2.1. Corporations

2.1.1. Economic and accounting depreciation

A key feature introduced to study the effects of the tax reform is the difference between economic and accounting depreciation. Economic depreciation refers to the way physical capital depreciates over time, while accounting depreciation refers to the way accounting capital is depreciated for tax purposes.

Let $E$ , $S$ , and $R$ denote, respectively, equipment, structures, and R&D. For $i=E,S,R$ , let $k^i_t$ be capital of type $i$ , and let $x^i_t$ be investment in type- $i$ capital. Capital depreciates at the constant economic depreciation rate $\delta ^i\gt 0$ . Its law of motion is

(1) \begin{align} k^i_{t+1} & = (1-\delta ^i) k^i_t + x^i_t - \frac{\psi }{2} \left (\frac{k^i_{t+1} - k^i_t}{\bar{k}^i}\right )^2 \bar{k}^i\qquad \mathrm{for}\ i=E,S,R, \end{align}

where the last term is a capital-adjustment cost, with $\psi \gt 0$ , and $\bar{k}^i\gt 0$ is the steady-state level of type- $i$ capital.

Accounting depreciation is modeled differently from economic depreciation. For tax purposes, a fraction $\chi ^i_t \geq 0$ of investment can be immediately depreciated, and the remaining part can be depreciated at the rate $\tilde \delta ^i\gt 0$ . I assume that $\tilde \delta ^i\gt \delta ^i$ , to model the fact that the tax system allows the use of an accelerated depreciation method to depreciate assets. In addition, to replicate the half-year convention, accounting capital is assumed to begin depreciating in the middle of the year in which investment occurs. Then, the fraction of investment that is depreciated in the year in which investment occurs is:

(2) \begin{align} \kappa ^i_t & \equiv \chi ^i_t + (1-\chi ^i_t)\frac{1}{2}\tilde \delta ^i\qquad \mathrm{for}\ i=E,S,R. \end{align}

Because of the difference between accounting depreciation and economic depreciation, we need to keep track of accounting capital separately from physical capital. Let $\tilde{K}^i_t$ be the nominal accounting capital available at the beginning of period $t$ , before accounting depreciation is subtracted and investment is added. Then, nominal accounting depreciation is

\begin{align*} Z^i_t & = \tilde \delta ^i \tilde{K}^i_t + \kappa ^i_t P_t x^i_t\qquad \mathrm{for}\ i=E,S,R, \end{align*}

and the law of motion of nominal accounting capital is

\begin{align*} \begin{split} \tilde{K}^i_{t+1} & = \tilde{K}^i_t + P_t x^i_t - Z^i_t \\[3pt] & = (1-\tilde \delta ) \tilde{K}^i_t + (1-\kappa ^i_t) P_t x^i_t\qquad \mathrm{for}\ i=E,S,R. \end{split} \end{align*}

Dividing the previous equations by the price level $P_t$ , we obtain

(3) \begin{align} z^i_t & = \tilde \delta ^i \frac{\tilde{k}^i_t}{1+\pi _t} + \kappa ^i_t x^i_t\qquad \mathrm{for}\ i=E,S,R, \end{align}

(4) \begin{align} \tilde{k}^i_{t+1} & = (1-\tilde \delta ^i) \frac{\tilde{k}^i_t}{1+\pi _t} + (1-\kappa ^i_t) x^i_t\qquad \mathrm{for}\ i=E,S,R, \end{align}

where $\tilde{k}^i_t \equiv \tilde{K}^i_t/P_{t-1}$ is real accounting capital, and $z^i_t \equiv Z^i_t/P_t$ is real accounting depreciation.

2.1.2. Taxable income

Production is a function of the three types of capital and labor demand $l_t$ :

(5) \begin{align} y_t & = A^C f(k^S_t,k^E_t,k^R_t,l_t), \end{align}

where $A^C\gt 0$ , $f(k^S,k^E,k^R,l) \equiv (k^S)^{\alpha ^S} (k^E)^{\alpha ^E} (k^R)^{\alpha ^R} l^{1-\alpha }$ , $\alpha \equiv \alpha ^S+\alpha ^E+\alpha ^R$ , $\alpha ^S\gt 0$ , $\alpha ^E\gt 0$ , $\alpha ^R\gt 0$ , and $\alpha \lt 1$ . Revenue is equal to production, $y_t$ , while wages are equal to the product between the wage rate, $w_t$ , and labor demand, $l_t$ . Earnings before interest and taxes, $\textrm{EBIT}_t$ , are equal to revenue minus wages and accounting depreciation:

(6) \begin{align} \textrm{EBIT}_t & = y_t - w_t l_t - \sum _{i=E,S,R} z^i_t \nonumber \\ \textrm{EBIT}_t & = y_t - w_t l_t- \sum _{i=E,S,R}\left ( \tilde \delta ^i \frac{\tilde{k}^i_t}{1+\pi _t} + \kappa ^i_t x^i_t \right ), \end{align}

where the last step uses (3).

Let $B_t$ be the nominal level of corporate debt issued in period $t-1$ , let $b_t \equiv B_t/P_{t-1}$ be the corresponding real level, and let $r^C_{t-1}$ be the nominal interest rate on the corporate debt. Then, in period $t$ , the nominal level of interest expenses is $r^C_{t-1} B_t$ , and the real level is $r^C_{t-1} B_t/ P_t = r^C_{t-1} b_t/ (1+\pi _t)$ .

Let $\zeta _t \in (0,1]$ denote the fraction of interest expenses that can be deducted for tax purposes. Then, taxable income, $\mathcal{I}_t$ , is equal to the difference between EBIT and the amount of interest expenses that can be deducted:

(7) \begin{align} \mathcal{I}_t & = EBIT_t - \zeta _t \frac{r^C_{t-1} b_t}{1+\pi _t} \nonumber \\ \mathcal{I}_t & = y_t - w_t l_t - \sum _{i=E,S,R}\left ( \tilde \delta ^i \frac{\tilde{k}^i_t}{1+\pi _t} + \kappa ^i_t x^i_t\right ) - \zeta _t \frac{r^C_{t-1} b_t}{1+\pi _t}, \end{align}

where the last step uses (6). Corporate income taxes are $\tau ^C_t \mathcal{I}_t$ , where $\tau ^C_t \in (0,1)$ is the corporate income tax rate.

