of goods sold and tax deductions. Wage payments form part of the cost of producing sold goods, while depreciation of equipment and property may be categorized either as a cost or, if in excess, as a tax deductible item. Investment in intangible assets may be also included in either category. For example, Research and Development expenses are one of the largest tax deductions at the Federal level, and marketing expenses usually count as a cost towards selling goods.7 In fact many investments in intangible capital are done inside the firm and are indistinguishable from other operating expenses (for example, a staff member using her time and equipment to design better production processes, establish a distribution network or train other workers). Indeed, the National Income and Product Accounts (NIPA) consider all intangible investment, except software, 5 This version differs from the original in two features. First, in McGrattan and Prescott (2010), the model captures intangible investment (sweat and expensed) and sets the managers “compensation at lower than market rates” but it does not capture that managers put effort with “the expectation of realizing capital gains”. As a short-cut of this, they assume that wage compensation is contemporaneous but not accounted. Second, they assume that firms rent the capital and distinguish between capital owners and workers (fixing the proportions of intangible investment financed by each group). Our version assumes that firms own the capital and that workers are themselves owners of the firm. 6 Our formulation ignores other important aspects of the U.S. tax law, such as tax credits on certain investments and tax deferrals on foreign profits. Although, not contemplated in this paper, they provide corporations with alternative channels to respond to changes in taxation. 7 For specific details of corporate taxation in the US see www.irs.gov/pub/irs-pdf/i1120.pdf.

986

J.C. Conesa, B. Domínguez / Journal of Monetary Economics 60 (2013) 983–995

as expenditures and not as an investment. Finally, tangible investment is generally not tax deductible in the U.S. corporate tax law, except for when otherwise specified to encourage certain types of investments. Notice how the presence of intangible assets can affect the corporations' decisions. Now corporations can react to changes in current taxes. If current corporate taxes are high, firms can lower current corporate income via investment in intangible assets, generating higher future corporate income. As a consequence, measured value added, f(km,t,ku,t,nt) xu,t, is smaller since activities such as advertisement, building a distribution network, developing new ideas, etc., are expensed. The after-tax corporate income is then used for investment in tangible capital. The difference, if positive, is distributed back as dividends and, if negative, is financed through new equity. Therefore, dividends and new equity issues are given by: dt st  vt ðst þ 1 st Þ ¼ ½ð1  τct Þ½f ðkm;t ; ku;t ; nt Þ  xu;t  wt nt  þ τct δm km;t  xm;t ;

ð4Þ

where vt is the price of a share. For simplicity, it is assumed that dividends are non-negative dt Z0. In the same spirit, equity issues are allowed but share repurchases are not, i.e. st þ 1 Zst. It should be noted however that – except for their different fiscal implications – issuing equity is equivalent to negative dividends and share repurchases would be equivalent to distributing dividends.8 For the sake of tractability, financing through firms' borrowing is assumed to be not possible. The trade-off between debt and equity financing has a long tradition in the public finance literature, see Auerbach (2002). Notice, as well, that firms can react to changes in dividend taxation by investing in tangible assets. 2.3. Government and policies The government collects tax revenues in order to finance an exogenously given stream of government expenditure (unproductive and not valued by households), denoted by fg t g1 t ¼ 0 , and issues one-period bonds bt. Tax revenues are collected through taxes on labor income, τnt , on corporate income, τct , and on dividend payments, τdt . We assume that the ~b government needs to levy distortionary taxes to fund fg t g1 t ¼ 0 . The after-tax interest rate on bonds is r t . To rule out government Ponzi schemes, it is assumed that government debt satisfies bt rB, with B 40 sufficiently large and not binding in equilibrium. The government sequential budget constraint is: τnt wt nt þ τct Π t þ τdt dt st þ bt þ 1 Z g t þ ð1 þ r~ bt Þbt :

ð5Þ

2.4. Preferences and endowments The preferences of the households are represented by a utility function defined as the discounted infinite stream of the instantaneous flow of utility derived from consumption, ct, and leisure, ℓt : 1

∑ βt uðct ; ℓt Þ;

ð6Þ

t¼0

where βA (0,1), and u is strictly increasing, strictly concave and continuously differentiable. Households own the initial stock of corporate shares and government bonds. As workers–owners of the firm, they devote some time to work nt and some time or effort to manage investment projects. For the second activity, they receive no wage but the value of their firm increases. Overall, total time used cannot exceed the time endowment (normalized to 1), em;t þ eu;t þ nt þℓt ¼ 1. 2.5. Characterization of the competitive equilibrium Households in this environment are at the same time workers and owners–managers of the firms in the corporate sector. A key assumption here is that households, as owners/managers behave independently of their interests as workers and vice versa.9 As working-saving units, households choose consumption, ct, labor supplied as a worker, nst , and savings in the form of corporate shares, sdtþ 1 , and bonds, bt þ 1, and collect income from after-tax wages, interest paid on bonds and dividends. As managers of firms, households choose tangible and intangible capital, km,t þ 1 and ku,t þ 1, managerial effort in tangibles and intangibles, em,t and eu,t, physical investment in tangible and intangible assets, xm,t and xu,t, dividend payments dt, number of shares offered, sst þ 1 ; and labor demand ndt . Through their choices they aim to maximize welfare, which in turn also maximizes the initial value of the firm (the discounted sum of future dividend payments net of equity issues). The maximization problem is as follows10: max

1
 ∑ βt u ct ; 1  nst  eu;t em;t

t¼0

s:t:

8

ct þ vt ðsdtþ 1 sdt Þ þ bt þ 1 r ð1  τnt Þwt nst þð1  τdt Þdt sdt þ ð1 þ r~ bt Þbt ;

In equilibrium, however, st ¼ 1 since there is a representative agent-firm, and therefore the only source of investment financing is retained earnings. A superscript s (d) is introduced to denote supply (demand) of the variables for which households and owners-managers decide upon but are on different sides of the market. The superscript disappears once equilibrium is imposed. 10 Households demand shares without taking into account the effect of shares on the firm’s income and dividend distribution. However, managers, as owners of the firm, take into account the effect of shares on the budget constraint. 9

