Knowledge that Transforms

B AINis (1956) analysis of the sources of barriers to new competition suggests that scale economies to the plant or firm allow sellers to elevate price somewhat above average cost without attracting new rivals. Multivariate statistical analyses of the determinants of seller concentration and profits henceforth have included measures of scale economies among their independent variables. However, direct measures, based on engineering or survey evidence, have been available to only a few investigators (Bain, 1956; Eastman and Stykolt, 1967). Others have employed various statistical proxies for the missing firsthand evidence. This paper proposes a new way to form these surrogate measures, compares its properties with those of previous approaches, and reports its performance in two recent studies of allocative efficiency in manufacturing industries.

det xoo'xoo 1 ) (N n + 1)/(n-2) has the det xo'xo F-distribution with n 2 and N (n 1) degrees of freedom, assuming normality of the underlying distributions. If the statistic is (almost) zero, det xoo'xoo (almost) equals det xo'xo, and the multicollinearity among the columns of xo is (almost) wholly attributable to the columns of xoo. Each step in the proposed third stage is virtually a replica of the second stage, the only difference being that fewer variables are involved. Thus, to show why the proposed third stage is effective in detecting multicollinearity patterns, it suffices to refer to the justification of the second stage, in footnote 3. 4 In practice, calculation of a few, strategically chosen, principil minors should suffice.

IN the empirical literature on market interferences a variety of numerical techniques have been used to analyse competitive equilibria which are not directly observable. Harberger (1963, 1966), and Johnson and Mieskowski (1970), for instance, in their analyses of factor market distortions in the United States economy use a mixture of differential calculus and linearization assumptions to estimate efficiency losses and distributional impacts of particular market interferences. Acceptance seems to be implied in these procedures of the reliability of approximate methods for calculating unobservable equilibria. This issue of reliability forms the subject matter of the present paper.' A recent joint paper (1972) examined the robustness of Harberger's results (1966) when a competitive for the United States economy in the absence of distortionary taxation was calculated using a procedure for the computation of competitive equilibria due to Scarf (1967, 1969, 1973). The results for particular parameterizations suggested that the gain in simplicity of approximate methods may in some circumstances counterbalance the precision of more refined computational devices. These results, however, were obtained for a problem of small dimensionality and limited complexity, and the comparison between Harberger's results and true general solutions was made only on the basis of one summary statistic. In addition, the approximate solution device used by Harberger (1966) does not correspond to conventional notions of either or general analysis. It is thus of some importance that the comparison between general solutions and various forms of analysis be carried further before any conclusions on computational experience are used as a guide in other contexts. These issues are taken up here in the context of a-particular model which allows different forms of analysis to be used and compared to general solutions. The results presented are put forward as evidence on computational experience. This paper considers a general model of the United Kingdom economy used in recent work on an assessment of tax changes in the United Kingdom economy (1973). Using this model the gain2 to the United Kingdom from the abolition of the distortionary features of capital income taxation is calculated by various methods and compared to the general solution. Section II presents a characterization of competitive equilibria for an economy with taxation used in a recent paper by Shoven and Whalley (1973) which underlies the United Kingdom tax model. As no explicit statement of partial equilibrium analysis is to be found in the literature, two alternative characterizations of such procedures which are later applied to the model, are devel-

The threshold regression assumes that value of dependent variable remains fixed until the concerted action of independent variables and error term induces it to overcome its reaction threshold. The existence of reaction thresholds in purchasing of private cars has been discussed and analyzed. Among main explanatory variables used in micro-economic studies, most significant appear to be household composition, age and education of head, number of earners, number and age of cars, value of stock of cars previously held, liquid assets, net worth, debts and place of residence. The independent variables finally retained in present study are permanent income, education of head household and number of children. To summarize, income appears to be most important variable affecting car purchases by households. There are no doubt other social and demographic characteristics of households which bear on this phenomenon, but nature of these variables as well as mechanisms through which they operate have not been sufficiently investigated and are not yet sufficiently well known to permit us to detect their effect very clearly, in statistical investigations.