2.1.3. Optimization problem

Corporate income and newly issued debt are used to pay taxes, repay existing debt, and distribute dividends. The corporate budget constraint is

(8) \begin{align} d_t + \frac{(1+r^C_{t-1})b_t}{1+\pi _t} + \tau ^C_t \mathcal{I}_t & = y_t - w_t l_t - \sum _{i=E,S,R} x^i_t + b_{t+1} + T^C. \end{align}

On the right-hand side, the first three terms represent revenue minus wages and investment expenses, the next term is newly issued debt, and the last term, $T^C$ , is a constant lump-sum government transfer that may be positive or negative (introduced to calibrate the steady-state level of corporate debt). On the left-hand side, the first term is dividends, $d_t\gt 0$ , the second term is gross-of-interest debt repayments, and the last term represents corporate income taxes.

Corporate owners receive dividends, $d_t$ , pay dividend taxes at the rate $\tau ^d_t\in (0,1)$ , and consume the rest:

(9) \begin{align} c_t & = (1-\tau ^d_t) d_t. \end{align}

The corporate owners’ optimization problem is:

(10) \begin{align} \begin{split} & \max _{\left \{c_t,d_t,y_t,l_t,b_{t+1},\mathcal{I}_t, \{x^i_t,k^i_{t+1},\tilde{k}^i_{t+1}\}_{i=E,S,R} \right \}_{t=0}^{\infty }}E_0 \sum _{t=0}^{\infty } (\beta ^C)^t u(c_t)\\[3pt] & \mathrm{subject\ to}\ (1), (4), (5), (7), (8)\ \mathrm{and}\ (9), \end{split} \end{align}

where the utility function is such that $u^{\prime }(c) \equiv c^{-\gamma }$ , $\gamma \gt 0$ , and $\beta ^C\gt 0$ .

2.1.4. First-order conditions

We now derive an equivalent optimization problem and the first-order conditions. Substituting the expression for $\mathcal{I}_t$ from (7) into (8), we obtain:

\begin{align*} d_t + & \frac{(1+r^C_{t-1})b_t}{1+\pi _t} + \tau ^C_t \left \{ y_t - w_t l_t - \sum _{i=E,S,R} \left ( \tilde \delta ^i \frac{\tilde{k}^i_t}{1+\pi _t}+ \kappa ^i_t x^i_t \right ) - \zeta _t \frac{r^C_{t-1} b_t}{1+\pi _t} \right \}\\[3pt] & = y_t - w_t l_t - \sum _{i=E,S,R} x^i_t + b_{t+1} + T^C \\[3pt] d_t + & \sum _{i=E,S,R} (1- \tau ^C_t \kappa ^i_t) x^i_t + \frac{(1+r^C_{t-1}-\zeta _t\tau ^C_tr^C_{t-1}) b_t}{1+\pi _t} \\[3pt] & = (1-\tau ^C_t) (y_t - w_t l_t) + \tau ^C_t \sum _{i=E,S,R} \tilde \delta ^i \frac{\tilde{k}^i_t}{1+\pi _t} + b_{t+1} + T^C. \end{align*}

Then, substituting the expression for $y_t$ from (5), we obtain:

(11) \begin{align} d_t & + \sum _{i=E,S,R} (1- \tau ^C_t \kappa ^i_t) x^i_t + \frac{(1+r^C_{t-1}-\zeta _t\tau ^C_tr^C_{t-1}) b_t}{1+\pi _t} \nonumber \\ & = (1-\tau ^C_t) [A^C f(k^S_t,k^E_t,k^R_t,l_t) - w_t l_t] + \tau ^C_t \sum _{i=E,S,R} \tilde \delta ^i \frac{\tilde{k}^i_t}{1+\pi _t} + b_{t+1} + T^C. \end{align}

Finally, substituting the expression for $c_t$ from (9), the corporate owner’s optimization problem (10) can be restated as:

(12) \begin{align} &\max _{\left \{d_t,l_t,b_{t+1}, \{x^i_t,k^i_{t+1},\tilde{k}^i_{t+1}\}_{i=E,S,R} \right \}_{t=0}^{\infty }} E_0 \sum _{t=0}^{\infty } (\beta ^C)^t u((1-\tau ^d_t) d_t)\\[3pt] &\mathrm{subject\ to}\ (11), (1),\ \mathrm{and}\ (4). \nonumber \end{align}

Let $\lambda _t$ , $\mu ^i_t$ and $\nu ^i_t$ be the Lagrange multipliers associated, respectively, with the constraints (11), (1), and (4). The first-order conditions with respect to $d_t$ , $l_t$ , $b_{t+1}$ , $x^i_t$ , $k^i_{t+1}$ , and $\tilde{k}^i_{t+1}$ are, respectively:

(13) \begin{align} (\beta ^C)^t u^{\prime }(c_t) (1-\tau ^d_t)& = \lambda _t \end{align}

(14) \begin{align} A^C \frac{\partial f(k^S_t,k^E_t,k^R_t,l_t)}{\partial l_t} & = w_t \end{align}

(15) \begin{align}\lambda _t & = E_t \frac{\lambda _{t+1}(1+r^C_t-\zeta _{t+1}\tau ^C_{t+1}r^C_t)}{1+\pi _{t+1}} \end{align}

(16) \begin{align}\lambda _t (1-\tau ^C_t\kappa ^i_t) & = \mu ^i_t + (1-\kappa ^i_t) \nu ^i_t \end{align}

(17) \begin{align} \mu ^i_t \left (1 + \psi \frac{k^i_{t+1} - k^i_t}{\bar{k}^i}\right ) = &E_t \left \{\lambda _{t+1} (1-\tau ^C_{t+1}) A^C \frac{\partial f(k^S_{t+1},k^E_{t+1},k^R_{t+1},l_{t+1})}{\partial k^i_{t+1}} \right .\nonumber \\ & \left. + \mu ^i_{t+1} \left (1-\delta ^i + \psi \frac{k^i_{t+2} - k^i_{t+1}}{\bar{k}^i}\right ) \right \} \end{align}

(18) \begin{align}\nu ^i_t & = E_t \left \{ \lambda _{t+1} \tau ^C_{t+1} \frac{\tilde \delta ^i}{1+\pi _{t+1}} + \nu ^i_{t+1} \frac{1-\tilde \delta ^i}{1+\pi _{t+1}} \right \}. \end{align}

