1. Growth driven by human capital

2. Growth driven by innovation

Technological innovation is identified as another important growth factor. The innovation approach of endogenous growth theory emphasizes deliberate efforts to develop new products and technology. In models of endogenous growth driven by knowledge spillover, returns to knowledge accumulation are external to firms. Knowledge is accumulated because it is the by-product of the accumulation of other factors whose returns are internal to firms. In models of endogenous growth driven by innovation, however, such returns are internal (at least partially) to firms so that firms have incentive to innovate. The market structure of imperfect competition is used in the innovation approach to model the profit-seeking innovation process. Here we specify a model of product variety based on Romer (1990). Models of quality differentials have the same essence as models of product variety according to Grossman and Helpman (1991).

In this model, the k-factor in equation (1) is human capital and the x-factor is the input of capital goods which are defined by

where x_i denotes capital good i produced according to the design i developed by a research sector in the economy, n_t is the number of product designs available at time t. All capital goods are assumed to be substitutes and symmetric. The index for designs is treated as a continuous variable.

To isolate the effects of human capital accumulation from those of product variety development, we assume there is no human capital accumulation over time, that is, k_t=k. The growth of the economy now is driven solely by the increase in the number of product designs. The production of product designs follows

where B is the productivity parameter of the production function for new designs and k_n is the human capital input in the production of new designs. Time subscripts are suppressed.

The key feature of this production function is that total number of product designs available, (n), has a positive external effect on the production of new designs. It is the linearity of ṅ in n that guarantees a constant growth rate of new product designs, which is also the steady-state growth rate of the economy. This growth rate is given by γ=Bk_n, k_n being a constant in the steady state. As the product variety expands, profit per product design declines. The offsetting factor in this model is the decline in design producing cost, which is due to the spillover from the total stock of knowledge (the total number of designs). It is this knowledge spillover in design production that maintains the research incentive and sustains the growth.

3. Growth driven by public infrastructure

Public infrastructure is sometimes thought to play an important role in offsetting the decline in the returns to private investment. Barro (1990) and Barro and Sala-i-Martin (1992a), among others, have modeled this idea in the endogenous growth framework. Based on the nature of public services, the following three cases have been considered.

1. Steady-state growth effects

a. Income taxation

Consider a flat income tax at a rate τ. The after-tax per capita income is given by and the after-tax rate of return to the k-factor is given by

$y_t\begin{array}{cc}=(1-\tau )A{k}_t^{1-\alpha }{x}_t^{\alpha }& (1\prime )\end{array}$

and the after-tax rate of return to the k-factor is given by

$r_t\begin{array}{cc}=(1-\tau )(1-\alpha )A{\left(\frac{x_t}{k_t}\right)}^{\alpha }\mathrm{.}& (4\prime )\end{array}$

The steady-state growth implications of this income tax in different endogenous growth models are summarized in Table 1.

Table 1.

Growth Implications of Income Taxation in Various Endogenous Growth Models

Note: H models and P models refer, respectively, to human capital driven and public infrastructure driven endogenous growth models. The steady-state growth rate in each type of model is derived from a certain benchmark model of that type discussed in Section II.

Table 1.

Growth Implications of Income Taxation in Various Endogenous Growth Models

	Steady-State Growth Rate	Growth Effects of Income Tax	Growth Maximizing Income Tax Rate
Ak models (Rebelo (1991))	τ=(1/σ)[(1-τ)A-ρ]	Negative	Zero
H models without spillover (Rebelo (1991))	τ=(1/σ) [(1-τ)1-β/1-β+α	Negative	Zero
H models without spillover (Lucas (1988))	τ=(1/σ)[B-ρ]	Zero	Irrelevant
H models with spillover (Romer (1986))	τ=(1/σ)[(1-τ)(1-α)A-ρ]	Negative	Ambiguous
Innovation models (Romer (1990))	τ=[(1-α)Bk-ρ]/(σ+1-α)	Zero	Irrelevant
P models with inputs as private goods (Barro and Sala-i-Martin (1992a))	τ=(1/σ)[(1-τ)τα/1-α(1-α)A1/1-α-ρ]	Positive or negative	Positive (=α)
P models with inputs as public goods (Barro and Sala-i-Martin (1992a))	τ=(1/σ)[(1-τ)τα/1-α(1-α)A1/1-αηα/1-α-ρ]	Positive or negative	Positive (=α)
P models with congestion (Barro and Sala-i-Martin (1992a))	τ=(1/σ)[(1-τ)τα/1-αA1/1-α-ρ]	Positive or negative	Positive (=α)

Note: H models and P models refer, respectively, to human capital driven and public infrastructure driven endogenous growth models. The steady-state growth rate in each type of model is derived from a certain benchmark model of that type discussed in Section II.

