Abstract

The surge in public debt triggered by the financial crisis has raised uncertainty about future tax pressure and economic activity. We examine the asset pricing effects of fiscal policies in a production-based general equilibrium model in which taxation affects corporate decisions by: (1) distorting profits and investment; (2) reducing the cost of debt through a tax shield; and (3) depressing productivity growth. In settings with recursive preferences, these three tax-based channels generate sizable risk premia, making tax uncertainty a first-order concern. We document further that corporate tax smoothing can substantially alter the effects of public expenditure shocks.

Fiscal stabilization policies arising in response to the recent financial crisis have led to a surge of public debt that will eventually require budget consolidation. At this stage, however, there is significant uncertainty about the future policies that will be implemented to achieve budget balance. The distortionary nature of the most relevant fiscal policy instruments raises concern that the effects of fiscal uncertainty on current economic activity, long-run growth, and welfare may be substantial.

We contribute to the public budget debate by examining the effects of fiscal policies affecting corporate decisions, and hence asset prices, through corporate taxation. We propose a production-based economy subject to risky government expenditure shocks that generate tax risk through the government's budget. The extent of this uncertainty depends on the government's financing policy, which pins down long-run tax dynamics. Our main results show that both volatility and the intertemporal distribution of tax rates are first-order determinants of the cost of equity and capital accumulation. Quantitatively, each of these features of the tax rate process is as important as the average level of taxation (Gomes et al. 2009a). At a broader level, therefore, our results are significant because they convey the need to include risk considerations in fiscal policy analysis.

We conduct a tax-based asset pricing and welfare analysis in the spirit of Lucas (1978, 1987), using a general equilibrium model with the goals of (1) capturing the most significant channels through which taxes can alter corporate decisions; and (2) producing reasonable implications for the cost of equity even in a baseline environment without tax uncertainty. We believe that a realistic model of corporate taxation that produces plausible results for both cost of equity and investment decisions will yield a reasonable assessment of the asset pricing role of corporate tax uncertainty.

We identify three primary channels through which corporate taxes mainly affect firm decisions. The first is the investment channel: taxes affect profits and therefore the after-tax marginal product of capital, which gives rise to investment distortions. Since we assume that capital accumulation is subject to adjustment costs as in Jermann (1998), our model features sizeable variations in the marginal price of capital that can be amplified by tax shocks.

Second, in line with the tax code in the United States, we assume that taxes lower the cost of debt, since interest payments on corporate debt are tax-deductible. Departing from the Modigliani and Miller (1958) benchmark, we capture this financing channel by explicitly modeling financial leverage. Specifically, we introduce a dynamic trade-off model of capital structure into an asset pricing model along the lines of Livdan et al. (2009). The marginal benefit of corporate debt corresponds to the expected tax shield. The marginal cost of debt is related to distress and debt adjustment costs in the spirit of Jermann and Quadrini (2012). Through this combination of frictions, in equilibrium, the volatilities of our net equity payouts and equity excess returns are closer to those observed in the data (see, among others, Larrain and Yogo 2008). Corporate financing, therefore, is a dimension that helps us better characterize the dynamics of equity returns and ultimately their exposure to tax risk. This is relevant to obtain reliable estimates on the effects of taxation on the cost of equity.

Third, reflecting recent empirical evidence (Lee and Gordon 2005; Djankov et al. 2010), we allow for a productivity channel that accounts for interdependence between taxation and productivity growth. Specifically, in our benchmark model, an increase in taxes produces a small but persistent slowdown in long-run productivity growth.1

In order to keep our fiscal analysis focused, we simplify government behavior in several ways. In particular, our government finances an exogenous cash-flow stream calibrated to mimic the corporate tax flows observed in the data (McGrattan and Prescott 2005). This cash-flow stream is financed through a mix of public debt and corporate taxes, according to an exogenous rule that determines the extent of fiscal stabilization through tax smoothing (i.e., the persistence and the volatility of the tax rate). Our exogenous fiscal policies can be interpreted as the fiscal counterpart of Taylor rules in monetary economics. In this sense, our approach is methodologically close to that of Gallmeyer et al. (2011) and Palomino (2012).

We consider three alternative policy scenarios. The government can either (1) implement a zero-deficit policy, implying that all tax shocks in the economy are absorbed by a one-to-one contemporaneous adjustment of corporate taxes (no tax smoothing); (2) use public debt to smooth corporate taxes in order to stabilize consumption over time and across contingencies; or (3) use public debt to stabilize investment. Under the zero-deficit policy, the tax rate dynamics reflect the exogenous fluctuations of the public liabilities. This policy is, therefore, a good benchmark to quantify the impact of purely exogenous expenditure shocks. Under the two alternative debt-financing policies, in contrast, the tax rate properties are endogenously pinned down by the tax-smoothing attitude of the government. The long-run budget balance determines the future tax adjustment required to consolidate public debt across different histories of expenditure and productivity shocks. These two alternative tax-smoothing policies enable us to determine under which circumstances public debt financing can endogenously amplify or reduce the asset pricing and welfare impacts of exogenous shocks. We find this second experiment particularly relevant for the current fiscal debate for a simple reason: while public liability shocks are mostly outside of government control, financing decisions are mainly within the discretion of the fiscal authorities and should be made to maximize welfare.

Since both our productivity channel and the government tax-smoothing rules generate significant trade-offs between current and future growth and taxation, we employ Epstein and Zin (1989) recursive preferences to capture agents' sensitivity to the intertemporal distribution of risk. The relevance of this last element of our model is twofold. On the one hand, it allows us to disentangle the intertemporal elasticity of substitution (IES) from relative risk aversion (RRA). This enables us to match several features of quantities, driven by the IES (Tallarini 2000), and asset prices, driven by RRA. On the other hand, recursive preferences make our household more or less favorable to public debt policies that alter the level of short-run and long-run consumption risk. In particular, as in Bansal and Yaron (2004), our household dislikes late resolution of uncertainty (i.e., long-lasting shocks to consumption prospects). Therefore, in our welfare investigation we treat tax-smoothing policies as a device to reallocate consumption risk across different horizons.

In this setup, we obtain three relevant results regarding corporate taxation. First, average corporate taxation matters for both the level and the composition of the cost of capital. When the tax rate is time invariant, higher taxation reduces capital accumulation and investment, the only hedging devices available in our economy. In equilibrium, higher average taxation results in a higher cost of equity, as in Gomes, Michaelides, and Polkovnichenko (2009a), and lower after-tax cost of debt.

Second, when the productivity channel is active, persistent government expenditure shocks affect long-run corporate productivity and thereby constitute a significant risk factor. We find that even a moderate increase in the volatility of the expenditure shocks can substantially increase the equity premium in the economy. This makes the level of fiscal risk as important as the average level of tax pressure in fiscal policy decisions.

The previous effects are independent of explicit financing policies; rather, they reflect production distortions arising from taxation. Our third result, however, relates to the intertemporal equilibrium effects resulting from tax smoothing. We show that conventional tax smoothing aimed at stabilizing short-run consumption volatility can produce a substantial increase in the equity premium and ultimately in the average excess return of total wealth. Since aggregate wealth mirrors welfare (Epstein and Zin 1989), this implies substantial welfare losses. This result can be explained as follows. In general equilibrium, the alteration of corporate tax rates to smooth consumption comes at the cost of an increase in the volatility of investment. This tax-smoothing scheme therefore increases the volatility of capital accumulation (i.e., the driver of long-run consumption growth). Since our household strongly dislikes long-run consumption uncertainty, welfare declines. The opposite occurs when the government smooths corporate taxation to stabilize corporate investment: in this case, tax smoothing acts as a stabilizer of long-run consumption growth, ultimately producing welfare benefits.

Our article belongs to a growing literature examining the links between government policies, economic activity, and asset prices. In two closely related studies, Pastor and Veronesi (forthcoming, 2011) examine the effect of uncertainty about government policy on stock prices. They stress learning about government interventions and political motives. Our article, in contrast, focuses on tax-related fiscal uncertainty and examines its implications for aggregate risk premia in a macroeconomic setting with perfect information and commitment. We view the learning channel of Pastor and Veronesi (forthcoming, 2011) as an important complementary mechanism to be incorporated into our macro model in future research.

Glover et al. (2010), like us, examine the effects of fiscal policy using calibrated models with realistic risk premia. In their incomplete market models with heterogeneous agents, they focus on portfolio reallocations between agents and crowding-out effects through the public supply of debt. In our article, we retain a representative agent framework but stress fiscal uncertainty and the intertemporal distributions of tax distortions and consumption as important determinants of risk premia and welfare. Our article is also related to work by Gomes et al. (2011), who calibrate a life-cycle model to measure the welfare losses from uncertainty about taxes and social security; however, they do not consider the cost of equity. Glover et al. (2010) also examine asset pricing and macroeconomic implications of corporate taxation in a model with endogenous financial leverage, but they focus on credit spreads and do not consider policy uncertainty.

While we focus on the government's financing problem, Belo et al. (forthcoming) and Belo and Yu (2011) empirically examine the effects of government spending on the cross-section of returns and the aggregate stock market. They find that government investment is an important risk factor that predicts aggregate stock returns.

Broadly, our article is related to a long list of studies examining the effects of fiscal policy on the macroeconomy. Among others, Dotsey (1990), Ludvigson (1996), Davig et al. (2010), and Leeper et al. (2010) examine the implications of dynamic fiscal policies for the macroeconomy in stochastic real business cycle models. In contrast to our study, these articles abstract from asset prices and risk considerations.

We link welfare costs to risk premia in asset markets similarly to Tallarini (2000), Alvarez and Jermann (2004), and Croce (2006). While these researchers focus on economic fluctuations abstracting from policy interventions, our work explicitly considers tax policies and their impact on asset markets and consumption at various frequencies.

Our article is also related to the growing literature examining asset pricing in production-based general equilibrium models with recursive preferences (Campanale et al. 2010; Kuehn 2008; Ai 2010; Backus et al. 2010; Kaltenbrunner and Lochstoer 2010; Gourio, forthcoming; Kuehn et al. 2011). In the spirit of the existing literature, we provide a handy production economy able to produce sizeable Sharpe ratios and equity premia. We differ from previous work, however, for our mix of investment and financing frictions and our focus on the link between long-run tax risk and equity premia.

The rest of the article is organized as follows. We present the model in Section 1, where we also detail the link between corporate taxation and productivity. Quantitative model results are presented and discussed in Sections 2 and 3. Section 4 concludes. Details concerning data construction and solution methods are presented in Appendix A and B, respectively.

1. Model

We use a general equilibrium model to quantitatively examine the links between fiscal shocks, leverage, macroeconomic aggregates, and asset prices. Our economy is populated by a representative firm that optimally chooses investment and financial leverage; a representative agent with Epstein and Zin (1989) preferences who supplies labor and saves using corporate equity, corporate bonds, and public bonds; and a government that determines the corporate tax rate. In this section, we describe in detail the behavior of these agents.

1.1 Government and productivity

1.1.1 Public liabilities.

In the tax literature it is common to assume that the government levies taxes in order to finance an exogenous demand for goods and services. Under this assumption, the role of government is twofold. On the one hand, the government generates distortionary effects (substitution effects) induced by proportional taxation. On the other hand, government expenditure reduces the amount of resources available to the private sector (a crowding-out or, equivalent, income effect). We focus only on the distortionary effect and, following Santoro and Wei (2011), we assume that all taxes are used to finance a lump-sum transfer to the household, TRt . By doing so, we ignore the negative income effect associated with government expenditure and obtain a lower (upper) bound on the potential costs (benefits) of corporate taxation.

The exogenous public cash flow to be financed, TRt , evolves as follows:  

(1)
$$\begin{align} T{R_t} & = \tau _t^* \cdot {\rm{tax}}\,{\rm{bas}}{{\rm{e}}_t}, \\ \tau _t^* & = \frac{1}{{1 + \exp ( - {\omega _t})}}, \\ {\omega _t} & = (1 - \rho ){\mu _\tau } + \rho {\omega _{t - 1}} + { \epsilon _{{\tau ^*},t}}, \\ { \epsilon _{{\tau ^*},t}} & \sim N(0,\sigma _\tau ^2). \\ \end{align}$$

This formulation guarantees that the expenditure–tax base ratio, τt* , is positive and smaller than 100%.