From the first-order conditions, one can derive the following Euler equation relating the corporate owners’ consumption, $c_t$ and $c_{t+1}$ , to the interest rate, $r^C_t$ :

(19) \begin{align} 1 & = E_t \left \{ \frac{\beta ^C u^{\prime }(c_{t+1}) (1-\tau ^d_{t+1})}{u^{\prime }(c_t) (1-\tau ^d_t)}\;\frac{1+(1-\zeta _{t+1}\tau ^C_{t+1})r^C_t}{1+\pi _{t+1}}\right \}. \end{align}

2.2. Financial frictions

The tax reform affected the balance sheets, credit risk, and cost of external funds of businesses. To capture these effects, I model the credit spread in a reduced form. Credit risk creates a spread between the interest rate faced by the borrower and the one faced by the lender. While the borrower faces the lending rate, the lender faces a lower interest rate, since the lender takes into account the default probability of the loan. Approximately, the lender faces an interest rate equal to the difference between the lending rate and the default probability. When the balance sheets of businesses weaken, credit risk increases and the credit spread widens. To replicate these features, I introduce a spread between the interest rate paid by businesses and the interest rate received by households, and I assume that the spread is an increasing function of business leverage.

More specifically, I introduce a financial frictions wedge, $\xi _t$ , between the bond payoff paid by corporations in period $t$ , $1+r^C_t$ , and the bond payoff received by households, $1+\tilde{r}^C_t$ :

(20) \begin{align} 1+\tilde{r}^C_t & \equiv \frac{1+r^C_t}{1+\xi _t}. \end{align}

The wedge is approximately equal to the difference $r^C_t-\tilde{r}^C_t$ , which in equilibrium is equal to the spread between the corporate bond yield and the government bond yield. With a larger wedge, corporations have to offer households a higher interest rate in equilibrium, which makes the cost of external funds higher and investment lower. (To be clear, both $r^C_t$ and $\tilde{r}^C_t$ are endogenous and vary with the wedge.)

I assume that the wedge, $\xi _t$ , is an increasing function of the aggregate leverage of corporations, $h_t$ :

(21) \begin{align} \xi _t & = \tilde A^C h_t^\rho \end{align}

(22) \begin{align} h_t & \equiv \frac{(1+r^C_t)b_{t+1}/(1+\pi _{t+1})}{k_{t+1}}, \end{align}

(with $\tilde A^C\gt 0$ and $\rho \gt 0$ ), so corporations face a higher cost of external funds when their aggregate leverage is higher.

To close the model, I assume that the difference between what is paid by corporations and what is received by households, $(r^C_t-\tilde{r}^C_t) b_t/(1+\pi _t)$ , is transferred to the households in a lump-sum way. With this assumption, the budget constraints of households and corporations are the same as the ones in a frictionless model with an interest rate equal to $r^C_t$ . Alternatively, one could assume that the difference, or part of it, is transferred to the corporations. The model results, however, would be very similar. Quantitatively, the main effect of the wedge is the one on the first-order conditions, not on the budget constraints.

2.3. Pass-through businesses

Pass-throughs are modeled in the same way as corporations, except for the following: there are no dividend taxes, so $\tau ^d_t$ is set equal to zero in the optimization problem for pass-throughs; the values of $A^P$ , $\tilde A^P$ , $\beta ^P$ , $\tau ^P_t$ , and $T^P$ are different from the values of $A^C$ , $\tilde A^C$ , $\beta ^C$ , $\tau ^C_t$ , and $T^C$ , as described later in the section on calibration, and the equilibrium values of $r^P_t$ may be different from the equilibrium values of $r^C_t$ (while $\tilde{r}^P_t=\tilde{r}^C_t$ in equilibrium).

In what follows, the values that solve the optimization problem for corporations are denoted by the superscript $C$ (for example, $\{c^C_t,x^{S,C}_t\}$ ), while the values that solve the problem for pass-throughs are denoted by the superscript $P$ (for example, $\{c^P_t,x^{S,P}_t\}$ ).

2.4. Households

Households consume $c^H_t$ and lend $\tilde{b}^P_{t+1}$ to pass-throughs, $\tilde{b}^C_{t+1}$ to corporations, and $D_{t+1}$ to the government. They receive a constant endowment of goods, $y^H$ ; supply labor, $n^H_t$ ; receive wages, $w_t n^H_t$ ; and receive gross-of-interest debt repayments from pass-throughs, corporations, and the government. They pay personal income taxes on wages and interest at the individual tax rate $\tau ^H_t$ and receive lump-sum government transfers, $T^H_t$ . They receive a lump-sum transfer, $\mathcal{H}_t$ , equal to the difference between the bond payoff paid by businesses and the bond payoff received by households:

(23) \begin{align} \mathcal{H}_t & \equiv \omega ^C (r^C_{t-1}-\tilde{r}^C_{t-1}) \frac{b^C_t}{1+\pi _t} + \omega ^P (r^P_{t-1}-\tilde{r}^P_{t-1}) \frac{b^P_t}{1+\pi _t}. \end{align}

Then, the households’ budget constraint is:

(24) \begin{align} \begin{split} c^H_t + \tilde{b}^C_{t+1} & + \tilde{b}^P_{t+1} + D_{t+1} = y^H + (1-\tau ^H_t) w_t n^H_t + \frac{1+(1-\tau ^H_t)\tilde{r}^C_{t-1}}{1+\pi _t} \tilde{b}^C_t \\ &+ \frac{1+(1-\tau ^H_t)\tilde{r}^P_{t-1}}{1+\pi _t}\tilde{b}^P_t+\frac{1+(1-\tau ^H_t)\tilde{r}^G_{t-1}}{1+\pi _t}D_t+ \mathcal{H}_t+ T_t^H. \end{split} \end{align}

The households’ optimization problem is:

(25) \begin{align} \begin{split} \max _{\left \{c^H_t,n^H_t,\tilde{b}^C_{t+1},\tilde{b}^P_{t+1},D_{t+1}\right \}_{t=0}^{\infty }} & E_0 \sum _{t=0}^{\infty } (\beta ^H)^t [u(c^H_t) - v(n^H_t)] \\ &\mathrm{subject\ to}\ (24), \end{split} \end{align}

where the utility function $u(c)$ is the same as the one for corporations and pass-throughs, $v(n) \equiv \Phi n^{1+1/\varphi }$ , $\Phi \gt 0$ , $\varphi \gt 0$ , and $\beta ^H\gt 0$ .