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Table 1.

Growth Implications of Income Taxation in Various Endogenous Growth Models

	Steady-State Growth Rate	Growth Effects of Income Tax	Growth Maximizing Income Tax Rate
Ak models (Rebelo (1991))	τ=(1/σ)[(1-τ)A-ρ]	Negative	Zero
H models without spillover (Rebelo (1991))	τ=(1/σ) [(1-τ)1-β/1-β+α	Negative	Zero
H models without spillover (Lucas (1988))	τ=(1/σ)[B-ρ]	Zero	Irrelevant
H models with spillover (Romer (1986))	τ=(1/σ)[(1-τ)(1-α)A-ρ]	Negative	Ambiguous
Innovation models (Romer (1990))	τ=[(1-α)Bk-ρ]/(σ+1-α)	Zero	Irrelevant
P models with inputs as private goods (Barro and Sala-i-Martin (1992a))	τ=(1/σ)[(1-τ)τα/1-α(1-α)A1/1-α-ρ]	Positive or negative	Positive (=α)
P models with inputs as public goods (Barro and Sala-i-Martin (1992a))	τ=(1/σ)[(1-τ)τα/1-α(1-α)A1/1-αηα/1-α-ρ]	Positive or negative	Positive (=α)
P models with congestion (Barro and Sala-i-Martin (1992a))	τ=(1/σ)[(1-τ)τα/1-αA1/1-α-ρ]	Positive or negative	Positive (=α)

Note: H models and P models refer, respectively, to human capital driven and public infrastructure driven endogenous growth models. The steady-state growth rate in each type of model is derived from a certain benchmark model of that type discussed in Section II.

It is clear from Table 1 that growth implications of income taxation are sensitive to model specifications. The effects of an increase in the income tax rate on the long-run growth rate of the economy could be negative, zero, or positive. The following discussions are aimed at clarifying the conditions behind these different growth implications.

The negative (steady-state) growth effects of income taxation are not difficult to understand, because an increase in income tax rate decreases the rate of return to the k-factor given the x-factor, as shown in equation (4’), which in turn has a negative impact on the steady-state growth rate. What we need to examine further is the possible indirect growth effects from the change in the x-factor due to the increase in the income tax rate.

By combining physical and human capital into broad capital and implicitly assuming identical production technology of physical and human capital, the Ak model lacks the necessary structure to discuss the indirect growth effects mentioned above. This drawback is partially overcome by the models specifying physical and human capital accumulation separately. Growth implications of income taxation are found to be very sensitive to the specification of the human capital accumulation process and its tax treatment.

Suppose the tax treatment is such that income from the goods producing sector is taxed at the rate τ, while income from the human capital producing sector is not taxed. People respond to an increase in the income tax rate by investing more in the human capital producing sector, which leads to a lower steady-state physical to human capital ratio. According to equation (4’), a lower steady-state physical to human capital ratio offsets the decline in the real rate of return to capital due to a direct disincentive from the income tax rate increase. If human capital accumulation is specified by equation (5) as in Rebelo (1991), that is, both physical and human capital are inputs in producing new human capital, the offset is partial and the net growth effects are negative, as shown in Table 1.

However, if only human capital is used as an input in the production of new human capital, as in Lucas (1988), the growth implications of income taxation will change dramatically. The real rate of return to capital is now given by

$\begin{array}{cc}r=(1-\tau )(1-\alpha )A{\left(\frac{x_y}{x}\frac{x}{k}\right)}^{\alpha }=B\left(\frac{x_h}{x}\right)& (4\prime \prime )\end{array}$

where x_y and x_h are human capital allocated to goods production and human capital production, respectively. In the steady state, X_y/x and x_h/x are constant. As τ rises, people respond by investing more in the human capital producing sector. This leads to a lower physical to human capital ratio in the long run which offsets completely the direct disincentive of an increase in the income tax rate on the real rate of return to capital; consequently, the net growth effects of this increase in the income tax rate are zero. The reason behind the different results of the Rebelo model and the Lucas model is that human capital accumulation, although not taxed directly due to the assumption on tax treatment, is taxed indirectly in the former through physical capital used in the sector producing new human capital, but is not taxed indirectly in the latter because only human capital is used in producing new human capital. If the tax treatment is such that income from both sectors is taxed, however, the growth effects of income taxation are negative even in the Lucas model.

