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

I. 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.

II. 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 impact on the growth rate; it however creates a direct effect on the marginal product of (effective) labor.

Define [z.sub.L] = k/L, we manipulate (3a,b) to get

[[Theta].sub.L] = [[Gamma][[z.sub.L].sup.-(1-[Gamma])] - [Rho] - n]/[Alpha]

[Mathematical Expression Omitted].

Totally differentiating the system (4a,b), we find

[Mathematical Expression Omitted].

Thus a higher labor tax rate decreases the balanced growth rate of the economy. To understand this result, we note that the introduction of a labor tax creates two distortionary margins. First, there is factor substitution on the production side that induces the adoption of capital-intensive technologies. Secondly, there is also a similar substitution on the preference side that shifts labor inputs away from productive activities toward leisure. Both effects raise the effective capital-labor ratio which can be seen from (4b) that d[z.sub.L]/d[[Tau].sub.L] [is less than] 0. With human capital accumulation, an intertemporal distortion emerges via the reallocation of goods and factors over time, as indicated in (4a). Since the human capital evolution is the engine of growth in this model, the decline in the effective labor-capital ratio then reduces the economic growth rate as shown in (5).

Capital Taxation

We next consider the capital income taxation case where T(t) = [[Tau].sub.k](t)r(t)k(t). Define the associated consumption growth rate as [Mathematical Expression Omitted]. Again, one can show that [Mathematical Expression Omitted], i.e., consumption, production inputs and outputs all grow at the same rate, [[Theta].sub.k]. By manipulation (see Appendix B for the details), we have

(1 - [[Tau].sub.k])[f.sub.1] = [Rho] + n + [Alpha][[Theta].sub.k] (6a)

[f.sub.2] = [Rho] + [Alpha][[Theta].sub.k]. (6b)

Aside from its indirect effect through the growth rate, the capital tax rate has a direct impact on the marginal product of capital. We next manipulate (6a,b) to obtain

[[Theta].sub.k] = [[Gamma][[z.sub.k].sup.-(1 - [Gamma])] - [Rho] - n]/[Alpha] (7a)

[Mathematical Expression Omitted]

where [z.sub.k] = [(1 - [[Tau].sub.k]).sup.-1/(1 - [Gamma])](k/L). Totally differentiating the system (7a,b), one gets

[Mathematical Expression Omitted]

From (7), an increase in the capital tax rate leads to a lower tax-adjusted effective capital-labor ratio ([z.sub.k]) due to distortions from factor substitution and intertemporal reallocation. Analogous to the labor taxation case, a higher capital tax rate reduces the balanced growth rate of the economy.

Factor Taxes Compared

In a balanced-growth equilibrium, we find that the effect of a higher (labor or capital) tax rate is to suppress the common growth rate of the economy.(11)

Generally speaking, consumption, production inputs and output may grow at different rates in transition. Lower consumption growth may emerge in an economy with saving rates higher than that derived from the Keynes-Ramsey equation under balanced growth, which is usually accompanied by an enhancement of net export to output ratio. Moreover, aside from the negative effect of tax rates on the above mentioned economic aggregates, an increase in the rate of change of tax rates ([Mathematical Expression Omitted] or [Mathematical Expression Omitted]) will also decrease the growth rates of macroeconomic aggregates, which can be seen by totally differentiating the equation system (4a,b) and (7a,b) around the balanced growth equilibrium solution. Qualitatively, the above balanced growth analysis provides a benchmark that enables us to characterize movements in the growth rates of macroeconomic aggregates, especially for a rapidly growing economy.

To examine which factor tax depresses economic growth more, we focus on the comparison of the magnitude of [[Theta].sub.L] and [[Theta].sub.k] with equal tax yield under a unitary-tax setup. Comparing (4b) with (7b), one can see that the two equations of z's are almost identical except for the coefficients attached to the highest order terms. By the implicit function theorem, we can easily find the negative relation between these coefficients and z's and hence conclude(12)

sign{[z.sub.L] - [z.sub.k]} = sign{Q}. (9)

where Q = [(1 - [[Tau].sub.k]).sup.[Gamma]/(1 - [Gamma])] - (1 - [[Tau].sub.L]) measures the difference in the magnitude of the coefficients attached to the highest order terms of z's. From (4a) and (7a), it is clear that the magnitude of the economic growth rate depends negatively on the effective capital-labor ratio measures ([z.sub.L] or [z.sub.k]) under diminishing returns. These together with (9), we have

sign{[[Theta].sub.k] - [[Theta].sub.L]} = sign{Q}. (10)

Capital taxation leads to relatively high economic growth compared to labor taxation if Q is positive.