The first-order conditions are:

(26) \begin{align} \frac{v^{\prime }(n^H_t)}{u^{\prime }(c^H_t)} & = (1-\tau ^H_t) w_t \end{align}

(27) \begin{align} 1 & = E_t \left \{\frac{\beta ^H u^{\prime }(c^H_{t+1}) }{u^{\prime }(c^H_t)}\;\frac{1+(1-\tau ^H_{t+1})\tilde{r}^j_t}{1+\pi _{t+1}}\right \}\qquad \mathrm{for}\ j=C,P,G. \end{align}

2.5. Government

The government receives a constant endowment of goods, $y^G$ , issues debt, $D_{t+1}$ , and collects tax revenue, $\mathcal{T}_t$ (net of taxes on government debt interest) from corporations, pass-throughs, and households:

(28) \begin{align} \mathcal{T}_t & \equiv \omega ^C \tau ^d_t d^C_t + \omega ^C \tau ^C_t \mathcal{I}^C_t + \omega ^P \tau ^P_t \mathcal{I}^P_t + \tau ^H_t w_t n_t + \tau ^H_t \frac{\tilde{r}^C_{t-1}\tilde{b}^C_t + \tilde{r}^P_{t-1} \tilde{b}^P_t}{1+\pi _t}. \end{align}

It uses the proceeds to finance government spending, $G$ ; distribute lump-sum transfers to corporations, pass-throughs, and households; and repay gross-of-interest debt to households:

(29) \begin{align} G + \omega ^C T^C + \omega ^P T^P + T^H_t + \frac{1+(1-\tau ^H_t)\tilde{r}^G_{t-1}}{1+\pi _t} D_t & = y^G + \mathcal{T}_t + D_{t+1}. \end{align}

I assume that the lump-sum transfers to households, $T^H_t$ , respond to changes in government debt and adjust so that government debt is stationary and an equilibrium exists. Provided that an equilibrium exists, the timing of the adjustment in $T^H_t$ affects only the evolution of government debt and does not matter for the dynamics of the other variables. Ricardian equivalence applies because households hold all the government debt.

Assuming that the government transfers to households adjust to make government debt stationary amounts to assuming that the tax reform will be financed by cuts in the government transfers to households. Alternatively, one could assume that the tax reform will be financed, at least in part, by cuts in the lump-sum transfers to businesses or by future increases in distortionary taxes. Under these alternative assumptions, the model results would be different. In particular, because households hold all the government debt, the size and the timing of the cuts in the transfers to businesses would have distributional effects, with implications for the financial frictions, and would matter for the equilibrium values of the aggregate variables. I will explore the sensitivity of the welfare and distributional effects to this assumption in Section 5.2.

2.6. Equilibrium

Let business output, $y^B_t$ , be the sum of corporate and pass-through output:

(30) \begin{align} y^B_t \equiv \omega ^C y^C_t + \omega ^P y^P_t, \end{align}

and let GDP be the sum of the household endowment, business output and the government endowment:

(31) \begin{align} \textrm{GDP}_t \equiv y^H + y^B_t + y^G. \end{align}

Since $y^H$ and $y^G$ are constant over time, percent changes in GDP are proportional to percent changes in business output, scaled by a factor equal to the ratio of business output to GDP.

The equilibrium condition for the goods market equates the demand for private consumption, government spending, and investment to GDP:

(32) \begin{align} c^H_t + \omega ^C c^C_t + \omega ^P c^P_t + G + \omega ^C \sum _{i=E,S,R} x^{C,i}_t + \omega ^P \sum _{i=E,S,R} x^{P,i}_t & = \textrm{GDP}_t. \end{align}

The other equilibrium conditions equate demand and supply in the labor market, in the market for corporate debt, and in the market for debt of pass-throughs:

(33) \begin{align} \omega ^C l^C_t + \omega ^P l^P_t & = n^H_t \end{align}

(34) \begin{align} \tilde{b}^C_{t+1} & = \omega ^C b^C_{t+1} \end{align}

(35) \begin{align} \tilde{b}^P_{t+1} & = \omega ^P b^P_{t+1}. \end{align}

An equilibrium is a set of sequences of quantities, prices, and Lagrange multipliers that satisfy:

1. 1. The constraints (1), (4), and (11) and the first-order conditions (13)–(18) of the corporate owners’ optimization problem (12), together with the additional equations (5), (7) and (9), which determine, respectively, $y_t$ , $\mathcal{I}_t$ and $c_t$ .

2. 2. The constraints, first-order conditions, and additional equations for pass-through owners analogous to the ones for corporate owners.

3. 3. The definitions (20), (21), and (22), which model the financial frictions for corporations, and the analogous definitions that model the financial frictions for pass-through businesses.

4. 4. The constraint (24) and the first-order conditions (26)–(27) of the households’ optimization problem (25).

5. 5. The tax revenue definition (28) and the government’s budget constraint (29).

6. 6. The definitions (2), (23), (30), and (31).

7. 7. The market equilibrium conditions (32)–(35).

2.7. Why a tax cut can decrease investment

As we will see in Section 4, while most TCJA provisions have an intuitive effect on investment, the tax cuts for corporations and pass-throughs have the somewhat surprising effect of decreasing investment. I explain why in this section.

The reason why a cut in the business income tax rate decreases investment is that, in the presence of interest deductibility and accelerated depreciation, the tax acts as an investment subsidy, so a tax cut reduces the subsidy.

To understand why a business income tax can act as an investment subsidy, let’s begin with a standard model of investment and let’s add accelerated depreciation and interest deductibility. As is well known, in a standard model of investment without accelerated depreciation and interest deductibility, a business income tax raises the user cost of capital and acts as a tax on investment. There are two ways to mitigate or solve this problem. First, allowing businesses to deduct their investment expenses early on (through accelerated depreciation, bonus depreciation, or other forms of depreciation faster than the economic depreciation of capital) creates a tax shield that mitigates the contractionary effect of the tax on investment. In the limit, if all investment expenses can be immediately deducted (full expensing of investment), the business income tax can become neutral, as can be shown in standard models of investment. Second, allowing businesses to deduct their interest expenses creates an additional tax shield that lowers the cost of funding investment and can, by itself, make the business income tax neutral. The combination of the two tax shields (interest deductibility and some form of accelerated depreciation) can make the tax act as an investment subsidy.Footnote ²

The just-described relationships between taxes and investment depending on interest deductibility and accelerated depreciation can be illustrated with a variety of models. In Appendix A in Supplementary Material, I illustrate these relationships with a partial-equilibrium, simplified version of the model used in this paper. Fullerton (Reference Fullerton and Fullerton1999) is the standard reference that shows how interest deductibility and accelerated depreciation allowances can lead to negative effective marginal tax rates on investment.