1.1.2 Corporate taxation and financing.

To keep the fiscal side of our model as focused as possible on corporate tax rate fluctuations, τt , we abstract from labor taxes and other non-corporate taxes and define the total tax in flow simply as  

(2)
$$\begin{align} {T_t} & = {\tau _t} \cdot {\rm{tax}}\,{\rm{bas}}{{\rm{e}}_t}, \\ {\rm{tax}}\,{\rm{bas}}{{\rm{e}}_t} & = ({Y_t} - {W_t}{H_t} - {r_{f,t - 1}}{B_{t - 1}}), \\ \end{align}$$
where Yt measures corporate sales, Wt is the real wage rate, Ht measures labor, and rf,t1Bt1 refers to corporate interest payments on corporate debt, Bt1 . We anticipate that at the equilibrium there will be no default and, therefore, corporate bonds pay the short-term risk-free rate, rf,t1 . The exclusion of corporate interest payments from the tax base captures the tax-shielding effects of corporate debt, in line with the U.S. tax code. This feature of the model represents a departure from the Modigliani and Miller (1958) assumptions typically maintained in the asset pricing literature and gives rise to an incentive to issue corporate debt.

To highlight the relevance of corporate tax smoothing, we allow the government to finance expenditure through a mix of corporate taxes, Tt , and public debt, BtG , according to the following budget constraint:  

(3)
$$\begin{align} B_t^G & = (1 + {r_{f,t - 1}})B_{t - 1}^G + T{R_t} - {T_t} \\ & = (1 + {r_{f,t - 1}})B_{t - 1}^G + (\tau _t^* - {\tau _t}){\rm{tax}}\,{\rm{bas}}{{\rm{e}}_t}. \\ \end{align}$$

1.1.3 Productivity.

Aggregate productivity is denoted by Zt . Empirical work in growth economics (e.g., Lee and Gordon 2005; Djankov et al. 2010) suggests that an increase in tax pressure reduces long-run growth. Croce et al. (2011) explain this empirical finding in a model in which growth is endogenously promoted by accumulation of patents (as in Romer 1990). They find that taxes inhibit profits and R&D activity, two main drivers of productivity growth. Since our analysis focuses mainly on the link between corporate tax uncertainty and the cost of equity, we abstract from endogenous growth and directly impose the condition that the log growth rate of productivity, Δztlog(Zt)log(Zt1) , evolves as follows:  

(4)
$$\begin{align} \Delta {z_t} & = \mu + {\phi _\tau } \cdot ({\tau _{t - 1}} - E[{\tau _t}]) + { \epsilon _t}, \\ { \epsilon _t} & \sim N(0,{\sigma _ \epsilon }),\qquad corr({ \epsilon _{{\tau ^*},t},{ \epsilon _t}}) = 0, \\ \end{align}$$
where Φτ0 captures the results of Croce et al. (2011). We assume that productivity is affected by the deviation of the tax rate, τt1 , from its unconditional mean, E[τt] , just to normalize the unconditional growth rate of the economy to $${\mu }$$. We impose the condition corr(ετ*,t,εt)=0 in order to study fiscal policy shocks purely unrelated to the productivity dynamics. In Section 2.1, we focus on U.S. data and provide direct empirical evidence supporting our productivity specification.

1.2 Representative household

Our household has Epstein and Zin (1989) preferences defined over consumption goods, Ct :  

$${U_t} = {\left\{ {(1 - \beta )C_t^{1 - \frac{1}{\psi }} + \beta {{({E_t}[U_{t + 1}^{1 - \gamma }])}^{\frac{{1 - \frac{1}{\psi }}}{{1 - \gamma }}}}} \right\}^{\frac{1}{{1 - \frac{1}{\psi }}}}},$$
where $${\gamma }$$ is the coefficient of relative risk aversion and $${\psi }$$ is the elasticity of intertemporal substitution. When ψ1γ , the agent cares about news regarding long-run growth prospects and taxation. In line with the literature on long-run risks in asset prices, we assume ψ>1γ , such that the agent dislikes shocks to long-run expected growth rates. This assumption allows the intertemporal distribution of tax rates to influence asset prices.

We assume that the agent experiences no disutility from working, so that the supply of hours worked, Ht , is fixed and normalized to 1 for simplicity. As shown in Epstein and Zin (1989), the stochastic discount factor in this setting is  

$${M_{t + 1}} = \delta {\left( {\frac{{{C_{t + 1}}}}{{{C_t}}}} \right)^{ - \frac{1}{\psi }}}{\left( {\frac{{{U_{t + 1}}}}{{{E_t}{{\left[ {U_{t + 1}^{1 - \gamma }} \right]}^{\frac{1}{{1 - \gamma }}}}}}} \right)^{\frac{1}{\psi } - \gamma }}.$$

The objective of the household is to maximize lifetime utility, subject to a standard budget constraint:  

(5)
$$\begin{align} {U_t} & = \mathop {\max }\limits_{\{ {C_j},{H_j},{S_j},{B_j},B_j^G\} _{j = t}^\infty } {\left\{ {(1 - \beta )C_t^{1 - 1/\psi } + \beta {E_t}{{[U_{t + 1}^{1 - \gamma }]}^{\frac{{1 - 1/\psi }}{{1 - \gamma }}}}} \right\}^{\frac{1}{{1 - \frac{1}{\psi }}}}} \\ & s.t. \\ {C_t} + {S_t}{P_t} + B_t^{tot} & \le (1 + {r_{f,t - 1}})B_{t - 1}^{tot} + {S_{t - 1}}({D_t} + {P_t}) + {W_t}{H_t} + T{R_t}, \\ B_t^{tot} & = {B_t} + B_t^G, \\ \end{align}$$
where St is number of equity shares (in equilibrium, St=1 for all $$t$$); Pt is the ex-dividend price per share; Dt is the equity payout; and Bttot is the sum of corporate and public bonds, as specified in Section 1.1. In each period, the household determines its consumption and its allocation of savings among equity, corporate debt, and public debt. The optimal investment policy implies the following no-arbitrage pricing equations:  
(6)
$$\begin{align} 1 & = {E_t}\left[ {{M_{t + 1}}\frac{{{P_{t + 1}} + {D_{t + 1}}}}{{{P_t}}}} \right], \\ {r_{f,t}} & = \frac{1}{{{E_t}[{M_{t + 1}}]}} - 1. \\ \end{align}$$
Equation (6) shows that in our economy the first-order conditions of the household are not directly affected by any marginal tax distortion. In this article, therefore, we consider only distortions that directly affect the firm side.

1.3 Representative firm and market clearing

1.3.1 Production technology.

The representative firm has access to a standard constant returns-to-scale production technology:  

$${Y_t} = {({Z_t}{H_t})^{1 - \alpha }}K_{t - 1}^\alpha ,$$
where Yt is output, Ht measures labor, and Kt denotes the physical capital stock that we specify as in Jermann (1998):  
$$\begin{align} {K_t} & = (1 - \delta ){K_{t - 1}} + \phi \left( {\frac{{{I_t}}}{{{K_{t - 1}}}}} \right){K_{t - 1}} \\ \phi \left( {\frac{{{I_t}}}{{{K_{t - 1}}}}} \right)& : = \left[ {\frac{{{\alpha _1}}}{{1 - 1/\xi }}{{\left( {\frac{{{I_t}}}{{{K_{t - 1}}}}} \right)}^{1 - 1/\xi }} + {\alpha _2}} \right]. \\ \end{align}$$

The introduction of investment adjustment cost, $${\Phi }$$, allows us to work with an upward-sloping supply curve of new capital and produces variations in marginal Tobin's Q that are required to match equity return dynamics.

1.3.2 Financing.

We assume that the firm can finance investment by issuing either equity or one-period bonds sold at par with face value $$B$$ and interest rate rf . Since we allow interest payments on corporate debt to be tax-deductible, there is scope for optimal leverage decisions, in line with the dynamic trade-off models of capital structure proposed in Hennessy and Whited (2005), Hennessy and Whited (2007), Livdan et al. (2009), and Gomes and Schmid (2010).

While the marginal benefit of debt is determined by the tax advantage, the cost of debt depends on indirect financial distress costs, CtE :  

$$C_t^E = {\phi _0}{e^{ - {\phi _1} \cdot \left( {\frac{{\eta {K_t}}}{{{B_t}}} - 1} \right)}} \cdot {Z_{t - 1}},$$
where $${\eta }$$, Φ1 , and Φ0 are positive constants, and the factor Zt1 ensures that these costs do not vanish along the balanced growth path. The parameter $${\eta }$$ captures the liquidation value of the collateral as a fraction of its book value, $$K$$, and is set so that η<(1δ) , implying that distressed capital is sold at a discount. The parameter Φ1 is set high to discourage the firm from borrowing more than the collateral value. The parameter Φ0 is set low so that the firm will choose B=ηK at the steady-state. We choose this cost formulation mainly to “convexify” the following occasionally non-binding enforcement constraint:  
(7)
$${B_t} \le \eta {K_t},$$

which allows the firm to borrow up to the value of its collateral, i.e., the liquidation value of the capital stock. Modeling CtE as a continuous and differentiable function approximating (7) enables us to easily solve the model with standard numerical methods. This modeling choice makes our production economy very straightforward to solve and versatile for future extensions.

The constraint (7) implies that all debt is secured by the firm's capital, and hence no default ever occurs in equilibrium. Similarly to Glover et al. (2010), our CE process captures indirect costs of financial distress, i.e., costs of financial leverage outside of bankruptcy. Such indirect costs arise in highly levered firms when, for example, they find it more difficult to find new lenders or recruit new employees. All these activities require more time and effort and are costly.

To generate realistically persistent dynamics for leverage (Leary and Roberts 2005; Lemmon et al. 2008), we introduce capital structure rigidities, modeled through the following quadratic debt adjustment cost function centered around the steady-state, BssYss :  

$$C_t^B = v \cdot {\left( {\frac{{{B_t}}}{{{Y_t}}} - \frac{{{B_{ss}}}}{{{Y_{ss}}}}} \right)^2} \cdot {Z_{t - 1}}.$$
Since in our model output, Yt , and earnings before interest and taxes (EBIT), YW=αY , are proportional to each other, variations in the cost of debt are a function of the debt-EBIT ratio, an accounting measure very frequently used in debt covenants. This formulation makes the issuance costs of new debt counter-cyclical, meaning that an increase in debt is more costly in downturns, when output is low, and cheaper in good economic times. Repaying debt, on the other hand, is less costly in bad times, when output is low. This friction generates an incentive for pro-cyclical debt issuance, consistent with the empirical findings of Jermann and Quadrini (2012) on aggregate debt payouts.

In each period, the objective of the firm is to maximize equityholders' wealth cum dividend ( Vt=Pt+Dt ) by optimally choosing physical investment, It , hours worked, Ht , and corporate debt, Bt :  

(8)
$$\begin{align} {V_t} & = \mathop {\max }\limits_{\{ {D_j},{I_j},{H_j},{K_j},{B_j}\} _{j = t}^\infty } {E_t}\left[ {\sum\limits_{j = t}^\infty {{M_{j\backslash t}}{D_j}} } \right] \\ & s.t. \\ {D_t} & \le {Y_t} - {W_t}{H_t} - {T_t} - {I_t} + {B_t} - (1 + {r_{f,t - 1}}){B_{t - 1}} - C_t^B - C_t^E, \\ {K_t} & \le (1 - \delta ){K_{t - 1}} + \phi \left( {\frac{{{I_t}}}{{{K_{t - 1}}}}} \right){K_{t - 1}}. \\ \end{align}$$

In the system of equations (8), Mj|t=Mt+1·...·Mt+j is the $$j$$-step stochastic discount factor, which is taken as given by the firm. If Dt<0 , then the firm is a net equity issuer at time $$t$$. Total corporate taxes are denoted by Tt . Taxes are proportional to corporate profits and embody a shield on corporate interest payments, as detailed in Section 1.1, Equation (2). We assume that the firm takes into account all tax margins implied by the tax code and knows the stochastic evolution of τt determined by the fiscal policies that we study in the next sections. The firm takes as given the evolution of productivity detailed in Equation (4).

