Taxation, Investment and Asset Pricing 1

Transcription

1 Taxation, Investment and Asset Pricing 1 Marika Santoro a Chao Wei b a Congressional Budget Office, Macroeconomic Analysis Division, Ford House Office Building, Washington, D.C b Department of Economics, George Washington University, 2115 G Street, N.W. Washington, D.C July 13, 2009 (Under Review, Review of Economic Dynamics) Abstract This paper studies the mechanism through which dividend and corporate profit taxesaffect investment and asset returns in a stochastic general equilibrium model. We find that proportional dividend taxes do not distort investment decisions, and have no impact on asset returns. By contrast, corporate profit taxes distort investment decisions, and introduce additional tax-related risk factors into the economy. We uncover a mechanism through which corporate taxes amplify the responses of consumption and investment to technology shocks, which leads to a lower risk-free interest rate and a higher equity premium. This amplification mechanism is the strongest when there exists a strong preference for consumption smoothing and high costs of adjusting the capital stock. 1 This paper is a substantially revised version of our earlier paper ciculated as "Taxation and Asset Pricing in a Production Economy". We would like to thank Marco Cipriani, Douglas Hamilton, Brett Rayner, Thomas Tallarini, Harald Uhlig, Anthony Yezer and seminar participants at the Midwest Macro Meetings 2009, Econometric Society Summer Meetings 2009, Federal Reserve Board, Society of Computational Economics Annual Meetings 2008, Atlanta Fed, and George Washington University for helpful comments and suggestions. addresses: Marika.Santoro@cbo.gov (Marika Santoro), cdwei@gwu.edu (Chao Wei). The views expressed in this paper are those of the authors and should not be interpreted as those of the Congressional Budget Office. 1

2 1 Introduction In the United States, taxes on shareholders (dividend taxes) are levied independently of the taxes on the profits of corporations they own (corporate taxes). Such double taxation of capital income has always generated interest in the respective impacts of dividend and corporate taxes on economic decisions. In this paper, we study the mechanism through which dividend and corporate taxes affect investment and asset returns in a stochastic general equilibrium model. We find that these two types of capital income taxes have different implications for both the real economy and the financial market, and those differences are theoretically and quantitatively important. There is a key difference with respect to investment between an economy with dividend taxes and one with corporate taxes. Dividends are taxed after investment is made. As a result, investment is exempt from dividend taxes. On the contrary, corporate profits are taxed before investment is made and thus reduce the firm s incentives to invest. These differences in investment decisions have different implications for asset pricing in a production economy. In our framework, taxes are fully capitalized into the value of the firm. In this type of environment, proportional dividend taxation affects the marginal cost and benefit of investment symmetrically, and therefore do not alter the firm s marginal investment decisions. Consequently, proportional dividend taxes have no impact on asset returns. By contrast, corporate taxes have distinctively different implications for investment and asset pricing. We find two mechanisms at work. The first mechanism is an insurance mechanism. Since corporate taxes are levied on procyclical profits, the tax liabilities increase during an expansion and decrease in a recession. Indeed, the procyclical corporate tax burden tends to be negatively correlated with the stochastic discount factor, thus generating a possibly negative tax-burden premium 2. However, we find that this insurance mechanism can be dominated by other forces in our general equilibrium setup. We uncover a new mechanism through which corporate taxes amplify the responses of consumption and investment to technology shocks, which can lead to a lower risk-free interest rate and a higher equity premium. The intuition behind this finding is as follows. Corporate taxes discourage 2 Gordon and Wilson (1989) argue that the welfare cost of corporate profit taxesis overstated if this insurance mechansim is ignored. 2

3 investment. Compared to an economy without taxes, investment constitutes a smaller share of the aggregate output in the steady state of an economy with corporate taxes. A lower investment-output ratio implies that investment has to respond more to a technology shock in order to smooth consumption. A strong preference for consumption smoothing implies that the response of investment has to be even more pronounced. However, any frictions in adjusting the capital stock can limit the ability of investment to smooth consumption, thus leading to more amplified responses of both consumption and investment. The amplification mechanism is the strongest when there exists both a strong preference for consumption smoothing, and high costs of adjusting the capital stock. We parameterize the model and use it as a laboratory to compare the quantitative investment and asset pricing implications of dividend and corporate taxes with those in an economy without taxes. The numerical analysis confirms that dividend taxes have no impact on investment and asset returns, despite their adverse impact on the firm value compared to a tax-free economy. For corporate taxes, we examine the importance of the insurance and amplification mechanisms for asset pricing. In one experiment we combine high habit formation and high capital adjustment costs to capture both a strong preference for consumption smoothing and frictions in adjusting the capital stock. We find that, in this case, almost all the macro variables, including consumption, investment, dividends, and the stochastic discount factor, respond more strongly to exogenous shocks in an economy with corporate taxes. As a result, the risk-free interest rate is lower, and a larger equity premium is required to compensate for the risk brought by corporate taxes. The increase in the equity premium dominates the insurance component attributed to the procyclical tax burden of corporate taxes. Alternative experiments show that the amplification mechanism is present even with lesser degrees of habit formation and lower adjustment costs, although its impact on the asset returns is markedly smaller. This paper relates to three strands of literature. It relates to the literature on production-based asset pricing models, including Jermann (1998) and Boldrin, Christiano, and Fisher (2001). Those papers do not consider any type of capital income taxes. Our paper shows that including such taxes can have a significant impact on both the real economy and asset prices. This paper also relates to the literature on taxation and asset pricing in an endowment economy. Brennan (1970), Lai (1989) and Sialm (2007) analyze the asset pricing implications of different taxes. However, they all assume 3