J.C. Conesa, B. Domínguez / Journal of Monetary Economics 60 (2013) 983–995

987

h h   i i dt sst  vt ðsst þ 1  sst Þ ¼ ð1 τct Þ f km;t ; ku;t ; ndt xu;t wt ndt þτct δm km;t  xm;t ;
 I m xm;t ; em;t ¼ km;t þ 1  ð1  δm Þkm;t ;
 I u xu;t ; eu;t ¼ ku;t þ 1 ð1  δu Þku;t ; ct Z 0; dt Z 0; sst þ 1 sst Z 0; sdt Z  S; bt Z  B; with s0 ; b0 ; km;0 ; ku;0 given;

t ¼ 0; 1; 2; :::;

where S and B are arbitrarily large constants to prevent Ponzi schemes. Rearranging the first order conditions and imposing equilibrium, we arrive to the following equations: u2;t ¼ u1;t ð1  τnt Þf 3;t ;

ð7Þ

u2;t u1;t ¼ ð1  τdt Þ m ; Im I 1;t 2;t

ð8Þ

u2;t u1;t ¼ ð1  τdt Þð1  τct Þ u ; I u2;t I 1;t

ð9Þ

ð1 τdt Þ

h iu   u1;t 1;t þ 1 m d c ; m ¼ βð1  τt þ 1 Þ I 1;t þ 1 ð1  τt þ 1 Þðf 1;t þ 1  δm Þ þ δm þð1  δm Þ m I 1;t I 1;t þ 1

ð10Þ

h iu u1;t 1;t þ 1 u d c ; u ¼ βð1  τt þ 1 Þð1  τ t þ 1 Þ I 1;t þ 1 f 2;t þ 1 þ ð1  δu Þ u I 1;t I 1;t þ 1

ð11Þ

ð1 τdt Þð1 τct Þ

as well as the conditions for bonds, pt ¼ pt þ 1 ð1 þ r~ btþ 1 Þ; and equity pt vt ¼ pt þ 1 ½ð1  τdtþ 1 Þdt þ 1 þvt þ 1 ; where pt ¼βtu1,t. These conditions together with feasibility, market clearing and the relevant transversality conditions, fully characterize the competitive equilibrium. Here (7) is the standard labor supply condition of workers. Conditions (8) and (9) establish that managers should be indifferent at the margin between enjoying one more unit of leisure and devoting effort to managing investment projects. These two conditions show that dividend and corporate taxes distort the intra-period allocation of time. Finally, conditions (10) and (11) are the Euler conditions for the accumulation of both types of capital. From these conditions, some mechanisms through which intangible investments might affect the optimal policy can be identified. On the one hand, conditions (10) and (11) show that constant dividend taxes do not distort the firms' capital accumulation decisions. On the other hand, conditions (8) and (9) show that managerial effort makes all capital taxes m distortionary. It is worth noting that (8) and (9) already incorporate the decisions on physical investment, ð1 τdt Þpt ¼ χ m t I 1;t u and ð1  τct Þð1  τdt Þpt ¼ χ ut I u1;t ; with χ m and χ the multipliers on (1) and (2) respectively. Then, increases in dividend taxes t t reduce the marginal cost of investing resources in both tangible and intangible capital, while increases in corporate taxes reduce the marginal cost of investing resources in intangibles. The rest of the paper defines the Ramsey problem, characterizes the Ramsey policy plan and explores quantitatively these effects. 3. The Ramsey problem This paper follows the primal approach in order to characterize the optimal fiscal policy. As standard in the literature (see Chari and Kehoe, 1999) the primal approach implies writing the Ramsey problem as a function of allocations only. Usually then it implies maximizing households' welfare subject to feasibility and an implementability condition (that summarizes the optimizing behavior of consumers and firms). In our case, these two constraints are not sufficient to characterize the set of feasible allocations that can be decentralized with the available tax instruments. To illustrate how decentralization works, look again at conditions (7)–(11). Say we are given a candidate allocation. Then conditions (7) and (8) uniquely determine τnt and τdt and, given this last one, (9) pins down τct . Notice that all tax rates are already determined but conditions (10) and (11) have not been taken into account yet. Therefore additional constraints need to be included in the Ramsey problem so as to guarantee that the tax rates that decentralize conditions (8) and (9) are also consistent with (10) and (11).  1 The government’s optimization problem is defined as follows. Given the stream of government spending g t t ¼ 0 , the 1 government at date 0 chooses the sequences fct ; nt ; em;t ; eu;t ; xm;t ; xu;t ; km;t þ 1 ; ku;t þ 1 gt ¼ 0 to maximize the welfare of the representative household (6) subject to feasibility and admissibility, given bt rB, and initial conditions on tangible and intangible capital, government bonds and after-tax interest rate on those bonds. Mathematically, the Ramsey problem is written as: max

1
 ∑ βt u ct ; 1  nt  em;t  eu;t

t¼0

s:t:

ct þ xm;t þxu;t þg t r f ðkm;t ; ku;t ; nt Þ;
 I u xu;t ; eu;t ¼ ku;t þ 1 ð1  δu Þku;t ; I m ðxm;t ; em;t Þ ¼ km;t þ 1  ð1  δm Þkm;t ; 1 
 ∑ βt u1;t ct  u2;t nt þem;t þ eu;t ¼ u1;0 ð1 þ r~ b0 Þb0 þ

