Knowledge that Transforms

T HIS research provides an estimate of the demand for educational attainment across states within a framework of optimal community choice. The communi,ty is envisioned as having the ability to choose a level of educational attainment for its students which will maximize its net benefits subject to the prevailing technical relationship. The technical relationship specified in this paper considers separately the impact of school inputs, pupil inputs, and social characteristics on educational attainment. Most previous studies of the educational industry have failed to specify a structural model of educational attainment which simultaneously accounts for supply and demand factors. Those which have attempted to measure the effects of inputs on educational attainment have failed to standardize for demand conditions. Expenditure studies have either ignored supply conditions or have resulted in reduced form equations in which the structural parameters cannot be identified. McMahon (1970) estimated the relationship between expenditures and inputs using state data. His conceptual framework did not, however, permit the estimation of the price and income elasticities of demand.' Estimates of income elasticities have been made by Hirsch (1960), Brazer (1959), and Pryor (1968). Their estimates utilized a single equation expenditure function approach which failed to take account of variations in price and the simultaneous aspects of the determination of price and quantity. With the exception of a recent paper by Barlow (1970) estimates of price elasticities have not been published in studies of educational expenditures.2 While Barlow's demand function is similar in form to our own, his single equation estimation procedure ignored the effects of supply changes and thereby introduced the possibility of simultaneous equation bias. The approach utilized in this research is to take account explicitly of the simultaneous nature of demand and supply. Our conceptual framework permits the identification of both price and income elasticities as well as output elasticities for the inputs. Our price and income elasticities are statistically significant and consistent with theoretical expectations. We find that school inputs, pupil inputs, and community characteristics all have important impacts on educational attainment.

N this paper, we first re-estimate the structural equations of the Puerto Rican Model (Dutta and Su, 1969) by seven alternative methods of estimation, and obtain predictions on endogenous variables by using seven sets of alternative estimates. We have obtained three different types of predictions -pure ex-post, pure ex-ante and partial ex-ante. We then compare the predictive power of the various estimators in terms of several descriptive criteria. The specification of the model remains as before (Dutta and Su, 1969). The model consists of 36 jointly determined variables and 36 equations. Twenty-three of these equations are stochastic, and the rest are definitional. Of the 23 behavioral equations, equations (1) to (6) explain consumption expenditures on food, services, other nondurable goods, housing, automobiles, and other durable goods; equations (7) and (8) describe private investment expenditures and changes in inventory investment; equations (9) to (16) cover imports including food, nondurable goods, automobiles, other durable goods, capital goods, raw material, payments on service account, and payments on all other service account; equations (17) to (19) determine exports, namely traditional exports, nontraditional exports, and exports of services; equations (20) to (22) deal with the production sector and explain gross product of three sectors, namely: agriculture, manufacturing, and all other industries and finally equation (23) explains wage share. The relations (24) through (36) are definitional. II Estimation

T HIS paper presents an empirical approach to the aggregation problem. An aggregate dependent variable is properly thought to depend on a long string of disaggregated explanatory variables. There are two extreme ways of analyzing an equation such as this. We may use all of the explanatory variables individually, or we may summarize them in an index and use only the index as an explanatory variable.1 Both of these approaches have serious shortcomings and the purpose of this paper is to consider methods that lie between these extremes. The difficulties with the two extreme approaches are well known. On the one hand data limitations in the form of degrees of freedom inadequacies or multicollinearity usually completely rule out the purely empirical approach. On the other hand, the use of indexes as explanatory variables implies a specification error with unhappy implications worked out by Theil (1954 and 1971), Klein (1946), Allen (1965) and others. It is useful to consider the role of prior judgement in these two approaches. The one analysis excludes prior information about the coefficients and estimates would depend entirely on data evidence if that were possible. The other approach is based on the assumption that the coefficients are known with certainty (up to a factor of proportionality) and no data evidence can alter that constraint. In this paper we will pursue an intermediate course that involves weakening the assumption that the index weights are known with certainty but not to the point that the weights are totally unknown. More formally, this means formulating a proper prior distribution on the coefficients in the unconstrained equation and updating that prior via Bayes Rule. We will analyze import demand functions. One phenomenon specific to import functions is that the domestic indexes that are typically used have weights that are quite unlikely to be adequate for analyzing competition between imports and domestic goods. For example, services substitute little if any with imports and should have low weight in the domestic price index. We hope from our analysis to identify the prices and incomes that are most critical in determining imports and also to obtain better estimates of the aggregate elasticities.

