Macroeconomic effects of factor taxation with endogenous human capital evolution: theory and evidence.

• Author: Wang, Ping

1. Introduction

   The distortionary effect of factor income taxation has been one of the central issues in public finance theory (for example, see Feldstein [4], Boadway [3], Homma [6], Summers [14] and Judd [8]). A tax on capital income, in contrast to a tax on labor income, has been claimed to create an intertemporal distortion that affects the future paths of macro aggregates adversely through the decumulation of physical capital. Hence, it is generally concluded in the aforementioned literature that capital taxation is more distortionary in the long run than labor taxation.(1)

   In this paper, we revisit this issue by constructing a dynamic general equilibrium model with infinitely lived, perfectly foresighted agents. Unlike most of the existing literature, we develop a growth model in which both physical and human capital are endogenously accumulated.(2) Within this framework, a tax on labor generates a distortionary effect on both human capital evolution and future dynamic paths of output and consumption, analogous to the case of capital taxation. In contrast to results in previous work, labor income taxation in our economy can be more distortionary than capital income taxation, even in the long run.

   Many studies, for years, have focused on welfare comparison of factor taxes. In most cases, calibration or simulation exercises are performed and there has been no empirical research to contrast one factor tax effect with another. (For instance, see Summers [14] and Judd [8]). Within our theoretical framework, welfare (lifetime utility of the representative agent) is a monotone function of the (endogenously determined) growth rate of the macroeconomy. Thus one can examine factor tax distortions by quantitatively measuring the adverse effect of factor taxation on the endogenous growth rate. This then enables us to implement empirical tests rather than relying on simulation exercises.

   To empirically test our theoretical hypothesis, we need to investigate an economy in which the evolution of human capital plays a crucial role in its economic development. This motivates us to shift our attention from developed countries, such as the U.S. and Japan, to newly industrialized countries. We have chosen Taiwan for our empirical study because it has the richest reliable data (for a study of the Taiwan economy, see Huang, Cheng, Chou and Lin [7]). The annual growth rate of per capita real GDP in Taiwan during 1954 through 1986 averaged about six percent; the percentage of the population completing higher education (colleges or universities), in the same period, increased by more than 14 times.(3) It is our belief that the improvement of labor skill over time plays a crucial role in the economic development of Taiwan.(4) The importance of human capital evolution in the development process of Taiwan prompts us to reexamine conventional conclusions on factor tax distortions.

   Tax reform has been one of the central concerns in Taiwan since 1960s and numerous studies have been undertaken.(5) More recently, Riew [12] provides a comprehensive study of possible linkage between tax policy and Taiwan's economic development. Generally speaking, the (factor) income tax policy implemented in Taiwan in the past three decades seems to be credited for having promoted Taiwan's economic growth without adverse effects on income distribution. However, such speculation has not been put to a rigorous empirical test based upon a dynamic general equilibrium framework. To examine the macroeconomic effects of factor taxation using the above mentioned endogenous growth framework, we need to construct a measure of the human capital skill level along with an empirical methodology to evaluate the relative magnitude of the distortions of the two factor income taxes. Using annual data for Taiwan covering the period from 1954 to 1986, our results suggest that a shift from capital taxation to labor taxation indeed depresses economic growth, contrary to the traditional perception.

   The remainder of the paper is organized as follows. Section II develops an endogenous growth model to analytically study the effects of unitary factor taxation on economic growth within the differential incidence framework. Section III implements empirical tests and employs the data for Taiwan to compare the two types of factor tax distortions in a mixed-tax environment. We then conclude the paper in section IV.

2. Analytical Framework

   This section constructs a general equilibrium framework with infinitely lived, perfectly foresighted agents. Different from previous work, we develop a dynamic factor taxation model with endogenously accumulated physical and human capital. Under this setup, we compare the effects of capital and labor taxation on economic growth.

   The Model

   Within a differential incidence framework, we assume that only one (real) factor tax T is imposed at each time in order to finance the (real) government spending g, which is simply assumed to be nonproductive expenditure.(6) Let [[Tau].sub.L] and [[Tau].sub.k] be the labor and capital income tax rates respectively. Define w and r as the (real) wage rate and the (real) rate of return of capital respectively. Further denote k as (per capita) physical capital and L = hl as (per capita) effective labor, where h and l represent the human capital skill level and the fraction of time allocated to work respectively. The fraction of time (1 - l) therefore indicates the leisure level. Following Becker's [2] theory of home production, we assume that the utility of leisure depends on the human capital skill level. Thus, the effective leisure measure is x = h (1 - l). Finally, the factor tax in our unitary-tax economy is imposed either on labor (T = [[Tau].sub.L]wL) or on physical capital (T = [[Tau].sub.k]rk).