1.3.3 Optimal investment and financing decisions.

The optimal investment policy must satisfy the following Euler equation:  

(9)
$$\begin{align} {q_t} = {E_t}& \left[ {{M_{t + 1}}\left\{ {(1 - {\tau _{t + 1}})\frac{{\partial {Y_{t + 1}}}}{{\partial {K_t}}} - \frac{{\partial C_{t + 1}^B}}{{\partial {K_t}}}} \right.} \right. \\ & \quad \left. { + {q_{t + 1}}\left. {\left( {1 - \delta - \frac{{{{\phi '}_{t + 1}}{I_{t + 1}}}}{{{K_t}}} + {\phi _{t + 1}}} \right)} \right\}} \right] - \frac{{\partial C_t^E}}{{\partial {K_t}}}, \\ \end{align}$$
where qt1Φt and Φ denotes the first derivative of the investment adjustment cost function $${\Phi }$$. Equation (10) differs from the optimality condition of Jermann's (1998) in three respects. First, the firm cares about the after-tax marginal product of capital and is exposed to tax rate uncertainty. Second, the term $$ - \frac{{\partial C_t^E}}{{\partial {K_t}}}$$ reflects the reduction in the distress costs, which is generated through additional capital. Third, the term $$ - \frac{{\partial C_{t + 1}^B}}{{\partial {K_t}}}$$ reflects the fact that each additional unit of capital also affects future borrowing costs by increasing output.

Turning our attention to capital structure, the following holds:  

(10)
$$\frac{{\partial C_t^B}}{{\partial {B_t}}} + \frac{{\partial C_t^E}}{{\partial {B_t}}} = {E_t}\left[ {{M_{t + 1}}{\tau _{t + 1}}} \right]{r_{f,t}}.$$

The left-hand side of this equation is related to marginal distress and debt adjustment costs (i.e., the marginal cost of debt). The right-hand side refers to the value of the tax advantage obtained with an extra unit of debt (the marginal benefit of debt). Further details of the firm's optimization are reported in Appendix B.

1.3.4 Market clearing.

Since we assume that all taxes are rebated lump-sum to the household, the market-clearing condition in the goods market is simply  

(11)
$${Y_t} = {C_t} + {I_t} - C_t^E - C_t^B.$$

Under our benchmark calibration, equilibrium financial costs are small:  

$$E\left[ {\frac{{C_t^E + C_t^B}}{{{Y_t}}}} \right] \lt 0.17\% ,$$
and therefore CE and CB will play no direct relevant role in the determination of output composition.

2. Exogenous Tax Uncertainty

We begin the quantitative analysis of our model by focusing on the special case in which the government is committed to a zero-deficit policy. Since we always initialize the economy with zero public debt, B0G=0 , Equation (3) implies that a zero-deficit policy requires the following:  

(12)
$${\tau _t} = \tau _t^*\quad \forall t.$$
For the purposes of this section, therefore, the corporate tax rate is a purely exogenous stochastic process. This case functions as a useful benchmark highlighting the basic features of our model. More realistic scenarios with time-varying public debt are addressed in Section 3.

2.1 Calibration

In order to disentangle the different mechanisms at work in our economy, we focus on the results of three different model specifications reported in Table 1. Model 1 is our benchmark. It features both short- and long-run productivity risk through the tax channel ( Φτ<0 ). In Model 2, we maintain stochastic tax fluctuations, but we shut down the growth channel by imposing the condition Φτ=0 . A comparison of Models 1 and 2 allows us to quantify the relevance of tax uncertainty when taxes affect the average drift of equity payouts.

Table 1

Calibrated parameter values

Model  
 Key Elements    
Tax Uncertianty  Yes Yes No 
Growth Channel  Yes No No 
 Zero-Deficit Tax Rate $$({\tau }^{*}_{t})$$    
Constant 11+eμτ 36.5% 36.5% 36.5% 
Volatility $${\sigma }_{{\tau }}$$ 1.19% 1.19% 
Long-run Risk Exposure $${\phi }_{{\tau }}$$ −.05 
Autocorrelation $${\rho }^{4}$$ 0.980 0.980 – 

 
Common Parameters     

 
 Preferences    
Discount Factor $${\beta }^{4}$$ 0.983   
Risk Aversion $${\gamma }$$ 10   
Intertemporal Elasticity of Substitution $${\psi }$$ 2.0   
 Technology    
Capital Share $${\alpha }$$ 0.33   
Depreciation Rate $${\delta }$$ 0.021   
Elasticity of Investment Adj. Costs $${\xi }$$   
Intensity of Debt Adj. Costs $${\nu }$$ .4   
Debt-Book Ratio $${\eta }$$ 33%   
Intensity of Distress Costs $${\phi }_{1}$$ 2000   
 Productivity    
Average Productivity Growth $${\mu }$$ .006   
Short-run Productivity Volatility $${\sigma }$$ 2.64%   
Model  
 Key Elements    
Tax Uncertianty  Yes Yes No 
Growth Channel  Yes No No 
 Zero-Deficit Tax Rate $$({\tau }^{*}_{t})$$    
Constant 11+eμτ 36.5% 36.5% 36.5% 
Volatility $${\sigma }_{{\tau }}$$ 1.19% 1.19% 
Long-run Risk Exposure $${\phi }_{{\tau }}$$ −.05 
Autocorrelation $${\rho }^{4}$$ 0.980 0.980 – 

 
Common Parameters     

 
 Preferences    
Discount Factor $${\beta }^{4}$$ 0.983   
Risk Aversion $${\gamma }$$ 10   
Intertemporal Elasticity of Substitution $${\psi }$$ 2.0   
 Technology    
Capital Share $${\alpha }$$ 0.33   
Depreciation Rate $${\delta }$$ 0.021   
Elasticity of Investment Adj. Costs $${\xi }$$   
Intensity of Debt Adj. Costs $${\nu }$$ .4   
Debt-Book Ratio $${\eta }$$ 33%   
Intensity of Distress Costs $${\phi }_{1}$$ 2000   
 Productivity    
Average Productivity Growth $${\mu }$$ .006   
Short-run Productivity Volatility $${\sigma }$$ 2.64%   

Notes: This table reports the parameter values used for our quarterly calibrations. The parameters in the top panel of the table refer to the process that determines taxation needs, $${\tau }_{t}^{*}$$, defined in Equation (1). The parameters in the bottom panel of the table are common to all model specifications considered in the article.

In Model 3, we eliminate tax uncertainty ( στ=0 ) in order to study the implications of a constant corporate tax rate. In this model, therefore, both quantity and price dynamics are purely driven by i.i.d. Gaussian shocks to productivity.

The parameters of the zero-deficit tax rate, τ* , are set to mimic U.S. data on average corporate taxation, measured as in McGrattan and Prescott (2005). For more details, see Appendix A. We believe that average taxation is a better measure of corporate tax pressure than the stated marginal tax rate, as it captures multiple margins. Inflation, accelerated depreciation changes, unexpected variations in the tax shield on investment, and R&D expenditures all are important sources of variation in the effective real corporate tax rate, as pointed out in Backus et al. (2008). Modeling the average corporate tax rate as an AR(1) process is a parsimonious way to include all these margins in our asset pricing model. Our AR(1) process for taxes can alternatively be seen as a continuous version of a persistent Markov process with “high” and “low” marginal taxation regimes. Using a Gaussian AR(1) process is particularly advantageous because it allows us to solve our model using very standard approximation methods. The annual volatility of the average corporate tax rate (measured starting from 1948) is 6.3%. To be as conservative as possible, we target a much lower level of zero-deficit tax-rate volatility, specifically, about 2.1% (i.e., one-third of that in the data), and we also make sure that under the active tax smoothing policy, this volatility does not exceed 3.2% (i.e., half of tax rate volatility measured in the data).

In order to calibrate the exposure of productivity to long-run tax rate uncertainty, Φτ , we estimate Equation (4) using U.S. annual data for the post–World War II sample. All details are reported in Section 1. We obtain a point estimate Φ^τ=0.058 with a Newey-West adjusted standard error of 0.026. Our estimate is significant at a 4% confidence level and is consistent with Lee and Gordon (2005). Specifically, using panel data from a multi-country data set, Lee and Gordon (2005) obtain an estimate of –0.05. Just to be conservative, we set Φτ=0.05 so that our results can be interpreted as a lower bound on the relevance of fiscal risk.

The preference and technology parameters are common across all specifications and are chosen in the spirit of the long-run risk and real business cycle literatures (e.g., Kydland and Prescott 1982; Bansal and Yaron 2004). The investment adjustment cost elasticity, $${\xi }$$, is set to a moderate level to avoid implausibly high adjustment costs. On average, these costs are in the order of .15% of GDP. The leverage level, $${\eta }$$, is consistent with U.S. data, while the intensity of the debt adjustment costs, $${\nu }$$, is set to match the volatility of investment. We describe our solution method in Section 2.

2.2 Taxation, financing, and investment

We begin our analysis by highlighting the basic implications of distortionary taxation for corporate financing and investment in our economy. Since the main intuition underlying these implications for corporate financing and investment can be explained even with a constant tax rate, in this subsection we focus only on Model 3. We compare it to other model specifications that more closely resemble standard production-based asset pricing models by removing debt adjustment costs ( ν=0 ) and financial leverage ( η=0 ). We consider the more general case with stochastic fluctuations in tax rates in the next subsection.

Figure 1 shows the impulse responses generated by Model 3, the model without debt adjustment costs, and the model without financial leverage (the RBC model), respectively. The RBC model with recursive preferences presents all the major problems already documented in the literature, namely, low volatility of the equity risk premium, smooth investment, and volatile consumption. By comparing the RBC model to the model with financial leverage and no debt adjustment costs, we see that financial leverage alone produces slightly more volatile excess returns, but it does not significantly alter the quantity dynamics. Quantitatively, therefore, the RBC model with leverage is close to a model in which the Modigliani and Miller (1958) assumptions hold. This result is due to the ability of the firm to costlessly substitute debt for equity. Essentially, in this specification, the preferential tax treatment of debt acts as a pure subsidy to debtholders.

Figure 1

Financial frictions and investment in Model 3

Notes: This figure shows quarterly log-deviations from the steady-state multiplied by 100. In each panel, the line marked with circles refers to Model 3, the solid line refers to the RBC model (Model 3 with ν=η=0 ), and the dashed line refers to Model 3 without debt adjustment costs ( ν=0 ). All the parameters are calibrated to the values reported in Table 1. We denote leverage as Lev. We use $$q$$ for the marginal value of capital; rex for the equity excess returns; $$m$$ for the pricing kernel; and Δi , Δc , and Δz for the growth rate of investment, consumption, and productivity, respectively.1

Figure 1

Financial frictions and investment in Model 3

Notes: This figure shows quarterly log-deviations from the steady-state multiplied by 100. In each panel, the line marked with circles refers to Model 3, the solid line refers to the RBC model (Model 3 with ν=η=0 ), and the dashed line refers to Model 3 without debt adjustment costs ( ν=0 ). All the parameters are calibrated to the values reported in Table 1. We denote leverage as Lev. We use $$q$$ for the marginal value of capital; rex for the equity excess returns; $$m$$ for the pricing kernel; and Δi , Δc , and Δz for the growth rate of investment, consumption, and productivity, respectively.1

The results change significantly after the introduction of counter-cyclical debt adjustment costs in Model 3. These costs eliminate the costless substitution between debt and equity and allow financing to have real effects. In good times, issuing more debt is cheaper and hence attractive. To avoid severe distress costs, all resources collected through the additional debt are used to increase the collateral stock, $$K$$, through investment, $$I$$. It is well known that when the IES is high enough, even small capital adjustment costs are enough to discourage investment volatility. For the same reason, in our economy even a moderate amount of counter-cyclical debt adjustment cost is sufficient to generate an incentive to significantly adjust debt and ultimately investment. Thanks to both distress and debt adjustment costs, the response of investment to exogenous productivity shocks is much more intense than in the RBC model with recursive preferences.