4 exogenously given dividends or stock prices. In our model, both dividends and stock prices are endogenously determined as a result of the endogenous responses of investment to taxation. That feature is crucial for understanding the asset pricing implications of dividend and corporate taxes. McGrattan and Prescott (2005) provide an important insight into the quantitative implications of the changing capital income tax rates on market valuations in a production economy. Since their focus is on the firm value, the model is deterministic and does not address risk premium issues related to taxes. This paper is also closely related to the literature on dividend taxes and investment. Hasset and Hubbard (2002) survey the research on the impact of dividend taxes on investment. This paper extends the analysis to the financial market. The organization of the paper is as follows. Section 2 describes the model. Section 3 compares the asset pricing implications of the two types of taxes. In Section 4, we parameterize the model and conduct a quantitative analysis of the impulse responses and financial statistics. Section 5 concludes. 2 Model In this section, we introduce dividend and corporate taxes into a dynamic stochastic general equilibrium model. There is a continuum of infinitely-lived identical households and a representative firm owned by the households. The government levies taxes and rebates them in a lump sum to the households. The economy grows at a constant trend g. 2.1 Households The representative household maximizes expected lifetime utility: max a t+1,f t+1,c t E 0 X β t U(C t,x t ), t=0 subject to a sequential budget constraint: C t +a t+1 V t +f t+1 V f t = a t h V t +(1 τ D ) bd t i +f t (V f t +D f t )+W t L t +ψ t. (1) 4

5 Here β is the subjective discount factor, C t is real consumption at time t and X t is a function of lagged consumption {C t j } n j=1. The preference specification allows for habit formation. We constrain the utility function so that the habit formation specification does not alter the steady state of the economy. Inthebudgetconstraint,a t represents shares of the representative firm held from period t 1 to t. V t is the firm s value and τ D is the proportional dividend tax rate. 3 bd t are the firm s dividends per share after corporate taxes. The vector f t represents the vector of other financial assets held at period t and chosen at t 1, including private bonds and possibly other assets. V f t and D f t are vectors of asset prices and current period payouts, respectively. W t represents the real wage and L t isthelaborsupplyattime t. Each household faces a (normalized) time constraint 1. Given that leisure does not enter the utility function, agents will allocate their entire time endowment to productive work. All the tax revenue is rebated back to the household as a lump-sum transfer, ψ t Production Production in the economy takes place in a representative firm operating in perfectly competitive markets using a constant returns to scale technology. We assume that the representative firm does not issue new shares and finances its capital stock solely through retained earnings. In each period, the representative firm maximizes the present value of a stream of after-tax dividends max I t E 0 X t=0 β t Λ t Λ 0 h (1 τ D ) bd t i. (2) Here β t Λ t Λ 0 is the marginal rate of intertemporal substitution, where Λ t represents the marginal value of consumption (as a numeraire) at time t. The dividends after corporate taxes, bd t, are defined as follows: 3 Santoro and Wei (2009) study the case of progressive dividend taxation. They find that the quantitative impact of a progressive dividend tax system on key economic variables is very similar to that of a proportional system for an income tax system as weakly progressive as in the United States. 4 We assume that the government rebates all of the tax revenues to the household in a lump-sum fashion. By doing that we abstract from the income effect of the tax system and focus on the distortionary aspect of the tax system. 5

6 bd t = D t τ c Π t (3) where the before-tax dividends, D t, are given by D t = Y t W t L t I t. (4) Here I t represents investment and τ c Π t represents the corporate taxes on corporate profits Π t, which is given by Π t = Y t W t L t. (5) Alternatively, the after-tax dividends, D b t, can also be written as 5 : bd t =(1 τ c ) Π t I t. (6) The output Y t is produced using Cobb-Douglas production technology: Y t = Z t Kt α L (1 α) t, (7) where K t is the capital stock, and the logarithm of the stochastic productivity level, Z t, follows a first-order autoregressive process given by z t = ρz t 1 + σξ t. (8) The firm s capital stock follows an intertemporal accumulation equation: K t+1 =(1 δ)k t + Φ (K t,i t ), (9) where δ isthedepreciation rateandthefunctionφ ( ) can potentially account for adjustment costs in capital accumulation. We constrain the functional form to a class which does not alter the steady state of the economy Equilibrium In equilibrium, all produced goods are either consumed or invested: Y t = C t + I t. (10) Labor is supplied inelastically at 1. Financial market equilibrium requires that a t equals 1 for all t and that all other assets are in zero net supply. In our model, the representative household cannot vary its labor supply or shareholdings to avoid income taxes. That allows us to isolate the impact of distortionary taxation on dynamic investment decisions. 5 Allowing for depreciation allowances or partial expensing does not change our main results. The details are contained in Appendix A. 6 We make such assumptions on the specifications of both habit formation and capital adjustment costs to focus on the distortionary effect of taxes on the steady state outcome. 6

