T HE response of government policy variables to the targets or objectives of policy has received increasing attention in the literature. All of the published studies have limited their investigations to the behavior of the monetary authority.1 This concern with the reaction function of the monetary authority can be traced to three factors: (1) Since the monetary authority is independent (or semiindependent) of the government, investigators have been concerned with whether the central bank has responded to the appropriate social objectives such as price stability and full employment; (2) Central banks have often expressed concern with short-run objectives (such as interest rate stability) and investigators have examined whether the pursuit of such objectives has hindered the implementation of the social goals; and (3) Econometric modelbuilders have become concerned with the statistical problems arising from the endogeneity of policy.2 This paper reports on an attempt at estimating the reaction function of the Federal Home Loan Bank System (FHLBS) and the Federal National Mortgage Association (FNMA). Both FNMA and the FHLBS are governmentsponsored agencies (the FHLBS being under more government control than FNMA) whose major objective concerns the mortgage market and housing activity. FHLBS makes loans (advances) to savings and loan associations which, in turn, use the funds for mortgage loans. FNMA buys (or sells) mortgages in the secondary market. During the 1960's these operations were aimed primarily at stabilizing the volume of mortgage credit with the implicit view towards stabilizing housing activity.3 There were a number of factors during the 1960's which might have prevented the FHLBS and FNMA from pursuing their objective of minimizing the variability in mortgage flows and housing starts. First, before 1968, FNMA purchases and sales of mortgages appeared in the United States budget, hence mortgage purchases, in particular, were carefully examined since such purchases added to the deficit. After 1968 this was no longer true since FNMA was made a private corporation and taken out of the federal budget. During the credit squeeze of 1966 the Johnson Administration placed severe restrictions on the debt issues of various government agencies, including the FHLBS. In effect, this meant that the FHLBS was not free to decide to raise funds to lend to savings and loan associations without severe scrutiny. In the next section, two alternative models of FHLBS behavior are derived within a utility function framework. Empirical estimates of the alternative reaction functions are presented. same is done for FNMA behavior in a subsequent section. remainder of the paper presents the implications of the results for a number of issues, including: (1) whether FNMA and the FHLBS have, indeed, used Received for publication June 29, 1972. Revision accepted for publication December 13, 1972. * author wishes to acknowledge the financial support of the Federal Home Loan Bank System. views expressed are not necessarily shared by the FHLBS. He also thanks M. J. Hamburger, S. M. Goldfeld, and an anonymous referee for their comments. 1See, for example, H. G. Johnson and W. G. Dewald, Analysis of the Objectives of in D. Carson (ed.), Banking and Studies, Irwin Inc., 1963; and J. H. Wood, Model of Federal Reserve Behavior, in George Horwich (ed.), Process and Policy, Irwin Inc., 1967. 2See F. de Leeuw and J. Kalchbrenner, Monetary and Fiscal Actions: A Test of Their Relative Importance in Economic Stabilization-Comment, in Review, Federal Reserve Bank of St. Louis, April, 1969, and the Reply by L. C. Anderson and J. L. Jordon in same issue. 3See Harry Schwartz, The Role of Government-Sponsored Intermediaries in the Mortgage Market, in Housing and Policy, Federal Reserve Bank of Boston, Boston, 1970; and Ernest Bloch, The Federal Home Loan Bank System, in Federal Credit Agencies, Commission on Money and Credit, Prentice-Hall, Englewood Cliffs, N.J., 1963.

IN recent years several research studies have used a data base consisting of a time series of cross-section samples. A primary reason is that panel data of this type are potentially richer in information than a single cross-section sample. To date, however, the question of how to best analyze data bases of this type has not been fully explored in any of the research. To illustrate, a number of prior research projects which have utilized this type of data base are briefly reviewed. Hoch (1962) used moving cross-section samples as the data base for estimating the parameters of a CobbDouglas production function by analysis of covariance. Specifically the data were collected on 63 Minnesota farms for the years 1946 to 1951. Hoch reported an observed difference between the least squares parameter estimates and covariance estimates and the elasticities developed from these estimates. In terms of method, the major conclusion was that the covariance model might produce less biased elasticities and marginal return estimates. Massy and Frank (1965) investigated the relationship between price changes and dealing activities on a -firm's market share for frequently purchased household and food products. Panel data covering a 101-week time period of family purchase history provided the data base for the study. However, the data were aggregated so no methodological insight could be inferred concerning the question of analyzing time series of cross-section data. Laughhunn and Lyon (1971) applied Bayesian regression in analyzing a time series of cross-section cigarette consumption data using the Tiao and Zellner (1964) approximation method. The primary methodological issue in this research was to observe differences that might exist between classical pooling and the Bayesian regression technique. Comparison of the two techniques revealed very little difference between either parameter estimates or standard errors. Schipper (1964) used covariance regression to analyze a series of cross-section samples (19541957) collected by the Survey Research Center, University of Michigan. The central focus of this study was to analyze consumer discretionary behavior particularly with respect to durable expenditures, short term debt, and discretionary saving. The major methodological finding was that several differences between the covariance regression model and individual cross-section regressions existed. Schipper suggested the individual cross-section analyses might be biased but could not prove this point since he did not use experimental data. Palda and Blair (1970) conducted an analysis of toothpaste demand by using multiple cross sections of data collected by MRCA during the period 1958-1962. One focus of their research was to investigate the potential cross-section specification bias, based on the rationale presented by Simon and Aigner (1970), that can exist because of omitted variables. An interpretation of the results led them to think that the covariance model may reduce the specification bias. This interpretation cannot be considered conclusive since the analysis was not conducted in an experimental framework. Since there is an interest on the part of economic and business researchers to use multiple cross-section sample data, this would appear to be a sufficient reason for evaluating the different methods available for combining and analyzing the samples. Earlier work in this area includes studies by Nerlove (1967, 1968). He assumed models of the form Yit = aYit-l + Uit and Yit = aYit-l + 1-Xit + Uit respectively with Uit = yi + Vit with yi and Vit uncorrelated where =o-2 = 2 +or2. The estimation methods used were OLS, generalized least squares utilizing known p (p = o-A2/o-X2) analysis-of-covariance estimates with cross-sectional effects only, two-round estimates based on an estimated value of p, and maximum likelihood estimates. Generally, Nerlove's findings indicated that generalized least squares (if p is known) produces good esti-

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