When knowledge spillover is introduced, whether the net growth effects of income taxation continue to be negative becomes ambiguous. First of all, since the private sector will not take the positive spillover effect into account, the equilibrium growth rate will be lower than the growth rate in a socially optimal solution. This implies that a subsidy or an investment tax credit can raise the steady-state growth rate above the equilibrium level. Both subsidy and investment tax credit, however, need to be financed with some taxation. If lump-sum taxation is infeasible and an income tax has to be imposed, the above discussed negative growth effects of income taxation will result. The net growth effects considering both effects from income taxation and effects from subsidy or investment tax credit are ambiguous.

The growth implications of tax revenue spending are very sensitive to where tax revenue is spent. If tax revenue is used to provide public services which enter people’s utility function but not production function, it will not have steady-state growth effects. ^1/ However, if tax revenue spending is productive, it may have effects on the long-run rate of growth. The nature of the public services on which tax revenue is spent also matters.

First consider the case that tax revenue is spent on the public inputs necessary for goods production and those inputs have the nature of private goods. The government budget is assumed to be balanced. The expression of the after-tax real rate of return to capital (4’) now tells us that in addition to the negative direct effect of an increase in τ on r, there is a positive indirect effect through the increase in the spending of tax revenue x=τy. From y=Ak^1-α(τy)^α we get y/k, and, substituting it into (4’), we obtain

$\begin{array}{cc}r=(1-\tau ){\tau }^{\frac{\alpha }{1-\alpha }}(1-\alpha )A^{\frac{1}{1-\alpha }}\mathrm{.}& (4\prime \prime \prime )\end{array}$

To see the effect of an increase in the income tax rate on the real rate of return to capital, we take the derivative of r with respect to τ

$\begin{array}{cc}\frac{dr}{d\tau }=\alpha A^{\frac{1}{1-\alpha }}{\tau }^{\frac{\alpha }{1-\alpha }}(\frac{1}{\tau }-\frac{1}{\alpha })\mathrm{.}& \left(8\right)\end{array}$

It is now clear that an increase in r will have a negative (positive) effect on r and therefore on the steady-state growth rate if the income tax rate is higher (lower) than the competitively determined income share of government, which is the supplier of public inputs. In other words, the steady-state growth rate and the income tax rate have an inverted-U relation. Before the optimal size of public infrastructure is reached, the long-run growth rate will rise with the increase in the income tax rate, because more tax revenue is needed to finance more public infrastructure. After the optimal size of public infrastructure is reached, however, a/any further increase in public infrastructure will be adverse to the long-run growth rate and, therefore, an increase in the income tax rate will have negative effects on the long-run growth rate.

In contrast to the Ak model and the Rebelo-type human capital driven (without spillover) growth model where the growth maximizing income tax rate is zero, the growth maximizing income tax rate is now positive and equal to α. The growth rate corresponding to τ=α is, however, a second-best outcome, due to the distortion caused by income taxation. The Pareto optimal growth can only be achieved in principle by lump-sum taxation.

Barro and Sala-i-Martin (1992a) considered two other cases. One is that public inputs have the nature of public goods (nonrival and nonexcludable); the other is that public productive services are subject to congestion. The above inverted-U relation between the steady-state growth rate and income tax rate and the result that the growth maximizing income tax rate is positive and equal to α maintain under their model specifications. The special feature for the case of congestion is that income taxation leads to a socially optimal growth rate because here the distortion in the decentralized equilibrium lies in the excessive use of the public services and income taxation acts like a user fee for public services, which corrects this distortion. In the solution to the public goods case as shown in Table 1, there is an additional scale factor (the number of firms denoted by n) affecting the steady-state growth. The number η is exogenous in their model, so that it is impossible to discuss further the possible effect of income taxation on this scale factor.

In all three cases that display the inverted-U relationship (discussed above) between the steady-state growth rate and the income tax rate, the ambiguity of the growth effects of income taxation arises from the presence of externalities (tax revenue is used to finance productive public goods). However, Zee (1994) has found that, even in a model without such externalities, but with endogenous time preference, the growth effects of an income tax would depend on the relative magnitudes of the income tax elasticity of the savings rate and the tax rate itself. Hence, the ambiguous growth effects of an income tax need not rely solely on the presence of externalities.

It is a surprise to find that income taxation is irrelevant to the steady-state growth in the benchmark model of endogenous growth driven by innovation, since the innovation approach emphasizes deliberate efforts to innovate and income taxation may well be negatively affecting innovation incentive, and therefore long-run growth. It turns out that this negative impact on innovation from income taxation does exist, but is offset entirely. This result follows from the assumption that the price of a design, by the free entry condition, is equal to the present value of monopoly profits from exploiting the design. The monopoly profits in turn are positively affected by the price of the capital goods.