7 3 Investment and Asset Pricing with Taxes In this section, we examine the investment decisions and asset pricing implications of dividend taxes and corporate taxes respectively. 3.1 Proportional Dividend Taxes We proceed to examine investment decisions and the corresponding implications for asset pricing in an economy with dividend taxes only. That is accomplished simply by setting τ c to zero Investment Decisions The first-order condition with respect to investment is: ½ (1 τ D ) Φ I (K t,i t ) = βe Λt+1 t (1 τ D ) Λ t α Y t+1 + (1 δ)+φ K (K t+1,i t+1 ) K t+1 Φ I (K t+1,i t+1 ) ¾. (11) The left-hand side of equation (11) represents marginal q, the shadow price of the installed capital in terms of the consumption good. Compared to an economy without taxes, marginal q is lower since investment can be used as a tool to avoid a dividend tax burden. The right-hand side represents the marginal benefit of investment, which is also lower because of the dividend tax burden. The proportional dividend taxes have a symmetric impact on the marginal cost and benefit of investment, which can be canceled out on both sides of the investment equation. That is the essence of the so-called new view, which argues that dividend taxation is not relevant for marginal investment decisions. 7 Because taxes are rebated as a lump sum to the household, the economy with only dividend taxes shares the same equilibrium consumption, investment, capital stock, and output as an economy without taxes. As a result, those two economies share the same Λ t and D t, two variables instrumental for asset pricing implications. 7 Poterba and Summers (1985) formalize the old view and the new view of dividend taxation in the public economics literature. 7

8 3.1.2 Asset Pricing Implications The equilibrium value of the firm, however, is modified by the introduction of dividend taxes. The household s first-order condition with respect to the real equity holding defines the value of the firm as the present discounted value of after-tax dividends. We add superscript D to underscore that the corresponding variables are derived in an economy with dividend taxes only. The value of the firm is given by ½ Λ Vt D D = βe t+1 t (1 τ Λ D D )Dt+1 D + Vt+1 ¾ D, (12) t where the before-tax dividends, D D t+1, are definedinequation(4). The risk-free rate is the reciprocal of the value of a claim to one unit of the consumption good in the next period: R f,d t,t+1 = 1 βe t ³ Λ D t+1 Λ D t (13) The gross return to the firm s equity a claim to the infinite sequence of after-tax dividends is given by Rt,t+1 D = V t+1 D +(1 τ D ) Dt+1 D, (14) V D t where V D t is defined in equation(12). Proposition 1 If two economies are identical except that (i) the dividend tax rate, τ D, is zero in the first economy but positive in the second, and (ii) the difference in lump-sum transfers offsets the difference in revenues from dividend taxes, then the equilibrium outcome, asset returns, and the equity premium are the same in both economies except for the firm s value. Proof. The representative firm in the two economies faces the same maximization problem except for a multiplicative factor, 1 τ D, in the objective function. Moreover, the budget constraints of households place the same constraints on consumption provided that condition (ii) holds. Labor is supplied inelastically in both economies. As a result, the two economies have the same equilibrium outcome. 8

9 The firm s value is reduced proportionally by (1 τ D ) in the economy with a positive dividend tax rate. Since the after-tax value and dividends of the firm are proportional to their respective before-tax counterparts, the equity return in the economy with a positive dividend tax rate, as defined in equation (14), is the same as that in the economy without dividend taxes. Similarly, the risk-free interest rate defined in equation(13) is determined by the equilibrium dynamics of the marginal rates of substitution, which are the same in the two economies. As a result, the equity premium, which captures the difference between the equity return and the risk-free rate, are the same in the two economies. In all, dividend taxes do not distort investment decisions and have no impact on the risk-free rate or the equity premium. 3.2 Corporate Taxes Now we consider an economy with corporate taxes only, which we do by setting τ D to zero. We show that corporate taxes have nontrivial implications for investment decisions and asset pricing Investment Decisions The first-order condition with respect to investment is 1 Φ I (K t,i t ) = βe Λ t+1 t Λ t α(1 τ C ) Y t+1 + (1 δ)+φ K (K t+1,i t+1 ) K t+1 Φ I (K t+1,i t+1 ). (15) As compared with dividend taxes, investment is made after the corporate taxes are paid. As a result, investment no longer has the benefit of avoiding taxes. In other words, corporate taxes affect the marginal benefit and cost of investment asymmetrically, which is different from what we have obtained from dividend taxes. This leads to different investment dynamics in response to technology shocks Asset Pricing Implications The firm s value is the present discounted value of dividends after corporate taxes. We add superscript C to emphasize that the corresponding variables are derived in an economy with corporate taxes only. ½ Λ Vt C C = βe t+1 t D C Λ C t+1 τ c Πt+1 ¾ C + V C t+1, (16) t 9

10 where Dt+1 C is defined accordingly as in equation (4), and τ c Π C t+1 is the corporate taxes levied on profits, Π C t+1, as definedinequation(5). The gross return to the firm s equity, a claim to the infinite sequence of dividends after corporate taxes, is given by R C t,t+1 = V C t+1 + D C t+1 τ c Π C t+1 V C t, (17) where V C t is defined in equation(16). Proposition 2 If two economies are identical except that the corporate tax rate, τ C, is zero in the first economy but positive in the second, then despite that the difference in lump-sum transfers offsets the difference in revenues from corporate taxes, the equilibrium outcome, including the firm s value, are different in both economies. In particular, an economy with corporate taxes is characterized by a lower investment-output ratio, bi, as compared to a tax-free economy or an economy with dividend taxes only. Proof. The differences in the equilibrium outcomes of the two economies follow from equations (15) and (16). In contrast to the economy without taxes or with dividend taxes only, the corporate taxes reduce the marginal product of capital, leading to lower investment, capital stock, and output. The steady-state investment-output ratio, (g + δ) K 1 α, decreases as the steadystate capital stock K decreases. Thus, the steady-state ratio of investment to output is smaller than their counterparts in the tax-free economy or the economy with dividend taxes only. The steady-state ratio of consumption to output is larger according to equation (10). The relative magnitude of the investment-output and consumption-output ratios turns out to have important implications for asset pricing. In most general equilibrium models, investment typically plays a major role in smoothing consumption. A lower investment-output ratio and a higher consumptionoutput ratio imply that investment has to respond differently to exogenous shocks to smooth consumption, especially when there exists strong preference for consumption smoothing. The altered dynamic responses of investment can lead to altered dynamic responses of consumption, the stochastic discount factor and dividends, the key determinants of the risk-free rate and the equity premium. 10