Our mix of financial and real frictions, therefore, alleviates a long-standing problem of RBC models with recursive utility and IES greater than one, by simultaneously producing more realistic dynamics for investment, equity payouts, and returns. As can be seen in Table 2, the volatility of investment is seven times greater than the consumption volatility in Model 3, consistent with the data. The high volatility of investment allows both equity payouts and the price of capital to be volatile and pushes the annualized volatility of equity excess returns to almost 10%. Although neither equity payouts nor excess returns are as volatile as in the data, we regard our results as very encouraging since, to the best of our knowledge, only Gomes et al. (2009b) and Kuehn et al. (2011) obtain similar results in economies with recursive preferences and fixed capital stock. Ultimately, our model generates an equity premium of 4.24% and an implied equity Sharpe ratio reasonably close to its empirical counterpart.

Table 2

Summary statistics

 Data Model 1 Model 2 Model 3 
First moments     
$$E[I/Y]$$ 0.23 0.21 0.21 0.21 
$$E[r_{f}]$$(%) 0.86 0.82 1.96 1.95 
$$E[r_{d} -- r_{f}]$$(%) 5.70 5.04 4.28 4.24 

 
Second moments     

 
$${\sigma }({\tau })(%)$$ 6.21 2.31 2.30 0.00 
$${\sigma }({\Delta }i)/{\sigma }({\Delta }c)$$ 6.95 6.70 6.97 7.07 
$${\sigma }_{{\Delta }c}(%)$$ 2.31 2.05 1.99 1.95 
$$ACF_{1}({\Delta }c)$$ 0.44 0.18 0.19 0.19 
σrdrf (%) 20.14 9.67 9.70 9.64 
$${\sigma }_{Lev}(%)$$ 8.65 2.65 2.65 2.57 
$${\sigma }\text {(NEPO/Profits) (%)}$$ 63.50 28.25 31.15 28.97 
σrf (%) 1.35 0.22 0.22 0.21 
 Data Model 1 Model 2 Model 3 
First moments     
$$E[I/Y]$$ 0.23 0.21 0.21 0.21 
$$E[r_{f}]$$(%) 0.86 0.82 1.96 1.95 
$$E[r_{d} -- r_{f}]$$(%) 5.70 5.04 4.28 4.24 

 
Second moments     

 
$${\sigma }({\tau })(%)$$ 6.21 2.31 2.30 0.00 
$${\sigma }({\Delta }i)/{\sigma }({\Delta }c)$$ 6.95 6.70 6.97 7.07 
$${\sigma }_{{\Delta }c}(%)$$ 2.31 2.05 1.99 1.95 
$$ACF_{1}({\Delta }c)$$ 0.44 0.18 0.19 0.19 
σrdrf (%) 20.14 9.67 9.70 9.64 
$${\sigma }_{Lev}(%)$$ 8.65 2.65 2.65 2.57 
$${\sigma }\text {(NEPO/Profits) (%)}$$ 63.50 28.25 31.15 28.97 
σrf (%) 1.35 0.22 0.22 0.21 

Notes: All models are calibrated as in Table 1 at a quarterly frequency. All entries for the models are obtained from 1,000 repetitions of short-sample simulations (320 periods, equivalent to 80 years). All figures are annualized. Our sample period is 1930 to 2008. Output is measured as $$Y = C + I$$. NEPO stands for net equity payout. Details about our data are reported in Appendix A.

Furthermore, under our debt adjustment cost function, the time-series properties of consumption growth are consistent with the data. Our results, therefore, are not driven by implausible consumption dynamics.

Finally, as seen in the bottom panel of Figure 1, we show that after a positive productivity shock, the value of equity increases more than the value of corporate debt, making corporate leverage counter-cyclical, consistent with that documented among others by Korajczyk and Levy (2003) and Covas and Den Haan (2011).

2.3 The role of corporate tax uncertainty

In this section, we turn our attention to the role of tax uncertainty. In Figure 2, we plot impulse response functions for Models 1 and 2. Because the corporate tax rate is stochastic, the figure shows two columns of plots. The plots on the right focus on an adverse tax shock, while those on the left refer to a negative short-run productivity shock, the opposite case from that shown in Figure 1.2 In Models 1 and 2, the response to short-run productivity shocks is the mirror image of that seen in Figure 1 for Model 3. The responses to a tax shock merit special attention, as they raise several noteworthy points.

Figure 2

Prices and quantities in Models 1 and 2

Notes: This figure shows quarterly log deviations from the steady-state multiplied by 100. In each panel, the solid (dashed) line refers to Model 1 (Model 2). The panels in the left column show responses to a negative short-run productivity shock. The plots to the right refer to a negative tax shock. Parameters values are reported in Table 1. Variables are the same as those described in Figure 1.2

Figure 2

Prices and quantities in Models 1 and 2

Notes: This figure shows quarterly log deviations from the steady-state multiplied by 100. In each panel, the solid (dashed) line refers to Model 1 (Model 2). The panels in the left column show responses to a negative short-run productivity shock. The plots to the right refer to a negative tax shock. Parameters values are reported in Table 1. Variables are the same as those described in Figure 1.2

2.3.1 Response of investment.

Although small, tax shocks are very persistent, and for this reason they have significant effects on both quantities and prices.3 On the one hand, a negative tax shock produces an incentive to invest less as after-tax profits persistently decrease (substitution effect). This effect is amplified when higher taxes depress productivity growth over the long horizon (Model 1). On the other hand, an increase in the tax rate causes the household to feel poorer and generates an incentive to decrease consumption (income effect). As in Croce (2006), when the intertemporal elasticity of substitution is calibrated above one, the substitution effect dominates. This implies that the representative investor finds it beneficial to invest less when the corporate tax rate increases, consistent with the empirical evidence in Leeper et al. (2010). In our model, therefore, when the tax rate rises, the demand of capital decreases, causing a strong decline in the price of capital. As shown in the bottom three panels of Figure 2 (right column), small adverse tax shocks produce significant negative adjustments in price of capital, excess returns, and capital structure.

2.3.2 Response of the pricing kernel when Φτ=0 .

Turning our attention to Table 2, we can see that Models 2 and 3 generate very similar average equity premia. As shown in the fourth panel of Figure 2, right column, this is because tax shocks do not generate significant adjustments in the log stochastic discount factor, $$m$$. A persistent increase in the tax rate produces bad news for long-run consumption and hence an increase in marginal utility. However, by the substitution effect, short-run consumption increases and the marginal utility tends to decrease. At the equilibrium, the final adjustment of the pricing kernel is negligible. When the growth channel is ignored ( Φτ=0 ), therefore, tax shocks produce sizeable endogenous long-run fluctuations in dividend growth—reflected in the persistent dynamics of the value of capital, $$q$$—that at the equilibrium effectively carry a zero risk-premium.

2.3.3 Response of the pricing kernel when Φτ<0 .

When adverse tax shocks have a negative impact on long-run productivity growth ( Φτ<0 ), they introduce a significant and persistent decline in expected consumption growth. With Epstein and Zin (1989) utility, our household is very averse to such expected consumption adjustments, as reflected by the significant move of the stochastic discount factor. This explains why in Model 1 an adverse tax shock (bad news for long-run productivity) produces such a strong increase in the marginal utility of the representative investor and a greater decline in the equity excess return (Figure 2, fourth and fifth panels, right column).

The equity premium generated by Model 1 is 5.04%, about 0.8% higher than in Model 2 (see Table 2). The risk-free rate, in contrast, is about 1% lower because of the additional precautionary saving motives generated by tax uncertainty. This variation in the composition of the equity returns shows that tax uncertainty can substantially increase risk premia and alter capital accumulation decisions. In our economy, therefore, small news about future taxes and productivity can have large and persistent effects on quantities and prices.

Figure 3 reports the effect of a permanent change in the average level of corporate taxation, μτ , on the cost of equity.4 Across all models considered so far, corporate taxation substantially depresses capital accumulation (top left panel) and investment (top right panel). Because of decreasing marginal returns to capital, this implies an increase in the average return on capital. In Model 3, where the tax rate is constant and known with certainty, the increase in the capital return appears as an increase in the cost of equity (bottom right panel), while the pretax cost of debt remains the same (bottom left panel). Average corporate taxation alone, therefore, strongly affects the cost of equity, consistent with the findings of Gomes et al. (2009a) in the context of a model with heterogeneous agents and incomplete markets.

Figure 3

Average taxation, investment, and cost of capital

Notes: The top two panels show the capital-productivity ratios (left panel) and investment-output ratios for different levels of average taxation in Models 1–3. The plots in the middle row show the volatility of the log stochastic discount factor (left panel) and the value of the firm (right panel). The bottom panels focus on pretax cost of debt (left) and the equity premium. All parameters are calibrated as in Table 1, except for μτ , which is allowed to vary.3

Figure 3

Average taxation, investment, and cost of capital

Notes: The top two panels show the capital-productivity ratios (left panel) and investment-output ratios for different levels of average taxation in Models 1–3. The plots in the middle row show the volatility of the log stochastic discount factor (left panel) and the value of the firm (right panel). The bottom panels focus on pretax cost of debt (left) and the equity premium. All parameters are calibrated as in Table 1, except for μτ , which is allowed to vary.3

Comparing Models 1 and 3 (bottom two panels, Figure 3), we see that when the growth channel is active, tax uncertainty plays an important role in the determination of the subcomponents of the cost of capital. In particular, the link between average tax rate and equity premium changes in at least two significant dimensions.

First, we observe that tax-driven productivity uncertainty can add 20–200 basis points to the cost of equity. This jump in the equity premium is explained by the simultaneous increase in the volatility of the stochastic discount factor (middle row, left panel) and the cum-dividend value of the firm (middle row, right panel) caused by long-run productivity risk. The additional long-run growth risk related to tax dynamics basically shifts the demand of assets toward riskless bonds, causing the cost of debt (bottom left panel) to decline and the cost of equity to increase for every possible μτ .

Second, when long-horizon productivity is affected by tax uncertainty, even a small increase in the average taxation level can produce a substantial run-up in the cost of equity. This is because as the average tax rate increases, the optimal level of accumulated capital falls, in turn reducing average investment and therefore the ability to hedge exogenous shocks. In an economy in which taxes generate long-run uncertainty, such a reduction in the consumption smoothing possibilities strongly penalizes equity value.

These results suggest that tax uncertainty should be a first-order concern in the current fiscal policy context, as uncertainty can actually amplify the effect of average tax pressure. To further highlight this point, in the left panel of Figure 4 we show the equity premium in Models 1 and 2 when the average taxation level is fixed at its benchmark level of 36.5% and tax volatility, στ , is allowed to vary. When the volatility of the tax rate is low, the equity premia produced by both Models 1 and 2 converges to 4.28%, the level obtained in Model 3 with a constant tax rate. When taxes do not directly affect long-run productivity growth (Model 2), tax rate volatility alters the cost of equity only marginally. However, when taxes affect growth (Model 1), even a marginal increase in the volatility of the tax rate can produce a substantial rise in the cost of equity. In the right panel of Figure 4, we let the persistence of the tax rate, $${\rho }$$, vary while fixing all other parameters. This graph shows that as long as $${\rho }$$ is sufficiently high, our small but persistent tax-based growth risk factor produces relevant effects on the cost of capital.

Figure 4

Cost of equity and tax rate volatility and persistence

Notes: This figure shows the annualized equity premia produced by Models 1 and 2 as a function of the tax rate volatility. All parameters are calibrated as in Table 1, except for στ , which is allowed to vary in the left panel, and for $${\rho }$$, which is allowed to vary in the right panel.4

Figure 4

Cost of equity and tax rate volatility and persistence

Notes: This figure shows the annualized equity premia produced by Models 1 and 2 as a function of the tax rate volatility. All parameters are calibrated as in Table 1, except for στ , which is allowed to vary in the left panel, and for $${\rho }$$, which is allowed to vary in the right panel.4

3. Public Debt And Endogenous Tax Uncertainty

In the previous section, we focused on a tax process, $${\tau }$$, that perfectly mimics the properties of an exogenously specified expenditure process, τ* . In this section, we now let the tax rate differ from τ* by allowing the government to accumulate public debt and thus reallocate taxation over time. We can therefore examine to what extent such tax-smoothing reduces or amplifies the cost of equity.

