Testing the Rational Expectations Hypothesis in an Agricultural Market

Abstract

A recent survey on models of agricultural supply equations listed over 500 studies in which variants of Nerlove's adaptive expectations model were employed.' One might naively assume that the scientific evidence overwhelmingly favored the adaptive expectations hypothesis, but this inference would not be warranted. In particular, there have been very few studies which have even attempted to estimate a expectations version of the traditional agricultural supply models and none that have explicitly tested the expectations hypothesis.2 In this paper we estimate a model of agricultural supply and demand for the chicken broiler industry under the maintained assumption of expectations in the sense of Muth (1961) and provide a series of tests of the model specification. We find that, in this case, the hypothesis of Muth rationality receives strong support. In recent years there has been increasing interest in models in which economic actors are assumed to form expectations of variables rationally. For the most part, empirical applications of the expectations hypothesis have employed single-equation econometric methods. These methods have permitted consistent estimation of equations under the assumption of the expectations hypothesis but do not allow for any explicit testing of the maintained hypothesis of rationality. This paper presents estimates of a simultaneous equation model of the chicken broiler industry using maximum likelihood methods and provides a joint test of the expectations hypothesis and the model specification. Our econometric procedure is related to the recent theoretical work of Wallis (1980) and combines time series analysis with traditional econometric estimation techniques. Under the assumption of expectations, the model can be solved for the expected price as a function of the expected values of the exogenous variables. This function can then be substituted into the model leading to a specification which contains the original endogenous and exogenous variables plus the expected values of the exogenous variables. In general, following this substitution, the model will contain overidentifying restrictions. Time series analysis is utilized to generate the necessary forecasts of the exogenous variables. The complete system of equations is estimated by full-information maximum likelihood, and the constraints are tested by a log-likelihood ratio test. The overidentifying constraints arise in the model because the suppliers are assumed to act as if they know both the underlying structure of the model and the stochastic processes governing the exogenous variables, the two requirements of expectations. While the expected price enters only the supply equation of our model, it is necessary, in the econometric formulation, to specify the demand equation. The instrumental variable procedures of McCallum (1976) and Nelson (1975b) are single-equation methods and do not permit a test of the expectations hypothesis. By specifying the complete model, the additional structure imposed on the problem allows us to estimate the coefficients and test the implied restrictions. There has not been universal agreement that the expectations hypothesis is the best theoretical device to model rational behavior. According to Muth's original formulation, economic actors forecast endogenous variables according to the true reduced form equations of the model. DeCanio (1979) and Friedman (1979) have argued that the economic actors actually Received for publication August 24, 1981. Revision accepted for publication March 2, 1982. ' University of New Mexico and University of California, Davis, respectively. We wish to thank G. King, R. L. Huntzinger, R. Pope, and L. Wegge for advice on this project. A. Nelson and E. Shaw contributed useful research assistance. I The paper by Askari and Cummings (1977) provides references for these studies. 2 Huntzinger's (1979) paper is one of the first attempts at estimatitng a expectations model of agricultural supply.