The result that a tax cut decreases investment can be mitigated or overturned in models with additional features. For instance, if businesses were subject to financial frictions, a tax cut would mitigate these frictions and would reduce the cost of external funds, thereby encouraging investment. Also, in a general equilibrium model, the interest rate on borrowed funds would respond to the tax cut and would decline as investment decreases, mitigating the decrease in investment.

In the end, whether a tax cut increases or decreases investment depends on the overall features and parameter values of the model. In the general equilibrium model used in this paper, which features interest deductibility, accelerated depreciation, financial frictions, and an endogenous interest rate, the combination of the two tax shields makes the tax on business income act as an investment subsidy for both corporations and pass-throughs. Since the business income tax acts as a subsidy, a tax cut decreases investment by decreasing the subsidy.Footnote ³

3.1. Parameters and steady-state values

The parameters and steady-state values are listed in Tables 1 and 2.

Table 1. Parameters and steady-state values

Note: The length of a period is 1 year.

Table 2. Policy parameters

One period corresponds to 1 year. A few parameter values are set in line with the literature. The households’ preference discount factor is set to $\beta ^H=0.96$ , the relative risk aversion parameter is set to $\gamma =2$ , the Frisch elasticity of labor supply is set to $\varphi =0.5$ , and the parameter $\Phi$ is set so that the labor supply $n$ is equal to $1/3$ .

The tax rates for corporations and pass-throughs are set to $\tau ^C=0.38$ and $\tau ^P=0.352$ , following the estimates (comprehensive of federal and local taxation) by Barro and Furman (Reference Barro and Furman2018). The tax rate for households is set to $\tau ^H=0.32$ , the sum of 29%, the effective marginal federal tax rate on labor income estimated by CBO (2018), and 3%, the average state income tax. The dividend tax rate is set to $\tau ^d=0.15$ . All interest expenses are deductible in the steady state, so $\zeta =1$ . The inflation rate, $\pi$ , is equal to 2%.

The parameters of the wedge function are set to approximate moments of the corporate bond spread [Flannery et al. (Reference Flannery, Nikolova and Öztekin2012), Table 1]. The scale parameters, $\tilde A^C$ and $\tilde A^P$ , are set so that the financial frictions wedge is $\xi =0.01$ , and the credit spread (1%) is, approximately, equal to the average corporate bond spread. The exponent, $\rho$ , is set so that the credit spread increases by 0.80 percentage points (equal to one standard deviation of the corporate bond spread) when leverage, $h$ , increases by 44% (equal to the ratio of the standard deviation to the mean of corporate leverage).

The values of $\tilde{r}^C$ , $r^C$ , and $\beta ^C$ for corporations are determined by the steady-state versions of the households’ first-order conditions (26), the equation defining the financial friction wedge (20), and the corporations’ first-order conditions (19):

\begin{align*} \begin{split} 1 & = \beta ^H \frac{1+(1-\tau ^H)\tilde{r}^C}{1+\pi } \\ 1+\tilde{r}^C & = \frac{1+r^C}{1+\xi } \\ 1 & = \beta ^C \frac{1+(1-\tau ^C)r^C}{1+\pi }. \end{split} \end{align*}

The values of $\tilde{r}^P$ , $r^P$ , and $\beta ^P$ for pass-throughs are determined in the same way. The resulting values for the preferences discount factors for owners of corporations and pass-throughs are, respectively, $\beta ^C=0.959$ and $\beta ^P=0.957$ .

The economic depreciation rates of equipment, structures, and R&D are, respectively, $\delta ^E=0.16$ , $\delta ^S=0.04$ , and $\delta ^R=0.2$ , to match, approximately, the BEA estimates of the average age of the three types of capital (6 years for equipment, software, and originals; 27 years for structures; and 5 years for R&D).

The fractions of initial investment that can be immediately depreciated are set as follows: for equipment, $\chi ^E_t=0.5$ , to replicate that a 50% bonus depreciation was allowed before the tax reform; for R&D, $\chi ^R_t=1$ , to replicate that investment in R&D could be fully expensed before the tax reform, and for structures, $\chi ^S_t=0$ , to replicate that the bonus depreciation was not allowed for structures.

The accounting depreciation rates for equipment and structures are set equal to double the economic depreciation rates, $\tilde \delta ^E=0.32$ , $\tilde \delta ^S=0.08$ , to approximate the fact that most businesses use accelerated depreciation (double declining balance method changing to straight line method at the point at which depreciation deductions are maximized). The accounting depreciation rate for R&D, $\tilde \delta ^R$ , does not play any role in the steady state because investment in R&D can be fully expensed (that is, $\chi ^R_t=1$ ).

The exponent of the production function is set to $\alpha =0.35$ , in line with standard values in the literature. To set $\alpha ^i$ , for $i=E,S,R$ , I follow a procedure similar to the one used in the literature to set $\alpha$ . Consider the following steady-state first-order conditions for the economy without taxes and financial frictions:

\begin{align*} {MPK}^i \equiv \alpha ^i \frac{y}{k^i} & = \frac{1}{{\beta ^H}} - (1-\delta ^i) \qquad \mathrm{for}\ i=E,S,R, \end{align*}

where $MPK^i$ is the marginal product of capital. Assuming that taxes and financial frictions raise the marginal product of capital proportionally for the three types of capital,

\begin{align*} {MPK}^i \equiv \alpha ^i \frac{y}{k^i} & \propto \left ( \frac{1}{{\beta ^H}} - (1-\delta ^i) \right )\qquad \mathrm{for}\ i=E,S,R, \end{align*}

where $\propto$ is the proportionality symbol. Substituting $x^i=\delta ^ik^i$ ,

\begin{align*} \alpha ^i & \propto \left ( \frac{1}{{\beta ^H}} - (1-\delta ^i) \right ) \frac{1}{\delta ^i} \frac{x^i}{y}\qquad \mathrm{for}\ i=E,S,R. \end{align*}

In 2017, the ratios of private investment to business output were approximately $x^E/y=0.11$ for equipment and intellectual property products other than R&D, $x^S/y=0.04$ for structures, and $x^R/y=0.03$ for R&D. These ratios, the previously set values for $\alpha$ , $\beta ^H$ and $\delta ^i$ , and the constraint $\alpha \equiv \alpha ^S+\alpha ^E+\alpha ^R$ imply $\alpha ^E=0.189$ , $\alpha ^S=0.111$ , and $\alpha ^R=0.05$ .

