Modeling Expectations of Bounded Prices: An Application to the Market for Corn

The presence of farm programs should directly affect the expectations of producers. This paper analyzes the formation of price expectations when price supports constitute an effective lower bound on the distribution of the expectations. We first investigate what the expected price would be if the usual rational expectations formula is used. This leads to a relationship that is not estimable. We suggest two alternatives -one based on a tobit approximation and the other based on a perfect prediction of when the support is going to be effective. Using a simplified model of the U.S. corn market, the methodology is demonstrated and compared to an alternative method of using futures prices as the expectation of harvest price. The analysis of supply response for the major U.S. field crops is made difficult due to government intervention in these markets. This intervention has been characterized by the use of price supports, acreage diversion, storage incentives, etc. during the last thirty years. Many studies have analyzed producer behavior in the presence of governmental involvement. Such studies have typically been concerned with modeling the effect of supports and diversions in an ex post sense rather than with how producers used the knowledge of farm programs to form their expectations. If producers are rational economic agents, their expectations of harvest prices should be conditioned both by free market forces and the type and degree of governmental intervention in the market. Of course, farm programs have varied in nature and extent during the past thirty years and it is doubtful that any structural model could capture their complexities. In this paper we attempt to introduce rational expectations in a simplified model of the U.S. corn market. In essence we focus on the formation of price expectations when price supports constitute an effective lower bound on the distribution of the expectations. We proceed by developing a theoretical model that connects the rational expectations model with a model of bounded price variation. It is shown that one representation that may characterize the corn market is a triangular structural system with endogenous switching. A full information maximum likelihood estimator is proposed for the system. Next an empirical model is specified and estimated. The model is evaluated in comparison to an augmented model that contains a futures price so that some inferences may be made concerning the rational expectations model's success in summarizing relevant market information. Expectations Under Bounded Prices Consider a market that may be represented by a simple supply and demand system Q= a,Pt* + a2W, + el, Supply Function Pt= b,Qt + b2Xt + e2t Demand Function (1) where P and Q represent market price and quantity, W and X represent supply and demand shifters, and P,* represents the rational expectation of product price at the time production decisions are made. Note that this system has a familiar recursive structure when the expected price variable is specified in terms of one or more lagged prices. When the restricted reduced form of the structural system is solved for in terms of the expected price and this expression is used to replace Pj* (Wallis (1980)) then models similar to those of Goodwin and Sheifrin (1982) and Shonkwiler and Emerson (1982)