Taxes, the Speed of Convergence, and Implications for Welfare Effects of Fiscal Policy

1. Introduction Economists' views on the relation between taxes and the long-run growth rate of per capita income have varied greatly as macroeconomic models have evolved. Neoclassical growth models leave no room for a relation between taxes and steady-state growth (Ramsey 1928; Solow 1956; Swan 1956; Cass 1965; Koopmans 1965). Tax policy can affect growth in early endogenous innovation models (Romer 1986, 1990; Segerstrom 1991; Grossman and Helpman 1991; Aghion and Howitt 1992). However, these models exhibit scale effects.1 When scale effects are removed, the relation between taxes and steady-state growth tends to disappear (Jones 1995b; Segerstrom 1998; Young 1998). Tax policy can affect the growth rate in some versions of endogenous human capital models (King and Rebelo 1990; Rebelo 1991; Jones, Manuelli, and Rossi 1993). However, Lucas's (1990) simulations indicate that the tax effects are tiny. Stokey and Rebelo (1995) support Lucas's conclusion. The short run may be the only run in which a relation between taxes and per capita income growth might hold. Nevertheless, a short-run relation could have important lasting implications. Whether this is true depends on the economy's convergence speed. For example, a capital income tax cut may increase the saving rate, increasing growth. Even if diminishing returns dictate that faster growth is merely transitory, the temporary growth spurt shifts upward the long-run trajectories of capital per person and welfare. But the increase in saving requires lower consumption in the short run. If the transition is slow, the short-run sacrifice could outweigh the long-run gain (Bernheim 1981; Judd 1987). The duration of the transition and, therefore, the size of the net welfare gain depend on the economy's convergence speed. The speed at which economies converge to their steady states has been analyzed extensively (Mankiw, Romer, and Weil 1992; Ortigueira and Santos 1997; Barro and Sala-i-Martin 1999). But even here, careful scrutiny suggests the absence of a relation between income taxes and growth. For example, income taxes do not affect the convergence speed in Barro, Mankiw, and Sala-i-Martin (1995) and Ortigueira and Santos (1997). Two points make it important to revisit the issue. First and foremost, as the example above suggests, convergence speed can alter the net welfare effects of fiscal policy. Second, though simple proportional income taxes do not affect the convergence speed, common features of realistic tax systems do. The purpose of this paper is to provide an example supporting both points. The particular example used here is the widely used depreciation deduction. However, the results are general: The analysis shows (i) that any tax parameter that affects required saving directly affects the convergence speed, and (ii) that any tax deduction causes the tax rate to affect convergence speed indirectly. Many features of realistic tax systems can affect required saving and, therefore, the economy's convergence speed. The accelerated depreciation allowances permitted by the U.S. tax code will have a larger effect than the example studied here. Tax benefits, such as deductions for charity, debt service, and amortization of goodwill and patents; investment tax credits for equipment and research and development (RD and the myriad other deductions in typical tax codes, as well as the personal income tax itself, affect required saving and can affect convergence speed. The next section of the paper incorporates a deduction for economic depreciation in the neoclassical model with exogenous saving (Solow model, hereafter) and explains the effect on the convergence speed. Section 3 explains the effect in the neoclassical model with endogenous saving (Ramsey model). Appendix C derives the same effect in a new growth model. The relation appears to be a robust feature of standard macroeconomic models. Section 4 compares the net welfare effects of income tax cuts with and without a depreciation deduction, under narrow and broad (human plus physical) capital. …