t¼0

988

J.C. Conesa, B. Domínguez / Journal of Monetary Economics 60 (2013) 983–995

! "u m #  u2;0 m I 1;0 I 2;0
u2;0 I f  δ Þ km;0 þ u ðI u1;0 f 2;0 þ ð1  δu ÞÞku;0 ; þδ þð1  δ m m m 1;0 u m Im I 2;0 I 1;0 1;0 I 2;0 2;0 "u # ! m I 1;t þ 1 I 2;t þ 1 u2;t u2;t þ 1 ¼ β Im ðf 1;t þ 1  δm Þ þ δm þð1  δm Þ m ; m 1;t þ 1 u Im I I I 2;t þ 1 2;t 2;t þ 1 1;t þ 1 u2;t u2;t þ 1 ¼ βðI u1;t þ 1 f 2;t þ 1 þ ð1 δu ÞÞ u ; I u2;t I 2;t þ 1 bt r B; for t ¼ 0; 1; 2; :::; with km;0 ; ku;0 ; b0 ; r~ b0 given: The set of feasible allocations is defined by the first three constraints: the resource constraint and the accumulation constraints for tangible (1) and intangible capital (2), respectively. Admissibility is imposed through the three constraints that follow, which respectively are the implementability condition and the two decentralization constraints.11 The right-hand side of the implementability condition corresponds to the households' initial wealth, which equals the sum of the value of initial bond holdings and the initial value of the firm (which is the sum of the last two terms). Since r~ b0 is taken as given, an implicit assumption is that the government at date 0 is committed to honor initial debt payments and therefore cannot directly lower the value of its debt obligations.12 As for the value of the firm, the above problem imposes no exogenous restrictions. For instance, there are no upper bounds on the initial corporate or dividend tax rates. In accordance with the primal approach, we have simply used the equilibrium conditions (8) and (9) to substitute the initial tax rates. Then, as it is written in terms of allocations only, the government can only attempt to reduce the value of the firm indirectly in order to relax the implementability condition. This action usually takes the form of an initial capital levy. In our environment, however, such a capital levy comes at the cost of distorting the allocation of sweat equity (8) and (9) and therefore may not be as large. 3.1. The Ramsey tax plan The solution to the Ramsey problem – the Ramsey allocation – satisfies feasibility and admissibility and the first order conditions presented in the online supplementary appendix.13 The Ramsey tax plan that decentralizes this allocation is obtained from the competitive equilibrium conditions (7)–(9) and, at steady state, is characterized as follows: Proposition 1. The Ramsey tax plan is characterized by zero corporate taxes and positive dividend taxes at steady state. The optimal level of the dividend tax rate equals that of the labor tax rate at steady state. Proof. See the online supplementary appendix, Conesa and Domínguez (2013) □ The Ramsey policy involves no intertemporal distortions in the accumulation of both tangible and intangible assets, as seen in (10) and (11), and an efficient allocation of managerial effort between tangibles and intangibles, as seen in (8) and (9). Moreover, the level of the Ramsey dividend tax rate is identical to that of the Ramsey labor tax rate in the long run. Through Eqs. (7)–(9), this implies that all labor activities (working, effort in intangible investment and effort in tangible investment) would be equally taxed and therefore the allocation of time across activities is not distorted. The proof of Proposition 1 follows the work of Albanesi and Armenter (2007). In a standard Ramsey problem, they derive the Chamley–Judd result by showing that there exists a welfare improving reform that transfers resources from a given period to the next whenever capital is taxed at steady state. For our setup, we can exploit that there are multiple labor activities and show that there exists a welfare improving reform that reallocates the time devoted to labor and managerial effort within a given period, whenever corporate taxes are not zero and/or dividend and labor taxes are not equalized at steady state.14 This illustrates the intimate connection between uniform “commodity” taxation and the optimality of zero taxation on intermediate goods. A corollary that can be drawn from Proposition 1 is that the decentralization constraints are not binding in the limit, which is the only outcome consistent with the optimality of no intertemporal distortions in the long run. Our results are therefore also in accordance with the general optimality principle of frontloading distortions uncovered by Albanesi and Armenter (2012). 4. Quantitative results This Section provides a numerical characterization of the Ramsey allocation and policy plan. First, the functional forms and the choice of parameter values are described. 11 The implementability condition is derived in detail in an online supplementary appendix, Conesa and Domínguez (2013), available online from the journal's website. The decentralization constraints are simply Eqs. (10)–(11) once the tax rates from (8) and (9) have been substituted in. 12 As shown by Armenter (2008), the assumptions about the ability to manipulate or not period 0 variables might affect the long-run Ramsey taxes. 13 As usual, the second order conditions are assumed to be satisfied. 14 This is shown for utility functions that are not logarithmic in consumption. For log utilities, income and substitution effects cancel out, and reallocation of labor and effort is not possible within one period. For this case, there exists welfare improving reforms across two periods.

J.C. Conesa, B. Domínguez / Journal of Monetary Economics 60 (2013) 983–995

989

4.1. Functional forms and parameterization The following functional form for the instantaneous utility function is assumed: uðct ; 1 nt  em;t  eu;t Þ ¼

c1t  s ðnt þem;t þeu;t Þ1 þ ð1=χÞ γ ; 1s 1 þ ð1=χÞ

ð12Þ

with γ 40 measuring the disutility of hours worked and effort, s 40 the coefficient of relative risk aversion and χ40 the labor supply elasticity. The production function is assumed to be Cobb–Douglas: α

α

m f ðkm;t ; ku;t ; nt Þ ¼ Akm;t ku;tu n1t  αm  αu ;

with A 40 and αm,αu A (0,1). Finally, the functional form for investment in tangible and intangible capital is assumed of the CES type: ρ