11 Since the risk-free interest rate is determined by the equilibrium dynamics of the stochastic discount factor, a different equilibrium outcome implies a different risk-free interest rate for an economy with corporate taxes. We further examine whether corporate taxes introduce additional taxrelated risk factors in the economy, and how the equity premium may be affected. Following Jermann (1998), we decompose the equity premium of a single-payout asset using log-linear approximation to identify different sources of risks. The value of the single-payout asset is a claim to the aftertax dividends in the n th period only. Proposition 3 If two economies are identical except that the corporate tax rate, τ C, is zero in the first economy but positive in the second, then despite that the difference in lump-sum transfers offsets the difference in revenues from corporate taxes, the following results about the equity premium hold: The risk premium for the asset with a single-period payout, EPM C,n t, can be decomposed into the following three components: EPM C,n t = exp cov t Et+1 λ C t+n λ C t+1,λ C t+1 exp cov ª t 1+θ C E t+1 d C t+n,λ C t+1 exp cov t θ C E t+1 π C t+n,λt+1 C, (18) where θ C = τ c Π C D C τ c Π C. where Π C and D C denote the steady-state values of corporate profits and before-tax dividends respectively, and d C,λ C and π C are defined as the logdeviations of dividends, the marginal value of consumption good and corporate profits from their steady-state values respectively. Proof. See Appendix B. As shown in Proposition 3, corporate taxes indeed explicitly introduce an additional tax-related risk factor, as represented in the third component of the equity premium in equation (18). The third term is related to the stochastic corporate tax liabilities. When profits arehighatthetimeof expansion, the tax liabilities are high as well. It is reasonable to expect E t+1 π C t+n to be negatively correlated with λ C t+1. If that is the case, a negative risk premium arises from desirable cyclical coincidence of a higher tax burden 11

12 and a lower marginal valuation of consumption goods. The procyclical tax burden eventually acts as an insurance mechanism for shareholders, thus possibly reducing the risk premium. We therefore define the third term as the tax burden uncertainty premium. The size of the premium critically depends on the ratio of tax liabilities to after-tax dividends, θ C.Thehigher the corporate tax burden, the more important the tax-related premium. In addition, corporate taxes magnify the risk premium related to uncertain before-tax dividends by a factor of 1+θ C. The second term of equation (18) compensates the household for risks related to uncertain before-tax dividends. We define the second term as the before-tax dividend uncertainty premium. Here θ C represents the ratio of tax liabilities to after-tax dividends. The coefficient 1+θ C adds weight on the correlation between before-tax dividends and the stochastic discount factor. The second and third terms together determine the premium for the after-tax dividend uncertainty. The first term, cov t Et+1 λ C t+n λ C t+1,λt+1 C, represents the term premium which compensates the household for the uncertainty attached to the valuation of given payout. Although this term shares the same functional form as in the tax-free economy, its value is quantitatively different due to different equilibrium solutions. It is important to note that even though the tax burden uncertainty premium may be negative, the equity premium as a whole may be larger than that of the tax-free economy because of different dynamics of the stochastic discount factor and dividends, as reflected in the different values of the term premium and the modified before-tax dividend uncertainty premium. 4 The Numerical Laboratory In this section we use our model as a numerical laboratory to compare the quantitative investment and asset pricing implications of dividend and corporate taxes with those in an economy without taxes, and examine the strengths of different mechanisms at work. 4.1 Specification and Parameterization We specify the preferences and the production technology to capture the preference for consumption smoothing and costs in adjusting the capital stock. We then parameterize the model for numerical experiments. 12

13 4.1.1 Specification We specify the utility function as U = (C t bc t 1 ) 1 γ. 1 γ The coefficient γ measures the curvature of the representative agent s utility function. When b>0, the utility function allows for habit persistence based on the household s own consumption in the previous period. The firm s capital stock follows an intertemporal accumulation equation with adjustment costs: µ It K t+1 =(1 δ)k t + Ψ K t, (19) where δ is the depreciation rate and the function Ψ ( ) takes the following form: µ µ 1 η It (g + δ)η It η (g + δ) Ψ = + K t 1 η K t η 1. (20) The capital supply is inelastic when η approaches infinity. The parameters that govern the function Ψ ( ) are set so that the model with adjustment costs has the same steady state as the model without adjustment costs and that near the steady state: Ψ > 0, Ψ 0 > 0, Ψ 00 < 0. 8 The concavity of this function captures convex costs of adjustment Preference and Production Parameters We set the quarterly trend growth rate, 1+g, to 1.005, the capital depreciation rate, δ, to 0.025, and the constant labor share in a Cobb-Douglas production function, 1 α, to We set the trend-adjusted subjective time preference, β (1 + g) 1 γ, to We fix the risk aversion parameter γ at 5. Estimates of the Solow residual, z t, typically yield a highly persistent AR(1) process in levels. We set ρ to We calibrate the standard deviation of the shock innovation to replicate U.S. postwar quarterly output growth volatility of 1%. All the parameter values are summarized in Table 1. 8 The functional form implies that Ψ I k = g + δ and Ψ 0 I K =1when evaluated at the steady state. K t 13