Hence, while income taxation does decrease the return to human capital in the final goods sector, it at the same time decreases the price of capital goods and, therefore the monopoly profits of purchasing a new design. Consequently, the price of design falls and returns to human capital in the research sector decline by the same proportion as that in the final goods sector. As a result, human capital allocated to the research sector does not change in equilibrium, hence the long-run rate of growth is not affected.

2. Transitional growth effects

An economy may well be along a transitional path toward the steady state instead of along a steady-state growth path. Most endogenous growth literature focuses on the steady-state growth path. To make our examination of the growth implications of taxation more complete, we provide the following discussion based mainly on Mulligan and Sala-i-Martin (1993).

Before examining the transitional growth effects of taxation implied by endogenous growth models, it is helpful to look at the transitional growth effects of taxation implied by the standard neoclassical model. Without population growth and technical change, the steady state in the standard neoclassical model is characterized by zero growth. However, if the current capital stock level is not equal to the steady-state level, the economy will experience a period of transitional growth. The growth rate during the transition is given by

Suppose the economy is initially on a steady-state (zero) growth path. At time 0, an income tax is imposed. The after-tax, steady-state capital stock has to be lower so that the after-tax real rate of return to capital equals the rate of time preference. The transition is characterized as follows: consumption jumps to a higher level in the saddle path at time 0, that is, part of the current capital stock is consumed. Along the saddle path, both consumption and capital stock decline until the lower steady-state level of capital stock is reached. It is clear from equation (12) that the growth rate of the economy during the transition is negative because capital stock keeps decreasing during this period. Consequently, income taxation has negative transitional growth effects.

The issue of transitional growth effects is more complex in the endogenous growth framework. The one-sector Ak model has no transitional dynamics, since the economy is always on the steady-state growth path. ^1/ Most endogenous growth models, however, fall into the framework of a two-sector model as laid out in Section II. Following Mulligan and Sala-i-Martin (1993), we discuss two possible cases of transitional dynamics in such a two-sector endogenous growth framework and their implications for income taxation. Assume the production of goods follows equation (1). Then the growth rate of the economy during the transition is a weighted average of the growth rates of different factors, as given by

To be concrete, we assume that the k-factor is physical capital, and the x-factor human capital. The economy is initially on a balanced growth path. In the human capital driven without spillover models laid out in Section II, an income tax imposed at time 0 results in a decline in the steady-state ratio of physical to human capital, that is, κ₀>κ^*, where κ₀ and κ* are the steady-state ratios of physical to human capital before and after tax, respectively.

Now there is an imbalance between the sector producing physical capital and the sector producing human capital with respect to the steady state. To reach the steady state, physical and human capital must accumulate at different rates during the transition.

One possibility is that transition is instantaneous. This happens when there is no adjustment cost between physical and human capital production. ^1/ Agents choose to invest (disinvest) at an infinite rate in the physical (human) capital-producing sector. The economy immediately jumps to the steady-state growth path.

When there exist adjustment costs between physical and human capital production, the economy will first jump to a saddle path, then converge to the steady-state growth path gradually. Mulligan and Sala-i-Martin (1993) prove that, in this case, there is global saddle path stability. Moreover, they find that if κ₀>κ^*, as in the above case of income taxation, agents will respond by lowering the ratio of physical capital allocated to the final goods production and raising the ratio of consumption to physical capital immediately to their respective saddle path levels. Afterwards, physical capital accumulates slower and human capital accumulates faster until the ratio of physical to human capital reaches the after-tax steady-state ratio. The growth rate of the economy at each point of the transition is given by (12’). With the knowledge of the relevant parameters, we may be able to determine the transitional growth effects of income taxation.

The transitional growth effects of income taxation implied by the one-sector neoclassical model and the two-sector endogenous growth model cannot be directly compared. The study by King and Rebelo (1993), however, shows that the transitional growth implied by the standard neoclassical model is not able to explain observed growth without resorting to a counterfactually high real rate of return to capital in the early development stage of a country. More research is needed to characterize the transitional dynamics of endogenous growth models qualitatively and quantitatively.

1. Some evidence from simple correlations

The U.S. economic history provides a natural experiment for examining the growth taxation relationship. Income tax revenue as a fraction of GNP increased dramatically in the United States in the early 1940s and the U.S. economy over the last century conforms well to the description of a balanced growth path. Figure 1 shows that although the growth rate of per capita real GNP in the United States dropped substantially following the jump in the ratio of income tax revenue to GNP, the long-run rate of growth seems to have been unaffected. ^1/ Stokey and Rebelo (1993) perform three statistical tests on the difference between the average growth rate before and after 1942. They find that this difference is statistically insignificant.