So far, the above discussion is valid based on the presumption that human capital accumulation is crucial in increasing productivity. Otherwise, labor is expected to be completely inelastic in the long ran. Once we endogenize human capital, the sign of Q becomes the most important criterion determining the relative magnitude of a factor tax distortion. Strictly speaking, there are two important sets of parameters involved in the Q expression: the capital income share ([Gamma]) and the existing tax distortion measured by the tax rates ([[Tau].sub.L] and [[Tau].sub.k]). An economy with highly labor-intensive production technologies is usually associated with a lower capital income share. To link with the traditional optimal income tax literature closely, we need to study how factor income share relates to the price elasticity of factor inputs. Notice that under constant returns, factor demand elasticity are not well defined. Nevertheless, for illustration, we may start with a general Cobb-Douglas production function with diminishing returns: f = [k.sup.[Gamma]][L.sup.m], where m [is less than] (1 - [Gamma]). The diminishing returns technology can be regarded as of an individual producer, while the constant returns one can be inferred as involving the aggregate economy. This is plausible in an economy with positive externalities in human capital (see a discussion in Romer [13]). For individual derived demands for factors, their elasticities can be calculated as

[Mathematical Expression Omitted]

[Mathematical Expression Omitted].

Thus, the price elasticities of factor demands are positively related to the income shares of the corresponding factors. In a labor-intensive economy in which labor income share is higher, one can expect that labor is very elastic in the long run as human capital is endogenously accumulated. In that case, a tax on labor may generate greater welfare costs.

In contrast with previous work, such as Homma [6], Summers [14] and Judd [8], we find that, in principle, capital taxation need not be more distortionary to economic growth (or welfare). Recall that the sign of Q depends crucially on the labor income share and the tax rates being levied. Causal empiricism suggests that labor income share is usually greater than capital income share, i.e., [Gamma] [is less than] 0.5.(13) On the other hand, the labor tax rate is likely to be smaller than the capital tax rate in practice. Therefore, Q is in general ambiguous in sign and no definitive theoretical conclusion can be drawn by comparing the associated economic growth rates under different tax schemes. Furthermore, if a mixed-tax economy is considered, there is no straightforward way to construct a theoretical measure parallel to Q to compare the negative effect of the two factor taxes on the growth rate of the economy. This then motivates us to pursue the issue of factor tax distortions from an empirical perspective.

III. Empirical Evidence

We now turn to an empirical investigation of the effects of factor taxation on economic growth. In examining the role of human capital, it would be desirable to focus on a country which exhibits a record of sustained growth and of notable improvement of the quality of labor. Taiwan fulfils our criterion and, to our great advantage, offers high quality time-series data pertinent to the analysis.

Data and Univariate Statistics

We employ the annual data of Taiwan from 1954 to 1986. Our first task is to find an appropriate measure for the human capital skill level. We construct an index of the percentage of the population completing college and university education (1981 = 100) and refer to it as a human capital skill index (H). The long-run growth rate of this skill index is 6.24% over the sample period. The (year-by-year) growth rate of the human capital skill index (GRH) appears to be trend-stationary.

[ILLUSTRATION OMITTED]

The raw labor measure is the employment rate, i.e., the ratio of employment to total population, denoted by E. Thus, effective labor is measured by L = EH, which is also trend-stationary. Other macro aggregates are (per capita) consumption (C), measured by per capita real private consumption; (per capita) income (Y), measured by per capita real domestic (aggregate) demand (i.e., the sum of private consumption, government spending financed by factor taxes and investment); and, physical capital (K), measured by per capita real gross capital stock owned by the private and public enterprises. Both consumption and output growth rates are trend-stationary, [TABULAR DATA OMITTED] while the growth rate of physical capital shows first-order autocorrelation. Moreover, output and effective labor are more volatile than consumption and physical capital.