ρ

I j ðxj;t ; ej;t Þ ¼ C j ½μj xj;tj þ ð1  μj Þej;tj ð1=ρj Þ ; for j ¼ fm; ug; μ

1μ

with C j xj;tj ej;t j ; if ρj ¼ 0; and Cj 4 0 and μj A [0,1]. Our benchmark economy is an equilibrium steady state with a given fiscal policy intended to represent the average features of the tax structure of the U.S. economy. We substantially rely on measurement done in McGrattan and Prescott (2005, 2010). In Table 1 some parameters are exogenously fixed or assumed, while others are determined in equilibrium to match empirical targets. The curvature parameters in the utility function are standard in the literature, representing a coefficient of relative risk aversion of 2 and a Frisch labor supply elasticity of 0.8. The parameters of our production technology and the depreciation rates of both types of assets are taken from measurement done by McGrattan–Prescott. For the technology to build tangible capital, the curvature parameter is assumed to be  2.0. The constant Cm is chosen so that I m t ðxm;t ; em;t Þ ¼ xm;t holds in the equilibrium of our benchmark economy. That is, tangible capital km is measured in the same units as the resources used to build it. In contrast, a Cobb–Douglas specification is assumed for the technology to build intangible capital. Our exercise incorporates an extensive sensitivity analysis with respect to the curvature parameter in the technologies to build tangible and intangible capital. The remaining five parameters are determined in equilibrium in order to target five key empirical observations. The discount factor targets a net after-tax interest rate of 2.6 percent. Given the presence of managerial effort, after-tax returns do not pin down the ratios of tangible capital to GDP and intangible capital to GDP. We use μm and μu to target them consistently with McGrattan–Prescott measurement. They estimate ratios of tangible capital and intangible capital to output, which are respectively 1.65 and 1.083. These ratios are the equivalent of a tangible capital-output ratio of 3 and an intangible capital-output ratio of 0.65 once it is taken into account that the corporate sector is 60% of the US value-added and that 1/3 of all tangible assets are in the corporate sector. The parameters γ and Cu target total hours worked (35 percent of the time endowment) and managerial effort (10 percent of total hours worked). The empirical target of managerial effort also comes from McGrattan–Prescott. The government policy in our benchmark economy is roughly consistent with average behavior over the last two decades (not including the sharp changes experienced since 2008). The tax rates for corporate, dividend and labor income are Table 1 Parameters. Parameter Preferences Discount factor CRRA Disutility of labor Frisch labor supply elasticity Final good technology Constant Share of tangible assets Share of intangible assets Depreciation of tangible assets Depreciation of intangible assets Tangible investment technology Constant Share of resources Curvature Intangible investment technology Constant Share of resources Curvature

β s γ χ A αm αu δm δu

Value

Target

0.975 2.00 11.20 0.80

Rate of return ¼ 2.6% Assumed, IES¼0.5 % time worked ¼35 Assumed

2.00 0.26 0.076 0.067 0.10

Normalization McGrattan–Prescott McGrattan–Prescott McGrattan–Prescott McGrattan–Prescott

Cm μm ρm

1.16 0.99  2.0

Cu μu ρu

7.8 0.09 0.0

Normalization Tang. K/GDP ¼ 1.65 Assumed Manag. Effort/Hours¼ 0.1 Intang. K/GDP ¼ 1.083 Assumed

Note: This table shows the assumed and calibrated parameter values used in the quantitative exercise.

990

J.C. Conesa, B. Domínguez / Journal of Monetary Economics 60 (2013) 983–995 0.5 0.4 0.3

Tax

Dividend Tax

0.2 Labor Tax

0.1 0

Corporate Income Tax

0

10

20

30

40

50

60

-0.1 -0.2

Period Fig. 1. Optimal Ramsey and constant taxes. Note: This figure depicts Ramsey corporate income, dividend and labor tax rates from date 0 onwards in solid blue, red and green respectively. The best constant tax rates are depicted in dashed lines following the same color pattern. The initial steady-state tax rates, those at and before date -1, are represented by a solid circle in the primary vertical axis with the respective same colors as before. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

initially fixed at 35, 21 and 20 percent respectively. The ratios of government consumption and government debt to GDP are set at 0.17 and 0.50 respectively.

4.2. The results for our benchmark exercise Given our benchmark economy, the Ramsey plan is solved numerically using a successive quadratic programming method provided by Schittkowski (1986) in the IMSL Fortran routines. The initial conditions for our Ramsey problem, r~ b0 , km,0, ku,0, and b0, are those found at the steady state of our benchmark economy. Given the second best allocation that solves the Ramsey problem, the corresponding taxes that decentralize it are represented in Fig. 1 (solid lines). Fig. 1 shows that the current dividend tax rate is very close to its optimal long run level, and that it would be optimal to eliminate corporate taxes. In the initial period, optimal corporate taxes increase from 35 to 45 percent and dividend taxes from 21 to 29 percent. This moderate increase in taxation is followed by an immediate drop in corporate taxes – becoming slightly subsidized – and a small decline in dividend taxes, and then both transit slowly towards their long-run levels. Labor taxes remain roughly at the current level. As a result of this policy welfare increases by 2 percent, measured in consumption equivalent units (relative to the steady state of the benchmark economy). The elimination of corporate income taxes appears roughly self-financing, since in the long run no other taxes have to be increased in order to make up for the lost revenues (more so considering that the reform implies lowering the level of debt). This finding can be explained using Proposition 1. The fall in corporate taxes reduces intra-temporal distortions in the allocation of labor activities and in the allocation of resources between tangible and intangible investment, and therefore increases the efficiency in production. Moreover, together with the close to constant dividend taxes, the corporate tax cut eliminates permanent intertemporal distortions and increases the stocks of both tangible and intangible capital in the long run. Both mechanisms make the tax cut self-financing. This feature is consistent with the results in Anagnostopoulos et al. (2012), who find that a cut in the capital gain tax increases the aggregate capital stock, and in Strulik and Trimborn (2012), who argue that the degree of self-financing of capital income tax cuts in a disaggregated model is larger than that obtained by Trabandt and Uhlig (2011).

4.3. The case for constant taxes We next evaluate the desirability of constant taxation in our environment. To do that, the Ramsey policy is compared to the solution to the government’s problem when tax rates are restricted to be constant. Fig. 1 shows the Ramsey policy (solid line) and the best constant tax policy (dashed line). Corporate income taxes are eliminated and become slightly negative (a seven percent subsidy), dividend taxes are increased to 28 percent (relative to the initial value of 21 percent) and labor income taxes are kept roughly unchanged. As a result of this policy the economy experiences welfare gains equivalent to 1.9 percent higher consumption in every period. These welfare gains are 98 percent of the gains attained with the Ramsey policy or, in other words, the initial higher capital taxes result in only 2 percent of those gains. Therefore, as in the public finance literature, constant capital taxation is desirable. But, in contrast to the standard Ramsey results, the initial capital levy is small. In terms of steady-state welfare, it is remarkable that the best constant tax policy achieves welfare gains equivalent to 5.1 percent permanent higher consumption, that is, 96 percent of the steady-state welfare gains of the Ramsey policy (5.4 percent). This indicates that a policy with constant taxes through adjusting the level of taxation is capable of frontloading a large proportion of the tax distortions, without relying on an initial capital levy.