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Economic Growth and Income Tax Rates in the U.S.

Income Taxes as Percentage of GNP

Citation: IMF Working Papers 1994, 038; 10.5089/9781451977554.001.A001

Source: Stokey and Rebelo (1993), Figure 6.¹Revenue from federal, state, and local individual income taxes as a fraction of GNP.²Revenue from social security and retirement taxes and from federal corporate profits tax are also included.

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The simple correlation of average tax rates on income and profits with average per capita GDP growth in OECD countries for the period 1960-89, however, is significantly negative, as pointed out by Plosser (1992). Figure 2 gives an illustration. ^2/

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Real Economic Growth and Tax Rates in OECD Countries

Citation: IMF Working Papers 1994, 038; 10.5089/9781451977554.001.A001

Source: Plosser(1992), Chart 6.

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These findings are based on simple correlations; although instructive, they do not provide solid empirical conclusions since there are many other variables affecting the economic growth rate which should be controlled when the growth taxation relationship is under examination. In the U.S. case, for example, there may exist positive growth effects from other sources which offset the negative effects from heavier income taxation, and those growth effects may have been larger after 1942 than before. For the result from OECD countries, Easterly and Rebelo (1993a) find that the negative correlation between growth and income taxes disappears once the level of income is controlled. This implies that the negative growth taxation correlation in Figure 2 may simply reflect the fact that average income tax rates tend to be higher in countries with higher income levels and that rich countries tend to grow slower. In the following two subsections, we review the results concerning the growth taxation relationship from cross-country regressions and simulations.

2. Cross-country growth regressions

There have been many studies using cross-country regressions to search for empirical linkages between long-run growth and economic policies. The basic form of these regressions can be expressed as

where:

• γ-rate of growth of real income per capita

• y=initial per capita real income

• x_i=variables explaining steady-state growth, i=2,3…n

• z=policy variable

• a_i,b=coefficients, i=0,1…n.

One derivation of this regression form is given by Barro and Sala-i-Martin (1992b). The endogenous growth theory gives a theoretical basis for the choice of the variables x_i. Typically x_i are proxies for human capital stock. Initial income level is used to control for transitory dynamics. A negative a₁ indicates conditional convergence, that is, poor countries tend to grow faster when controlling the factors determining the steady-state growth rate. The policy experiment is to see whether the estimate of b has a statistically significant sign.

Among the 41 cross-section growth studies listed by Levine and Renelt (1991), 17 studies examine the growth effects of fiscal policy. More recent studies include Engen and Skinner (1992), Dowrick (1992), Canning, Fay, and Perotti (1992), and Easterly and Rebelo (1993a, 1993b). These studies, however, are far from reaching any consensus.

As far as tax policy is concerned, the difficulty of establishing a proxy for the tax policy in the cross-country regression remains a problem. Most researchers who use government consumption as a proxy for the distortionary taxes that must be raised to support the spending find negative partial correlation between growth rate and the proxy, although a few find that this correlation is insignificant, or even positive (Ram (1986)). ^1/ Total government spending, a more complete proxy for distortionary taxes, is also found to be negatively correlated with growth rate in the base regression of Levine and Renelt (1991). The partial correlation between growth rate and government investment, however, is found insignificant in most studies, although a positive sign is obtained in some investigations.

There are also a number of studies which use indicators of taxes directly in their regressions. Their results seem to indicate a negative partial correlation between the economic growth rate and tax variables. Table 2 summarizes these studies.

Table 2.

Cross-Country Studies of Economic Growth and Taxation

Table 2.

Cross-Country Studies of Economic Growth and Taxation

	Partial Correlation with Growth Rate	Tax Variable	Data
Marsden (1983)	Negative	Ratio of tax revenue to GDP	20 countries 1970-79
Mañas-Anton (1987)	Negative or insignificant	Ratio of income taxes to total tax revenue or to GDP	39 countries 1973-82
Skinner (1987)	Negative	Ratio of tax revenue to GDP	31 countries 1965-82
Koester and Kormendi (1989)	Insignificant	Average and marginal tax rates	63 countries 1970-79
Martin and Fardmanesh (1990)	Negative	Ratio of tax revenue to GDP	76 countries 1972-81
Engen and Skinner (1992)	Negative	Change in ratio of tax revenue to GDP	107 countries 1970-85
Easterly and Rebelo (1993a)	Negative	Marginal income tax rate	53 countries 1970-88
Easterly and Rebelo (1993b)	Insignificant	Income-weighted average of marginal tax rates	32 countries 1970-88

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Table 2.