[ILLUSTRATION OMITTED]

There are some points worth emphasizing. First, there are only three major recessions in terms of output growth: 1975, 1982 and 1985. The first two are due to oil crises, while the last one is a result from the so-called "Tenth-Trust financial panic." Secondly, one can see that physical capital does not move closely with output, as compared to effective labor. In particular, in 1967, 1975 and 1985, physical capital growth seems inversely related to output growth. Thus, the role of effective labor can perhaps help to explain the movements in output. Thirdly, without the consideration of human capital, the two major inputs, K and E grow at very different rates over the sample period (7.92% and 0.77% respectively). Such a significant diffusion in the rates of factor input growth contrasts with the prediction of the neoclassical growth theory, which suggests that the mismatch of the two major factor inputs cannot have generated the rapid output growth witnessed in Taiwan. By introducing endogenous human capital, the effective labor measure grows at 7.01%, which is very close to the capital growth rate and thus consistent with the prediction of the balanced growth model (see King, Plosser and Rebelo [9]). Finally, even with a human capital skill level measure, output variation still cannot be fully explained by the two input factors, especially in 1965, 1973, 1979 and 1982. This motivates us to consider some exogenous variables that are not present in our theoretical framework.

Two crucial exogenous variables that are missing in our theoretical analysis are government spending and international trade. In the past three decades, the government of Taiwan essentially operates at balanced budget. Inasmuch as our concern is with taxes on capital and labor, we can simply compute the government spending, denoted by G, as the sum of labor and capital income taxes. We then use the ratio of real exports to real imports to measure the structure of international trade.(14) By providing productive services to the public, a higher growth rate of the government sector (GRG) is expected to increase the economic growth rate, especially in such a government-directed developing country. On the other hand, a large export-import ratio (GRX) is, in an export-oriented developing country like Taiwan, expected to increase demand for domestic goods and thus to raise production. Therefore, a higher growth rate of GRX promotes domestic [TABULAR DATA OMITTED] output growth. In the longer run, higher output growth induces higher rates of consumption growth.

For tax rate variables, we measure the capital tax rate (TRK) by real business and profit tax collections as a ratio to the sum of corporate earnings and government and public enterprise property income. The ratio of personal income tax collections to wages and compensations is used to measure the labor tax rate (TRL). The labor tax share (TSL) is thus the ratio of personal income tax to total factor income tax collections. Both tax rates have upward trends, especially after the Tax Reform Act of 1969-70. Since labor income tax increases at a higher rate than does capital income tax, the labor tax share has exhibited an upward trend since the early 1960s.

Finally, it is worth noting that our computed series of government spending and output are in fact highly correlated with the actual government consumption expenditure and real GDP, respectively (with correlation coefficients at or above 0.977).

Distortionary Effects of Factor Taxation

Before examining factor tax distortions, we first study how each factor tax affects factor accumulation. This is done by regressing the growth rates of physical capital and effective labor on capital and labor income tax rates, respectively. Table II shows that each factor tax rate and its growth rate have significantly negative effects on factor accumulation. Specifically, a percentage point increase in the capital (labor) tax rate lowers the rate of physical capital (effective labor) growth by 0.25% (3.78%). Notably, effective labor in Taiwan appears to be rather elastic and so it is extremely sensitive to changes in the labor income tax rate. Moreover, simple growth accounting indicates that enlargement in employment and enhancement in human capital have accounted for 60 percent of the output growth in Taiwan, while physical capital accumulation have contributed only 32 percent. From these preliminary analyses, one can see that labor income taxation is likely to generate greater macroeconomic distortions than capital income taxation.

In practice, consumption and output may not grow at a common rate. Thus, we examine the distortionary effects of factor taxation on the growth rates of both variables (GRC and GRY, denoting consumption and output growth, respectively). From (5), (8) and the discussions on the characteristics of transition paths presented in section II above, we can specify the following regression equation:

[GRZ.sub.t] = [a.sub.0] + [a.sub.1]TIME + [a.sub.2][TRF.sub.t] + [a.sub.3][GRTRF.sub.t] + [a.sub.4][GRG.sub.t] + [a.sub.5][GRX.sub.t], (11)

where GRZ denotes the growth rate of an endogenous variable Z(Z = C, Y); TRF represents the tax rate on a production factor F(F = K,L); GRTRF is the rate of change of the tax rate on F; GRG and GRX are the growth rates of government spending (G) and the export-import ratio (X), respectively; and, t is the time index. Applying the univariate properties mentioned above, we incorporate a time trend variable (TIME) into the regressions.