SINCE World War II there has been a tremendous increase in the number of men and women attending college, an increase in the attachment of women to the labor force, and more recently, widespread concern with the economic position of women. Despite these developments, there has been little investigation of the impact of higher education on women's earnings.' This study undertakes such an investigation. Its scope will be limited to considering only monetary costs and benefits associated with education since only these can be measured directly.

T HE micro-economic foundation for most analyses of price and wage decisions is based on the optimizing behavior of familiar objective functions; employers maximizing profit and workers optimizing utility. The functions typically contain variables that measure opportunity cost (the unemployment rate), real income, and price-deflated wages. But neither objective function contains any variable that measures the situation of other actors in the economic system. Behavior in the real world, however, frequently depends on relative wages, profit margins, and so forth. There is a body of literature on the relationship between relative wages and the macro-economic variables of inflation and unemployment. Wachter (1970), finds that low wage workers tend to get relatively larger wage increases in periods of low unemployment, and thus, the interindustry spread among manufacturing wage-rates diminishes with low unemployment and increases with inflation. Wachter deals with the influence of the macro-economic variables on the relative wage structure. number of studies (1962, 1967, 1968, 1969) have been directed to the effect of relative wages on the general wage or price level.1 It is the latter subject that is the primary focus of this paper. Our micro-economic hypothesis is that wage and price behavior is influenced by both general and relative factors. Therefore, we added a measure of the relative wage structure to the typical Phillips curve relationship. This formulation will reflect the idea that under a given set of overall demand conditions, an individual will attempt to obtain a larger wage increase if he feels relatively underpaid. Our second hypothesis is that rapid inflation is unanticipated and leads to the distortions in the relative wage structure. These two hypotheses lead to the following dynamics. given Phillips curve exists at any point in time. If the economy operates at a point of low unemployment and high inflation rates, then distortions are created which move the Phillips curve to the northeast, i.e., the tradeoff is worsened. If the economy operates at a point of high unemployment and low inflation rates then the distortions tend to diminish and the trade-off improves.2 Thus, while a Phillips curve exists, there is only one point on it (i.e., one unemployment and inflation rate) that is stable; moreover, the stable point is determined by the previous historical experience which has created the distortions in the economy. This series of stable points defines a long-run trade-off that is steeper than the shortrun curve but is still less steep than the vertical line hypothesized by the accelerationists. These dynamics suggest that the absence of unanticipated inflation in the early 1960's brought about the stable wage structure of the 1963-1965 period and, with it, the favorable trade-off. The unanticipated inflation of the late sixties, however, again distorted relative wages and produced the worsened trade-off of 1969-1971. The short-term relationships will then take the general form: DP = f (1/U, DST) T ( ) Received for publication May 12, 1972. Revision accepted for publication August 17, 1972. * This work was performed as part of the CED project entitled A Reconsideration of Policies for Economic Stabilization. The authors thank Frank Schiff for his suggestions in the initiation of this work and George Perry, Charles Schultze, Arthur Okun, William Branson, Gary Fromm and the referee for their comments on preliminary drafts. The errors and omissions remain the responsibility of the authors. The views expressed are our own and not necessarily those of the officers, trustees or other members of the Committee for Economic Development. ' See Eckstein and Wilson (1962), Perry (1967, 1968) and Throop (1968). 2 One of the factors that gives an inflationary bias to our economy is the asymmetrical nature of the distortion process; that is, larger than average wage increases cause the distortion and the return to the normal structure is also achieved by larger than average increases.

IN this paper is examined some of the determinants of earnings of males in a high powered occupation, chemical engineering. Models such as those developed here can be useful to researchers interested in earnings functions, the theory of occupational choice, economic growth and returns to investments in human capital. In addition, earnings models can be help'ful to individuals who must make promotion and salary decisions. The impact of education on earnings has received a great deal of attention in social, political and economic circles. Previous studies show that persons who obtain higher levels of education earn higher incomes. However, comparing average incomes of individuals who differ only in levels of educational attainment may overstate the influence of education since schooling and non-schooling factors other than the amount of formal schooling cause differences in individual incomes. Such factors include socio-economic background, demographic characteristics, innate ability and the quality of formal education. Emphasis in this study is on the quality of education and student ability. The author was able to find only two attempts at simultaneously estimating the impact of student ability and school quality on the earnings of persons in professional occupations.' This paper is viewed as an exploratory effort in this direction. The basic earnings functions to be estimated are described in section I. The data sources, key proxy variables in the regression analysis and the regression findings are discussed in section II. Section III is a summary of the main findings.