Cross-Country Studies of Economic Growth and Taxation

	Partial Correlation with Growth Rate	Tax Variable	Data
Marsden (1983)	Negative	Ratio of tax revenue to GDP	20 countries 1970-79
Mañas-Anton (1987)	Negative or insignificant	Ratio of income taxes to total tax revenue or to GDP	39 countries 1973-82
Skinner (1987)	Negative	Ratio of tax revenue to GDP	31 countries 1965-82
Koester and Kormendi (1989)	Insignificant	Average and marginal tax rates	63 countries 1970-79
Martin and Fardmanesh (1990)	Negative	Ratio of tax revenue to GDP	76 countries 1972-81
Engen and Skinner (1992)	Negative	Change in ratio of tax revenue to GDP	107 countries 1970-85
Easterly and Rebelo (1993a)	Negative	Marginal income tax rate	53 countries 1970-88
Easterly and Rebelo (1993b)	Insignificant	Income-weighted average of marginal tax rates	32 countries 1970-88

Although there exist certain specifications that yield significant coefficient estimates between tax policy indicators and growth, these results are generally very sensitive to regression specifications, as found by Levine and Renelt (1992). By slightly altering the set of explanatory variables in any regression, the resulting estimates become insignificant.

Another problem is that those linear cross-country regressions are not capable of capturing the inverted-U relation between the steady-state growth rate and income tax rate in cases of productive public inputs discussed in Section II. The income tax rate and the growth rate are positively correlated when the income tax rate is higher than the competitively determined income share of government (the supplier of public inputs), and negatively correlated when the opposite is true. Thus, we expect zero cross-country correlation when the income tax rates are optimally set. This means that the insignificant coefficient estimate obtained in some cross-country regressions cannot be interpreted as indicating no correlation between the growth rate and the income tax rate. ^1/

3. Simulations

The steady-state growth effects of taxation can be estimated through simulation. The existing estimates, however, vary wildly from nearly zero in Lucas (1990) to 3.5 percentage points in Jones, Manuelli, and Rossi (1993). Table 3 shows the benchmark estimates of these simulations.

Table 3.

Simulation Results of Steady-State Growth Effects of Taxation

Table 3.

Simulation Results of Steady-State Growth Effects of Taxation

	Experiments	Change in the Growth Rate
Lucas (1990)	Eliminate capital tax and raise labor tax to 46 percent	−0.0003
King and Rebelo (1990)	Increase income tax by 10 percent	−0.0152
	Increase capital tax by 10 percent	−0.0052
Kim (1992)	Eliminate all taxes	0.0085
Jones, Manuelli, and Rossi (1993)	Eliminate all taxes	0.0350

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Table 3.

Simulation Results of Steady-State Growth Effects of Taxation

	Experiments	Change in the Growth Rate
Lucas (1990)	Eliminate capital tax and raise labor tax to 46 percent	−0.0003
King and Rebelo (1990)	Increase income tax by 10 percent	−0.0152
	Increase capital tax by 10 percent	−0.0052
Kim (1992)	Eliminate all taxes	0.0085
Jones, Manuelli, and Rossi (1993)	Eliminate all taxes	0.0350

The divergence of simulation results, according to Stokey and Rebelo (1993), are due to different model specifications and parameter choices of different authors. For example, the trivial growth effect found by Lucas (1990) is due to his assumptions that new human capital is produced using human capital only, and human capital production is not taxed. The no growth effect result of the human capital (without spillover) model of Lucas (1988) has already been analyzed in Section III. In addition, labor taxation affects equally both the cost side and the benefit side of the marginal condition governing the learning decision, except through the labor-leisure choice which results in the small change in the rate of growth in Lucas (1990).

Some critical parameters affecting the size of the steady-state growth effects of income taxation have been identified by Stokey and Rebelo (1993). The shares of physical capital in total capital stock in the sector producing physical capital and the sector producing human capital are found to be extremely important in predicting the growth effects of income taxation. The elasticity of labor supply becomes important to growth effects when the share of physical capital in total capital stock is small. The low share of physical capital in the sector producing human capital (v=0.17) combined with the high elasticity of labor supply in Jones, Manuelli, and Rossi (1993) are what result in the large steady-state growth effects of income taxation in their study.

Table 4 illustrates the different growth effects calculated by Stokey and Rebelo (1993) based on their model using the parameter values in the above-mentioned simulations. The growth effects reflect the change in the steady-state growth rate when all taxes are eliminated.