The capital-adjustment cost parameter is set equal to $\psi =10$ , in line with common values used in models with a unique type of capital.

The endowment and production parameters are set so that $y^B=75$ , $y^H=12.5$ , $y^G=12.5$ , and $GDP=y^H+y^B+y^G=100$ , to match the fact that in 2013 the business sector accounted for about 75% of gross value added, while both the household sector and the government sector accounted for 12.5% (BEA, National Income and Product Accounts, Table 1.3.5). More specifically, the production function scale parameters, $A^C$ and $A^P$ , are set so that $y^C=y^P=75$ . The two parameters are different because the tax rates are different for corporations and pass-throughs, implying different first-order conditions and capital levels. With this choice, business output, $y^B$ , is also equal to $75$ : $y^B = \omega ^C y^C+\omega ^P y^P =75$ .

The measures of corporations and pass-throughs are set to $\omega ^C=0.43$ and $\omega ^P=0.57$ so that corporate output $\omega ^C y^C$ represents 43% of business output, $y^B$ , and pass-through output represents the remaining 57%. This setting matches the fact that in 2013 C corporations and pass-through businesses accounted for, respectively, 43% and 57% of net business income (IRS, SOI Tax Stats—Integrated Business Data, Table 1).

The lump-sum government transfers to corporations and pass-throughs, $T^C$ and $T^P$ , are set to target the levels of debt, $b^C$ and $b^P$ . In turn, the levels of debt are set so that the coverage ratio, defined as the ratio of EBIT to interest expenses, is 3.7 for both corporations and pass-throughs, matching the average coverage interest ratio for US nonfinancial corporate publicly traded firms [Palomino et al. (Reference Palomino, Paolillo, Perez-Orive and Sanz-Maldonado2019)].

Government spending, $G$ , is set to 18% of GDP. The lump-sum government transfers to households, $T^H$ , are set so that government debt, $D$ , is equal to 76% of GDP, to match gross federal debt held by the public as a percentage of GDP in 2017.

As a result of the calibration, investment is 17% of GDP (10.7% in equipment, 3.2% in structures, and 3% in R&D) and consumption is 65% of GDP (1.5% of corporate owners, 2.6% of pass-through owners, and 60.9% of households).

3.2. Changes in policy parameters to model the tax reform

Before detailing how I model the tax reform, let me highlight the role played by agents’ expectations in the model. The initial effect of the tax reform depends on agents’ initial expectations about the future of the TCJA provisions. Therefore, to obtain accurate model estimates, it is important that the agents’ expectations in the model are as close as possible to the ones held by the public in reality.

Of course, there is large uncertainty about the future of the TCJA provisions—partly because of political uncertainty—and large uncertainty about agents’ initial expectations. On the one hand, there will be political pressure to make the temporary provisions on individual income tax rates permanent, to extend the bonus depreciation of equipment, and to mitigate the switch from expensing to amortizing R&D expenses. On the other hand, the rise in government debt will create pressure in the opposite direction and may even lead to a partial repeal of the corporate tax rate cuts. Indeed, in the President’s Budget for fiscal year 2023, President Biden has already proposed that Congress raise the corporate tax rate to 28%.

The large uncertainty notwithstanding, to obtain accurate model estimates, we need to incorporate expectations that are as realistic as possible. To that end, I present the main results for a case where agents hold what I consider realistic expectations about the future of the TCJA provisions. Specifically, I construct a plausible future scenario for the TCJA provisions (called plausible scenario), and I assume that agents have perfect foresight, so their current expectations are consistent with that scenario. With this strategy, I aim at generating expectations that are as close as possible to the ones that the public plausibly holds in reality.

After presenting the main results for the plausible scenario, I show the results for a scenario where the TCJA provisions will evolve as prescribed by current legislation (called legislation scenario), and agents’ expectations are consistent with it. Agents have perfect foresight in this scenario as well. In my view, agents’ expectations in this scenario are less realistic, so the model estimates are less accurate. For instance, in this scenario, agents believe that the corporate tax cuts will be permanent and don’t place any probability on a possible partial repeal, while in reality a partial repeal has always been publicly considered. However, I include this scenario because it may be of interest in itself, and because, by comparing the two scenarios, we can gain some insights about how the estimated effects of the tax reform depend on the future paths of the TCJA provisions.

In what follows, I begin describing the parameter settings for the legislation scenario, and then, I describe the parameter settings for the plausible scenario.

3.2.1. Parameter settings for the legislation scenario

The parameter settings that model the tax reform in the legislation scenario are described by the dashed lines in Figure 1.

Figure 1. Changes in policy parameters designed to model the tax reform. Note: For the second subplot, the solid line refers to both the plausible scenario and the legislation scenario. For the other subplots, the solid and dashed lines refer, respectively, to the plausible scenario and the legislation scenario.

Beginning with the permanent corporate income tax cuts, Barro and Furman (Reference Barro and Furman2018, Table 4 and page 275) estimate that the tax rate on corporate income dropped by 11 percentage points, taking into account the new limits on the deduction of net operating losses, as well as other details of the tax legislation. Following their estimate, I model the corporate income tax cuts as a permanent drop by 11 percentage points from $\tau ^C=0.38$ to $\tau ^C=0.27$ from 2018 on (first subplot of Figure 1).