14 4.1.3 Dividend and Corporate Tax Rates We set the dividend tax rate to 41.1 percent, and the corporate tax rate to 43.2 percent, as the dividend and corporate tax rates estimated by McGrattan and Prescott (2005) 9. For the sake of expositional clarity, we do not take into account the depreciation allowance in the theoretical setup. In reality, investment that is used to replace the depreciated capital stock is exempt from corporate income taxation, and some fraction of investment is exempt from taxes as well. We take those into account in computing the statistics of the economy with corporate taxes. The depreciation allowance narrows the tax base and, to some extent, moderates the impact of corporate income taxation on the economy. We set the fiscal depreciation rate to be the same as the economic rate. We also set the allowed rate of immediate expensing of investment to 2 percent. Even after accounting for depreciation allowance, the statistics are still markedly different from those in an economy without corporate taxes The Four Cases: Varying Habit Formation and Adjustment Costs We form numerical laboratories by varying b and η, which index the degrees of habit persistence and capital adjustment costs respectively. By doing this, we examine the robustness of the mechanisms through which taxes impact both dynamic responses and financial statistics. We start with the laboratory of high habit formation and high capital adjustment costs. As shown in Jermann (1998) and Boldrin, Christiano and Fisher (2001), in a model environment like ours, a combination of high habit formation and high frictions in adjusting the capital stock can deliver an equity premium and a risk-free interest rate of magnitudes close to the data. We examine in this laboratory whether and how dividend and corporate taxes alter the dynamic responses of consumption, investment and the stochastic discount factor. In particular, we explore whether the introduction of taxes alters the responses of these key variables to exogenous shocks, and how 9 McGrattan and Prescott (2005) estimates for the tax rates are based on the data in the 1960s. The corporate tax rate is slightly lower in the 1990s. We have performed numerical experiments using the lower tax rate in the 90s and our main results remain robust. Alternative estimation, such as Gravelle (2004), suggest that those estimates are close to the average over the period from 1959 to

15 different dynamic responses are reflected in the risk-free interest rate and the components of the equity premium. We then conduct numerical experiments by reducing the degree of habit formation and capital adjustment costs to examine their importance for the mechanism through which taxes affect the real and financial aspects of the economy. We examine in total four numerical cases: Case I: high habit formation (b =0.8) and high costs of capital adjustment (η =4); 10 Case II: high habit formation (b =0.8) and moderate costs of capital adjustment (η =2); Case III: moderate habit formation (b =0.4) and high costs of capital adjustment (η =4);and Case IV: standard real business cycle setup (b =0,η =0). 11 For each numerical case, we examine the impulse responses and the financial statistics for three economies: a benchmark economy without taxes, an economy with dividend taxes only, and an economy with corporate taxes only. Given the particular specifications of habit formation and capital adjustment costs, different parameterization of b and η have no impact on the deterministic steady state of the economy. 4.2 Insurance and Amplification Mechanisms at Work This section starts with describing the deterministic steady state of the economy, in particular, the different investment-output ratios in the steady state of the three economies with different tax environments. These differences turn out to have important implications for dynamic responses and asset prices. We then presents the impulse responses and financial statistics of the three economies with different tax environments for each of the four numerical cases. We focus mainly on the insurance and amplification mechanisms introduced by corporate taxes, since dividend taxes do no change the equilibrium outcome, as shown in the previous section. 10 The values of these two parameters in Case I are close to those used in Jermann (1998). 11 We have conducted numerical analyses for a full range of parameters for b [0, 0.8] and η [0, 4]. Theresultsareavailablefromtheauthorsuponrequest. 15

16 4.2.1 The Deterministic Steady State Table 2summarizes thesteady-state valuesofrealandfinancial variables for the three economies. Within each of the four numerical cases, the economy with dividend taxes only and the benchmark economy share the same steady state in terms of real economy variables and asset returns. That is true for any dividend tax rates as long as we assume that the tax revenues are rebated to the households in a lump sum. The steady state in an economy with corporate taxes only, however, features a lower capital stock level and lower investment-output ratio within each case. Due to the absence of uncertainty, the equity premiums are zero in the steady state. The market value of the firm in the economy with dividend taxes only is (1 τ D ) times lower than that of the benchmark economy due to dividend taxation. The market value of the firm in the economy with corporate taxes only also reflects an adverse impact on investment when investment is made out of after-tax profits Impulse Responses This section analyzes the impulse responses of key economic variables in the three economies with different tax environment for each numerical case. Figure 1 displays the impulse responses of consumption, investment and the stochastic discount factor to a 1 percent positive technology shock in the three economies. The jth column corresponds to Case j. The impulse responses are the same in the benchmark economy and the economy with dividend taxes only. This result is consistent with our earlier finding that proportional dividend taxation has no impact on log-deviations of key economic variables from their steady state values. For this reason, the dashed lines in all the figures can be interpreted as the impulse responses of key variables in both the tax-free economy and the economy with dividend taxes only. By contrast, the introduction of corporate taxes into the benchmark economy alters the impulse responses of consumption, investment and the marginal value of consumption good (λ), as shown in the four columns of Figure 1. Both consumption and the marginal value of consumption good respond more strongly to a given technology shock in the initial period for Cases I to IV. In other words, the introduction of corporate taxes amplify the immediate responses of consumption and the marginal value of consumption 16

