[In this paper we construct a model that describes the behavior of the foreign exchange market and Exchange Fund. Cross-spectral and regression analysis of daily data are used to show that official intervention contributed significantly to the short-run stability of Canadian exchange rates.]

They asserted that Gt is a function of Rt but that R* is in no way a function of Gt (see p. 51). From this identity it of course follows that the cycles in R* will generate cycles in R unless offset by G. Investigating the period April 4, 1951-May 31, 1967 as a whole, B-S found 1) monthly cycles in R* and G, 2) no monthly peak in R, and 3) no cross covariance between G and R.' Based on these results they concluded that the effect of Federal Reserve open market operations since the Accord has been practically to eliminate the very strong monthly element cycling in member bank reserves, . (p. 59). In addition, they found a monthly cycle in currency outside all and significant coherence between this series and both R* and G. On the basis of these data they suggested an interpretation of open market operations as being undertaken, or at least having the effect of existing primarily, for the purpose of offsetting a monthly cycle in currency outside all banks (p. 60). But B-S committed important methodological and analytical errors which require us to set aside their results and conclusions and search for correct ones.

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.

D ISTRIBUTION of the population by urban, rural nonfarm and farm residence is one of the oldest and most established causes of differentials in fertility cited by demographers.' Geographical region is also frequently mentioned in demographic studies as a source of variation in fertility in the United States. Race and social class, the latter often measured by occupational status, are additional variables popular with both demographers, and less specialized sociologists, as sources of variation in fertility.2 In most of the studies by demographers, a major difficulty with the factors proposed as causes of variation in fertility is that there is no way of knowing whether the variables are separate and independent explanations of birth rate differentials. To some extent, this is due to the fact that the statistical methodology consists of simple correlations, or more frequently, tabular and graphical presentations, which limit the analysis to two or three dimensions. A more fundamental criticism is that the discussion of the causal relationship between the independent variables and the fertility differentials does not attempt to assay whether basic factors, such as income and economic conditions, and the costs and benefits of having children, are common explanations of the variations in fertility by community of residence, geographical region, class, race, etc. Analyses of birth rate differentials by economists usually are based on a stronger statistical methodology than the studies by demographers but suffer from a similar weakness in their analytical formulation. independent contribution of the variables to fertility differentials is determined by means of multiple regression or partial correlation analysis. Although meaningful statistically, the regression results usually afford little insight into the fundamental relationship between population growth and economic development and/or economic conditions. One source of confusion in economic crosssection studies of birth rates may be the unfortunate choice of data. Some economists apparently ignore the demographers' findings that a considerable portion of the variance in fertility within a country is due to geographical differentials, and attempt a cross-section analysis of fertility on a very heterogeneous sample composed of different countries.3 It would seem that a more homogeneous sample of observations within a country is a more propitious beginning for an interpretation of the relationship between birth rates and economic variables. Economists have benefited from one of the findings of demographers. A popular variable for inclusion is the fraction of the population classified as farm or the per cent of the labor force employed in nonagricultural industries. Weintraub suggests that the ratio of the popu* This paper is a revision of an earlier version presented at the annual meeting of the Western Economic Association at Corvallis, Oregon, August, 1968. It has benefited from a critical reading by our colleague Jerzy F. Karcz who made a number of helpful suggestions. Our appreciation goes to Dana Burtness who assisted us in all phases of this study but especially in making our interactions with the IBM 360 Computer pleasant. Additional credit goes to John Danforth and Ken Gralla who assisted us in the early stages of this study. 'Ben Franklin noted this causal relationship between birth rate differentials and population distribution as early as 1786. 2The following references are typical of the analysis of differential fertility by demographers. Donald J. Bogue, of the United States, Free Press of Glencoe, Illinois (1959), chapter 12 -The Fertility of the United States Population (contributed by Wilson H. Grabill). Warren S. Thompson, Problems, McGraw-Hill Book Co. (1965), chapter 11 -Some Factors Affecting Fertility. As an example in the same vein by a sociologist, refer to the book by T. Lynn Smith, Fundamentals of J. P. Lippincott Co. (1960), chapter 13Differential Fertility. 3 Typical of the multiple regression cross-section analysis of fertility differentials in different countries conducted by economists are Irma Adelman, Econometric Analysis of Growth, American Economic Review, 52, no. 3 (1963); Robert Weintraub, The Birth Rate and Economic Development, An Empirical Study, Econometrica, 40, no. 4 (Oct. 1962).