I. The optimum income distribution from a voluntary theory of exchange, 329. — II. A complication, 333. — III. The mathematics, 333. — IV. Conclusions, 335.
The Review of Economics and Statistics196951(4), 431
M ODERN investment functions, springing from the work of Jorgenson,' differ from earlier investment functions in that they start with an explicit assumption about the economy's aggregate production function. In particular, Jorgenson assumes a Cobb-Douglas production function. Starting with an explicit production function means that it is possible to calculate algebraically the impact of factors, such as interest rates, that could not be isolated in earlier investment functions. Choosing the correct production function is important in estimating partial effects, but the proper definition of the cost of capital variable is also central to their correct estimation. Formulations other than those of Jorgenson are possible. If one had priors about the differences in the opportunity cost of capital under the Duesenberry supply of funds hypothesis,2 the cost of capital could be defined to embody these priors. Doing so would lead to different estimates of the partial effects of tax rates, interest rates, and depreciation policies. Thus, the partial effects that emerge from a modern investment function are a product of the initial specifications of the production function and the cost of capital variable. In addition to choosing the correct production function and the correct definition of the cost of capital, there are other directions in which the modern investment function can be modified. In Jorgenson's neoclassical equilibrium world the cost of capital and the marginal product of capital are always identical. Thus, the desired capital stock at any moment of time is equal to output divided by the marginal product of capital (the cost of capital) multiplied by the elasticity of output with respect to capital. Thus, the only problems are ones of correct data measurement and estimation of the lag structure. This formulation has some theoretical problems. Introducing lags means that the economy is not in equilibrium. actual capital stock lags behind the desired capital stock. Therefore, the cost of capital and the marginal product of capital are not equal. Even if they were equal, the marginal product of capital will differ before and after expansion of the capital stock. Thus output should be divided by the expected cost of capital rather than the actual cost of capital to determine the desired capital stock.3 In a disequilibrium world, the cost of capital and the marginal product of capital can diverge. Profit maximizing firms invest to eliminate the gap between the marginal product of capital and the cost of capital. investment necessary to eliminate this gap depends upon the economy's production function. This paper investigates a disequilibrium investment function based on a Cobb-Douglas production function and Jorgenson's definition of the cost of capital. I was led to investigate such a model in the process of attempting to use the Jorgenson investment function.4 Several problems emerged in addition to those investigated elsewhere.5 (1) Although the Jorgenson investment function fit quarterly time series data for producers' * author would like to thank the referee for many useful comments. 'Dale W. Jorgenson, Anticipations and Behavior, in J. S. Duesenberry, E. Kuh, G. Fromm, and L. R. Klein (editors), Brookings Quarterly Econometric Model of the United States (Chicago: Rand McNally, 1965). Rational Distributed Lag Functions, Econometrica, XXXIV (Jan. 1966), 135-149. With Calvin D. Siebert, A Comparison of Alternative Theories of Corporate Behavior, American Economic Review, XVIII (Sept. 1968). Optimal Capital Accumulation and Corporate Behavior, Journal of Political Economy, LXXVI (Nov./Dec. 1968), 1123-1151. With J. A. Stephenson, The Time Structure of Behavior in United States Manufacturing, 1947-60, this REvIEw, XLIV (Feb. 1967), 16-27. Investment Behavior in U.S. Manufacturing, 1947-60, Econometrica, XXXV (April 1967), 169-220. 2J. Duesenberry, Business Cycles and Economic Growth (New York: McGraw-Hill, 1968), 87-112. 3This was pointed out to me by my colleague Duncan Foley. 'Anyone wishing the detailed econometric results of my attempts to fit the Jorgenson model to producer's durable equipment and nonresidential structures can have them by writing to me. 'Robert Eisner and M. I. Nadiri, Investment Behavior and Neoclassical Theory, this REvIEw, L (Aug. 1968).
The Review of Economics and Statistics196850(1), 23
D IFFERENTIATING a production function with respect to capital and labor yields equations for the marginal productivity of capital and the marginal productivity of labor. The variables that determine the marginal products in these equations are the same as those in the production function. If the data used to estimate the parameters of the production function are inserted into the equations for the marginal products, the marginal productivities of both capital and labor can be estimated empirically. The same data and equations also make it possible to determine the causes of any changes in the marginal products. How much of the rising marginal productivity of labor is caused by technical progress; how much is caused by a rising capital-labor ratio? If the economy is in equilibrium and there are no economies or diseconomies of scale, actual and marginal returns should be identical. Any differences between the estimated marginal products and the actual returns to capital and labor means that the economy is in disequilibrium; the size of the differences measures the extent of disequilibrium. If disequilibrium does exist, what causes the observed pattern? What are its implications for investment decisions in both human and physical capital? This paper applies the above approach to the American economy from 1929 to 1965.
Arthur Okun wrote Equality And Efficiency: The Big Tradeoff in 1974. The book focused on the tradeoffs between tax-transfer systems and the work or savings incentives necessary for economic growth. If society wished more equality it faced a leaky bucket where the amount given to the poor was inevitably less than the amount taken from the rich. If the book had been written ten years earlier, Okun would not have focused on the big tradeoff. The conventional wisdom (circa 1964) held that any society could have both more output and a more equal distribution of output if only it invested in more education-human capital. If a more equal distribution of education was pumped into the economy, the economy would automatically pump back a more equal distribution of earnings. As educational gaps diminished between blacks and whites, or men and women, earnings gaps would similarly disappear. The War on Poverty and Great Society programs as they were conceived by Presidents Kennedy and Johnson were based upon education-not tax-transfer-strategies. With more education, higher earnings for the poor would mean higher, not lower, incomes for the rich. Strangely, Equality and Efficiency says nothing about education. The only reference to education is a brief discussion of the Yale Plan where tuition loans could be repaid based on future earnings rather than some fixed repayment schedule. Nowhere in the book does Okun justify his association of equality with the tax-transfer system on the grounds that education empirically failed to deliver what was earhler promised. Without argument he just assumes that the tax-transfer system is the only way to get a more equal distribution of income. Between the mid-1960's and the mid-1970's, I am unaware of anyone who was advancing the argument that education had empirically failed as an economic strategy for generating both growth and equality. Yet Okun was not alone in ignoring education. Without explicit discussion, education had ceased to be seen as a viable economic strategy by almost everyone. Intellectually it is interesting to speculate as to why equality, which was so closely associated with education in 1960's, came to be just as closely associated with tax-transfer systems in the 1970's without any hard analysis that would have forced the shift in strategy. Perhaps it had something to do with the public's disgust with education flowing out of the student rebellion of the late 1960's and early 1970's. More education was not a politically viable strategy for promoting equality and efficiency whatever its economic merits. But more importantly, the evidence, at least on the surface, now indicates that the educational strategy of the 1960's did fail economically. The educational attainments of the labor force continued to accelerate in the 1970's, but productivity stopped growing by the end of the decade. (See the Economic Report of the President, 1981.) There is no educational gap between men and women who work at year-round full-time jobs (both have 12.0 median years of education in 1978), but women continue to earn 58 percent of what men earn. (See Current Population Reports... 1978, No. 123, pp. 213; 218.) Education has been much more equally distributed since World War II, but the earnings of the top quintile rose from 19 times that of the bottom quintile in 1948 to 27 times that of the bottom quintile in 1980 (Current Population Reports... 1968, No. 6, p. 28; No. 123, p. 271). Why didn't education deliver the growth and rising equality that was promised? One can quickly think of many reasons why education may appear to be failing as a strategy for promoting growth and equality *Massachusetts Institute of Technology.