A NY econometric equation representing a complex behavioral or technical relationship is, of necessity, an approximation of reality. As such, it is subject to errors in specification and structural change over time. This problem is well recognized by econometricians. Duesenberry and Klein (1965) point out that *'. . . as technology, institutional arrangements, tastes and managerial techniques change over time, the relationships represented by our equations inevitably change. Furthermore, when statistical tests are applied to econometric relationships, the hypothesis of structural stability is frequently rejected.' Some methods for dealing with structural change have evolved. Quandt (1957) has developed a maximum likelihood technique for estimating a point of structural change within a sample.2 Klein and Evans (1967) adjust the intercepts of the Wharton Model to account for structural change.3 The purpose of this paper is to test the robustness of Adaptive Regression (1973) to specification errors causing structural change over time, relative to ordinary least squares analysis with and without the autoregressive correction.4 Since econometricians are inevitably faced with structural change and errors in specification, they should use a technique which is robust rela-tive to such problems. The device most commonly used is to assume that the disturbances are subject to an autoregressive process. The autoregressive correction may frequently ameliorate the effects of misspecification and structural change, but it is doubtful whether such processes, except in rare instances, describe the true distribution of the disturbances. The economics literature seldom gives any justification for this scheme except that omitted variables may be subject to an autoregressive process or the structure of the model may be changing.5 We suspect the reasons for the widespread use of the autoregressive correction are that it is a simple hypothesis, explains serial correlation in the disturbances, and can be dealt with efficiently. The adaptive regression model considered in this paper is equally simple but more general, explains serial correlation, and can also be dealt with efficiently.6 In the next section the adaptive regression model is presented and the Bayesian estimators are developed. In section II the results of a Monte Carlo Study are presented. Two models are considered for which data are generated by eleven different schemes. The estimation and forecasting efficiency of adaptive regression, and ordinary least squares with and without the autoregressive correction are compared. Section III contains an analysis of the role of time trends in econometric relationships. In section IV the relative forecasting ability of the three estimation techniques is tested on real data. The three models suggested by Received for publication February 10, 1972. Revision accepted for publication November 30, 1972. *The authors acknowledge helpful comments of Professors F. G. Adams, R. Roll and R. Summers and the participants of the NBER conference on Bayesian Statistical Inference in Economics. Computations were executed on the University of Pennsylvania computer. 'Examples of such tests include Brown (1966), Goldfield (1969) and Howrey (19-70). One of the most extensive studies was done by Duffy (1969). 'The Quandt technique is limited by the fact that it is mainly useful for finding stable subsamples. If structural change occurs often, it is not very useful. Rosenberg (1968) has used stepwise composition to develop the computationally efficient Aitken estimates of a model subject to structural change over time. His procedure, however, requires that the true covariance matrix of the disturbances be known up to a constant scale factor. 'Adjusting the intercepts is an ad hoc method for keeping the model on track for ex ante forecasting. The intercepts are not assumed to change over the sample period which is always much longer than the forecasting period. 'The autoregressive correction assumes the error is subject to a first or second order autoregressive scheme. See Dhrymes (1969) for the maximum likelihood approach and Zellner and Tiao (1965) for the Bayesian development. The latter approach is used in this paper. 'In fact, if omitted variables are subject to an autoregressive process, the disturbances will, in general, be subject to a more complicated process. 6 A test with sufficient power to differentiate betweer these two models (or others which result in serial correlation) using sample sizes generally available to econometricians does not appear to exist. Further, if one did, its usefulness would be limited as neither structure is likely to be an exact representation of reality. That one structure is more likely on the basis of the data does not imply thai it will forecast better if, in fact, a third structure is generating the data.

DESPITE historical importance of Populist uprising in late nineteenth century, causes of agrarian unrest which culminated in that movement remain obscure. Economic historians have become increasingly dubious of justifications advanced by Populists themselves, partly because many of Populist programs (such as Free Silver plan) were little more than schemes for an involuntary redistribution of wealth in favor of farmers, and partly because many of farmers' stated grievances fail to appear in aggregate economic statistics of period (Bowman, 1965; DeCanio, 1974a; Bowman and Keehn, 1974; North, 1974). The most comprehensive recent study concludes that the agrarian protest of late nineteenth century was not a simple, straightforward consequence of economic factors as many economic historians have believed (Klepper, 1974, p. 285). There is some evidence that cyclical economic fluctuations coincided with upsurges of protest (Bowman and Keehn 1974; Klepper 1974), but agrarian spokesmen of time (as well as subsequent historians) attempted to identify long-standing structural problems of agricultural sector as ultimate explanation of farmers' distress. One recurring theme in historical explanations of agrarian unrest locates source of farmers' difficulties in their perceptions of and responses to economic requirements of market. Thus, Mayhew suggests that protests of Grangers and Alliancemen were a reaction to commercialization of agriculture. This commercialization may have increased farm incomes, but it also made farmers subject to impersonal market forces (Mayhew, 1972). Farmers' failure to understand operation of markets for their products is featured in textbook accounts of Populist period (Davis, Hughes, and McDougall, 1969, p. 368; Gray and Peterson, 1974, p. 320; and North, 1974, p. 134). Econometric studies of price-responsiveness of late nineteenth and early twentieth century American agriculture have shown that sector as a whole responded properly to market prices in both choice of crop mix and choice of technique (Nerlove, 1958; Fisher and Temin, 1970; Hayami and Ruttan, 1971; DeCanio, 1973). These investigations of farmers' responses to output and input prices, however, do not indicate whether estimated agricultural response parameters were in any sense optimal, nor can their fixed-parameter estimation techniques reveal whether farmers' behavior changed in an appropriate manner as underlying market conditions changed. This paper goes beyond previous studies by testing directly a rational expectations hypothesis for American agriculture during Populist period. Using a varying-parameter estimation methodl it is possible to trace changes in supply response parameters over time, and to compare those parameter variations with variations implied by a model of rational price expectations. We will show that changes in farmers' price expectations were indeed consistent with theory of rational expectations. Since our estimates are based on same statewide aggregate data used in previous supply response studies, it is not possible to conclude from our results that all farmers formed rational expectations, but existence of rational expectations in aggregate leads us to reject notion that farmers as a group were unable to Received for publication October 10, 1975. Revision accepted for publication March 15, 1976. ' The helpful comments of Paul David, Stanley Engerman, Jacob Metzer, Joel Mokyr, Marc Nerlove, William Parker, Merton Peck, Edward Prescott, Joe D. Reid, Jr., Peter Temin, and participants in seminars at University of Pennsylvania and Columbia University are gratefully acknowledged. Responsibility for errors remains ours. The research was supported in part by NSF Grant GJ-l 154X3 to National Bureau of Economic Research, and by NSF Grant SOC75-08056. I Recent developments in theory of models with varying parameters are discussed in Cooley (1971) Rosenberg (1973) and Cooley and Prescott (1973a, 1973b, 1973c, and 1976).