Knowledge that Transforms

IT sometimes happens that when a new mathematical or statistical procedure is adopted from one discipline into another, it arrives complete with terminology, usage and (these days) computer software devised for specialized application to problems in the parent area. This is probably inevitable, but until the new method is more broadly perceived its application may fall considerably short of its potential in the adopting discipline. A recent example is the spline function. Briefly put, spline functions are a device for approximating the shape of a curvilinear stochastic function without the necessity of pre-specifying the mathematical form of the function. That is, it is unnecessary to restrict the estimate to a straight line, a polynomial of pre-specified degree, an exponential, or any other particular form. Brought over from engineering and the mathematics of interpolation, spline functions have appeared in several places in economic statistics in recent years. Application to economic problems has been made by Barth, Kraft and Kraft (1976), McGee and Carlton (1970) and Poirier (1973, 1976). Buse and Lim (1977) have shown spline functions to be a special case of restricted least squares. Yet because the idea is still wrapped in its original packaging, it is frequently overlooked when it might be a powerful adjunct to research. Moreover, even in some of the work where the spline function has been employed, it has not always been used to best advantage. For example, Barth and others in the article cited above, although admitting that it might improve their analysis to employ a multivariate spline function, were constrained by the fact that the software package at their disposal unfortunately ... permits only bivariate specification. Yet, in fact, the procedure is readily adapted to bivariate or multivariate analysis. In this article we show that by use of appropriately defined composite variables, spline functions are easily fitted by any standard package for ordinary least squares regression. Some of the examples given below were fitted by the familiar SPSS package, others were fitted by members of an undergraduate class in econometrics at the University of Hawaii, using the TSP routine. In the presentation, piece-wise linear regression is employed as a general introduction to the procedure. This is followed by development of the bivariate and the multivariate spline functions. The procedures are then illustrated by their application to the relationship of interest rates to money supply and inflation. Once the spline function is understood as a least squares regression model, additional variations become possible. As an example we present a modified or truncated spline function and apply it to the relationship of fertility to per capita income. We conclude with a few general remarks on the limitations of the method.

THE purpose of this paper is to empirically examine whether security prices and volume are causally related. Existing models that attempt to analyze the interdependence of price and volume in speculative markets have been generally built on basic underlying demand and supply conditions. Crouch (1970), Clark (1973), Westerfield (1973), and others have postulated that the absolute value of price change is positively and linearly related to volume. The rationale is that given an initial equilibrium position and assuming a net increase (decrease) in demand for a security, the market will eventually clear that security at some price above (below) the equilibrium price. During the process of adjustment transactions are constantly occurring as a function of demand. Under these conditions one would expect a rise in the volume of transactions with both a rise or fall in the price level. Copeland (1974) refined this theory by establishing the direction of the relationship between the absolute value of price changes and volume under two assumptions of information arrival. Using trading volume as a proxy for the rate of information arrival in the market, Copeland concludes that i the relationship is positive and linear if a hypothesis of sequential information is valid. An inverse correlation would support the notion of simultaneous information arrival. An alternative approach is to view a degree of association between price change per se and volume. The research of Ying (1966), Hsu (1973), and Epps and Epps (1976) are in this category. Illustrative of this line of reasoning Epps and Epps (E&E) developed a theory of financial markets based on a two-parameter portfolio model. Their rationale is that news reaching the market is generally accompanied by a change in the overall average of investors' expectations. And if investors are classified as either buyers or sellers (these groups are identified by their response to news entering the market) then the news reaching the market will result in changes in the average expectations of each of the two groups. Combining these two notions, the major premise of their model is that the extent of disagreement between these two groups of investors tends to increase with the absolute value of the overall average change in expectations. Building upon this assumption, E&E are able to imply that their theory (and empirical evidence) supports the notion of positive stochastic dependence between volume and security price change. In this paper additional empirical evidence is provided to support the thesis that price change per se and volume for individual securities are positively interrelated. The main methodological novelty is the use of a direct test of independence/causality developed by Haugh (1976), which is outlined in section II. In section III the results of the empirical tests are presented. The hypotheses are tested on stock data and warrant data. To date no empirical evidence has been published concerning the stochastic process generating warrant volume or the interrelationships between warrant price, warrant volume, stock price, and stock volume. Section IV contains a summary and conclusions.