J.C. Conesa, B. Domínguez / Journal of Monetary Economics 60 (2013) 983–995

991

Table 2 Welfare gains from reevaluation and continuation with the Ramsey plan. Period

WR

WC

Diff

1 5 10 25 50 100

0.0228 0.0367 0.0461 0.0539 0.0546 0.0543

0.0226 0.0363 0.0456 0.0533 0.0540 0.0536

0.0001 0.0004 0.0005 0.0006 0.0006 0.0007

Note: The first column presents the period in which both welfare gains are calculated. The second shows the Welfare gains of Reevaluating the Ramsey at the current period, denoted WR. The third shows the Welfare gains of Continuing with the Ramsey plan chosen at date 0, denoted WC. The last column displays the difference between those two, that is Diff¼ WR  WC. The welfare gains are measured in terms of increased consumption relative to the initial steady state.

4.4. One-period deviations from the optimal plan The desirability of constant capital taxation and the smallness of the initial capital levy suggest that the time inconsistency problem of our Ramsey policy is not so severe. Now the optimal plan is reevaluated along the transition to quantify the additional welfare gains of deviations from the optimal plan. In doing so, we still retain the assumption of governments honoring their debt commitments. Table 2 reports the welfare gains of reevaluating the optimal plan at a given period, WR, the welfare gains of continuing with the Ramsey evaluated at date 0, WC, and the difference between those two welfare gains, WR–WC. This difference constitutes a rough measure of the incentives to revise the optimal policy at a given period (assuming a revision would entail no penalty). As reported in Table 2, there are some gains to revise the optimal policy and therefore there is a time inconsistency problem. However, these gains are small. The highest incentives to revise the optimal policy come at the final steady state, and for our calibrated economy they are around 0.07% in terms of (initial steady state) consumption. Alternatively, this small number suggests that a very small penalty, perhaps a reputational cost or reform cost as in Farhi et al. (2012), would suffice to deter a potential deviation by the government. These results are in any case only tentative. A complete characterization would imply endogenizing the costs of a potential deviation and computing the entire game. Of course, there is no guarantee that the optimal policy in such a game would be close to the one we identify. 4.5. Distinctive features of our model Our quantitative exercise shows that corporate taxes should be eliminated, while dividend taxes should be positive, that a policy of constant taxes is nearly optimal and that future temptations to deviate from such a policy are minimal. The distinctive features of our setup are: (i) a disaggregated tax structure incorporating corporate income taxes and dividend taxes, (ii) expensed intangible investment, and (iii) sweat investment in the form of managerial effort. 4.6. Our results in relation to the key features Distinguishing between corporate and dividend taxes allows constant dividend taxes to mimic the missing lump-sum instrument. However, sweat equity renders constant dividend taxes distortionary. Overall our theoretical setting generates a non-trivial trade-off between the timing and the level of dividend taxes. Our quantitative results show that the desirability of constant dividend taxes prevails. The intuition for constant dividend taxes can be explained in two ways. First, our dividend tax is a tax on managerial effort and standard results on optimal taxation prescribe the optimality of constant labor taxes. Second, since firms can choose the timing of distributions, it is optimal not to distort this timing. Notice that a constant dividend tax would just collect as tax revenues a fraction of the initial value of the firm. In a different setup with only tangible capital and no managerial effort, Abel (2007) proposes immediate expensing of all investment and finds that a constant capital income tax is lump-sum. He also points out that this policy is time-consistent. This is clear because, as Fischer (1980) points out, time inconsistency arises because of the need to use distortionary taxation. Notice that, absent managerial effort, Abel's constant capital tax would be equivalent to our constant dividend tax. In contrast, in our setup, constant dividend taxes are desirable even though dividend taxes are distortionary. These distortions, brought in by sweat intangibles, make the Ramsey dividend tax deviate only slightly from constant taxation through a short run increase. The tax rise and the firm’s reaction are shown in Fig. 2. When facing an increase in dividend taxes, firms respond increasing their investment in tangibles and reducing their dividend payments. The existence of expensed and sweat intangible investment allows firms to contemporaneously respond to changes in corporate taxation. However, at the same time, sweat intangibles make all taxation distortionary. Corporate taxation is

J.C. Conesa, B. Domínguez / Journal of Monetary Economics 60 (2013) 983–995

Dividend Income, tax and investment

992

0.4 Dividend Tax

0.35 0.3 0.25

Tangible Investment

0.2 0.15

Dividend Income

0.1 0.05 0 0

1

2

3

4

5

6

7

8

9

10

Period Fig. 2. Dividend tax, before tax dividend income and tangible investment. Note: This figure depicts the Ramsey dividend tax rate, before tax dividend income and tangible investment from date 0 onwards in blue, red and green respectively. The respective variables in the initial steady state, those at and before date -1, are represented by a solid circle in the primary vertical axis following the same color pattern. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

0.5

0.15

0.4 0.1 0.3 Corporate Income

0.2

0.05

Sweat Investment

0.1

ExpensedInvestment

Investment

DividendIncome and tax

CorporateTax

0 0 0

1

2

3

4

5

6

7

8

9

-0.1

10 -0.05

Period Fig. 3. Corporate tax, before tax corporate income and intangible investment. Note: this figure depicts the Ramsey corporate tax rate, before tax corporate income, sweat intangible investment and expensed intangible investment from date 0 onwards in blue, red, orange and green respectively. Corporate tax and income are shown in the primary vertical axis. Sweat and expensed intangible investments are shown in the secondary vertical axis. The respective variables in the initial steady state, those at and before date -1, are represented by a solid circle in their respective vertical axis following the same color pattern. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

