Knowledge that Transforms

A large number of econometric studies have focused on possibilities for capital-labor in U.S. manufacturing. The evidence, however, indicates substantial disagreement over value of of (cr). Studies based on cross-sectional data provide estimates which are quite close to unity, but time series studies generally report lower estimates. Furthermore, estimates of or seem to vary systematically with choice of functional form: regressions based on marginal product of capital relation generally produce lower estimates of cr than regressions based on marginal product of labor relation. A variety of hypotheses have been advanced to explain diversity of results, including cyclical changes in utilization of factors (Nerlove, 1967), random measurement errors (Leontief, 1964), systematic variation of input prices with product prices (Nerlove, 1967), embodied and disembodied technical change and problems in measurement of inputs (Griliches, 1967a; Hildebrand and Liu, 1965), simultaneous equations bias (Maddala and Kadane, 1966; Nerlove, 1967), serial correlation (Griliches, 1967a), and lagged adjustment (Griliches, 1967a; Lucas, 1969; Jorgenson, 1972). In general, empirical studies attempting to take account of these deficiencies have produced unsatisfactory results. Zvi Griliches, for example, finds that the labor quality variables . . . contribute little in elasticity-of-substitution context (1967a, p. 296), while R. E. Lucas, Jr. concludes that lagged adjustment hypotheses make essentially no contribution to reconciling of time series and cross-sectional evidence of substitution (1969, p. 259). In this paper we report results of a rather successful attempt to reconcile differing estimates of cr. While it may be desirable to consider separately and systematically contribution of each of above hypotheses in reconciling cr estimates, here we limit our concern to two principal areas: (1) data -we attempt to construct time series data on cost of capital services in a more detailed manner than previous researchers have, taking into account real and nominal rates of return, asset prices, depreciation, tax policies, and compositional changes in aggregate capital between equipment and structures; (2) stochastic specification -we estimate cr by a two-stage least squares (2SLS) procedure to circumvent problem of simultaneous equations bias by ordinary least squares (OLS). We then compare estimates of abased on six different functional forms, five alternative measures of rental price of capital services, and two estimation methods. Our most sobering result is that estimates of Cr are extremely sensitive to differences in measurement and data construction. In this respect we concur with Nerlove who finds that even slight variations in period or concepts tend to produce drastically different estimates of elasticity (1967, p. 58). However, with our preferred set of data we obtain OLS and 2SLS time series estimates of owhich exhibit robustness over a variety of functional forms and time periods, and are consistent with cross-sectional evidence.

Direct and Cross Demand Elasticities in a Model with Many Sectors, Econometrica (Apr. 1959). Goldberger, A. S., Econometric Theory (New York: John Wiley & Sons, Inc., 1964). Jorgenson, D. W., Lecture Notes: Economics 241 Part IV: The Multivariate Structural Model (Berkeley, California: Committee on Econometrics and Mathematical Economics, Institute of Business and Economic Research, University of California at Berkeley, 1962). Lemke, C. E., A Method of Solution for Quadratic Programs, Management Science (Aug. 1962), 442-453. Mangasarian, 0. L., Duality in Nonlinear Programming, Quarterly Journal of Applied Mathematics 20 (1962), 300-302.

A question central to the issue of optimal city size is whether scale economies exist in urban production. Over a third of all Americans who currently live in metropolitan areas live in one of the dozen largest. If it can be shown that these areas have a significant production advantage over the remaining ones, then welfare analysis could be applied to learn whether the extra output produced in these metropolitan areas outweighs the drawbacks of 'their greater disamenities. Economists have long recognized that wages and output per worker in large cities exceed those in smaller ones (Alonso, 1970; Fuchs, 1967; Hoch, 1972; and Izraeli, 1973). Workers have apparently known about this too, and as a result the size distribution of cities has been shifting in favor of the largest cities for much of the past century. But before one can pass welfare judgments about this trend it is necessary to have in hand an empirically-based theory of production and income in urban areas and of the role, if any, played by city size. Our main concern is to develop such a theory -to explain variation in worker incomes across a set of metropolitan areas. We do this for 58 areas using data for 1967. As a part of the study capital stock data were estimated for each of the areas. A marginal productivity theory of factor incomes is assumed and justified empirically. Two-thirds of the variation in gross metropolitan income per worker is explained. We found that the largest SMSAs-those with a population of two million or more had a return to factors 8% higher than the remaining SMSAs. The reason for this was not increasing returns to scale in production -we observed constant returns both across the entire sample and within several smaller city/larger city partitionings of the sample. Rather, there is an effect that seems to obtain for areas of more than two million -a change in the constant term causing a shift in the production function. The reason for this effect, apparently, is that economies exist in transport and communication in the very largest cities with the result that the benefits from agglomeration more than offset congestion costs. A marginal productivity theory of distribution in cities is developed briefly in the next section. This is followed by an empirical section which describes the data and relates the findings.