As shown in Leeper et al. (2010), there are several ways to specify tax-smoothing behavior. One of the main technical problems with using an exogenous tax smoothing rule is the need to guarantee stationarity of the debt-output ratio in order to rule out “unsustainable” public debt paths. One possible way to solve this problem is to define the public financing rule directly:  

(13)
$$\frac{{B_t^G}}{{{Y_t}}} = {\rho _G}\frac{{B_{t - 1}^G}}{{{Y_{t - 1}}}} + {\phi _G} \cdot \epsilon _t^G,$$
where εtG is a stationary variable summarizing the state of the economy and ρG(0,1) is a measure of the speed of repayment of debt; i.e., the higher the value of ρG , the slower the repayment of debt relative to output. The fact that ρG<1 guarantees stability of the debt-output ratio.5 It is possible to show that there is a positive monotonic mapping between ρG and the persistence of the tax rate process determined by Equations (1)–(2) and (13). Choosing a higher ρG is equivalent to increasing the degree of tax smoothing.

The parameter ΦG>0 measures the intensity of the government's fiscal response to changes in the state of the economy, εtG . In our analysis, we consider two different specifications for εtG . We first focus on the case in which the government responds to short-run consumption growth:  

(14)
$$\epsilon_t^G \equiv \Delta {c_t} - \mu .$$

This policy rule captures the behavior of a government that reduces current corporate taxes every time the economy is affected by a positive shock to consumption growth. By decreasing corporate taxes, the government attempts to stimulate a reallocation of resources toward investment in order to smooth consumption growth and keep it close to its unconditional average, $${\mu }$$.6

In a second step, we highlight the relevance of tax policies aimed to stabilize the long-run dynamics of consumption:  

(15)
$$\epsilon_t^G \equiv \mu - {E_t}\left[ {\Delta {c_{t + 1}}} \right].$$

The properties of the corporate tax rate, therefore, are now endogenously pinned down by our public debt policy. In what follows, we first show that a tax-smoothing policy aimed at stabilizing short-run consumption growth can produce substantial welfare costs. We then show that a tax-smoothing policy stabilizing long-run consumption dynamics can generate, in contrast, significant welfare benefits. The main goal of this section is to illustrate that in a model with recursive preferences built to replicate several asset price features, welfare-enhancing tax smoothing is quite different from that normally obtained in the macroeconomic-RBC literature.

3.1 Short-run consumption growth tax smoothing

Equations (13) and (14) jointly imply the following debt policy:  

$$\frac{{B_t^G}}{{{Y_t}}} = {\rho _G}\frac{{B_{t - 1}^G}}{{{Y_{t - 1}}}} + {\phi _G} \cdot (\Delta {c_t} - \mu ).$$

To explain what this public financing policy does, in Figure 5 we show the response of tax rate, consumption, and investment growth after an adverse shock to productivity (top panels) and to expenditure (bottom panels). The intensity of the active policy, ΦG , is set to 0.3 to ensure that the implied annualized volatility of the tax rate does not exceed 3.1%, i.e., half of the observed standard deviation of the average corporate tax rate. We set the parameter ρG initially to 0.98 to replicate the persistence of the public debt-output ratio observed in the U.S. data (see Appendix A); we then allow this parameter to vary in order to alter the persistence of the corporate tax rate. All other parameters are calibrated as in Model 1. We let ΔcZD and ΔiZD denote consumption and investment growth, respectively, under the zero-deficit policy adopted for Model 1 in the previous section.

Figure 5

Short-run tax smoothing at work

Notes: This figure shows corporate tax rate, consumption, and investment growth responses to an adverse shock to productivity (top panels) and to government expenditure (bottom panels). In each panel, the solid line refers to Model 1 under the zero-deficit policy obtained by setting ΦG=0 in Equation (13). The dashed line refers to the model with active tax smoothing aimed to stabilize short-run consumption growth, as determined by Equations (13) and (14). In this case, we set ΦG=0.3 in Equation (13) and let all other parameters be calibrated as in Model 1 (see Table 1). We let ΔcZD and ΔiZD denote consumption and investment growth, respectively, under the zero-deficit policy adopted for Model 1.5

Figure 5

Short-run tax smoothing at work

Notes: This figure shows corporate tax rate, consumption, and investment growth responses to an adverse shock to productivity (top panels) and to government expenditure (bottom panels). In each panel, the solid line refers to Model 1 under the zero-deficit policy obtained by setting ΦG=0 in Equation (13). The dashed line refers to the model with active tax smoothing aimed to stabilize short-run consumption growth, as determined by Equations (13) and (14). In this case, we set ΦG=0.3 in Equation (13) and let all other parameters be calibrated as in Model 1 (see Table 1). We let ΔcZD and ΔiZD denote consumption and investment growth, respectively, under the zero-deficit policy adopted for Model 1.5

3.1.1 Adverse productivity shock.

Under the zero-deficit policy, an adverse productivity shock produces a decline in consumption growth (top middle panel of Figure 5) both on impact (time 1) and in subsequent periods, leaving the tax rate constant. Thus, in the top left panel of Figure 5, the solid line is flat. Under the active short-run tax-smoothing policy, however, the government actually increases the corporate tax rate to discourage the demand for new capital (top right panel of Figure 5) and to allow more resources to be allocated toward private consumption. The top middle panel of Figure 5 shows that the government is indeed able to mitigate the immediate drop in consumption growth (at time 1, ΔctΔctZD>0 ), but at the cost of actually depressing further long-run consumption growth or, equivalently, the recovery speed. This long-run effect occurs because the short-run stabilization of consumption is obtained through a more severe decline in investment and, ultimately, a slower process of capital accumulation. Thus, this policy reduces short-run volatility of consumption, i.e., StD t(Δct+1) , at the cost of amplifying long-run volatility, i.e., StD( Et[Δct+1] ).

3.1.2 Adverse fiscal shock.

The bottom left panel of Figure 5 compares the dynamic behavior of the tax rate under the active policy against the tax rate required to perfectly balance the public budget. Under our specification, at time 1 the government increases the tax rate less than required to fully finance current expenditure, consistent with tax-smoothing behavior. This comes at the cost, however, of having to increase taxation further later on to pay back the accumulated debt. Given the moderate size of our fiscal shocks, these tax fluctuations are actually small and produce less severe adjustments in the dynamics of consumption and investment. Nevertheless, after the moderate increase in taxes prescribed by the smoothing policy, private investment increases less than it would under the zero-deficit policy. Although this might appear counterintuitive at first, note that such tax smoothing comes at the cost of persistent increases in future taxation and reductions in future growth over the long horizon. At equilibrium, the representative firm actually has less incentive to invest and accumulate capital. With respect to expenditure shocks, therefore, the active financing policy is not capable of smoothing investment and consumption volatility over the long run.

3.1.3 Implications for cost of equity and welfare.

In the middle row panels of Figure 6, we report key moments of the distribution of consumption under the zero-deficit and the active policy considered so far, for different values of speed of debt repayment, ρG . In the spirit of the long-run risk literature, we report short-run volatility of consumption growth, $$StD_{t}$$(Δct+1) ; the persistence of the conditional mean of consumption growth, ACF1(Et[Δct+1]) ; and the volatility of the long-run component in consumption, StD (Et[Δct+1]) .7 The solid line is flat in all panels because in our zero-deficit economy there is no debt and therefore the speed of repayment does not matter. The dashed line shows the effects of our fiscal policy parameters {ρG,ΦG} on the endogenous distribution of consumption.

Figure 6

The costs of short-run tax smoothing

Notes: In each panel, the solid line refers to Model 1 under the zero-deficit policy obtained by setting ΦG=0 in Equation (13). The dashed line refers to the model with active tax smoothing aimed to stabilize short-run consumption growth, as determined by Equations (13) and (14). In this latter case, we set ΦG=0.3 in Equation (13) and calibrate all other parameters as in Model 1 (see Table 1). All moments are obtained through quarterly simulations and are annualized. 6

Figure 6

The costs of short-run tax smoothing

Notes: In each panel, the solid line refers to Model 1 under the zero-deficit policy obtained by setting ΦG=0 in Equation (13). The dashed line refers to the model with active tax smoothing aimed to stabilize short-run consumption growth, as determined by Equations (13) and (14). In this latter case, we set ΦG=0.3 in Equation (13) and calibrate all other parameters as in Model 1 (see Table 1). All moments are obtained through quarterly simulations and are annualized. 6

As anticipated by the analysis of the impulse response functions of the model, a tax-smoothing policy aimed to stabilize short-run consumption volatility amplifies both the consumption volatility in the long run (middle right panel), and the investment volatility at all horizons (bottom row of plots). This effect is intensified by higher levels of debt persistence, implying that a government prone to repay debt at a very slow pace ends up stabilizing short-run consumption variations only by making them more and more long-lasting (higher ACF1(Et[Δct+1]) ). Our representative consumer, however, dislikes persistent sources of uncertainty and attaches to them a high market price of risk. Consistent with Bansal and Yaron (2004), in our economy the annualized returns of the consumption and equity claims are mainly driven by long-run dynamics. For this reason, their risk premia increase by 40 and 8 basis points, respectively, even though short-run consumption volatility is lower under the active public financing policy.

Using Lucas (1987) computations, we are able to map this change in risk premia into the percentage of lifetime consumption that the agent would be willing to give up to live in an economy without this sort of tax smoothing.8 As shown in the top right panel of Figure 6, short-run tax smoothing can generate substantial welfare costs, on the order of 5%. Furthermore, these costs are increasing in ρG , suggesting that the slow repayment of public debt (or, equivalently, persistent tax adjustments) increases the cost of the fiscal intervention. Since we abstract from relevant sources of potential benefits of government intervention (e.g., productive public investment or reduction of long-run unemployment), our welfare results should not be interpreted as discouraging any sort of public intervention. This analysis simply suggests that common tax-smoothing and debt financing policies can generate long-run swings in productivity and private investment that are quite costly when the agent cares about the timing of resolution of tax uncertainty.9 Since the alteration of consumption uncertainty introduced by tax smoothing can be sizeable, it should be explicitly considered in fiscal policy design. In the next section, we show that a tax-smoothing scheme aimed at stabilizing long-run consumption growth, Et[Δct+1] , instead of short-run consumption growth, Δct+1 , can actually significantly enhance welfare.

3.2 Long-run consumption growth tax smoothing

3.2.1 Altering taxes to smooth Et[Δct+1] .

In this section, we focus on a financing policy of government expenditure aimed at stabilizing long-horizon consumption dynamics measured by Et[Δct+1] :  

$$\frac{{B_t^G}}{{{Y_t}}} = {\rho _G}\frac{{B_{t - 1}^G}}{{{Y_{t - 1}}}} + {\phi _G} \cdot (\mu - {E_t}[\Delta {c_t} - \mu ]).$$

Under this fiscal rule, the government increases public debt whenever expected consumption growth is below its unconditional average. The implied tax rate dynamics are depicted in Figure 7. When an adverse productivity shock materializes, expected consumption growth drops below steady-state and the government reduces taxes to stimulate investment. While this stimulus allows consumption growth to fall even further in the first period than under the zero-deficit policy, the implied faster accumulation of capital actually improves the recovery speed of consumption over the subsequent periods. This policy, therefore, is effective in reducing long-run consumption growth risk by stabilizing investment growth and capital accumulation after productivity shocks.