0.80 0.70

Ratios

0.60 0.50 0.40 0.30 0.20 0.10 0.00 0

10

20

30

40

50

Period Fig. 4. The ratios of intangible to tangible capital and government debt to output. Note: This figure depicts the ratios of intangible to tangible capital and government debt to output from date 0 onwards in blue and red respectively. The respective ratios in the initial steady state, those at and before date -1, are represented by a solid circle in the primary vertical axis following the same color pattern. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

particularly distortionary as it alters the firms' allocation of investment between tangibles and intangibles. As a consequence, a Ramsey planner initially increases the corporate tax but quickly eliminates it. The effect of this initial increase in taxation on resource allocation is shown in Fig. 3, as firms face a higher corporate tax they invest more in expensed intangibles, which reduces their current corporate income. Fig. 4 plots the ratios of intangible to tangible capital and government debt to output over time. The first illustrates the corporate tax distortion between tangibles and intangibles. An initial increase in corporate taxes leads to a sizable rise in the stock of intangibles relative to tangible. This also explains the relatively low initial corporate taxes (as the increase in

J.C. Conesa, B. Domínguez / Journal of Monetary Economics 60 (2013) 983–995

993

intangible capital comes together with distortions in sweat equity) and the subsequent medium-run subsidies (as after the phase with higher corporate taxes, the intangible to tangible capital ratio is well above the long-run optimal level). The properties of optimal policy in our environment also have differential implications for the level and dynamics of government debt. In the standard framework, the Ramsey allocation is characterized by a sharp reduction in government debt and a massive accumulation of assets by the government. As Fig. 4 shows, this is not the case in our environment since government debt falls moderately in the short run and then slowly converges to a relatively small level in the final steady state. The lack of severity of the time inconsistency problem is illustrated by the small and short-lived initial period of high capital taxation, but it is also reflected in the labor tax at period 0. In the standard Chamley–Judd setup, Ramsey labor taxes are usually negative in period 0 to make individuals consume more in that period, which lowers the real value of the initial wealth and the need for distortionary taxation. In our economy, however, lowering the initial wealth may require individuals to enjoy more leisure (that is, depressing the term u2,0 on the right-hand-side of the implementability condition). This can be achieved with an initial increase in both corporate and dividend taxes that reduces the marginal gain of sweat equity. By non-arbitrage between the different labor activities, then labor taxes cannot fall too much. In fact, as Fig. 1 shows, the optimal labor tax falls only slightly. 4.7. Sensitivity analysis Since the degree of complementarity between resources and effort in building both types of capital has been arbitrarily chosen, this Section presents a sensitivity analysis with respect to these parameters. For each of these exercises our economy is recalibrated, so that the initial steady states are observationally equivalent. First, we examine the importance of the curvature in building tangible capital. In our benchmark, this parameter was fixed at  2.0. The same policy exercise is performed for a set of values for this parameter between 10 and 0.95 (a value of Table 3 Sensitivity analysis with respect to ρm. ρm

 10 5 2 0 0.95

Ramsey Taxes at 0

St. St. Ramsey Taxes

τct

τdt

τnt

τct

τdt

τnt

0.41 0.43 0.45 0.48 0.49

0.34 0.32 0.29 0.26 0.19

0.16 0.16 0.16 0.17 0.18

0.00 0.00 0.00 0.00 0.00

0.18 0.18 0.18 0.19 0.19

0.18 0.18 0.18 0.19 0.19

Welfare Gain R

0.020 0.020 0.020 0.020 0.022

St. St. Welfare Gain R.

0.054 0.054 0.054 0.054 0.065

Best Constant Taxes

τct

τdt

τnt

 0.15  0.11  0.07  0.02 0.01

0.34 0.31 0.28 0.24 0.21

0.20 0.20 0.20 0.20 0.20

Welfare Gain C.

St. St. Welfare Gain C.

C/R

St. St. C/R

0.020 0.020 0.019 0.019 0.022

0.052 0.051 0.051 0.051 0.062

0.98 0.98 0.98 0.98 0.98

0.96 0.96 0.96 0.95 0.95

Note: The first column presents the different values of ρm for which the sensitivity analysis is conducted. The second and third show the Ramsey corporate, dividend and labor tax rates in period 0 and at steady state. The fourth and fifth show the ex-ante and steady-state welfare gains (in consumption equivalents) associated with the Ramsey tax reform. The sixth column presents the best constant corporate, dividend and labor tax rates. The seventh and eighth show the ex-ante and steady-state welfare gains associated with the best constant taxes. The last two columns show the proportion of the ex-ante and steady-state welfare gains of the Ramsey reform that can be achieved with constant taxes, that is the values of the seventh column divided by those in the fourth column and the values of the eighth column divided by those in the fifth column. Highlighted in bold are the results for our benchmark parameterization.

Table 4 Sensitivity analysis with respect to ρu. ρu

 10 5 2 0 0.95

Ramsey Taxes at 0

Ramsey Taxes at ss

τct

τdt

τnt

τct

τdt

τnt

0.93 0.89 0.79 0.45 0.17

0.32 0.32 0.32 0.29 0.27

0.17 0.16 0.15 0.16 0.18

0.00 0.00 0.00 0.00 0.00

0.18 0.18 0.18 0.18 0.19

0.18 0.18 0.18 0.18 0.19

Welfare Gain R

0.020 0.020 0.020 0.020 0.022

St. St. Welfare Gain R.

0.054 0.054 0.054 0.054 0.055

Best Constant Taxes

τct

τdt

τnt

 0.07  0.07  0.07  0.07  0.07

0.28 0.28 0.28 0.28 0.28

0.20 0.20 0.20 0.20 0.20

Welfare Gain C.

St. St. Welfare Gain C.