IN making dividend decisions, the firm determines the division of earnings between reinvestment and distribution to stockholders. There are two general issues in the area of dividend policy: The first concerns the determinants of the firm's payout ratio (the ratio of dividends to earnings). The second issue concerns the intertemporal change of dividends. The focus of this paper is on the second issue. There are two prevailing views on the behavior of corporate dividend policies over time; the informational content and the partial adjustment hypothesis. In the following sections, both hypotheses are shown leading to empirically equivalent expressions. To avoid this confusion, we suggest an approach that would differentiate between the two hypotheses. Empirical results analyzing dividends behavior of twenty broad industry categories are summarized.

M IGRATION studies using aggregate data IYL have noted the importance of differences in economic opportunity between areas on migration flows (Greenwood, 1969; Bowles, 1970; Fabricant, 1970). Studies using survey data have provided a more detailed profile of the characteristics identifying migrants, but have not incorporated the effects of economic incentives as fully as aggregate studies. Both approaches have noted significant differences in migration behavior among race or age groups, but neither has generated results which can be readily generalized to other groups of interest such as the poor. Recent interest in anti-poverty policies and income maintenance programs directed toward the poor suggest the need for explicit analysis of this group. The objective of this study is to examine the effects of economic incentives on migration for households grouped first by race and then by poverty level. The data, covering annual observation periods 1968-1969 and 1969-1970, focuses on households headed by persons less than fortyfive years old who are in the labor force at the beginning of an observation period (Institute for Social Research, 1970). The model takes the basic form

David J. Smyth, William J. Boyes, Dennis E. Peseau, The Measurement of Firm Size: Theory and Evidence for the United States and the United Kingdom, The Review of Economics and Statistics, Vol. 57, No. 1 (Feb., 1975), pp. 111-114

provide a criteria for rejecting the importance of substitution in ERP calculations. In addition, it is no less restrictive to assume a priori that all industries have the same value for a, whether it be 0.5, 2.0 or the traditional value of zero. It has been pointed out elsewhere that the realistic case to consider is what happens to the rankings when different industries have different values for a'.3 A meaningful approach would involve answering the question of what is the highest and lowest ranking an industry could obtain under any combination of different hypothetical values for o-. The data for the 135 industries in the investigation indicate that applying these criteria creates scope for the rank correlations to be somewhat less than the observed figures of 0.99, but the author's contention of a high correlation still stands. Nevertheless this result, while being interesting and useful, can however be misleading if applied as a general case. There is in fact considerable scope for variation in industry rankings when there is a wide disparity in the magnitude of the calculated ERP across the industries. This is the experience of some countries4 and it is also the case when, for a variety of practical purposes, industries are classified in smaller groups according to the intensity of their protection. For the group of highly protected industries, for example, there is traditionally a wide spread in the magnitude of the ERP and therefore considerable scope for variation in industry rankings. The result being that in the study under discussion for the 10 most highly protected industries there are 9 industries that could fill the top 4 positions and 7 industries that could fill the bottom 2 positions in the industry rankings.5

THE market for new law school graduates has undergone considerable change in recent years, with starting salaries increasing rapidly following the enormous increase in rates of the major New York firms in 1968' and enrollments into law programs skyrocketing in the late 1960's. What explains these and earlier developments in the market for new lawyers? Does the influx of students reflect economically responsive supply behavior with respect to salary and other labor market incentives? What factors underly changes in the salaries of starting lawyers? This paper investigates these questions with a variant of the recursive model of the market for highly-trained workers originally used to analyze engineering shortages and surpluses (Freeman, 1971). Application of the model to a profession which differs substantially from engineering and related sciences but has a similar fixed time delay in producing new specialists provides a test of its general validity, as well as insight into the operation of the legal labor and education markets. This paper begins with a brief description of the empirical phenomenon under study -patterns of change in the number of law students, legal salaries, and activity in the profession. Section II develops a recursive cobweb-type model to explain these developments. Section III presents estimates of the supply and salary equations of the model. The final section examines the endogenous cyclic fluctuations in the market and summarizes the major findings.