The provision on corporate earnings held overseas amounts to a lump-sum tax cut for corporations, since the earnings held overseas were subject to a higher tax rate (35%) under the old tax system, and became subject to a lower tax rate (15.5% on liquid assets and 8% on illiquid assets). The lump-sum tax cut is equal to the product of the tax rate cut and the amount of overseas earnings. The amount of earnings held overseas is, approximately, $\$ $ 2.6 trillion [McKeon (Reference McKeon2017)]. Assuming that one-third of assets held overseas are liquid, the tax rate cut is equal to $0.35-(1/3 \times 0.155+2/3 \times 0.08)=0.245$ . The product of the tax rate cut and the amount of overseas earnings is $\$ $ 637 billion, corresponding to 3.3% of GDP, so I model the provision as a lump-sum tax cut for corporations equal to 3.3% of GDP. Since corporations can pay the new tax in installments over 8 years, I assume that the lump-sum tax cut is equally spread over the 8 years starting in 2018 (second subplot of Figure 1).

As to the temporary individual tax cuts, Barro and Furman (Reference Barro and Furman2018, page 298) estimate a cut in the average marginal income tax rate of about 2.3 percentage points. Following their estimate, I model the individual tax cuts as a temporary drop by 2.3 percentage points to $\tau ^H=0.297$ in the years 2018–2025, followed by a return to $\tau ^H=0.32$ from 2026 on (third subplot of Figure 1).

Turning to the temporary tax cuts for pass-throughs, Barro and Furman (Reference Barro and Furman2018, Table 4 and page 283) estimate a drop by 4.1 percentage points, reflecting the limits on the pass-through deduction. Following their estimate, I assume a temporary cut by 4.1 percentage points, and set $\tau ^P=0.311$ in the years 2018–2025, followed by a return to $\tau ^P=0.352$ from 2026 on (fourth subplot of Figure 1).

To model the bonus depreciation for equipment, I set $\chi ^E_t=1$ for the years 2018–2022, then $\chi ^E_t=0.8, 0.6, 0.4, 0.2$ , respectively, for the years 2023–2026, and finally $\chi ^E_t=0$ from 2027 on (fifth subplot of Figure 1).

The amortization of R&D expenses starting in 2022 is modeled by keeping $\chi ^R_t=1$ for the years 2018–2021 and then setting $\chi ^R_t=0$ from 2022 on (sixth subplot of Figure 1). The value for the accounting depreciation rate for R&D is set to $\tilde \delta ^R=0.2$ , to model that R&D expenses need to be amortized over 5 years ( $\tilde \delta ^R$ does not play any role unless $\chi ^R_t\lt 1$ ).

With regard to the limits on interest deductibility, Barro and Furman (Reference Barro and Furman2018, pages 275–276) assume that the limits on interest deductibility are constraining 5% of investment in the initial years (when the limit is 30% of EBITDA) and will constrain 15% of investment in the long run (when the limit will be 30% of EBIT). Motivated by their assumption, I approximate the limits on the deductibility of interest expenses by setting $\zeta _t=0.95$ for the years 2018–2021, followed by $\zeta _t=0.85$ for the years from 2022 on (seventh subplot of Figure 1).

The final point regards the financing of the tax reform and the evolution of government debt. As I stated in Section 2.5, I assume that the lump-sum government transfers to households, $T^H_t$ , adjust to make government debt stationary, and insure the existence of an equilibrium. This assumption implies that, after the tax reform, the transfers decrease enough to balance the government’s intertemporal budget constraint, so the tax reform is financed by cuts in the government transfers to households. The timing of the adjustment in $T^H_t$ does not affect the dynamics of any variable, except for government debt, $D_t$ . Intuitively, if the transfers decrease in the initial years of the tax reform, the path of government debt is lower than in the case where the transfers decrease in the distant future. To be able to evaluate the costs of the tax reform in terms of increases in government debt, I assume that all of the adjustment in $T^H_t$ takes place in the distant future, after 20 years, that is, the transfers remain constant and equal to their steady-state value for the initial 20 years, and they decrease only afterwards. With this assumption, the path of government debt in the initial 20 years (which is the time horizon in the figures) is entirely the result of the tax reform.

5.1. Comparison between the two scenarios and sensitivity to the paths of the policy parameters

The model results depend significantly on the assumptions about the paths of the policy parameters, as can be seen by comparing the plausible scenario and the legislation scenario (solid and dashed lines of Figures 2–9).

Focusing on the cumulative effect of the seven TCJA provisions (Figure 9), the estimate of the immediate effect on labor and output is smaller in the legislation scenario than in the plausible scenario. The estimate of the immediate effect on investment is negative in the legislation scenario, while it is positive in the plausible scenario. The difference in the estimates of the immediate effects is due to the difference in the agents’ expectations about the paths of the bonus depreciation of equipment, the amortization of R&D expenses, and the limits on interest deductibility (Figures 2–8).

The two scenarios estimate different future effects as well. According to the legislation scenario, tax revenue will remain above steady state for several years, helping to stabilize government debt. The improvement in fiscal conditions in the legislation scenario will be due to the expiration of the bonus depreciation of equipment, the amortization of R&D expenses, the expiration of the income tax cuts for individuals and pass-throughs, and the stricter limits on interest deductibility. However, the legislation scenario estimates worse future macroeconomic conditions than the plausible scenario. According to the legislation scenario, the labor supply will drop below steady state after 2026, when the income tax cuts for individuals expire. By 2036, investment will plunge by 10%, because of the expiration of the bonus depreciation of equipment, the amortization of R&D expenses, the expiration of the income tax cuts for individuals, and the stricter limits on interest deductibility. As labor, investment and capital drop, output will decrease by more than 2%.

The welfare implications of the two scenarios are different as well (first four columns vs. last four columns of Table 3). Most of the welfare effects are qualitatively similar, but differ in size depending on the settings of the provisions in each scenario. For instance, the corporate tax cuts are more persistent in the legislation scenario, so the related welfare effects are larger in size. Symmetrically, the individual and pass-through tax cuts are more temporary in the legislation scenario, so the related welfare effects are smaller in size. The limits on interest deductibility are stricter in the legislation scenario, so the related welfare effects are larger in size. Overall, the tax reform has larger distributional effects in the legislation scenario than in the plausible scenario. Moreover, the total welfare effect is negative in the legislation scenario (equivalent to a 0.05% permanent decrease in aggregate consumption), while it is positive in the plausible scenario.