Table 4.

Comparison of Growth Effects Due to Different Parameter Values

Source: Stokey and Rebelo (1993), Tables 1-4. Notes: w = share of physical capital in total capital stock in the sector producing physical capital. v = share of physical capital in total capital stock in the sector producing human capital. δ^k = depreciation rate of physical capital. δ^h = depreciation rate of human capital. 1/σ = elasticity of intertemporal substitution. τ_i,j = tax rate on the return to factor i in sector j, i=k,h, j=k,h. Growth effects = changes in growth rate when all taxes are eliminated. Numbers in parenthesis = different values used in the same experiment with values of other parameters unchanged.

Table 4.

Comparison of Growth Effects Due to Different Parameter Values

	Growth Effects	w	v	δk	δh	1/σ	Labor Supply Elasticity	Tax Rates
								τ k,k	τ h,k	τ k,h	τ h,h
Lucas (1990)	0.0000	.24	.00	.0	.0	.5	Small	.26	.40	.00	.00
King and Rebelo (1990)	0.0330 (.0143)	.33	.33 (.05)	.1	.1 (.012)	1.0	No	.20	.20	.20	.20
Kim (1992)	0.0091	.34	.34	.05	.01	.52	No	.34	.17	.34	.17
Jones, Manuelli, Rossi (1993)	0.0211 (.0333)	.36	.17	.1	.1	.5 (.91)	Large	.21	.31	.00	.00

Source: Stokey and Rebelo (1993), Tables 1-4. Notes: w = share of physical capital in total capital stock in the sector producing physical capital. v = share of physical capital in total capital stock in the sector producing human capital. δ^k = depreciation rate of physical capital. δ^h = depreciation rate of human capital. 1/σ = elasticity of intertemporal substitution. τ_i,j = tax rate on the return to factor i in sector j, i=k,h, j=k,h. Growth effects = changes in growth rate when all taxes are eliminated. Numbers in parenthesis = different values used in the same experiment with values of other parameters unchanged.

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Table 4.

Comparison of Growth Effects Due to Different Parameter Values

	Growth Effects	w	v	δk	δh	1/σ	Labor Supply Elasticity	Tax Rates
								τ k,k	τ h,k	τ k,h	τ h,h
Lucas (1990)	0.0000	.24	.00	.0	.0	.5	Small	.26	.40	.00	.00
King and Rebelo (1990)	0.0330 (.0143)	.33	.33 (.05)	.1	.1 (.012)	1.0	No	.20	.20	.20	.20
Kim (1992)	0.0091	.34	.34	.05	.01	.52	No	.34	.17	.34	.17
Jones, Manuelli, Rossi (1993)	0.0211 (.0333)	.36	.17	.1	.1	.5 (.91)	Large	.21	.31	.00	.00

Source: Stokey and Rebelo (1993), Tables 1-4. Notes: w = share of physical capital in total capital stock in the sector producing physical capital. v = share of physical capital in total capital stock in the sector producing human capital. δ^k = depreciation rate of physical capital. δ^h = depreciation rate of human capital. 1/σ = elasticity of intertemporal substitution. τ_i,j = tax rate on the return to factor i in sector j, i=k,h, j=k,h. Growth effects = changes in growth rate when all taxes are eliminated. Numbers in parenthesis = different values used in the same experiment with values of other parameters unchanged.

The size of growth effects is also sensitive to the size of depreciation rates (δ^k,δ^h). If depreciation of capital is tax deductible, then the growth effects of taxation will be overstated assuming income is taxed gross of depreciation. If the King and Rebelo (1990) model is recalibrated with δ^k and δ^h equal to 0.06 instead of 0.1, eliminating all taxes will raise the long-run growth rate by 2.5 percentage points rather than 3.3, according to Stokey and Rebelo (1993).

It is easy to understand that different choices of the elasticity of intertemporal substitution (1/σ) result in very different growth effects, since it acts like a multiplier in calculating the steady-state growth rate. If the Jones, Manuelli, and Rossi model (1993) is resimulated with σ equal to 1.1 instead of 2, eliminating all taxes will raise the long-run growth rate by 3.3 percentage points rather than 2.1.

The results from simulations, like that from cross-country regressions, are inconclusive. As Stokey and Rebelo (1993) indicate, further efforts are needed to improve the estimates used in simulations, in particular the estimate of physical capital’s share in the sector producing human capital and the estimates of the elasticity of intertemporal substitution and the elasticity of labor supply.