C/R

St. St. C/R

0.019 0.019 0.019 0.019 0.022

0.051 0.051 0.051 0.051 0.053

0.95 0.96 0.96 0.98 0.99

0.94 0.94 0.95 0.96 0.97

Note: The first column presents the different values of ρu for which the sensitivity analysis is conducted. The second and third show the Ramsey corporate, dividend and labor tax rates in period 0 and at steady state. The fourth and fifth show the ex-ante and steady-state welfare gains (in consumption equivalents) associated with the Ramsey tax reform. The sixth column presents the best constant corporate, dividend and labor tax rates. The seventh and eighth show the ex-ante and steady-state welfare gains associated with the best constant taxes. The last two columns show the proportion of the ex-ante and steady-state welfare gains of the Ramsey reform that can be achieved with constant taxes, that is the values of the seventh column divided by those in the fourth column and the values of the eighth column divided by those in the fifth column. Highlighted in bold are the results for our benchmark parameterization.

994

J.C. Conesa, B. Domínguez / Journal of Monetary Economics 60 (2013) 983–995

1 would imply perfect substitutability between resources and managerial effort). The results of this sensitivity analysis are summarized in Table 3. First, the more substitutable resources and effort are in building tangible capital, the more the initial capital levy relies on taxation of corporate income rather than on dividend taxation. Second, higher complementarity implies that in the long run optimal dividend and labor taxes are slightly lower in the Ramsey policy, and it becomes optimal to subsidize corporate income in the best constant tax policy. Finally, the welfare gains are not substantially changed, and a strategy of constant taxes achieves 98 percent of the potential ex-ante welfare gains and between 95 and 96 percent of the steady-state welfare gains irrespectively of the chosen parameter value. Now we turn to the sensitivity analysis with respect to the degree of complementarity between resources and effort in building intangible capital. The results are reported in Table 4. The only substantial change is in the nature of the capital levy. The more complementary resources and effort are, the higher the capital levy, especially in the form of an initial jump in corporate taxes. For higher complementarity, effort on its own is less responsive to changes in taxation and then tolerates higher initial taxes. In the long run, optimal dividend and labor taxes are again slightly lower. However, constant optimal policies are unaffected by changes in this parameter value. Again, welfare gains from the Ramsey policy are roughly unchanged and a substantial fraction of the ex-ante (between 95 and 99 percent) and the steady-state gains (between 94 and 97 percent) are already achieved with constant taxes. In particular, the more substitutable resources and effort become, the lower the incentive for an initial capital levy and constant taxes achieve virtually all of the welfare improvement. Overall, the degree of complementarity between resources and effort affects slightly the optimal long-run level of dividend taxes. The higher the complementarity the lower the ability of firms to respond to changes in taxation making the initial capital levy a little bit larger. This contributes to a modest decrease in dividend and labor taxation in the long run. The degree of complementarity between resources and effort in building tangible capital determines whether the initial capital levy relies on dividend taxation or on corporate taxation, while the degree of complementarity in building intangible capital affects the size of the initial capital levy. However, it is a robust finding that most of the ex-ante and steady-state welfare gains from changing to the optimal policy can be achieved with constant taxes.

5. Conclusions To study optimal fiscal policy, this paper considers a disaggregated model with different types of assets, multiple labor activities and a variety of labor and capital taxes. In the long run, we find that the optimal policy features no distortions on investment and no distortions on the allocation of time into different labor activities. The first is achieved through zero corporate taxes but constant and positive dividend taxes. The second is attained through the equality of the different labor wedges. In the short run, the optimal policy features a small capital levy. In our environment, firms can react contemporaneously through resources and managerial effort to any change in taxation, which makes an immediate hike in taxes less desirable. The contribution of this paper is normative. In contrast, the history of capital taxation reforms since the seventies (from the tax cuts of the Reagan era until the JGTRA of 2003) presents a different picture. According to the calculations of McGrattan and Prescott (2004), effective dividend taxes have decreased from around 40% to around 18%, with most of the decrease happening in the early eighties under the Reagan administration. At the same time, statutory corporate income taxes have fallen from around 45%, but still remain substantial at 35%. One question left open is what features of the structure of capital taxation might explain the high corporate income taxes observed in the data. Our results suggest that time inconsistency alone might not be such a plausible explanation as suggested by previous literature. Otherwise, perhaps there are substantial welfare gains of reforming the structure of capital income taxation. The policy prescription is simple: eliminate corporate income taxes, and treat dividend income and labor income equally in individuals' income taxation. References Abel, A.B., 2007. Optimal capital income taxation. Unpublished Manuscript. Anagnostopoulos, A., Cárceles-Poveda, E., Lin, D., 2012. Dividend and capital gains taxation under incomplete markets. Journal of Monetary Economics 59, 599–611. Albanesi, S., Armenter, R., 2007. Understanding capital taxation in Ramsey models. Unpublished Manuscript. Albanesi, S., Armenter, R., 2012. Intertemporal distortions in the second best. Review of Economic Studies 79, 1271–1307. Armenter, R., 2008. A note on incomplete factor taxation. Journal of Public Economics 92, 2275–2281. Atkeson, A., Chari, V.V., Kehoe, P.J., 1999. Taxing capital income: a bad idea. Federal Reserve Bank of Minneapolis Quarterly Review 23, 3–17. Auerbach, A.J., 1979a. Wealth maximization and the cost of capital. Quarterly Journal of Economics 93, 433–446. Auerbach, A.J., 1979b. The optimal taxation of heterogeneous capital. Quarterly Journal of Economics 93, 589–612. Auerbach, A.J., 1983. Welfare aspects of current U.S. corporate taxation. American Economic Review Papers and Proceedings 73, 76–81. Auerbach, A.J., 2002. Taxation and corporate financial policy. In: Auerbach, A.J., Feldstein, M. (Eds.), Handbook of Public Economics, vol. 3. Elsevier, Amsterdam, pp. 1251–1292. Auerbach, A.J., Hassett, K.A., 2006. Dividend taxes and firm valuation: new evidence. American Economic Review 96, 119–123. Bradford, D.F., 1981. The incidence and allocation effects of a tax on corporate distributions. Journal of Public Economics 15, 1–22. Chamley, C., 1986. Optimal taxation of capital income in general equilibrium with infinite lives. Econometrica 54, 607–622. Chari, V.V., Christiano, L.J., Kehoe, P.J., 1994. Optimal fiscal policy in a business cycle model. Journal of Political Economy 102, 617–652.