More generally, the model results depend significantly on the paths of the policy parameters set to model the seven TCJA provisions. In particular, the provision on overseas earnings and the limits on interest deductibility could be modeled differently, so the estimated effects of these provisions are subject to especially large uncertainty. The sensitivity of the results to the modeling of each provision can be inferred from Figures 2–8, which show the effect of each individual TCJA provision. For instance, I model the provision on corporate earnings held overseas as a lump-sum tax cut for corporations equal to 3.3% of GDP. One may judge that it should be modeled as a lump-sum tax cut equal to, say, half that size, perhaps because corporations, in the past, may have anticipated a provision with similar effects. In this case, the effect of the provision would be half of what is shown in Figure 3, and the other half should be subtracted from the cumulative effect of the seven TCJA provisions shown in Figure 9.

5.2. Sensitivity to the assumption about the financing of the tax reform

The model’s baseline results are derived under the assumption that the tax reform will be financed by cuts in the government’s lump-sum transfers to households. Because of Ricardian equivalence, the timing of the cuts does not affect the equilibrium, except for the path of government debt. Under alternative assumptions about the financing of the tax reform, the model results are somewhat different, especially the results about the welfare and distributional effects.

One possible alternative assumption is that the tax reform will be financed, at least in part, by cuts in the government’s lump-sum transfers to businesses. With this assumption, the cuts in the lump-sum transfers to businesses weaken the balance sheets of businesses and worsen the financial frictions, mitigating the expansionary effects of the tax reform. Also, since businesses are subject to financial frictions, Ricardian equivalence does not hold, and the timing of the cuts matter for the equilibrium.

The welfare and distributional effects of the tax reform are different as well. Table 6 lists the welfare effects of the tax reform under the assumption that the tax reform will be entirely financed by cuts in the transfers to corporations and pass-throughs (in proportion of their measures $\omega ^C$ and $\omega ^P$ ). Specifically, in each period, the government’s transfers to businesses are assumed to adjust to maintain the government’s primary budget deficit constant. In other words, the government’s transfers to businesses are cut when a provision tends to generate a fiscal deficit, while they are increased when a provision tends to generate a fiscal surplus.

Table 6. Welfare effect of the tax reform under the alternative assumption that the tax reform is financed by cuts in the government’s transfers to businesses

Note: Effect of the TCJA provisions on the welfare of households, corporate owners, and pass-through owners, measured as equivalent permanent change in their consumption, expressed as a percentage of aggregate consumption. The total is the sum of the three welfare effects. The first four columns refer to the plausible scenario, while the last four refer to the legislation scenario.

Comparing Table 6 (which is derived under the assumption that the transfers to businesses adjust) and Table 3 (which is derived under the assumption that the transfers to households adjust), the differences in the distributional effects are intuitive. For the first five provisions, which tend to generate budget deficits and transfers cuts, the welfare of business owners (/households) is lower (/higher) in the case where the transfers cuts involve the businesses, rather than the households. For the last two provisions, which tend to generate budget surpluses and transfers increases, the welfare of business owners (/households) is higher (/lower) in the case where the transfers increases involve the businesses, rather than the households.

The differences in the total welfare effects are also intuitive. For the first five provisions, the ones that generate transfers cuts, the total welfare effect is lower in the case where the transfers cuts involve the businesses, since the transfers cuts worsen the financial frictions. For the last two provisions, the ones that generate transfers increases, the total welfare effect is higher in the case where the transfers increases involve the businesses, since the transfers increases mitigate the financial frictions.

In aggregate, for the seven TCJA provisions, the welfare of business owners is lower and the welfare of households is higher in the case where the transfers cuts involve the businesses, rather than the households. In the case where the transfers cuts involve the businesses, the transfers cuts worsen the financial frictions to the point that the total welfare effect is negative.

Another possible alternative assumption is that the tax reform will be financed, at least in part, by future increases in distortionary taxes. Table 7 lists the welfare effects of increasing the individual tax rate, the corporate tax rate, and the pass-through tax rate by 10 percentage points, starting in the year 2026, under the baseline assumption that the government’s transfers to households adjust to keep government debt stationary. Intuitively, an increase in the corporate (/pass-through) tax rate decreases the welfare of corporate (/pass-through) owners and increases the welfare of households, who benefit from the increase in government’s transfers. In contrast, an increase in the individual tax rate decreases the welfare of households, since this experiment amounts to an increase in a lump-sum transfer financed by an increase in a distortionary tax. The total welfare effect is negative when any of the three distortionary taxes increases. Quantitatively, the increase in the individual tax rate has, by far, the largest welfare effects.

Table 7. Welfare effect of future tax increases

Note: Effect of future tax increases on the welfare of households, corporate owners, and pass-through owners, measured as equivalent permanent change in their consumption, expressed as a percentage of aggregate consumption. The total is the sum of the three welfare effects. Each tax rate increases by 10 percentage points starting in the year 2026.

5.3. Three mechanisms that may play some role

Although the model incorporates the key mechanisms for the effect of the tax reform, it abstracts from three mechanisms that may play some role.

First, because the tax reform decreases the tax rate for corporations more than for pass-throughs, it may encourage some pass-through businesses to change their legal form into corporations (besides shifting the demand for labor and capital as captured by the model). Based on regressions of the corporate share of business income on the wedge between corporate and noncorporate business tax rates, a 10 percentage point drop in the differential between the income tax rates for corporations and pass-throughs is associated with an increase in the corporate share of about 3.4 percentage points [Prisinzano and Pearce (Reference Prisinzano and Pearce2018), Section III.3]. In the plausible scenario, the long-run drop in the tax rate differential is only 3.35 percentage points, corresponding to an increase in the corporate share of about 1.1 percentage points. In the legislation scenario, the long-run drop in the tax rate differential is 11 percentage points, corresponding to a more significant increase in the corporate share of about 3.75 percentage points.

Second, inflation may respond to the tax reform, and monetary policy may respond to changes in output and inflation, thereby modifying the effects of the tax reform. It is plausible that monetary policy may mitigate the effect of the tax reform on output, by tightening in response to an increase in output. However, it is also possible that monetary policy may amplify the effect of the tax reform on output: For instance, monetary policy amplifies the effect of tax shocks on output, owing to its response to inflation, in the New Keynesian model of Sims and Wolff (Reference Sims and Wolff2018, Figure 5).

Third, the model predicts that the tax reform will persistently depress investment in R&D, by about 7%. Following Romer (Reference Romer1990), the endogenous growth literature indicates that the drop in R&D investment may have a negative effect not only on the levels but also on the growth rates of productivity and output, although the uncertainty around this effect is especially large. See Chu and Wang (Reference Chu and Wang2022) for a recent model of R&D investment, innovation, and growth.