The distortionary taxes considered are the two major factor income taxes. Our theory predicts that an increase in factor tax rates or their growth rates suppresses economic growth: [a.sub.2] [is less than] 0 and [a.sub.3] [is less than] 0. Further, from the discussion in section III, one expects that [a.sub.4] [is greater than] 0 and [a.sub.5] [is greater than] 0. We note that the purpose of constructing these regressions is not to forecast, but to perform hypothesis testing that enables us to examine the effects of factor taxation on economic growth after isolating impacts from other major internal and external exogenous factors, such as government spending and the export-import ratio.

The regression results are summarized in Table III. We find that all the regressions from our simple OLS estimation have significant explanatory power at the 5% level (using F-test). The signs of all significant coefficient estimates of the growth rates of government spending and export-import ratio are consistent with our theoretical predictions.(15) Since our main purpose is to investigate the effects of factor taxation on the growth rates of macroeconomic aggregates, we will not report the coefficient estimates of constant and time trend terms.

Notice that both tax rates and their growth rates affect negatively the growth rates of consumption and output. When we separate the two tax rates, the adverse effects of TRK and GRTRL are significant (at the 5% level) in both consumption and output regressions. TRL significantly suppresses consumption growth, while GRTRK is not influential in either regression. When we combine both taxes into each regression, the labor income tax rate and its growth rates have significant negative effects on consumption growth. The capital income tax rate is, though its growth rate is influential, not very important in explaining consumption growth. For the output regression, neither tax rates have significant effect, but their growth rates are rather influential. Overall, labor taxation appears to generate greater distortionary effects on the rates of growth of consumption and output (especially the former). A percentage point increase in the labor income tax rate decreases the growth rate of consumption by 1.46%, while a percentage point increase in the growth rate of the labor tax rate reduces the growth rates of consumption and output by 0.42% and 0.59%, respectively.

Using results from Tallman and Wang [15], the output elasticity of capital for Taiwan is around 0.2 and the constant-returns-to-scale hypothesis cannot be rejected in the presence of endogenous human capital evolution. For the major OECD countries, the capital income share ranges from 0.25 to 0.40, far higher than Taiwan's figure. Thus, Taiwan can be called a relatively labor-intensive economy and so labor input is rather elastic. This may explain why labor taxation is more distortionary to economic growth (see the discussion in section II).

[TABULAR DATA OMITTED]

Alternative Comparison between Factor Taxes

Section II has suggested that with endogenous human capital accumulation, labor income taxation may be more distortionary than capital income taxation. Within the unitary-tax, differential-incidence framework, such a comparison depends crucially on the criterion described in (10). Specifically, we need to check the sign of Q which is a function of tax rates and the output elasticity of capital (or capital income share under constant returns). The long-run average values of (average) labor and capital tax rates in Taiwan over the sample period are estimated as 3.9 percent and 13.3 percent, respectively.(16) By regressing tax revenues on the corresponding tax bases, we can obtain the estimated marginal tax rates of labor and capital income taxes, which are 5.4% and 14.3%, respectively. Combining these tax rate measures with the output elasticity of capital (around 0.2), we get Q [is greater than] 0. This indicates that labor taxation is likely to be more distortionary.(17)

In practice, Taiwan is a mixed-tax economy in which the long-run average labor tax share (to total factor tax collection) is 64.6%. Thus, the above calibration focusing on the sign of Q may not be completely convincing without further empirical investigation. This motivates us to provide an additional regression analysis. Aside from GRG, GRX and a time trend, our regression equation can be specified as:

[GRZ.sub.t] = [b.sub.0] + [b.sub.1][(TSL).sub.t] + [b.sub.2][(TSL - 1).sub.t] + ... + [b.sub.s + 1][(TSL -S).sub.t], (12)

where (TSL -j) denotes the j-year lagged labor income tax share (to total factor tax collection). Under the Cobb-Douglas production specification, it can be easily shown that TSL = (1 - [Gamma])[[Tau].sub.L]/[(1 - [Gamma])[[Tau].sub.L] + [Gamma][[Tau].sub.k]], which can be treated as exogenous, given that both tax rates are [TABULAR DATA OMITTED] government's instruments. The optimal lag length S is determined by the Akaike information criterion (which is found to be one). From 1954 to 1986, the long-run growth rates of (average) capital and labor tax rates are 0.46% and 1.98%, respectively. Thus, Taiwan is an increasing-tax-rate economy in which the government tends to move toward labor taxation over time (since the capital tax growth rate is smaller than the labor tax growth rate). In this case, labor taxation is said to be more distortionary to economic growth than capital taxation if the cumulative effect of TSL in (12) is negative, i.e., [summation of] [b.sub.i] [is less than] 0 where i = 1 to S + 1.

Standard correlation analysis shows that the growth rates of consumption and output are negatively correlated with the labor tax share. Using OLS estimation for (12), we can examine how the labor tax share affects the economic growth rates. We find that the cumulative effects of the labor tax share on the growth rates of consumption and output are all negative. When GRG and GRX are excluded from the regressions, better statistical results are obtained. A percentage point increase in the labor tax share is found to permanently decrease the growth rates of consumption and output by 0.31% and 0.20%, respectively.(18) This corroborates with our earlier result that labor taxation has been more distortionary to economic growth than capital taxation in Taiwan.

[ILLUSTRATION OMITTED]

To summarize, we reiterate that both factor taxes would slow down economic growth. We note that the accumulation of human capital plays a crucial role in the economic development of Taiwan. Since Taiwan's production technologies are mostly labor-intensive, labor taxation can seriously suppress the growth rates of output and consumption. Our results suggest, in contrast with the conventional perception, that a shift from capital taxation to labor taxation, as in Taiwan, in effect reduces the economic growth rate.

IV. Conclusions

This paper provides a first empirical attempt to examine the effect of factor taxation on the growth rates of macroeconomic aggregates based on an endogenous growth model. Since both physical and human capital accumulation are endogenously determined, both labor and capital income taxation have similar dynamic impacts on the macroeconomy. This then calls for reevaluation of the distortionary effects of factor taxes on economic growth.

We find that within a differential incidence framework in which only one particular distortionary tax is imposed at a time, capital income taxation need not be more distortionary than labor income taxation, with the ultimate outcome depends mainly on factor intensity and existing tax distortions. In our empirical study, we use time-series data of Taiwan where the evolution of human capital has played a crucial role in its economic development. Since most of the production technologies in Taiwan are highly labor-intensive, the labor income share is high and labor input becomes rather elastic. A tax on labor turns out to be very distortionary to human capital accumulation and goods production. We find that a shift from capital taxation to labor taxation can slow down economic growth, contrary to traditional beliefs.

It is our belief that our conclusion may be applied to other developing countries with similar labor-market and income-tax structures: production technologies are labor-intensive, the labor income share is large, the improvement in education is significant, and labor and capital income taxes are the major sources of government revenue. However, we would like to caution our readers that the tax system in Taiwan does have some special features: (i) personal interest and dividend incomes are virtually tax-free; (ii) small businessmen, who create value-added mainly from labor input, are allowed to file the personal (labor) income tax only; (iii) school teachers, about one-sixth of the labor force, receive full tax exemption on their earnings; and (iv) custom duties on intermediate investment goods are negligible after accounting for import rebates. The first feature enables us to differentiate labor from capital income tax more clearly. While the second feature may enlarge the distortionary effects of labor taxation, the third may reduce them. The last feature, on the other hand, lowers the potential adverse effects of capital taxation.

Along our research lines, the application of a complete calibration and simulation analysis and the incorporation of a productive government sector are possible extensions for future work. Moreover, an evaluation of factor taxation in the context of "equity" or "stabilization" (rather than "growth") would also be in order.