J.C. Conesa, B. Domínguez / Journal of Monetary Economics 60 (2013) 983–995

995

Chari, V.V., Kehoe, P.J., 1999. Optimal fiscal and monetary policy. In: Taylor, J., Woodford, M. (Eds.), Handbook of Macroeconomics, vol. 1. Elsevier, Amsterdam, pp. 1671–1745. Chetty, R., Saez, E., 2005. Dividend taxes and corporate behavior: evidence from the 2003 dividend tax cut. Quarterly Journal of Economics 120, 791–833. Conesa, J.C., Domínguez, B., 2013. Intangible investment and Ramsey capital taxation. Online supplementary appendix. Conesa, J.C., Kitao, S., Krueger, D., 2009. Taxing capital? Not a bad idea after all!. American Economic Review 99, 25–48. Diamond, P.A., Mirrlees, J.A., 1971. Optimal taxation and public production, I: production efficiency. American Economic Review 61, 8–27. Erosa, A., Gervais, M., 2002. Optimal taxation in life-cycle economies. Journal of Economic Theory 105, 338–369. Farhi, E., Sleet, C., Werning, I., Yeltekin, S., 2012. Non-linear capital taxation without commitment. Review of Economic Studies 79, 1469–1493. Feldstein, M., 1970. Corporate taxation and dividend behavior. Review of Economic Studies 37, 57–72. Feldstein, M., Slemrod, J., Yitzhaki, S., 1980. The effects of taxation on the selling of corporate stock and the realization of capital gains. Quarterly Journal of Economics 94, 777–791. Feldstein, M., 1990. The second best theory of differential capital taxation. Oxford Economic Papers 42, 256–267. Fischer, S., 1980. Dynamic inconsistency, cooperation and the benevolent dissembling government. Journal of Economic Dynamics and Control 2, 93–107. Fullerton, D., Lyon, A.B., 1988. Tax neutrality and intangible capital. In: Summers, L.H. (Ed.), Tax Policy and the Economy, vol. 2. MIT Press, Cambridge, pp. 63–88. Gordon, R.H., Hines, J.R., 2002. International taxation. In: Auerbach, A.J., Feldstein, M. (Eds.), Handbook of Public Economics, vol. 4. Elsevier, Amsterdam, pp. 1935–1995. Gourio, F., Miao, J., 2010. Firm heterogeneity and the long-run effects of dividend tax reform. American Economic Journal: Macroeconomics 2, 131–168. Gravelle, J., 1982. Effects of the 1981 depreciation revision on the taxation of income from business capital. National Tax Journal 35, 1–20. Gravelle, J., Kotlikoff, L.J., 1989. The incidence and efficiency costs of corporate taxation when corporate and noncorporate firms produce the same good. Journal of Political Economy 97, 749–780. Grubert, H., Slemrod, J., 1998. The effect of taxes on investment and income shifting to Puerto Rico. Review of Economics and Statistics 80, 365–373. Hall, R.E., Jorgenson, D.W., 1971. Application of the theory of optimal capital accumulation. In: Fromm, G. (Ed.), Tax Incentives and Capital Spending. Studies of Government Finance, The Brookings Institution, Washington, D.C., pp. 9–60. Hanlon, M., Mills, L., Slemrod, J., 2007. An empirical examination of corporate tax noncompliance. In: Auerbach, A.J., Hines, J.R., Slemrod, J. (Eds.), Taxing Corporate Income in the 21st Century, Cambridge University Press, Cambridge, pp. 171–210. Harberger, A.C., 1962. The incidence of the corporation income tax. Journal of Political Economy 70, 215–240. Hines, J.R., 2001. Corporate taxation. In: Smelser, N.J., Baltes, P.B. (Eds.), International Encyclopedia of the Social & Behavioral Sciences, Elsevier, Oxford, pp. 2810–2812. Judd, K.L., 1985. Redistributive taxation in a simple perfect foresight model. Journal of Public Economics 28, 59–83. King, M.A., 1977. Public policy and the corporation. Chapman and Hall, London. Kydland, F.E., Prescott, E.C., 1977. Rules rather than discretion: the inconsistency of optimal plans. Journal of Political Economy 85, 473–492. McGrattan, E.R., Prescott, E.C., 2004. Data appendix: taxes, regulations and the value of U.S. and U.K. corporations. Staff Report 309, Federal Reserve Bank of Minneapolis. McGrattan, E.R., Prescott, E.C., 2005. Taxes, regulations and the value of U.S. and U.K. corporations. Review of Economic Studies 72, 767–796. McGrattan, E.R., Prescott, E.C., 2010. Unmeasured investment and the puzzling U.S. boom in the 1990 s. American Economic Journal: Macroeconomics 2, 88–123. Poterba, J., Summers, L.H., 1985. The economic effects of dividend taxation. In: Altman, E., Subrahmanyam, M. (Eds.), Recent advances in corporation finance, Richard D. Irwin Publishers, Homewood, IL, pp. 227–284. Poterba, J., 2004. Taxation and corporate payout policy. American Economic Review 94, 171–175. Schittkowski, K., 1986. NLPQL: A FORTRAN subroutine solving constrained nonlinear programming problems. Annals of Operations Research 5, 485–500. Summers, L.H., 1987. Should tax reform level the playing field? NBER Working Paper 2132. Strulik, H., Trimborn, T., 2012. Laffer strikes again: dynamic scoring of capital taxes. European Economic Review 56, 1180–1199. Trabandt, M., Uhlig, H., 2011. The Laffer curve revisited. Journal of Monetary Economics 58, 305–327.