RICE and quantum indexes (P, Q) are dual to each other if PQ = E where E is the expenditure index. They satisfy the weak factor reversal test.' If they share an identical weighting formula as weighted averages of price and quantity relatives, they satisfy the strong factor reversal test, that is, they are ideal. The most celebrated ideal economic index is the one associated with the name of Irving Fisher though it was discovered before him. No ideal index as simple as Fisher's has been discovered since. Log-change index numbers have become increasingly popular in recent years, particularly as an approximation to the theoretically desirable Divisia index. Theil (1973) proposed a new log-change index number that alhnost satisfies the strong factor reversal test. I derived several alternative formulas that improve in the degree of approximation (Sato, 1974b). But neither Theil nor I was able to obtain the ideal log-change index. In section II, I report its discovery. Our pessimism has proved premature. Indeed, the formula was self-evident from the very beginning -we simply failed to see it.2 There are dual dualities between economic indexes and homothetic preferences (Samuelson and Swamy, 1974). A price or quantum index is associated with a homothetic indirect or direct preference ordering. If P and Q are dual to each other, so are the direct and indirect preference orderings corresponding to them. If P and Q are ideal, the latter are not only dual but also share an identical mathematical form. They are strictly self-dual as I call them elsewhere.3 An obvious example is the association of Cobb-Douglas indexes and preferences. A less obvious example is the association of Fisher's ideal indexes and quadratic preferences. The association itself was discovered by Konuis and Buscheguence a half century ago in 1926.4 Note that homothetic quadratic preferences are self-dual. Then, what is the selfdual preference ordering that corresponds to our ideal log-change index? We shall show in section III that it is the CES function that has become so popular in the economic literature, originally discussed by Bergson (1936), rediscovered by Solow (1956), and popularized by Arrow et al. (1961). The CES function is known to be self-dual (Samuelson, 1965) and yet the economic index associated with it has eluded discovery until now. Economic indexes are useful because they apply even when underlying preferences are not homothetic.5 We shall show in section IV that the ideal log-change index corresponds to the addilog preference ordering introduced by Houthakker (1960).

Journal Article Incidence of a Capital Income Tax in a Growing Two-Class Economy Get access Kanhaya L. Gupta Kanhaya L. Gupta University of Alberta Search for other works by this author on: Oxford Academic Google Scholar The Review of Economic Studies, Volume 43, Issue 3, October 1976, Pages 561–562, https://doi.org/10.2307/2297238 Published: 01 October 1976 Article history Received: 01 April 1975 Accepted: 01 February 1976 Published: 01 October 1976

Journal Article A Note on Complementarity Over Time Get access Tapan Biswas Tapan Biswas University of Manchester Search for other works by this author on: Oxford Academic Google Scholar The Review of Economic Studies, Volume 43, Issue 1, February 1976, Pages 179–181, https://doi.org/10.2307/2296611 Published: 01 February 1976 Article history Received: 01 May 1974 Accepted: 01 December 1974 Published: 01 February 1976

Journal Article M. J. Farrell Get access Peter Hammond, Peter Hammond Search for other works by this author on: Oxford Academic Google Scholar Stephen Nickell Stephen Nickell Search for other works by this author on: Oxford Academic Google Scholar The Review of Economic Studies, Volume 43, Issue 1, February 1976, Page 1, https://doi.org/10.1093/restud/43.1.1 Published: 01 February 1976

The proof of Theorem 4 in [1] is incorrect. We offer another, longer one.

Journal Article General Equilibrium with a Replenishable Natural Resource: A Comment Get access Jacques Lesourne Jacques Lesourne Conservatoire National des Arts et Métiers Search for other works by this author on: Oxford Academic Google Scholar The Review of Economic Studies, Volume 43, Issue 3, October 1976, Pages 557–560, https://doi.org/10.2307/2297237 Published: 01 October 1976 Article history Received: 01 June 1975 Accepted: 01 March 1976 Published: 01 October 1976