Figure 7

Long-run tax smoothing at work

Notes: This figure shows corporate tax rate, consumption, and investment growth response to an adverse shock to productivity (top panels) and to government expenditure (bottom panels). In each panel, the solid line refers to Model 1 under the zero-deficit policy obtained by setting ΦG=0 in Equation (13). The dashed line refers to the model with active tax smoothing aimed to stabilize long-run consumption growth, as determined by Equations (13) and (15). In this latter case, we set ΦG=0.3 in Equation (13) and calibrate all the other parameters as in Model 1 (see Table 1). We let ΔcZD and ΔiZD denote consumption and investment growth, respectively, under the zero-deficit policy adopted for Model 1.7

Figure 7

Long-run tax smoothing at work

Notes: This figure shows corporate tax rate, consumption, and investment growth response to an adverse shock to productivity (top panels) and to government expenditure (bottom panels). In each panel, the solid line refers to Model 1 under the zero-deficit policy obtained by setting ΦG=0 in Equation (13). The dashed line refers to the model with active tax smoothing aimed to stabilize long-run consumption growth, as determined by Equations (13) and (15). In this latter case, we set ΦG=0.3 in Equation (13) and calibrate all the other parameters as in Model 1 (see Table 1). We let ΔcZD and ΔiZD denote consumption and investment growth, respectively, under the zero-deficit policy adopted for Model 1.7

When an adverse expenditure shock materializes, the government smooths taxes in the first period, but with a much lesser intensity than that seen in the previous section. This strategy allows the government to keep the corporate tax rate below the zero-deficit level over a much longer horizon. By doing so, the government mitigates the long-run negative effects of corporate taxation on productivity growth and stimulates investment and capital accumulation (bottom right panel of Figure 7). Thus, in this case also, this policy promotes fast long-run capital accumulation exactly when needed the most.

3.2.2 Welfare benefits.

As documented in the bottom row of plots depicted in Figure 8, this policy is able to stabilize investment growth, and therefore capital accumulation, in both the short and long run. Although this financing scheme increases short-run consumption volatility, it also results in a strong stabilization of long-run consumption risk. Such stabilization can reduce the cost of equity up to 15 basis points, equivalent to welfare benefits on the order of 2.5%. Note that our previous intuition on the speed of repayment of debt continues to hold: when the government does not repay debt fast enough, it effectively makes the consumption shocks last longer and reduces the welfare benefits. Overall, this simple policy shows that corporate taxation and the way in which it is altered over time can have significant impacts on asset prices and welfare.

Figure 8

The benefits of long-run tax smoothing

Notes: In each panel, the solid line refers to Model 1 under the zero-deficit policy obtained by setting ΦG=0 in Equation (13). The dashed line, instead, refers to the model with active tax smoothing aimed to stabilize long-run consumption growth, as determined by Equations (13) and (15). In this case, we set ΦG=0.3 in Equation (13) and let all other parameters be calibrated as in Model 1 (see Table 1). All moments are obtained through quarterly simulations and are annualized. 8

Figure 8

The benefits of long-run tax smoothing

Notes: In each panel, the solid line refers to Model 1 under the zero-deficit policy obtained by setting ΦG=0 in Equation (13). The dashed line, instead, refers to the model with active tax smoothing aimed to stabilize long-run consumption growth, as determined by Equations (13) and (15). In this case, we set ΦG=0.3 in Equation (13) and let all other parameters be calibrated as in Model 1 (see Table 1). All moments are obtained through quarterly simulations and are annualized. 8

At a broader level, these results show that the current fiscal debate should focus not only on average tax pressure on corporations, but also on the way in which the government intends to vary corporate tax rates over time and across different future states of the world. Equity market participants disliking long-run uncertainty would benefit from corporate tax policies able to stabilize long-run capital accumulation even at the cost of more severe short-run consumption fluctuations.

3.3 Asset prices and welfare

In the previous sections, we have documented tight links between risk-premia and welfare across our fiscal policy specifications. Here, we analyze to which extent our welfare implications change when the information encoded in asset prices is neglected.

The ability of our model to account for basic asset pricing data relies on two main channels: (1) a preference for early resolution of uncertainty in conjunction with tax-induced long-run consumption risk; and (2) tax-driven corporate leverage. In what follows, we show that removing either of these two channels can significantly alter our welfare results on corporate tax smoothing.

3.3.1 Role of preferences.

The top panels of Figure 9 illustrate the role of preferences by describing the welfare costs and benefits that our tax-smoothing policies could produce in an economy with standard time-additive preferences (in the spirit of Sialm 2006). The left panel refers to the policy designed to reduce the volatility of consumption over the long horizon, as stated by Equations (13) and (15). If we assume that our household has no preference for the timing of resolution of uncertainty, this tax-smoothing strategy becomes undesirable with respect to a simple zero-deficit fiscal rule: with time-additive preferences, the agent simply does not care about the implied stabilization of the long-horizon growth of consumption. In this economy, only the higher volatility of short-run consumption growth matters for welfare.

Figure 9

Welfare costs, preferences, and frictions

Notes: This figure shows the welfare costs (benefits) achievable when either the representative household has time-additive CRRA preferences (top panels), or all financial frictions are removed (bottom two panels). Our benchmark is Model 1. For the CRRA case, all parameters are calibrated as in Model 1, except the IES that is set to 0.1, so that γ=1/ψ=10 . In the model with no frictions, we set ν=η=1/ξ=0 . The left panels refer to a tax-smoothing scheme aimed at stabilizing long-run consumption growth, Equations (13) and (15). The right panels refer to the tax-smoothing policy that stabilizes capital accumulation and long-run consumption growth, Equations (13) and (14). The intensity of the tax policy, ΦG , is set to 0.3 in all cases.9

Figure 9

Welfare costs, preferences, and frictions

Notes: This figure shows the welfare costs (benefits) achievable when either the representative household has time-additive CRRA preferences (top panels), or all financial frictions are removed (bottom two panels). Our benchmark is Model 1. For the CRRA case, all parameters are calibrated as in Model 1, except the IES that is set to 0.1, so that γ=1/ψ=10 . In the model with no frictions, we set ν=η=1/ξ=0 . The left panels refer to a tax-smoothing scheme aimed at stabilizing long-run consumption growth, Equations (13) and (15). The right panels refer to the tax-smoothing policy that stabilizes capital accumulation and long-run consumption growth, Equations (13) and (14). The intensity of the tax policy, ΦG , is set to 0.3 in all cases.9

For the same reason, the tax-smoothing policy aimed at stabilizing short-run consumption growth, as stated by Equations (13) and (14), is now able to produce benefits (top right panel, Figure 9). These results suggest that choosing preferences that are inconsistent with asset pricing could completely overturn our fiscal policy assessments.

3.3.2 Role of frictions.

The two bottom panels of Figure 9 illustrate the welfare implications of fiscal policies in economies with and without financial frictions. The model without financial frictions abstracts from any preferential tax treatment of corporate debt so that corporations are optimally unlevered. This specification differs from the RBC one mentioned in Section 2 because we further remove adjustment costs to replicate the volatility of investment and consumption observed in the data. As shown in Table 3, this frictionless model produces quantity dynamics in line with Model 1, but fails on the asset pricing side. Specifically, excess returns are tiny and have minimal volatility.

Table 3

Summary statistics for the model with no frictions

 Data Model 1 Model 2 Model 3 
First moments     
$$E[I/Y]$$ 0.23 0.22 0.21 0.21 
$$E[r_{f}]$$ 0.86 1.78 2.26 2.26 
$$E[r_{d} -- r_{f}]$$ 5.70 0.12 0.08 0.08 

 
Second moments     

 
$${\sigma }_{{\Delta }c}(%)$$ 2.31 2.07 2.12 1.92 
$${\sigma }({\Delta }i)/{\sigma }({\Delta }c)$$ 6.95 6.48 6.05 6.29 
$${\rho }$$$${\Delta }c, {\Delta }i$$ 0.44 0.71 0.64 0.92 
σrf (%) 1.35 0.13 0.13 0.12 
σrdrf (%) 20.14 0.05 0.05 0.05 
ρΔc,rdrf 0.22 0.78 0.71 0.99 
$${\sigma }({\tau })(%)$$ 6.21 2.31 2.31 0.00 
$$ACF_{1}({\Delta }c)$$ 0.44 0.16 0.13 0.16 
 Data Model 1 Model 2 Model 3 
First moments     
$$E[I/Y]$$ 0.23 0.22 0.21 0.21 
$$E[r_{f}]$$ 0.86 1.78 2.26 2.26 
$$E[r_{d} -- r_{f}]$$ 5.70 0.12 0.08 0.08 

 
Second moments     

 
$${\sigma }_{{\Delta }c}(%)$$ 2.31 2.07 2.12 1.92 
$${\sigma }({\Delta }i)/{\sigma }({\Delta }c)$$ 6.95 6.48 6.05 6.29 
$${\rho }$$$${\Delta }c, {\Delta }i$$ 0.44 0.71 0.64 0.92 
σrf (%) 1.35 0.13 0.13 0.12 
σrdrf (%) 20.14 0.05 0.05 0.05 
ρΔc,rdrf 0.22 0.78 0.71 0.99 
$${\sigma }({\tau })(%)$$ 6.21 2.31 2.31 0.00 
$$ACF_{1}({\Delta }c)$$ 0.44 0.16 0.13 0.16 

Notes: All models are calibrated at a quarterly frequency. The parameters are set as in Table 1, except for the following restriction: $${\nu } = {\eta } = 1/{\xi } = 0$$. All entries for the models are obtained from 1,000 repetitions of short-sample simulations (320 periods, equivalent to 80 years). All figures are annualized. Our sample period is 1930 to 2008. Output is measured as $$Y = C + I$$. Details about our data are reported in Appendix A.

The asset pricing implications of this specification are again key to understanding the welfare assessments of fiscal policy objectives. While qualitatively the welfare implications are similar to those obtained in Model 1, quantitatively they differ sharply. The intuition is simple: since the model is not able to produce any relevant amount of risk for unlevered returns, the impact of tax shocks is negligible as well. In our model with financial frictions, instead, levered returns are significantly exposed to aggregate risk and capital accumulation is very sensitive to long-run tax dynamics. Accounting for financial frictions thus allows the model to generate realistic asset price movements that entail more reliable policy assessments.

3.3.3 Asset prices, growth, and fiscal policy design.

Our welfare results can be recast in terms of long-run growth. In Figure 10, we depict cumulative output growth gap between an economy with a zero-deficit policy and one with active tax smoothing. When the cumulative growth gap is positive, the active policy is generating growth benefits with respect to the zero-deficit case. In each panel, we depict the impulse responses generated by Model 1, the model with CRRA preferences, and the model featuring no frictions. This figure shows three important results. First, while all these models produce very similar implications for output growth over the short horizon, over the long run they differ substantially. Second, as in the case of the welfare analysis, the long-run growth implications of Model 1 are overturned when focusing on CRRA preferences. Finally, the milder welfare costs (benefits) obtained in the model without frictions are the result of the milder response of capital accumulation and hence output over the long run.

Figure 10

Cumulative output gains/losses

Notes: This figure shows the response of the cumulative output growth gap between tax-smoothing policies and the zero-deficit policy to adverse productivity (top panels) and expenditure (bottom panels) shocks. Our benchmark is Model 1. For the CRRA case, all parameters are calibrated as in Model 1, except the IES that is set to 0.1, so that γ=1/ψ=10 . In the model with no frictions, we set ν=η=1/ξ=0 . The left panels refer to a tax-smoothing scheme aimed at stabilizing long-run consumption growth, Equations (13) and (15). The right panels refer to the tax-smoothing policy that stabilizes capital accumulation and long-run consumption growth, Equations (13) and (14). The intensity of the tax policy, ΦG , is set to 0.3 in all cases.10

Figure 10

Cumulative output gains/losses

Notes: This figure shows the response of the cumulative output growth gap between tax-smoothing policies and the zero-deficit policy to adverse productivity (top panels) and expenditure (bottom panels) shocks. Our benchmark is Model 1. For the CRRA case, all parameters are calibrated as in Model 1, except the IES that is set to 0.1, so that γ=1/ψ=10 . In the model with no frictions, we set ν=η=1/ξ=0 . The left panels refer to a tax-smoothing scheme aimed at stabilizing long-run consumption growth, Equations (13) and (15). The right panels refer to the tax-smoothing policy that stabilizes capital accumulation and long-run consumption growth, Equations (13) and (14). The intensity of the tax policy, ΦG , is set to 0.3 in all cases.10

Taken together, Figures 6, 8, 9, and 10 show the relevance of including asset pricing considerations in the current policy context. Asset prices dictate and discipline our calibration of preferences and financial frictions, i.e., the two main drivers of our welfare results. A model that abstracts from either financial frictions or preference for early resolution of uncertainty, even though able to replicate short-run quantity dynamics, may substantially misspecify the role of tax-based long-run growth risk.