1. Endogenous tax policy

So far, tax policy has been taken as exogenously determined. Redistribution of income due to tax policy change is implicitly assumed to have no effect on the steady-state growth rate. However, tax policy is typically made through a certain political process, and political process is characterized by conflicts and compromises. Recently there have been studies that endogenize tax policy as well as economic growth (see Perroti (1992b) and Persson and Tabellini (1992) for a review). These studies shed new light on the growth taxation relationship.

Distributional conflict and political process are modeled explicitly in this type of political economy model. In Alesina and Rodrik (1991), for example, individuals are assumed to own different amounts of capital in addition to one unit of labor endowment. They vote on the capital tax rate according to simple majority rule. The higher the labor-capital ratio of an individual, the higher the capital tax rate that the individual will vote for. The capital tax rate in the political equilibrium is the one chosen by the median voter. The more unequal the wealth distribution, the less the capital owned by the majority of the population and the higher the capital tax rate chosen in the political equilibrium. In Persson and Tabellini (1991), a capital tax ^1/ is used for redistribution purposes. The income an individual can own depends on his skill to utilize his capital. Different skill endowments correspond to different income levels. Individuals have the same initial capital stock, but their levels of capital stock vary because of their different skills in accumulating capital. As in Alesina and Rodrik (1991), the poorer the median voter is, the higher the capital tax rate he prefers.

Now the link between distribution and economic growth can be established by specifying an endogenous growth mechanism discussed in Section II. In Alesina and Rodrik (1991), tax revenue is used as public investment in such a way that the real rate of return to private investment is constant, therefore growth is sustained. The steady-state growth rate is negatively correlated with the tax rate on capital because capital taxation reduces the real rate of return to capital. Consequently, the more unequal the wealth distribution, the higher the capital tax rate and the lower the long-run growth rate of the economy. In Persson and Tabellini (1991), long-run growth is sustained by capital accumulation with knowledge spillover. The steady-state growth rate is again negatively correlated with the tax rate on capital; consequently, unequal distribution is harmful for growth. In Perotti (1992a, 1992b), growth is the result of private investment in education and only those individuals whose after-tax income is no less than the cost of education will invest in human capital and will have a higher pretax income next period. As a result, the level of the tax rate and, therefore, the level of redistribution determine which classes of agents can invest in human capital. This in turn determines the rate of growth and how income distribution evolves.

The above studies have also conducted some empirical investigations which generally support their theoretical findings.

2. Tax policy in an open economy setting

Diversity in growth rates across countries is a stylized fact. The endogenous growth models discussed in Section II imply that the difference in the real rates of return to capital is the reason for growth rate diversity, provided that preferences and policies are the same across countries. However, in an open economy with perfect capital mobility and under the source principle of international taxation, rates of return to capital across countries will be equalized, hence growth rate differences across countries will disappear. The long-run growth effects of a national tax policy derived from a closed economy setting will be washed out.

This drawback in many endogenous growth models has been recognized and efforts have been made to preserve growth rate differences in an open economy framework. Razin and Yuen (1992) point out that under the residence principle of international income taxation, growth differences across countries due to different national tax policies can be consistent with international capital mobility. The residence principle implies symmetrical tax treatment of domestic-source and foreign-source incomes for residents of each country, but asymmetrical treatment across countries. Residents of a country have to pay the same tax rate on capital income, whether the income comes from investment at home or abroad. According to Razin and Yuen (1992), when people are more individualistic, residents of countries with higher tax on capital income will tend to substitute human capital investment for physical capital investment (either at home or abroad) if they care more about their own consumption, leading to a higher growth rate in per capita income; when people are more altruistic, they will tend to substitute fertility for physical capital investment, leading to a lower growth rate in per capita income.

The study of Frenkel, Razin, and Sadka (1991) shows that the residence principle is the dominant tax principle among countries in the world. Thus the asymmetry in cross-country capital taxes is a plausible explanation of growth rate diversity across countries. Razin and Yuen (1993) calibrate an open economy growth model to the Group of Seven data over the period 1965-87 under the residence principle. They find that low capital tax rates tend to be associated with faster growth in per capita income. Moreover, they find that the growth effects of changes in capital income tax rates can be much larger with than without capital mobility due to cross-border policy spillovers. The closed economy growth models may thus have underestimated the potentially large growth effects due to tax changes.

A few studies have tried to modify model specifications to make growth diversity consistent with capital mobility. By adding a subsistence consumption term in utility function, Rebelo (1992) establishes a case that the growth rate difference is consistent with perfect international capital markets. Jones and Manuelli (1990) also give an example where growth divergence can be preserved in an open economy. However, these examples are exceptional.