Appendix A: Derivation of the Keynes-Ramsey Rule (Labor Taxation Case)

In order to solve for the balanced growth equilibrium in the labor taxation case, we first specify the current-value Hamiltonian as

[H.sub.L](c, l, [Psi], k, h, [[Lambda].sub.L1], [[Lambda].sub.L2], t) = u(c, h(1 - l)) + [[Lambda].sub.L1]([Psi]f - nk - [[Tau].sub.L]whl - c) + [[Lambda].sub.L2][(1 - [Psi])f],

where [Lambda]'s are costate variables. Given the production function specification, application of Pontryagin's Maximum Principle yields

[u.sub.1] - [[Lambda].sub.L1] = 0 (A1)

- [u.sub.2]h + [[[Lambda].sub.L1]([Psi] - [[Tau].sub.L]) + [[Lambda].sub.L2](1 - [Psi])][f.sub.2]h = 0 (A2)

[[Lambda].sub.L1] = [[Lambda].sub.L2] (A3)

[Mathematical Expression Omitted]

[Mathematical Expression Omitted]

[Mathematical Expression Omitted]

[Mathematical Expression Omitted].

The transversality conditions are lim [e.sup.-[Rho]t] [[Lambda].sub.L1](t)k(t) where t [approaches] [infinity] = 0 and lim [e.sup.-[Rho]t] [[Lambda].sub.L2](t)h(t) where t [approaches] [infinity] = 0. Recall that [Mathematical Expression Omitted] and that l is constant along a balanced growth path. Applying the utility function specification and using (A1)-(A3), we have

[(1 - [Beta])/[Beta]][c/(1 - l)] = (1 - [[Tau].sub.L)[f.sub.2]h. (A8)

Equations (A3) and (A4) together result in

[Mathematical Expression Omitted].

Similarly, using (A2), (A3) and (A5), we obtain

[Mathematical Expression Omitted].

Equations (A9) and (A10) imply that both [f.sub.1] and [f.sub.2] are constant along balanced growth paths. Thus, total differentiation of (A8) with respect to time leads to

[Mathematical Expression Omitted].

Substituting (A11) into (A9) and (A10) gives (3a) and (3b) in the text.

Appendix B: Derivation of the Keynes-Ramsey Rule (Capital Taxation Case)

For the capital taxation case, the current-value Hamiltonian can be written as

[H.sub.k](c, l, [Psi], k, h, [[Lambda].sub.k1], [[Lambda].sub.k2], t) = u(c, h(1 - l)) + [[Lambda].sub.k1]([Psi]f - nk - [[Tau].sub.k][f.sub.1]k - c) + [[Lambda].sub.k2][(1 - [Psi])f],

where [Lambda]'s are costate variables. Given the production function specification, application of Pontryagin's Maximum Principle yields

[u.sub.1] - [[Lambda].sub.k1] = 0 (B1)

- [u.sub.2]h + [[[Lambda].sub.k1] [Psi] + [[Lambda].sub.k2](1 - [Psi])][f.sub.2]h = 0 (B2)

[[Lambda].sub.k1] = [[Lambda].sub.k2] (B3)

[Mathematical Expression Omitted]

[Mathematical Expression Omitted]

[Mathematical Expression Omitted]

[Mathematical Expression Omitted].

The transversality conditions are lim [e.sup.-pt][[Lambda].sub.k1](t)k(t) where t[approaches][infinity] = 0 and lim [e.sup.-pt][[Lambda].sub.k2](t)h(t) where t [approaches][infinity] = 0. Recall that [Mathematical Expression Omitted] and that l is constant along a balanced growth path. Applying the utility function specification and using (B1) - (B3), we have

[(1 - [Beta])/[Beta]][c/(1 - l)] = [f.sub.2]h. (B8)

Equations (B3) and (B4) together result in

[Mathematical Expression Omitted].

Similarly, using (B2), (B3) and (B5), we obtain

[Mathematical Expression Omitted].

Equations (B9) and (B10) imply that both [f.sub.1] and [f.sub.2] are constant along balanced growth paths. Thus, total differentiation of (B8) with respect to time leads to

[Mathematical Expression Omitted].

Substituting (B11) into (B9) and (B10) gives (6a) and (6b) in the text.