4. Conclusion

The surge in public debt associated with the fiscal stabilization policies implemented in response to the financial crisis has raised uncertainty about future tax pressure and its potential effects on economic activity. In this article, we examine the effects of tax shocks and fiscal stabilization policies on important aspects of economic activity, namely, asset prices and capital accumulation. We propose a production-based general equilibrium asset pricing model with recursive preferences in which fiscal policies affect corporate investment and financing decisions through corporate taxes.

We document three significant results. First, in settings with constant tax rates, tax distortions can have severely negative effects on the cost of equity and investment. Second, in our equilibrium model, tax risk generated by exogenous shocks to government liabilities produces first-order effects on capital accumulation. Specifically, high tax uncertainty has a negative impact on capital accumulation that is as severe as that of high average taxation. Third, corporate tax smoothing affects the intertemporal distribution of consumption risk and welfare. While this last effect can be dismissed with standard time-additive preferences, it is of paramount importance in our setting with recursive preferences. When the agent prefers early resolution of uncertainty, tax-smoothing policies aimed at short-run consumption stabilization increase the cost of equity and result in welfare losses. Public financing policies aimed at stabilizing capital accumulation, in contrast, reduce both long-run consumption risk and the cost of capital, ultimately producing relevant welfare benefits.

More broadly, these result highlight the relevance of risk and asset pricing considerations in the current fiscal policy debate. Future research should incorporate sovereign default risk considerations (e.g., Li and Leeper 2010; Laubach 2010) and explore the relevance of credit shocks as in Jermann and Quadrini (2012). It will also be important to explore optimal fiscal policy in our setting using the techniques developed in Karantounias (2011).

We thank Matthew Spiegel, two anonymous referees, Andy Abel, David Backus, Ravi Bansal, Frederico Belo, Michael Brandt, Gian Luca Clementi, Vito Gala, Francisco Gomes, João Gomes, Urban Jermann, Sydney Ludvigson, Alex Michaelides, Chris Parsons, Vincenzo Quadrini, Nick Souleles, Vish Viswanathan, Amir Yaron, Stan Zin, and seminar participants at Wharton, LBS, Duke, UNC, NYU, USC, LSE, CEPR 2010 meetings, and SED 2010 meetings for their comments.

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Appendix A: DATA

A.1 Macroeconomic quantities and tax rate.

Data for real annual consumption, investment, corporate profits, and corporate taxes are from the Bureau of Economic Analysis (BEA). Output is computed as the sum of consumption and investment; government expenditures and net exports are excluded. Following McGrattan and Prescott (2005), the aggregate corporate tax rate is computed as the ratio of taxes on corporate profits to corporate profits before taxes. The sample period comprises the years 1929 to 2008. In Table 2, we report the volatility of the average corporate tax rate in the sample period 1948–2007. This is a conservative choice, as the standard deviation of the measured tax rate increases to 10% for the sample period that includes the 1930s. Our results, therefore, can be amplified by targeting pre-war data.

A.2 U.S. public debt data.

We collect data on U.S. debt from the CBO website: http://www.cbo.gov/doc.cfm?index=11766&zzz=41113.

We divide debt by US total GDP to compute the persistence of debt-output ratio.

A.3 Corporate debt and equity net payouts.

We compute net debt and equity payouts using Flow of Funds data as in Larrain and Yogo (2008). We thank these authors for making their data set available on the Web: http://www.nber.org/∼myogo/data/FirmValue_Data.xls.

A.4 Returns and financial leverage.

Monthly returns, dividends, and equity values are from CRSP. Debt values are obtained from Compustat. The risk-free rate is measured by the 3-month T-bill return. Annual dividends and returns are obtained by time-aggregating the monthly values. To compute the aggregate leverage ratio, we first compute equity and debt values at the firm level. Specifically, for firm i, the market value of equity is computed as the product of the number of shares outstanding and the price per share, mvequityi,tPRCi,t·SHROUTi,t . Since the market value of debt is unavailable at the firm level, we use the book value of both short- and long-term debt to determine total debt: totdebti,tDLCi,t+DLTTi,t . Then, for a given year t, we add these figures over all firms to obtain aggregate values, totdebtt=itotdebti,t and mvequityt=imvequityi,t . The aggregate leverage ratio is then computed as the ratio of the value of debt to the total value of the firm,  

$$le{v_t} \equiv \frac{{totdeb{t_t}}}{{totdeb{t_t} + mvequit{y_t}}}.$$

A.5 Deflator.

All nominal variables are converted to real units using the CPI index. The sample period is the financial variables from 1929–2008, except for the leverage ratio, which is only available for the sample period 1950–2008.

A.6 Productivity.

We compute productivity according to the following expression:  

$${Z_t} = \frac{{{Y_t}}}{{K_t^\alpha H_t^{1 - \alpha }}},$$
where Yt measures annual output; Kt measures capital and is computed as in Equation (8) with the following initialization: K1929=I1929/δ ; and Ht measures annual labor and considers both full-time and part-time employees (NIPA Table 6.4).

A.7 Estimation of Equation (4).

We regress our measure of U.S. productivity growth on the first lag of the corporate tax rate. We implement this regression in Eviews and compute Newey-West adjusted standard errors considering three lags. Focusing on the 1950–2007 sample (58 included observations), we obtain a point estimate of Φτ equal to –0.058 with a standard error of 0.267 and an implied t-stat of –2.179.

Appendix B: Model Solution

B.1 Definitions.

We start by listing key components of the technology in our economy:

 
$$\begin{align} {Y_t} & = {\left( {{Z_t}{H_t}} \right)^{1 - \alpha }}K_{t - 1}^\alpha \\ C_t^B & = v{Z_{t - 1}}{\left( {\frac{{{B_t}}}{{{Y_t}}} - \frac{{{{\widehat B}_{ss}}}}{{{{\widehat Y}_{ss}}}}} \right)^2} \\ C_t^E & = {\phi _0}{Z_{t - 1}}{e^{ - {\phi _1}\left( {\frac{{\eta {K_l}}}{{{B_t}}} - 1} \right)}}. \\ \end{align}$$

We can compute the following derivatives:

 
$$\begin{align} \frac{{\partial {Y_t}}}{{\partial {K_{t - 1}}}} & = \alpha {({Z_t}{H_t})^{1 - \alpha }}K_{t - 1}^{\alpha - 1} \\ \frac{{\partial C_t^B}}{{\partial {K_{t - 1}}}} & = 2v{Z_{t - 1}}\left( {\frac{{{B_t}}}{{{Y_t}}} - \frac{{{{\widehat B}_{ss}}}}{{{{\widehat Y}_{ss}}}}} \right)\left( {\frac{{ - \alpha {B_t}}}{{{Y_t}}}} \right)\frac{1}{{{K_{t - 1}}}} \\ \frac{{\partial C_t^E}}{{\partial {K_t}}} & = C_t^E\frac{{ - {\phi _1}\eta }}{{{B_t}}} \\ \frac{{\partial C_t^B}}{{\partial {B_t}}} & = 2v{Z_{t - 1}}\left( {\frac{{{B_t}}}{{{Y_t}}} - \frac{{{{\widehat B}_{ss}}}}{{{{\widehat Y}_{ss}}}}} \right)\frac{1}{{{Y_t}}} \\ \frac{{\partial C_t^E}}{{\partial {B_t}}} & = C_t^E\frac{{{\phi _1}\eta {K_t}}}{{B_t^2}} \\ \frac{{\partial {Y_t}}}{{\partial {H_t}}} & = (1 - \alpha )Z_t^{1 - \alpha }H_t^{ - \alpha }K_{t - 1}^\alpha \\ \frac{{\partial C_t^B}}{{\partial {H_t}}} & = 2v{Z_{t - 1}}\left( {\frac{{{B_t}}}{{{Y_t}}} - \frac{{{{\widehat B}_{ss}}}}{{{{\widehat Y}_{ss}}}}} \right)\frac{{(\alpha - 1){B_t}}}{{{Y_t}{H_t}}}. \\ \end{align}$$

B.2 Firm's problem.

Define the vector At(Zt1,Zt,τt,Kt1,Bt1) as the aggregate state at time t. The Lagrangian formulation associated with the firm's problem described in Equation (8) can be stated as  

$$\begin{align} {V_d}({{\rm{A}}_t}) = & \mathop {\max }\limits_{{l_t},{K_t},{B_t},{H_t}} (1 - {\tau _t})({Y_t} - {W_t}{H_t}) - {I_t} + {B_t} - (1 + (1 - {\tau _t}){r_{b,t - 1}}){B_{t - 1}} - C_t^B - C_t^E \\ & + {E_t}\left[ {{M_{t + 1}}{V_d}({{\rm{\bf A}}_{t + 1}})} \right] \\ & + {q_t}\left( {(1 - \delta ){K_{t - 1}} + \phi \left( {\frac{{{I_t}}}{{{K_{t - 1}}}}} \right){K_{t - 1}} - {K_t}} \right), \\ \end{align}$$
where qt is the multiplier associated to the capital accumulation constraint.

B.3 Optimality with respect to debt.

The first-order condition with respect to corporate debt and the envelope theorem jointly imply  

$$\begin{align} 1 & = \frac{{\partial C_t^B}}{{\partial {B_t}}} + \frac{{\partial C_t^E}}{{\partial {B_t}}} - {E_t}\left[ {{M_{t + 1}}\frac{{\partial {V_{d,t + 1}}}}{{\partial {B_t}}}} \right] \\ \frac{{\partial {V_{d,t}}}}{{\partial {B_{t - 1}}}} & = - (1 + (1 - {\tau _t}){r_{b,t - 1}}). \\ \end{align}$$

Taking into account the fact that at equilibrium rb is equal to the risk-free rate,  

$$\frac{{\partial C_t^B}}{{\partial {B_t}}} + \frac{{\partial C_t^E}}{{\partial {B_t}}} = {E_t}[{M_{t + 1}}{\tau _{t + 1}}]{r_{f,t}}.$$

The left-hand side refers to the total marginal cost of issuing an extra unit of debt. The right-hand side measures the value of the corporate interest tax advantage.

B.4 Optimality with respect to capital.

Envelope and first-order conditions with respect to investment and capital imply the following:  

$$\begin{align} {q_t} & = \frac{1}{{{{\phi '}_t}}} = {E_t}\left[ {{M_{t + 1}}\frac{{\partial {V_{d,t + 1}}}}{{\partial {K_t}}}} \right] - \frac{{\partial C_t^E}}{{\partial {K_t}}} \\ \frac{{\partial {V_{d,t}}}}{{\partial {K_{t - 1}}}} & = (1 - {\tau _t})\frac{{\partial {Y_t}}}{{\partial {K_{t - 1}}}} - \frac{{\partial C_t^B}}{{\partial {K_{t - 1}}}} + {q_t}\left( {1 - \delta - \frac{{{{\phi '}_t}{I_t}}}{{{K_{t - 1}}}} + {\phi _t}} \right). \\ \end{align}$$

B.5 A stationary system of first-order stochastic difference equations.

Given a stochastic process Xt , we define its normalized counterpart, X^t , as follows:  

$${\widehat X_t} \equiv \frac{{{X_t}}}{{{Z_{t - 1}}}}.$$

Using this convention, we write the following set of first-order stochastic difference equations.

