This PDF is a selection from an out-of-print volume from the National Bureau of Economic Research Volume Title: Inflation, Tax Rules, and Capital Formation Volume Author/Editor: Martin Feldstein Volume Publisher: University of Chicago Press Volume ISBN: 0-226-24085-1 Volume URL: http://www.nber.org/books/feld83-1 Publication Date: 1983 Chapter Title: Inflation, Income Taxes, and the Rate of Interest: A Theoretical Analysis Chapter Author: Martin Feldstein Chapter URL: http://www.nber.org/chapters/c11328 Chapter pages in book: (p. 28 - 43) Inflation, Income Taxes, and the Rate of Interest: A Theoretical Analysis Income taxes are a central feature of economic life but not of the growth models that we use to study the long-run effects of monetary and fiscal policies. The taxes in current monetary growth models are lump sum transfers that alter disposable income but do not directly affect factor rewards or the cost of capital. In contrast, the actual personal and corporate income taxes do influence the cost of capital to firms and the net rate of return to savers. The existence of such taxes also in general changes the effect of inflation on the rate of interest and on the process of capital accumulation.1 The current paper presents a neoclassical monetary growth model in which the influence of such taxes can be studied. The model is then used in sections 3.2 and 3.3 to study the effect of inflation on the capital intensity of the economy. James Tobin's (1955, 1965) early result that inflation increases capital intensity appears as a possible special case. More generally, the tax rates and saving behavior determine whether an increase in the rate of inflation will increase or decrease steady-state capital intensity. The analysis also shows that the net real rate of interest received by savers may be substantially altered by the rate of inflation. Section 3.3 Reprinted by permission horn American Economic Review 66 (December 1976): 809-20. I am grateful to the University of California at Berkeley for the opportunity to prepare this paper while I was Ford Research Professor. The National Science Foundation sup- ported the project on the effects of fiscal programs on capital accumulation and income distribution, of which the current study is a part. I am grateful for discussions with Stanley Fischer, Steven Goldman, and David Hartman. 1. Income taxes have been studied in nonmonetary growth models by Peter Diamond (1970,1975), Feldstein (1974a, b), and Kazuo Sato (1967). Of course, the effects of inflation cannot be examined in such models. 28 29 Inflation, Income Taxes, and the Rate of Interest discusses the desirability of adjusting the taxation of interest income to eliminate these arbitrary effects of inflation. The fourth section discusses the implications of this for the welfare effects of inflation and the optimal rate of growth of the money supply. 3.1 A Growing Economy with Inflation and Income Taxes This section presents a one-sector neoclassical model of economic growth with inflation and income taxes. The model differs from that of Tobin (1965) in two fundamental ways: (1) the savings rate depends on the net real rate of return earned by savers; (2) there are personal and corporate interest income taxes as well as a lump sum tax.2 Because the analysis of the model in section 3.2 will focus on comparative steady-state dynamics, only these steady-state properties will be discussed here. The steady-state economy will be characterized by an inflation rate ir = Dp/p and a nominal interest rate of /. The real rate of interest is, by definition, r = / - TT . In order to consider the effects of adjusting the tax treatment for the rate of inflation, separate tax rates will be specified for the real and inflation components of the nominal rate of interest. The personal income tax will tax real interest payments at 6X and the inflation component at 82. The net nominal rate of return is thus iN - (1 - 6J r + S0 (1 - 82)TT. In our current tax law Q1 = Q2 ^^iN = (1 ~ &)(? + IT) = (1 - Q)i. With complete inflation indexation, 62 = 0 and iN = (1 - O^r + IT; the net real rate of interest received by households is thus rN = iN - TT = (1 - e^r. The economy is characterized by an exogenously growing population (1) N The labor force is a constant fraction of the population. Production can be described by an aggregate production function with constant returns to scale. The relation between aggregate output per capita (y) and aggre- gate capital stock per capita (k) is (2) y=f{k) with /' > 0 and /" < 0. For simplicity, both technical progress and depreciation are ignored. 