17 good to technology shocks. In Case I, there exist a strong preference for consumption smoothing (b =0.8), and high costs of capital adjustment (η =4). All the key variables, including investment, respond more strongly to technology shocks. Two forces are at work. On the one hand, in response to a positive technology shock, procyclical corporate tax liabilities discourage investment. On the other hand, a weaker investment response due to corporate taxes would imply a larger increase in current consumption, thus leading to a higher valuation of future consumption goods, which ultimately encourages investment. In economies with a strong preference for consumption smoothing, such as high habit formation, the latter force dominates, resulting in a stronger response of investment to technology shocks in presence of corporate taxes. The intuition behind the amplified responses of both consumption and investment is as follows. Investment constitutes a lower fraction of output in the steady state of an economy with corporate taxes. A lower investmentoutput ratio implies that investment has to respond more strongly to a given technology shock in order to smooth consumption. The investment responses are even more pronounced under the assumption of habit persistence. However, the presence of capital adjustment costs limits the ability of investment to smooth consumption, thus leading to amplified responses of both consumption and investment. We define this mechanism as the amplification mechanism. In Case II, there is still a strong preference for consumption smoothing (b =0.8), however, the capital adjustment costs are moderate (η =2). The amplification mechanism described above is still robust as both consumption and investment respond more strongly to technology shocks in presence of corporate taxes. The marginal value of consumption good also responds more strongly to technology shocks, but the magnitude of the responses are lower than those of Case I, as consumption is smoothed to a larger degree due to lower capital adjustment costs. In Case III, the capital adjustment costs remain high (η =4), but the habit persistence is moderate (b =0.4). In the initial period, both consumption and the marginal value of consumption good still respond strongly to technology shocks. This result implies that even when the preference for consumption smoothing is moderate, the amplification mechanism is still atwork. Wefocusontheimmediateresponsesofthemarginalvalueof consumption good to exogenous shocks, because amplified initial responses imply a stronger precautionary motive due to unanticipated movement of 17

18 the stochastic discount factor. The stronger precautionary motive leads to a lower risk-free interest rate. 12 Case IV features a standard real business cycle model with no habit formation (b =0)and no adjustment costs (η =0). In this case, both consumption, and consequently the marginal value of consumption good respond more strongly to technology shocks compared to the benchmark economy and the economy with dividend taxes only. The amplification mechanism is robust in the standard real business cycle setup. The amplified responses of the marginal value of consumption good have a major impact on the term premium, as captured by the first component of equation (18). In particular, as the marginal value of consumption good declines more in response to positive technology shocks, its correlation with the value of a discount bond becomes larger in absolute magnitude. A larger correlation between the two implies a larger term premium. Since the marginal value of consumption good also enters the second and third components of the risk premium in equation (18), both the pre-tax dividend uncertainty premium and tax burden uncertainty premium are modified. Figure 2 displays the impulse responses of before-tax dividends and corporate tax liabilities for the four cases. In the benchmark economy (or equivalently, an economy with dividend taxes only), before-tax dividends decline in the initial periods to accommodate procyclical investment and become procyclical later because of rising capital income in response to a positive technology shock. In an economy with corporate taxes, before-tax dividends are more procyclical. The impact of investment on before-tax dividends is smaller because of the smaller investment-output ratio. Thus, despite stronger responses of investment to the technology shock, the initial countercyclical responses are not as pronounced as in the benchmark economy. Such responses of pre-tax dividends imply a higher pre-tax dividend uncertainty premium in an economy with corporate taxes, as compared to the economy without taxes or with dividend taxes only. As shown in Figure 2, the corporate tax liabilities are procyclical in all four cases. The procyclical responses of corporate tax liabilities imply a 12 As is well known, the risk-free interest rate can be approximated by ½ ¾ R f 1 t,t+1 = β (1 + g) γ exp 2 [var (E tλ t+1 λ t ) var (λ t+1 E t λ +1 )] The second component of the above equation captures the precautionary motive. 18

19 negative correlation between the tax liabilities and the marginal value of consumption captured in the tax burden uncertainty premium, the third component of equation (18). This can be interpreted as the insurance mechanism induced by procyclical tax liabilities. In all, we examine the impulse responses of key variables in four cases with varying degrees of habit formation and capital adjustment costs. Both insurance and amplification mechanisms are at work in all four cases in the presence of corporate taxes. The insurance mechanism is present even in a partial equilibrium setup. However, the amplification mechanism is present only in a general equilibrium framework and is the strongest in the presence of both high habit formation and high capital adjustment costs (Case I). The amplification mechanism is even stronger when there is no depreciation allowance or partial expensing of investment, as shown in Figures 3 and Financial Statistics In this section, we examine the implications of taxes on the risk-free interest rate and the equity premium in the four cases. 13 Table 3 reports the risk-free interest rate and the equity premium in the benchmark economy and in the two economies with alternative tax environments. In an economy with dividend taxes only, the financial statistics are the same as in the benchmark case, as reflected in their identical impulse responses. The column no tax also can be interpreted as containing the statistics for the economy with dividend taxes only. The column tax contains the financial statistics for the economy with corporate taxes only. Panel A reports the risk-free interest rate and equity premium when both depreciation allowance and partial expensing are taken into account when computing the financial statistics for the economy with corporate taxes only. As discussed above, the amplification mechanism leads to a strong precautionary motive and thus a lower risk-free interest rate. In Case I (b =0.8,η =4), 13 One of our numerical cases, Case I, is similar to Jermann (1998). Thus it inherits a major shortcoming of the type of production economy in Jermann (1998), namely the overly volatile interest rate. The fact that models like Jermann (1998) and Boldrin, Christiano and Fisher (2001) do poorly on risk-free rate volatility is well known. Since the main goal of our analysis is to examine the mechanism through which taxes affect the real and financial aspects of the economy, we choose instead to focus on comparing the benchmark economy with the economies under alternative tax environments. Case I is only one of the cases we study, and the amplification mechanism is present in all four cases. 19

