Prediction-Oriented Estimation Methods for the Canonical Disequilibrium Model

Abstract

Most of the proposed econometric models for a single and isolated market in disequilibrium are variations of the canonical disequilibrium model (for an overview see Quandt (1982)). This model consists of a demand and a supply equation $${\rm D}_{{\rm t}\,} \,{\rm = }\,{\rm f(x}_{\rm t}^{\rm D} )\, + \,{\rm u}_{\rm t}^{\rm D},$$ (1a) $${\rm S}_{{\rm t}\,} \,{\rm = }\,{\rm g(x}_{\rm t}^{\rm s} )\, + \,{\rm u}_{\rm t}^{\rm s},$$ (1b) where t is time index, D is demand and S is supply. XD and XS are vectors of independent variables appearing in the demand function f and the supply function g, respectively. The functions f and g must be derived from theoretical considerations about the considered market. They might be non-linear but they contain unknown coefficients which have to be estimated. uD and uS denote the error terms. They are assumed to be serially uncorrelated and independently normally distributed: $${\rm u}_{\rm t}^{{\rm D} } \;^\sim \;{\rm N(0,}\sigma _{\rm D}^{\rm 2} )\;\;,\;\;{\rm u}_{\rm t}^{{\rm S} }\;\;^\sim \;\;{\rm N(0,}\sigma _{\rm S}^{\rm 2} ).$$ (2)