B.6 Production side:

 
$$\begin{align} {\widehat Y_t} & = \Delta z_t^{1 - \alpha }\widehat K_{t - 1}^\alpha \Delta z_{t - 1}^{ - \alpha }, \\ \widehat C_t^B & = v{\left( {\frac{{{{\widehat B}_t}}}{{{{\widehat Y}_t}}} - \frac{{{{\widehat B}_{ss}}}}{{{{\widehat Y}_{ss}}}}} \right)^2},\quad \widehat C_t^E = {\phi _0}{e^{ - {\phi _1}\left( {\frac{{\eta {{\widehat K}_t}}}{{{{\widehat B}_t}}} - 1} \right)}}, \\ {\widehat K_t} & = (1 - \delta - {\phi _t}){\widehat K_{t - 1}}{e^{ - \Delta {z_{t - 1}}}},\quad {q_t} = \frac{1}{{{{\phi '}_t}}}, \\ 1 & = {E_t}[{M_{t + 1}}{R_{I,t + 1}}], \\ {R_{I,t}} & \equiv \frac{1}{{{q_{t - 1}}}}\left( {(1 - {\tau _t})\frac{{\alpha {{\widehat Y}_t}\Delta {z_{t - 1}}}}{{{{\widehat K}_{t - 1}}}} + 2v} \right.\left( {\frac{{{{\widehat B}_t}}}{{{{\widehat Y}_t}}} - \frac{{{{\widehat B}_{ss}}}}{{\widehat {{Y_{ss}}}}}} \right)\left( {\frac{{\alpha {{\widehat B}_t}}}{{{{\widehat Y}_t}}}} \right)\frac{{\Delta {z_{t - 1}}}}{{{{\widehat K}_{t - 1}}}} \\ & \quad \left. { + {q_t}\left( {1 - \delta - \frac{{{{\phi '}_t}{{\widehat I}_t}\Delta {z_{t - 1}}}}{{{{\widehat K}_{t - 1}}}} + {\phi _t}} \right)} \right) + \frac{{{\phi _1}\eta \widehat C_t^E}}{{{{\widehat B}_t}}}, \\ 1 & = 2v\left( {\frac{{{{\widehat B}_t}}}{{{{\widehat Y}_t}}} - \frac{{{{\widehat B}_{ss}}}}{{{{\widehat Y}_{ss}}}}} \right)\frac{1}{{{{\widehat Y}_t}}} + \frac{{{\phi _1}\eta {{\widehat K}_t}\widehat C_t^E}}{{\widehat B_t^2}} + {E_t}[{M_{t + 1}}(1 + (1 - {\tau _{t + 1}}){r_{b,t}})], \\ {\widehat W_t} & = (1 - \alpha ){\widehat Y_t} - \frac{1}{{(1 - {\tau _t})}}2v\left( {\frac{{{{\widehat B}_t}}}{{{{\widehat Y}_t}}} - \frac{{{{\widehat B}_{ss}}}}{{{{\widehat Y}_{ss}}}}} \right)\frac{{(\alpha - 1){{\widehat B}_t}}}{{{{\widehat Y}_t}}}. \\ \end{align}$$

B.7 Consumption side:

 
$$\begin{align} {{{\widehat C}_t}} & { = {{\widehat Y}_t} - {{\widehat I}_t} - {{\widehat G}_t} - {{\widehat{{C^E}}}_t} - {{\widehat{{C^B}}}_t},} \\ {{{\widehat U}_t}} & { = {{\left\{ {(1 - \beta )\widehat C_t^{1 - 1/\psi } + \beta {e^{\Delta {z_t}}}{E_t}{{[\widehat U_{t + 1}^{1 - \gamma }]}^{\frac{{1 - 1/\psi }}{{1 - \gamma }}}}} \right\}}^{\frac{1}{{1 - \frac{1}{\psi }}}}},} \\ {{M_{t + 1}}} & { = \delta {{\left( {\frac{{{{\widehat C}_{t + 1}}{e^{\Delta {z_t}}}}}{{{{\widehat C}_t}}}} \right)}^{ - \frac{1}{\psi }}}{{\left( {\frac{{{{\widehat U}_{t + 1}}}}{{{E_t}{{\left[ {\widehat U_{t + 1}^{1 - \gamma }} \right]}^{\frac{1}{{1 - \gamma }}}}}}} \right)}^{\frac{1}{\psi } - \gamma }}.} \\ \end{align}$$

B.8 Cost of equity and cost of debt:

 
$$\begin{align} {\widehat D_t} & = (1 - {\tau _t})({\widehat Y_t} - {\widehat W_t}) - {\widehat I_t} + {\widehat B_t} - (1 + (1 - {\tau _t}){r_{b,t - 1}}){\widehat B_{t - 1}}{e^{ - \Delta {z_{t - 1}}}} - \widehat C_t^B - \widehat C_t^E \\ {\widehat V_{d,t}} & = {\widehat D_t} + {e^{\Delta {z_t}}}{E_t}\left[ {{M_{t + 1}}{{\widehat V}_{d,t + 1}}} \right] \\ {r_{d,t}} & = \frac{{{{\widehat V}_{d,t}}}}{{{{\widehat V}_{d,t - 1}} - {{\widehat D}_{t - 1}}}} \cdot {e^{\Delta {z_{t - 1}}}} \\ {r_{b,t}} & = {r_{f,t}} = \frac{1}{{{E_t}[{M_{t + 1}}]}}. \\ \end{align}$$

B.9 Deterministic steady-state.

At the deterministic steady-state, we assume that the firm pays zero financial distress costs. This is equivalent to impose B^ss=ηK^ss . For given Φ1 , we use the following two Euler equations to solve for Φ0 and K^ss :  

$$\begin{align} 1 & = {M_{ss}}\left\{ {(1 - {\tau _{ss}})\alpha \Delta Z_{ss}^{2 - 2\alpha }\widehat K_{ss}^{\alpha - 1} + 1 - \delta } \right\} + \frac{{{\phi _1}\eta }}{{{{\widehat B}_{ss}}}}{\phi _0}{e^{ - {\phi _1}\left( {\frac{{\eta {{\widehat K}_{ss}}}}{{{{\widehat B}_{ss}}}} - 1} \right)}} \\ 1 & = \frac{{{\phi _1}\eta {{\widehat K}_{ss}}}}{{\widehat B_{ss}^2}}{\phi _0}{e^{ - {\phi _1}\left( {\frac{{\eta {{\widehat K}_{ss}}}}{{{{\widehat B}_{ss}}}} - 1} \right)}} + {M_{ss}}\left( {1 + (1 - {\tau _{ss}})\left( {\frac{1}{{{M_{ss}}}} - 1} \right)} \right). \\ \end{align}$$

At the steady state, the following holds:  

$$\begin{align} {\widehat K_{ss}} & = {\left\{ {\left( {\frac{{1 - \eta {\tau _{ss}}(1 - {M_{ss}})}}{{{M_{ss}}}} - 1 + \delta } \right)\frac{1}{{(1 - {\tau _{ss}})\alpha \Delta Z_{ss}^{2 - 2\alpha }}}} \right\}^{\frac{1}{{\alpha - 1}}}} \\ {\phi _0} & = \frac{{\eta {{\widehat K}_{ss}}{\tau _{ss}}(1 - {M_{ss}})}}{{{\phi _1}}}. \\ \end{align}$$

Given K^ss , it is possible to compute the steady-state value of all other variables.

B.10 Solution method.

We solve the model in dynare++4.2.1 using a second-order approximation. The policies are centered about a fix-point that takes into account the effects of volatility on decision rules. In the MatLab workspace file generated by dynare++, the vector with the fix-point for all our endogenous variables is denoted as dyn_ss. All conditional moments are computed by means of simulations with a fixed seed to facilitate the comparison across fiscal policies.

B.11 Welfare costs.

Consider two consumption bundle processes, {C1} and {C2} . We express welfare costs as the additional fraction λ of life time consumption bundle required to make the representative agent indifferent between {C1} and {C2} :  

$${U_0}(\{ {C^1}\} ) = {U_0}(\{ {C^2}\} (1 + \lambda )).$$

Since we specify U so that it is homogeneous of degree one with respect to C, the following holds:  

$$\frac{{{U_0}(\{ {C^1}\} )}}{{C_0^1}} \cdot C_0^1 = \frac{{{U_0}(\{ {C^2}\} )}}{{C_0^2}} \cdot C_0^2 \cdot (1 + \lambda ).$$

This shows that the welfare costs depend on both the utility-consumption ratio and the initial level of our two consumption profiles. In our production economy, the initial level of consumption is endogenous, so we cannot choose it. The initial level of productivity, Z0ii{1,2} , instead, is exogenous:  

$$\frac{{{U_0}(\{ {C^1}\} )}}{{C_0^1}} \cdot \frac{{C_0^1}}{{Z_0^1}} \cdot Z_0^1 = \frac{{{U_0}(\{ {C^2}\} )}}{{C_0^2}} \cdot \frac{{C_0^2}}{{Z_0^2}} \cdot Z_0^2 \cdot (1 + \lambda ).$$

We compare economies with different tax regimes but the same initial condition for productivity: $$Z^1_0=Z^2_0.$$ After taking logs, evaluating utility– and consumption–productivity ratios at their unconditional mean and imposing $$Z^1_0=Z^2_0,$$ we get the following expression:  

$$\lambda \approx \overline {\ln {U^1}/Z} - \overline {\ln {U^2}/Z} ,$$
where the bar denotes the unconditional average which is computed using the values stored by dynare++ in the vector dyn_ ss.

Our welfare costs are computed comparing the steady-states of two separate economies subject to two different fiscal regimes. Therefore, our welfare comparisons abstract from any transition dynamics required to move from one policy regime to another.

1
For the sake of simplicity, we model this link in reduced form, similarly to Pastor and Veronesi (forthcoming). This channel can be micro-founded in models with endogenous growth in which innovation and R&D sustain balanced growth, as in Croce et al. (2011). Croce et al. (2011) focus on the link between the return of the consumption claim and labor taxation and abstract from physical capital, capital structure, and corporate taxes.
2
Since in the next section we describe the main intuition of our tax-smoothing policy in reference to either bad productivity or fiscal shocks, we focus on adverse shocks in Figure 2 as well. The impulse response functions (IRFs) produced by the model after positive productivity or tax shocks are the reverse of those shown in Figure 2.
3
Under our benchmark calibration, the impact of tax shocks on the productivity growth rate is quite small ( Φτστ2.2%σε ); hence, our results are not driven by implausibly high long-run productivity risk.
4
In most of the panels, the dotted line that we use for Model 3 is not visible because it coincides with the dashed line used for Model 2. Consistent with our previous findings, therefore, Models 2 and 3 produce similar results.
5
In economies with standard time-additive preferences, the debt-output ratio tends not to be stationary because the risk-free rate puzzle makes E[(1+rf,t1)/exp(Δyt)]>1 . In our economy, however, at the stochastic steady-state, E[(1+rf,t1)/exp(Δyt)]<1 . Intuitively, the high growth rate of output dominates on the low risk-free rate.
6
In principle, tax smoothing and debt sustainability could be enforced by a fiscal rule of this kind:  
$${\tau _t} = \phi _1^G\tau _t^* + \phi _2^G(\mu - {E_t}[\Delta {y_{t + 1}}]) + \phi _3^G\frac{{B_{t - 1}^G}}{{{Y_{t - 1}}}},$$
in which Φ1G(0,1) defines the intensity of smoothing with respect to expenditure shocks, Φ2G defines the counter-cyclicality of the tax policy, and Φ3G>0 captures repayment attitude. While this policy specification might appear easier at first sight, we find it less parsimonious as it requires us to examine the role of three parameters, instead of simply two. It is also more opaque in regard to the cross-parameter restrictions required to guarantee a stationary debt-output ratio.
7
To be precise, we plot E[StDt(Δct)] , i.e., the average conditional volatility of consumption growth. Since in the model the variation of the conditional second moment is negligible, we do not stress it in the figures. In order to better link our results to the asset pricing investigation of Bansal and Yaron (2004) and the welfare analysis of Croce (2006), we recall their exogenous consumption process:  
$$\begin{align} \Delta {c_{t + 1}} & = \mu + {x_t} + {\sigma _c}{\epsilon_{c,t + 1}} \\ {x_t} & = {\rho _x}{x_{t - 1}} + {\sigma _x}{\epsilon_{x,t + 1}} \\ \left[ {{\epsilon_{c,t + 1}},{\epsilon_{x,t + 1}}} \right] & \sim i.i.d.N(0,{I_2}). \\ \end{align}$$
What we denote as StDt(Δct+1) is the equivalent of σc , the amount of short-run risk. ACF1(Et[Δct+1]) is our measure of ρx , and StD (Et[Δct+1]) is the volatility of the long-run component xt .
8
We describe in detail our welfare cost computations in Appendix B. Here, we point out that our welfare analysis compares steady-states of different fiscal regimes and abstracts from transition dynamics.
9
Since in our model public debt is on average zero and there is no government expenditure waste, our results are not driven by crowding-out effects. Our experiment isolates the pure redistribution of intertemporal consumption risk generated by corporate tax smoothing.