Knowledge that Transforms

THIS ANALYSIS EXTENDS THE CONVENTIONAL MODEL OF HOUSING CHOICE, DEFINING HOUSING AS A MULTIDIMENSIONAL COMMODITY WITH SEVERAL QUALITY ATTRIBUTES WHOSE PRICES VARY THROUGHOUT THE CITY IN A DISCONTINUOUS FASHION. WORK SITE AND ACCESSIBILITY HAVE SIGNIFICANT EFFECTS ON HOUSEHOLDS' CHOICE OF A LOCATION AND THE AMOUNT OF HOUSING CONSUMED. DESPITE HOUSEHOLDS' WILLINGNESS TO ALTER THEIR WORK TRIP WHEN CONFRONTING DIFFERENT PRICES, RESIDENTIAL LOCATION CHOICES ARE SIGNIFICANTLY AFFECTED BY THE SPATIAL DISTRIBUTION OF EMPLOYMENT. /DOT/

U NFORTUNATELY, economic theory and existing empirical evidence provide little insight into the effects of diversification on industry performance. This is partially due to the fact that most previous empirical studies of diversification have been concerned with tabulating the extent of,1 or motives for,2 diversification. In order for the antiitrust authorities to develop a rational policy toward conglomerate mergers, it will be necessary to determine the competitive consequences of diversification. This study attempts to provide some empirical evidence on the effects of diversification by examining the relationship between industry price-cost margins and diversification.3 Specifically, the study examines the general proposition that diversification is an element of industry structure and the more narrow hypothesis that diversification raises barriers to entry into an industry. The study is based on a sample of 241 four-digit manufacturing industries from the 1963 Census of Manufactures. The primary testing technique is multivariate regression analysis. Results of the analysis provide tentative support for the proposition 'that diversification has a systematic influence on price-cost margins which may be attributable to certain barriers to entry.

COMPARISONS of the extent of poverty at different times are greatly affected by whether the dividing line between the poor and the rest of the population changes as average income grows over time, and if so to what degree.1 The absolute income standard and the relative income standard are polar hypotheses about the income elasticity of the poverty line. Under an absolute standard of poverty, the poverty line is constant (in deflated dollars). In terms of what people thought of as poverty a century ago, the absolute standard implies that today almost no one is poor in the United States. Under a relative standard of poverty, the poverty line changes in the same proportion as average income if the relative income distribution is constant. The relative standard implies that if the shape of the income distribution is the same today as a century ago, the poverty problem is now no less.2 Probably more likely than either of these extremes is that people's judgment about the dividing line between poverty and a more adequate standard of living is determined by a mixture of concerns over both absoluteand relative conditions.3 If so, growth in average income increases the poverty line, but by less than in the same proportion. This proposition -that the income elasticity of the poverty line is between zero and one-is the hypothesis tested in this paper. I Time Series Analysis of Gallup Poll Results

T HIS study investigates the effect of financial leverage, or relatively greater use of debt capital, on industry profitability. Recently at least two cross-section studies have yielded the surprising result that systematically higher rates of return are earned by firms with relatively low leverage. Measuring leverage inversely as the ratio of equity to assets,' one would expect the rate of return on equity and this ratio to vary in opposite directions, lower values of equity/assets and the associated riskier bond intensive capital structures implying higher equilibrium profit rates, ceteris paribus.2 But so far the evidence has gone the other way. Fred D. Arditti (1967) calculated expected profit rates for firms as a geometric average of past rates of return and regressed this variable on the ratio of debt to equity.3 His measure of leverage appeared with a negative sign in all of his regressions. And in a paper dealing with the determinants of firm profitability, Marshall Hall and Leonard Weiss (1967) found that equity/assets, which is inversely related to leverage, had a significantly positive effect on profits on equity when market structure conditions were held constant.4 They noted, . . a possible after-the-fact explanation is that relatively profitable firms take some of the exceptional returns in the form of reduced risks. (1967, p. 328.) Thus profitability may affect leverage, and leverage may affect profitability. On grounds that the direction of causation between leverage and profitability may run in both directions, this paper develops and tests a model consisting of two equations, one explaining industry profitability in terms of the usual market structure variables plus leverage and the other a new equation incorporating risk variables to explain leverage.

This paper estimates a housing demand function from a four year panel study.The findings indicate that the income elasticity of housing demand is around .6 or .7 for owners and around .5 for renters.This means that the percentage of income spent on housing declines as income rises, and that the property tax falls more heavily on the poor than on the rich.This finding differs from earlier studies which were based on city averages rather than panel studies, and is therefore more reliable.The study also found that, other things equal, the old demand more housing than the young, whites more than nonwhites, and female headed households more than male headed households.