20 the risk-free interest rate is reduced from 1.29 to 0.48 percent after the introduction of corporate taxes. In Cases II and III with either moderate adjustment costs or moderate habit formation, the risk-free interest rates are higher than that in Case I in the tax-free economy. In Case II, when the adjustment cost parameter is reduced by half, corporate taxes bring about a 0.17 percentage point decrease in the risk-free interest rate. In Case III, the habit formation parameter is reduced by half. The risk-free interest is reduced after the introduction of corporate taxes, albeit by a lesser amount. Case IV represents a standard real business cycle setup. As is well known, the risk-free interest rate in the tax-free economy is high. In this case, the introduction of corporate taxes reduces the risk-free interest rate by 2 basis points. Since higher degree of habit persistence transforms any amplified consumption responses into larger responses in the marginal value of consumption good, the amplification mechanism is stronger with higher habit formation, resulting in strong implications for asset prices. Panel A also reports the equity premium in the four cases under different tax environments. In Case I, the equity premium increases from 5.38 to 6.87 percent after the introduction of corporate taxes. In Case II, when the habit formation parameter remains at 0.8, but the adjustment cost parameter is cutbyhalf,theequitypremiumincreasesfrom1.99 to 2.35 percent. In Case III, when the habit formation parameter is cut by half, the equity premium increases by 4 basis points from 1.76 to 1.81 percent. In Case IV, the standard real business cycle setup, the equity premium is close to zero with or without taxes. The amplification mechanism is stronger when there is no depreciation allowance or partial expensing, as shown in Panel B of Table 3. Case I (b =0.8,η =4) demonstrates the strong effect of the amplification mechanism on the financial statistics when there is no depreciation allowance or partial expensing. In this case, the risk-free interest rate decreases from 1.29 to 1.95 percent, and the equity premium increases from 5.38 to percent after the introduction of corporate taxes. 14 In terms of the decomposition of the equity premium in equation (18), in the first three cases, the positive term and before-tax payout uncertainty premiums dominate the negative tax burden uncertainty premium. In other 14 The parameterization in Case I is similar to that of Jermann (1998) except for taxes. The large increase in the equity premium implies that we can relax his strong restrictions on habit persistence and capital adjustment costs, but still retain a reasonable equity premium, if we account for the effect of corporate taxes. 20

21 words, even though there is an insurance component due to the presence of corporate taxes, the amplified responses of dividends and marginal value of consumption good lead to a higher equity premium. The risk-free rate declines the most, and the equity premium increases the most in presence of corporate taxes in Case I, reflecting the fact that the amplification mechanism is the strongest in this case. 5 Conclusion This paper studies the investment and asset pricing implications of dividend and corporate taxes in a dynamic stochastic general equilibrium model. In particular, we examine whether these two types of taxes introduce additional tax-related risk factors in the economy, and how the risk-free interest rate and the equity premium may be affected. We find that proportional dividend taxes reduce the firm value proportionally, but have no impact on the risk-free rate or the equity premium. This result comes from the fact that proportional dividend taxes affect the marginal cost and benefit of investment symmetrically and therefore do not affect any marginal decisions. Corporate taxes, by contrast, have strong implications in terms of both investment decisions and asset pricing. Corporate taxes reduce the marginal benefit of investment, thus discouraging investment. We uncover a mechanism through which corporate taxes amplify the responses of consumption and investment to technology shocks, which lead to a lower risk-free interest rate and higher equity premium. This amplification mechanism is the strongest when there exists a strong preference for consumption smoothing and high costs of adjusting the capital stock. 21

22 References [1] Auerbach A. J. and L. Kotlikoff, 1987, Dynamic Fiscal Policy, Cambridge MA, Cambridge University Press. [2] Auerbach, Alan, J. 2002, Taxation and Corporate Financial Policy, in Handbook of Public Economics, Vol 3, edited by Alan Auerbach and Martin Feldstein, Amsterdam: North Holland. [3] Boldrin, Michele, Christiano, Lawrence J. and Jonas Fisher, 2001, Habit Persistence, Asset Returns and the Business Cycle, American Economic Review, 91(1), March, pp [4] Brennan, Michael, 1970, Taxes, Market Valuation and Corporate Financial Policy, National Tax Journal, pp [5] Constantinides, G.M., 1990, Habit Formation: A Resolution of the Equity Premium Puzzle, Journal of Political Economy, 98, pp [6] Griffoli, Tommaso Mancini, 2007, Dynare User Guide: An Introduction to the Solution & Estimation of DSGE Models. [7] Feldstein, Martin, 2006, The Effect of Taxes on Efficiency and Growth, NBER Working Papers [8] Gordon, Roger and John Wilson, 1989, Measuring the Efficiency Cost of Taxing Risky Capital Income, American Economic Review, vol. 79(3), pp [9] Gravelle, Jane, 2004, Historical Effective Marginal Tax Rates on Capital Income, CRS Report for Congress, RS [10] Gourio, Francois, and Jianjun Miao, 2006, Firm Heterogeneity and the Long-Run Effects of Dividend Tax Reform, Working Paper. [11] Gouveia M. and R. Strauss, 1994, Effective Federal Individual Tax Functions: An Exploratory Empirical Analysis, National Tax Journal 47, [12] Graham, John and Alok Kumar, 2006, Do Dividend Clienteles Exist? Evidence on Dividend Preferences of Retail Investors, Journal of Finance, Vol. LXI, No. 3, pp