Appendix C: Description of the Data

A. Primary Data

C = per capita real private consumption expenditure

I = per capita real private and public enterprise gross domestic fixed capital formation (gross investment)

TK = per capita real business and profit tax (deflated by government spending deflator)

TL = per capita real personal income tax (deflated by government spending deflator)

YK = per capita real corporate savings and government public enterprise property income (deflated by national income at factor price deflator)

YL = per capita real compensation of employees (deflated by national income at factor price deflator)

K = per capita real gross capital stock owned by private and by public enterprises (deflated by gross investment deflator)

H = index of higher educated population at ages of 6 and over

E = employment ratio (per capita employment)

N = population

X = export-import ratio

(TK and TL are computed using 2-year moving average of fiscal-year data)

B. Computed Data

L = effective labor index, L = E x H (%)

G = per capita real government spending financed by factor taxation, G = TK + TL

Y = per capita real income, Y = C + I + G

YKA = per capita real capital income, YKA = Y x YK/(YK + YL)

YLA = per capita real labor income, YLA = Y x YL/(YK + YL)

TRK = capital income tax rate, TRK = TK x 100/YKA (%)

TRK = labor income tax rate, TRL = TL x 100/YLA (%)

TSL = labor tax share, TSL = TL x 100/(TK + TL) (%)

UNITS:

(1) C, I, TK, TL, YK, YL and K: in thousands of New Taiwan Dollars per person at 1981 constant prices

(2) N: in thousands of persons

(3) E: %

(4) H: % (1981 = 100)

SOURCES:

(1) C, I, YK, YL and X: from the National Income (NI) of the Republic of China (ROC), 1988, Directorate-Generate of Budget, Accounting, and Statistics (DGBAS), and the Taiwan Statistical Data Book (TSDB), 1989, Council for Economic Planning and Development (CEPD)

(2) TK and TL: from the Yearbook of Financial Statistics of the ROC, 1988, and the Yearbook of Tax Statistics, ROC, 1988, Ministry of Finance

(3) N: from the Yearbook of Interior Statistics, ROC, 1988, Ministry of Interior

(4) E: from the Yearbook of Labor Statistics, ROC, 1988, DGBAS

(5) H: from the TSDB

(6) K: from the NI and the Input-Output Survey, 1979, CEPD

1. Boadway [3] showed that labor taxation may be more distortionary in the short run than capital taxation.

2. The importance of human capital accumulation in neoclassical growth theory has been addressed by Lucas [10], which yields predictions in accord with international evidence.

3. The annual growth rate of a variable is computed by the slope coefficient estimate of the OLS regression of its log value on the time trend.

4. Using the Denison accounting for potential output growth given the labor income share of 0.8, more than 64% of the growth of per capita real GDP cannot be explained by the two major production inputs, physical capital stock and employment.

5. Notable among them are the 1969-70 study by the Tax Reform commission of the Executive Yuan, the 1985 one by the Economic Renovation Commission, and the 1988-89 one by the ministry of Finance.

6. For discussion concerning an active government sector that directly affects preferences and production technologies, the reader is referred to Burro [1].

7. For [Alpha] = 1, we have u (c, x) = [Beta] In (c) + (1 - [Beta]) ln(x). This utility function is a minor variation of Lucas [11].

8. This specification of production technology has been often used in endogenous growth models. For example, see Lucas [10] and Barro [1].

9. See King, Plosser and Rebelo [9] for further discussion.

10. The relationship between c(0) and [Theta] is ambiguous in nature. However, for the long-run effect on welfare, one may focus merely on the effect of [Theta]. It can be shown that welfare (U) is increasing in [Theta] if and only if [Theta] is bounded below by -[1 - [Alpha](1 - [Beta])][Rho]/[[Alpha] + [Alpha](1 - [Alpha])(1 - [Beta])]. According to Hall [5], the intenemporal elasticity of substitution is very tow and of is usually above 5. Following Barro [1] and Lucas [11], we take [Beta] = 1/3 and [Rho] = 0.02. Then this lower bound of [Theta] turns out to be negative. Therefore, for any growing economy, U is a monotone increasing function of [Theta].

11. This result needs modification if a productive government sector is introduced. For instance, the government can use the tax revenues to subsidize the education sector or to invest in productive public sector capital such as infrastructure. This then generates a secondary growth-enhancing effect of taxation. However, our result that factor taxation suppresses growth will hold up with if the government is not more efficient than the private, i.e., the secondary growth-promoting effect of factor taxation is dominated by its primary growth-retarding effect.