T HE problem of collinear data sets in the context of the univariate multiple regression model has generated a confusing array of papers, comments and footnotes. Perusal of this literature does not lead the reader to conclude the problem has even been rigorously defined. The purpose of this paper is to offer several rigorous definitions and to suggest several substantive quantitative summaries of the degree of the problem. Specifically we address our attention to the regression model Y = X,B + u where ,B is a k-dimensional parameter vector with elements 81,12, ... *k, where Y and u are T X 1 vectors and where X is a T X k matrix. Inferences are to be made about the vector ,B from observations of Y and X. When the columns of X are orthogonal, the design matrix X'X is diagonal. Correlated columns of X imply a nondiagonal design matrix. The collinearity problem has to do with the differences in the inferences may be drawn in these two situations. The principal claim of this paper is the most important aspects of the collinearity problem derive from the existence of undominated prior information which causes major problems in interpreting the data evidence. It is claimed here if our a priori knowledge of parameter values were either certain or completely uncertain the aspects of the collinearity problem most of us worry about would disappear.' As an empirical test of this proposition consider the situations when collinearity is identified as a culprit. Usually signs are wrong or point estimates are otherwise peculiar. Occasionally confidence intervals overlap unlikely regions of the parameter space. Yet to say these things is to say there exists undominated prior information. Classical inference, with the possible exception of the pretesting literature, necessarily excludes undominated prior information. As a result most discussions of the collinearity problem miss a critical point. The textbook discussions including Theil (1971, p. 149), Malinvaud (1970, p. 218), and Goldberger (1964, p. 192), observe when the design matrix X'X becomes singular, the least squares estimator is non-unique and the sampling distribution has finite variance only for certain estimable functions. Thus extreme collinearity is implicitly defined as total lack of sample information about some parameters. The case of less extreme collinearity is not dealt with so trivially since there is nothing in the least-squares theorems is obviously dependent on the near non-invertibility of the design matrix. This fact has led Kmenta (1971, p. 391) to conclude that a high degree of multicollinearity is simply a feature of the sample contributes to the unreliability of the estimated coefficients, but has no relevance for the conclusions drawn as a result of this unreliability. To put this another way, the problem of defining collinearity may be solved by identifying a distance function for measuring the closeness of the design matrix to some noninvertible matrix in which the collinearity problem is unambiguously extreme. Since the extreme case is associated with infinite marginal variances on the parameters, authors such as Theil (1971, p. 152), Malinvaud (1970, p. 218), and Goldberger (1964, p. 193) use a distance function informally related to the sampling variance of the coefficients. Collinearity is defined as large variances. The failure of this definition is instead of defining a new problem, it identifies a new cause of an already well-understood problem weak evidence. Although collinearity as a cause of the weak evidence problem can be distinguished from other causes such as small samples or large residual error variances, collinearity as Received for publication November 7, 1972. Revision accepted for publication January 23, 1973. * Research for this paper was supported by NSF Grant GS 319.29. The author has benefited from conversations on the subject with Gary Chamberlain and Richard Kopcke. Both the discussion and the content have benefited significantly from a referee's comments. An earlier version was presented at the NBER-NSF Seminar in Bayesian Inference in Econometrics at the University of Minnesota, October, 197,2. 1 See Zellner (1971, chapter 2) for a discussion of the problem of defining complete uncertainty.

PpT HE purpose of this paper is to investigate the systematic covariation between stock prices in developed countries. Covariation may reflect causation or it may indicate similar reactions to external stimuli. Causal relationships may be lasting or temporary and may accordingly result in sustained periods or in rather brief periods of covariation. For example, developments in the Canadian stock market are continuously influenced by those in the United States stock market. An example of the second type of causal covariation is the relationship between Japanese and United States stock prices in mid-1970. Because of a decline in United States stock prices at this time and the liquidity needs of large institutional investors in the United States, it was necessary for these investors to reduce their holdings of foreign assets.1 The reduction of their investment in Japanese equities resulted in an outflow of capital from Japan and stimulated a decline in Japanese equity prices. For markets outside the United States, the introduction of the Interest Equalization Tax by the United States in mid-1963 is an example of an external development that caused similar responses in several stock markets. This measure caused many stock indices to decline, especially those in Japan and Canada. To the extent that stock prices reflect domestic economic conditions and conditions are similar across countries, stock prices will show systematic covariation that is a result of developments external to the national stock markets. Covariation between stock prices in different countries is of interest to individual investors who wish to allocate their investment portfolios so as to maximize the rates of return on their portfolios for a given risk. The return on stock consists of the dividend paid on the stock and the change in the price of the stock. For most stocks the price is more variable than the dividend so that price movements account for a larger part of the change in the rate of return. Thus investors seeking effective portfolio diversification wish to determine the countries whose stock prices move together, those whose stock prices move in opposite directions, and those whose stock price movements are unrelated to one another. Covariation between stock prices in different countries is of interest to the forecaster and policy maker because stock movements affect domestic consumption and investment expenditures. The wealth of consumers is affected by changes in stock prices and changes in wealth affect consumption decisions. The mechanism through which stock price changes affect investment decisions is more complex, but the influence of these changes may still be significant. An economist is frequently interested in establishing the extent to which financial markets are integrated or the extent to which developments in one market are reflected in the developments in a second market. Measures of financial integration are traditionally based on the dispersion of interest rates between markets, with a smaller dispersion measure corresponding to a higher degree of integration.2 This study concentrates exclusively on the covariation between equity prices as a measure of integration since aggregate information on dividend payments is not available for most countries. In an attempt to measure the extent of covariation between national stock markets and to isolate and identify the patterns of linkage Received for publication June 28, 1972. Revision accepted for publication January 12, 19,73. * The views expressed in this paper are those of the author and not necessarily those of the International Monetary Fund. 1Legal constraints on the share of a United States institution's portfolio that may be invested in foreign assets may also have influenced the repatriation of portfolio capital. 2See R. N. Cooper, Towards an International Capital Market?, Center Discussion Paper number 68, Economic Growth Center, Yale University, July 1969. The question of the integration of national stock markets is briefly raised but is not pursued because price earnings ratios are not available in many countries.

Focuses on additive and homogeneous production possibility frontiers that have played an important role in formulating statistical tests of the theory of production. Characterization of the class of production possibility frontiers that are homogenous and additive; Representation of the production possibility frontier; Statistical tests of the theory of production. (Из Ebsco)