   Given the two factor prices, w and r, the representative agent's optimization problem is to choose c (per capita consumption), l (labor), k (physical capital) and h (human capital) to solve

   [Mathematical Expression Omitted]

   subject to

   c(t) + k(t) = [Psi](t)f(k(t),h(t)l(t)) - nk(t) - T(t) (1)

   h(t) = (1 - [Psi](t))f(k(t),h(t)l(t)) (2)

   where n and [Rho] are rates of population growth and time preference respectively, while [Psi] represents the fraction of output devoted to consumption, investment and tax payments (and so 1 - [Psi] indicates the fraction of output used for education). Equation (1) is a standard budget constraint or, more precisely, the goods production/spending constraint. This constraint determines the evolution of physical capital. Equation (2) can be called an education production technology, which determines the evolution of human capital. Here, education output is assumed to be tax-exempt. To get a closed-form solution for the balanced growth equilibrium, the instantaneous utility function u exhibits constant intertemporal elasticity of substitution of consumption: u(c,x) = [([c.sup.[Beta]][x.sup.1-[Beta]]).sup.1-[Alpha]]/(1 - [Alpha]).(7) Moreover, the production function f is assumed to take the Cobb-Douglas form: f (k,hl) = [k.sup.[Gamma]] [(hl).sup.1-[Gamma]].(8)

   In equilibrium both factors must receive their marginal product: r = [f.sub.1] and w = [f.sub.2], where numerical subscripts denote partial derivatives in the usual manner. Thus, with the above specification, we can compute the collections from labor and capital taxes by [[Tau].sub.L]whl = [[Tau].sub.L][f.sub.2]L = [[Tau].sub.L] (1 - [Gamma])f and [[Tau].sub.k]rk = [[Tau].sub.k][f.sub.1]k = [[Tau].sub.k][Gamma]f respectively. Within a differential incidence framework in which only one factor tax is imposed at a time, balanced government budget requires g(t) = T(t) = [[Tau].sub.L](t)w(t)h(t)l(t) = [[Tau].sub.k]r(t)k(t) for all t.

   Along a balanced growth path, the rate of growth of each endogenous variable is by definition constant, given a constant tax rate ([[Pi].sub.L] or [[Pi].sub.k]). It is well known that a balanced growth equilibrium generally induces a common economic growth rate of macro aggregates, such as consumption, human capital, physical capital and output (see the derivation below).(9) Denote [Mathematical Expression Omitted] as the common growth rate. To derive the representative agent's welfare, U, we assume p [is greater than] (1 - [Alpha])[Theta] such that U is bounded. Then aside from a constant term, U is governed by

   U = [c [(0).sup.[Beta]] x [[(0).sup.1-[Beta]]].sup.1-[Alpha]]/{(1 - [Alpha])[[Rho] - (1 - [Alpha])[Theta]]},

   which can be shown as a monotone increasing function of the balanced growth rate, [Theta].(10) This then enables us to restrict our attention to the growth rate of the economy ([Theta]) rather than the welfare measure (U).

   Labor Taxation

   First, we consider the labor income taxation case where T (t) = [[Pi].sub.L](t)w (t)h (t)l (t). Let [Mathematical Expression Omitted], representing the growth rate of consumption in this case. In equilibrium, constant (unit) time endowment implies that the fraction of time devoted to work (l) has to be constant along balanced growth paths. Under the specified constant-returns-to-scale production technology, one can easily show that both production inputs (k and L) and output (f) have to grow at the same balanced rate. Manipulating the budget constraint (1), we obtain the consumption-capital ratio as [Mathematical Expression Omitted], which is constant along a balanced growth path. Hence, [Mathematical Expression Omitted]. In words, [[Theta].sub.L] is the "common" balanced growth rate of the economy under labor taxation.

   We apply Pontryagin's maximum principle and manipulate to get the following Keynes-Ramsey role equations (see Appendix A for details):

   [f.sub.1] = [Rho] + n + [Alpha][[Theta].sub.L]

   (1 - [[Pi].sub.L])[f.sub.2] = [Rho] + [Alpha][[Theta].sub.L].

   Equations (3a-b) demonstrate the efficient evolution of physical and human capital. Interestingly, a change in the labor income tax rate affects the marginal product of capital only through its...