STATISTICAL analyses of the structureperformance relationship in manufacturing industries have invariably assumed that an industry's member firms differ only in their market shares. This paper demonstrates that this assumption is often incorrect, and that the complexity of the structure of strategic groups populating an industry exerts a significant influence on its performance. In the following sections we explain the sources and significance of strategic groups, derive hypotheses about their influence on an industry's profitability, and test these hypotheses on a sample of producer-good industries.

Prepared in association with the Sloan School of Management and the Dept. of Economics

A DAM Smith (1937) observed that "the whole of the advantages and disadvantages of the different employments of labor and stock must, in the same neighborhood, be either perfectly equal or continually tending to equality."If a job poses health and safety risks that are especially great, a worker will require higher levels of compensation or greater non-pecuniary benefits in order for him to accept the risky job.Despite the fact that the theory of compensating differentials is almost two centuries old, it has been only recently that this theory has been subjected to successful empirical tests.'The purposes of this essay are twofold.First, in section II, I will formalize the theory of individual choice among potentially hazardous jobs for the general situation in which worker preferences are contingent on the health state outcome.An important implication of this analysis is that the job risk that a worker selects will be negatively related to his wealth.The second purpose of the investigation is to test the two principal conceptual hypotheses.The characteristics of the principal data source to be used are summarized in section III.The University of Michigan Survey of Working Conditions, which is the data set used in the compensating differentials analysis, provides very extensive information concerning the nature of the worker's particular job and his personal characteristics.Section IV presents the analysis of the earnings differentials generated by job hazards and other job attributes.In section V, I consider the responsiveness of the job risk to a worker's wealth.The empirical findings, which are consistent with the theoretical predictions, are summarized in section VI. II. Optimal Choice among Hazardous Job AlternativesRecent economic analyses of choices among potentially hazardous jobs have generalized Adam Smith's notion of compensating wage differentials to probabilistic contexts.The study by Oi (1973) views adverse job consequences as being tantamount to a drop in income.He concludes that jobs posing greater risks will command compensating wage differentials.A more detailed analysis along similar lines is presented by Thaler and Rosen (1976), who develop Oi's approach and also consider the situation in which individuals face lotteries on life and death.2The payoff after an adverse outcome (death) is represented by a bequest function.The approach taken here also can be viewed as a probabilistic generalization of the compensating differential analysis.It differs in that individuals' utility functions are assumed to be dependent on one's health state.The static model in this section illustrates the properties of the optimal job choice of a worker who is choosing from a set of job opportunities that involve the same number of work hours but have differing probabilities of an adverse consequence.3This approach does not impose assumptions that are unduly restrictive since most job opportunities offer little individual leeway in the choice of hours.

Migration is a means of improving the allocation of human resources. People living in places where they are not fully employed or most highly valued are expected to move to destinations having brighter prospects but both policymakers and migration analysts seem to have mixed opinions as to whether private market forces alone are sufficient to induce them to do so. On the one hand there has been considerable discussion of policies (e.g. relocation assistance programs) designed to affect migration directly by enabling or inducing the unemployed to move to more promising labor markets the implication being that the unemployed are not themselves sufficiently responsive to economic conditions. On the other hand policies of investment in depressed areas are based largely on the premise that expanded local economic opportunities will reduce economically forced outmigration. Available evidence has provided little guidance to policymakers and others concerned with the influence of personal and area unemployment on outmigration. Several studies using survey data (e.g. Saben 1964; Lansing and Mueller 1967) have confirmed that certain unemployed workers are more likely to migrate than employed workers; but because these studies do not use adequate controls for other characteristics that may affect migration the direct contribution of unemployment to migration cannot be determined. Studies using aggregate data to assess the relationship between unemployment and migration (e.g. Lowry 1966) have obtained mixed results but unemployment is often measured at the end of the migration period an hence may have been affected by the intervening migration. (excerpt)