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25 Appendix A. Corporate Taxes with Depreciation Allowance and Partial Expensing Production in the economy takes place in a representative firm operating in perfectly competitive markets using a constant returns to scale technology. We assume that the representative firm does not issue new shares and finances its capital stock solely through retained earnings. Each period the representative firm maximizes the present value of a stream of after-tax dividends: max I t E 0 X t=0 ½ β t Λ t Λ 0 h (1 τ D ) bd t i ¾ (21) where the post corporate-income-tax dividends, bd t, are given by: bd t = D t τ c Πt δ f K t ζi t. (22) Here we take into account the depreciation allowance with a fiscal depreciation rate of δ f. Such depreciation allowance narrows the tax base of corporate taxes. The fiscal depreciation rate δ f can be different from the economic depreciation rate δ. The rate ζ is the allowed rate of immediate expensing of investment. The first-order condition for investment is now given by: 1 ζτ ³ c = βe 0 Ψ 0 I t K t ½ Λt+1 Λ t (1 ζτ c ) + α(1 τ c ) Y t+1 + τ c δ f K t+1 h ³ ³ (1 δ)+ψ It+1 K t+1 Ψ 0 It+1 It+1 K t+1 ³ Ψ 0 It+1 K t+1 K t+1 i.(23) We conduct numerical experiments with depreciation allowance and partial expensing by setting δ f to the benchmark value of δ, and setting the rate ζ to

26 B. The Derivation of Equity Premium with Taxes Here we prove Proposition 3, which decomposes the strip premium in an economy with corporate taxes. First, we consider a claim to the after-tax dividends in the n-th period only. The value of that asset, V C,t+n t, is approximated by Ã!# V C,t+n t = V C,n E t "exp λ C D C τ c Π C t+n + D C τ c Π C dc t+n D C τ c Π C πc t+n λ C t, (24) wherethelowercaselettersarethelog-lineardeviationsofthecorresponding variables from their steady-state values, and V C,n is the steady-state value of the asset. The steady-state values are denoted with an upper bar above the corresponding variables. We further define the one-period holding return of this asset as: R t,t+1 h b D t+n i = V C,t+n t+1 V C,t+n t, (25) wherethevariableinthesquarebracketrepresentstheone-timepayoutat period t + n. ³ h i In order to solve for the conditional expected return E t R t,t+1 D bt+n, we first take the expectation of V C,t+n t+1 at time t. Under the assumption of lognormality, the expression of the conditional expected return can be greatly simplified. After some manipulations, we get that: ³ h i E t R bdt+n t,t+1 = R t,t+1 [1 t+1 ] exp cov t Et+1 λ C t+n λ C t+1,λ C t+1 exp cov ª t 1+θ C E t+1 d C t+n,λ C t+1 exp cov t θ C E t+1 π C t+n,λt+1 C, (26) where θ C = τ c Π C D C τ c Π C. Here R t,t+1 [1 t+1 ] represents the risk-free rate computed under the assumption of lognormality. The derivations above follow the descriptions in Jermann (1994) closely. 26

27 Table 1 Benchmark Parameterization Parameters Production g δ α Preferences β (1 + g) 1 γ γ Technology Process ρ σ Table 2: The Deterministic Steady State C I τ D τ C R f R V Y Y The Benchmark Economy Economy I: Dividend Taxes Only Economy II: Corporate Income Taxes Only

28 Table 3: Financial Statistics Panel A: with Depreciation Allowance and Partial Expensing Case I Case II Case III Case IV b =0.8,η =4 b =0.8,η =2 b =0.4,η =4 b =0,η =0 no tax tax no tax tax no tax tax no tax tax Risk-free Rate Equity Premium Panel B: without Depreciation Allowance or Partial Expensing Case I Case II Case III Case IV b =0.8,η =4 b =0.8,η =2 b =0.4,η =4 b =0,η =0 no tax tax no tax tax no tax tax no tax tax Risk-free Rate Equity Premium The statistics are computed from 10,000 simulations. All the numbers are in percentage terms. 28

29 Figure 1: Comparison of Impulse Responses - I (with depreciation allowance and partial expensing) The impulse is a 1% positive productive technology shock. 29

30 Figure 2: Comparison of Impulse Responses - II (with depreciation allowance and partial expensing) The impulse is a 1% positive productive technology shock. 30

31 Figure 3: Comparison of Impulse Responses - I (without depreciation allowance or partial expensing) The impulse is a 1% positive productive technology shock. 31

32 Figure 4: Comparison of Impulse Responses - II (without depreciation allowance or partial expensing) The impulse is a 1% positive productive technology shock. 32