12. Let [Mathematical Expression Omitted] and [Mathematical Expression Omitted] where [A.sub.L] = (1 - [[Tau].sub.L]) and [A.sub.k] = [(1 - [[Tau].sub.k]).sup.[Gamma]/(1 - [Gamma])]. Thus, by implicit function theorem, d[z.sub.i]/d[A.sub.i] = -([Delta][G.sub.i]/[Delta][A.sub.i])/([Delta][G.sub.i]/[Delta][z.sub.i]) [is less than] 0. Define Q = [A.sub.k] - [A.sub.L], we obtain (9).

13. For the U.S., [Gamma] falls in between 25% and 34%. For a recent reference, see Lucas [10].

14. In Taiwan, more than 92% of imports are raw materials and capital goods and these imports, as the record indicates, are used largely for producing exportables. Imports, in fact, are shown to be highly correlated with exports. The import-export ratio may then be regarded as an exogenous measure of the structure of international trade.

15. For all explanatory variables with unambiguous theoretical predictions, we use a one-tailed t-test to examine their significance.

16. Under the Taiwan government's policy, the labor tax rate has been low compared to most developed countries. Moreover, school teachers, account for about 16% of the labor force, earn full tax exemption. This further lowers the average labor tax rate.

17. Our conclusion is invariant to the selection of the tax rates; i.e., one can use either average or marginal tax rate. Further, over the range of all plausible output elasticity of capital, from 0.16 to 0.23, our conclusion remains unchanged.

18. The joint F-test values of these cumulative effects are 3.11 and 5.46, significant at the 10% and 5% levels, respectively.

References

1. Barro, Robert J., "Government Spending in a Simple Model of Endogenous Growth." Journal of Political Economy, October 1990, S103-25.

2. Becker, Gary S., "A Theory of the Allocation of Time." Economic Journal, September 1965, 493-517.

3. Boadway, Robin W., "Long-run Tax Incidence: A Comparative Dynamic Approach." Review of Economic Studies, September 1979, 505-11.

4. Feldstein, Martin S., "Tax Incidence in a Growing Economy with Variable Factor Supply." Quarterly Journal of Economics, November 1974, 551-73.

5. Hall, Robert E., "Intertemporal Substitution in Consumption." Journal of Political Economy, April 1988, 339-57.

6. Homma, Masaaki, "A Dynamic Analysis of the Differential Incidence of Capital and Labour Taxes in a Two-class Economy." Journal of Public Economics, June 1981, 363-78.

7. Huang, Cliff, Jen-Chi Cheng, Ching-Sheng Chou and Shun-Ying Lin, "The Substitutability of Monetary Assets in Taiwan." Southern Economic Journal, October 1991, 975-87.

8. Judd, Kenneth L., "The Welfare Cost of Factor Taxation in a Perfect-Foresight Model." Journal of Political Economy, August 1987, 675-709.

9. King, Robert G., Charles Plosser and Sergio Rebelo, "Production, Growth and Business Cycles: I. The Basic Business Cycle Model." Journal of Monetary Economics, March/May 1988, 195-232.

10. Lucas, Robert E., Jr., "On the Mechanics of Economic Development." Journal of Monetary Economics, August 1988, 3-42.

11. -----, "Supply-side Economics: An Analytical Review." Oxford Economic Papers, February 1990, 293-316.

12. Riew, John. "Taxation and Development: the Taiwan Model." Working Paper, University Park: Pennsylvania State University, 1988.

13. Romer, Paul M. "Human Capital and Growth: Theory and Evidence." Working Paper, Cambridge: NBER, 1989.

14. Summers, Lawrence H., "Capital Taxation and Accumulation in a Life Cycle Growth Model." American Economic Review, September 1981, 533-44.

15. Tallman, Ellis and Ping Wang. "Human Capital and Endogenous Growth: Evidence from Taiwan (1954-86)." Working Paper, Atlanta: Federal Reserve Bank, 1989.

16. Tax Reform Commission. Commission Report, Taipei: Tax Committee, 1970/1985/1989.