3.1.1 The Demand for Capital The investment and financing behavior of firms is influenced by the corporate income tax. An important feature of the corporation tax is that the interest paid on corporate debt may be deducted by firms in calculat- ing taxable profits while dividends paid on corporate equity may not be 2. In the more general model of David Levhari and Don Patinkin, the savings rate does depend on the rate of return but there are no corporate or personal income taxes. 30 Inflation and Tax Rules in Macroeconomic Equilibrium deducted. Although the method of finance need not affect the analysis in models without a corporate income tax, it is necessary in the current model to identify the method of finance. Because the focus of the current paper is on the effect of inflation on the rate of interest, I will assume that all corporate investment is financed by issuing debt.3 The tax deduction of interest payments may also be adjusted for inflation: let J1 be the tax rate at which the real component of interest payments is deducted and let T2 be the tax rate at which the inflation component can be deducted. The net 4 rate of interest paid by firms is then (1 - T^r + (1 - T2)TT. In the absence of the corporation tax, the firm maximizes its profit by investing until the marginal product of capital is equal to the real rate of interest, i - TT. Stated somewhat differently, the firm's capital stock is optimal when the marginal product of capital [/'(&)] plus the nominal appreciation in the value of the capital stock per unit of capital (ir) is equal to the nominal rate of interest: (3) /'(*) +IT = i The effect of the corporation tax on this optimality condition depends on the way that depreciation is treated by the law. Consider first the simple case in which capital lasts forever, i.e., in which there is no depreciation. The corporation tax then reduces the net-of-tax marginal product of capital to (1 - ^/'(k). There is no tax on the unrealized appreciation of the capital stock. The firm maximizes profits by increasing the capital stock until the net nominal return on capital (1 — Ti)f'(k) + TT is equal to the net nominal rate of interest, (1 — J{) r + (1 — T2)TT. The first-order optimum of equation (3) therefore becomes (4) f'{k) = r- TT 1-Ti If the capital stock does depreciate, f'{k) can be interpreted as the marginal product of capital net of the cost of replacing the capital that has been used up in production. If the corporation tax allows the deduction of 3. It would, of course, be desirable to have a more general model in which corporate debt and equity coexist. The exclusion of equity in the current analysis and the full deductibility of corporate interest payments imply that the present value of corporation taxes is zero. The present model might therefore be regarded as an approximation to a model in which equity profits are intramarginal and all marginal investments are financed by debt (see Joseph Stiglitz 1973). Dale Henderson and Thomas Sargent (1973) studied the effect of inflation in an economy in which firms finance all investment by issuing equity. Because they use a short-run analysis with no accumulation of capital, their conclusions cannot be compared with those of the current analysis. After this paper was accepted for publication, Jerry Green, Eytan Sheshinski, and I (1978; chap. 4 below) developed a more general extension of the current analysis in which firms use an optimal mix of equity and debt finance. 4. In steady-state growth with fully anticipated inflation there is no need to distinguish between short-term debt and long-term debt. 31 Inflation, Income Taxes, and the Rate of Interest the replacement cost of this depreciation, the net-of-tax marginal product of capital is again (1 - T\)f'{k) and equation (4) continues to hold. I will use this condition to describe the demand for capital.5 3.1.2 Liquidity Preference The real value of household assets is the sum of the real values of outside money (M/p) and corporate bonds (B/p): Since outside money bears no interest, the ratio of money to bonds that households will hold is a decreasing function of the after-tax nominal rate of return on bonds, iN = (1 - 8x)r + (1 - 82)^. The real value of bonds (B/p) is also the real value of the capital stock (K). The liquidity prefer- ence relation can therefore be written in per capita terms as (6) f = L[(l - eOr + (1 - 62H,L'<0 where m = M/pN, the real money balances per capita. In steady state, mlk must remain constant. Equivalently, M/pK remains constant, i.e., the rate of growth of M is equal to the rate of growth of pK or TT + n.