I. Introduction and summary, 264. — II. The model, 265. — III. A brief review of the Hood and Scott, and Johnson results, 276.

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.

[This paper derives the asymptotic distribution of restricted and unrestricted reduced form estimators and compares their asymptotic efficiency. It also shows that the same techniques yield the asymptotic distribution of dynamic multipliers.]

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.

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

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 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.

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 1950's. This study covers the period 1937-59.

There are two primary questions confronting program planners of educational facilities: 1) At what is the minimum cost per pupil achieved, i.e., what is the of school? 5 2) Ascertaining if economies of exist and the magnitude of such economics, i.e., at what rate does expenditure per pupil decrease as 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 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 $12.74. 2) Change in cost from 500 to 1000 students is -$16.74. 3) Change in cost from 1,000 to 1,500 students is -$11.14 per pupil. 4) Change in cost from 1,500 to 2,000 students is $5.53. 5) Change in cost from 2,000 to 2,244 is -$.66 per pupil. In other words, the total net effect of increasing school from 200 to 2,244 students would result in a savings of approximately $47 per pupil. Riew, on the other hand, found the total savings would amount to well over $200 per pupil from a school with 200 to 1,675 students. A possible explanation for such a large discrepancy in the rate of decrease in per pupil expenditures is that Riew excluded transportation costs from his expenditure variable. The results of this analysis regarding the net relationship between current expenditures per pupil and of school provides guidelines regarding the added costs incurred if the optimum size school was not provided. Note that most of the economies had been realized as student numbers approached 1500. 5 DY/DX8 =-.0503 + 2 (.00001121) X8. Setting DY/DX8 equal to zero and solving for X8 yields 2,244 students. TABLE 1. REGRESSION RESULTS OF CURRENT PER PUPIL EXPENDITURES REGRESSED ON SELECTED INDEPENDENT VARIABLES MISSOURI SCHOOL SYSTEMS, 1966

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]. Lintner's 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. Lintner's 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.