There also exist tax maximizing rates for various types of taxes. Using a similar empirical specification, we find that the tax maximizing rate for the income tax, sales tax and trade taxes expressed as a fraction of GDP are 22.5, 12.5 and 13.2 percent, respectively. A revenue maximizing government will set all tax rates to their tax maximizing levels.

The growth rate in the estimation of the relationship between tax rates and economic growth is the compound growth rate in per capita real domestic product over the period 1960 to 1980. It is calculated from the data on per capita real gross domestic product from Summers and Heston.1 The independent variables are the growth rate in real capital per head over the same period, real gross domestic product per capita in 1980, the difference between taxes and expenditures as a share of GDP, the tax rate and the tax rate squared.

Note that the growth rate is over the period 1960 to 1980 and the tax rate is for 1980. There is a sound theoretical reason for using the end state tax rate. The period was one in which the size of government grew. The growth in government is viewed as a growth in tax liability. Presumably, people make behavioral adjustments in expectation of future tax liability.

Real gross domestic product per capita in 1980 is in the equation to adjust for convergence of growth rates. According to neoclassical economic theory, high income (capital intensive) economies grow more slowly than low income (labor intensive) economies because the marginal returns to capital are low in the former and high in the latter. In theory, capital flows to its highest valued use. In fact, capital probably has been flowing, from the high-risk, less-developed world to the safer havens in the West. Contrary to the predictions of neoclassical theory, the high per capita income countries are growing at the faster rate.

All of the variables in the estimation are highly significant (the regression equation is presented in Table A-1). The variables of interest here are the tax variables. The coefficient of the tax rate on the growth rate is 0.1339 (0.0688). The coefficient of the tax rate squared on the growth rate is -0.0035 (.000089). The growth maximizing tax rate is 19.3 ( = .1339/.0069) percent.

The growth maximizing tax rates for various types of taxes were also calculated. The empirical specification essentially is the same as reported above. The growth maximizing tax rates for the income tax, sales tax and trade taxes are 11.9, 4.6 and 9.4 percent, respectively. Note that, like aggregate taxes, the growth maximizing tax rates are about half that of the revenue maximizing tax rates.

1Robert Summers and Alan Heston, "Improved International Comparisons of Real Product and Its Composition: 1950-1980," Review of Income and Wealth, 30, June 1984, pp. 207-262.