Phoebus J. Dhrymes

TECHNOLOGY AND SCALE IN ELECTRICITY GENERATION

The question of returns to scale in public utilities is a much debated issue. In this study, the productive process of electricity generation is examined and a modified substitution model is employed, permitting differentiation between returns to scale to labor and to other factors. The method employed here allows us to isolate the impact of technological progress on (steam) electricity generation. We find that increasing returns to scale prevail throughout, and that the main impact of technology was registered during the 1950s. This study covers the period 1937-59.

Some Extensions and Tests for the CES Class of Production Functions

IN a recent pioneering paper Arrow, Chenery, Minhas, and Solow, hereafter referred to as Arrow, et al., have proposed a new class of production functions of great flexibility. Essentially, they address themselves to the following problem: If it is given that a certain relationship exists between wages and output per man-hour, then what sort of production function rationalizes this relationship. Specifically if it is given that

Small Sample and Asymptotic Relations Between Maximum Likelihood and Three Stage Least Squares Estimators

This paper deals with similarities and differences in the equations defining the full information maximum likelihood and three stage least squares estimators. It shows that the twp sets of equations are similar, the difference being that the two estimators purge the jointly dependent variables differently. Hence, even if three stage least squares is iterated, it will not give an estimator which is the same as the maximum likelihood one. On the other hand, it is quite apparently asymptotically equivalent to full information maximum likelihood. A number of other results are also obtained.

On an Efficient Two-Step Estimator for Dynamic Simultaneous Equations Models with Autoregressive Errors

where R is a stable matrix and { E : . : t = 0, k1, k 2 , , . .) is a sequence of independent identically distributed (i.i.d.) random variables having mean zero and nonsingular covariance matrix Z. It is assumed that whatever the process generating {w:.:t = 0, kl, +2, ..-) the latter sequence is independent of (6:. : t = 0, A 1, t2, ...). In Dhry~nes [I] under the additional assumption of normality for the E-process the full information maximum likelihood (ML) estimator wasobtai ned as well as the three-stage-least-squares-like estimator, termed there the full information dynamic autoregressive (FIDA). The converging iterate of the latter (CIFIDA) was compared with the ML estimator and it was determined that the difference between the two lies in the way in which the (jointly) dependent variables of the system are purged of their stochastic component. In Dhryines and Erlat [3] the asymptotic distribution of the converging iterate of FIDA was obtained. The purpose of this paper is twofold: First, to show that the asymptotic distributions of the converging iterate of FIDA and the ML estimator are identical and second, to provide a simple two step procedure which is fully as efficient as CIFIDA and ML estimators. This is a natural extension of the results in Dhrymes [2] and Hatanaka [5].

On Devising Unbiased Estimators for the Parameters of a Cobb Douglas Production Function

1. IN MANY empirical investigations the geometric mean of observed factor shares serves as an estimator of the factor exponents in a Cobb-Douglas2 production function. This particular estimator is due to Klein [7, p. 194]. It is here shown that such an estimator is biased. Under certain conditions an alternative estimator is derived which is unbiased, sufficient, efficient, and consistent.

On the Dividend Policy of Electric Utilities

D URING the past twenty years a great deal of econometric research has been directed toward the study of the saving behavior of economic units. Thus, personal saving has been explored quite intensively through (personal) consumption studies, especially so in the post-war period. The question of corporate saving, however, has in large measure been neglected, although a casual look at the data would disclose that it has ranged in magnitude from about 300 per cent of personal saving in 1947 to just under 50 per cent in recent years. Undeniably, this is a very significant component of total savings. By corporate saving we mean, of course, undistributed profits; hence, this question could be studied equivalently by studying the dividend policies of firms. On the latter topic some studies have been made and some tentative hypotheses have been formulated. The most widely held view in the recent literature is that propounded by Lintner in his pioneering contribution, [2] and [3]. Lintners hypothesis states that corporations are conservative in their financial policy, and, consequently, their dividend disbursement activity is characterized by a considerable degree of inertia, and more precisely, that there exists some optimal or target dividend payment (per share) to which corporations adhere. Departures from this level are made only reluctantly, following a change in the level of profits which is deemed to be more or less permanent. Lintners statistical analysis is based on time series data pertaining to aggregate corporate dividend disbursements and profits. His model has dividends at time t, explained by dividends at time t 1, and profits at time t. This is not a very satisfactory approach, except for shortrun prediction (of aggregate dividends), since it fails to account for apparently wide (intertemporal) variations in the dividend policy of various corporations, and does not go sufficiently far in elucidating the motives and factors involved in deciding the amount of corporate profits to be retained.

A Comparison of Productivity Behavior in Manufacturing and Service Industries

F OLLOWING a pioneering article by Solow [71 the problem of measuring technical change has been investigated by many authors, viz., Hogan [4], Massell [i], Pasinetti [6], Solow [7]. What almost all the papers above attempt to do is to construct a series which indexes or measures technical change. The term is slightly inaccurate in that the series really purport to describe the time profile of that part of output which is not explained by the specified inputs, viz., capital and labor. It may be preferable to employ the term productivity in accounting for such variations in observed output, a terminology which will be adhered to below. We shall provide a simple method of estimating a productivity parameter in a firm or sectoral or global production function. We shall then apply this method in estimating the appropriate parameter for the Manufacturing and Service Sector of the United States post-war economy. Finally, we shall indicate a method for testing a statistical hypothesis on the equality of two parameters so estimated. It will be found that the data does not warrant the conclusion that the rate of change of productivity differs significantly as between the two sectors.

A Comparison of Some Limited Information Estimators for Dynamic Simultaneous Equations Models with Autocorrelated Errors

In this paper we consider a number of estimators for the linear structural simultaneous equations model containing lagged endogenous variables and autocorrelated errors. The special case is considered in which the matrix of autocorrelation coefficients of the (vector) structural error process is diagonal. We consider the two stage least squares analogue (C2SLA) in this case, its relation to the estimators proposed earlier by Fair, the estimator obtained when the autocorrelation matrix is known, and a number of instrumental variables estimrators, as well as a modification of the method of scoring which yields an estimator that is asymptotically equivalent to the C2SLSA estimator. The asymptotic distributions of such estimators are obtained and we determine their relative asymptotic efficiencies.

Elasticities of Substitution for Two-Digit Manufacturing Industries: A Correction

There are two primary questions confronting program planners of educational facilities: 1) At what size is the minimum cost per pupil achieved, i.e., what is the optimum size of school? 5 2) Ascertaining if economies of size exist and the magnitude of such economics, i.e., at what rate does expenditure per pupil decrease as size increases? Table 1 provides the results of expenditures per pupil regressed on selected independent variables. Use of the regression equation to find the net relationship between cost and size is as follows for the different school sizes: 1) Change in cost from 200 to 500 pupils .0503 (500) + .00001121 (500)2 .0503 (200) + .00001121 (200)2

On the Strong Consistency of Estimators for Certain Distributed Lag Models with Autocorrelated Errors

12.74. 2) Change in cost from 500 to 1000 students is -