SPECIFICATION ANALYSIS AND CONSISTENT ESTIMATION FOR MODELS OF MARKETS IN DISEQUILIBRIUM (IDENTIFIABILITY, NONLINEAR REGRESSION, MIXTURE MODEL, MOMENT GENERATING FUNCTION)

This study provides results of specification analysis and a consistent estimator appropriate to the estimation of econometric disequilibrium markets models with unknown regime classification. These models are related to a class of limited dependent variables regression models. However, unlike the well known probit, Tobit, truncated regression, and selectivity models, a consistent estimator beyond the maximum likelihood approach is unknown and unexplored.;Secondly, an effort to correct the sample selection bias is made following the method of moments. Due to the absence of sample separation information, the now familiar probit two-stage approach, which requires the selectivity term related to Mills ratio, is not applicable. Incidentally, a basic model of disequilibrium market is found quite analogous to the mixture model studied by Karl Pearson, who obtained a nonic equation for solving the moment estimator in 1894. Indeed, another nonic equation is also found in the context of disequilibrium model. It sheds some light on the complicated solution space of these types of models without regime classification.;Thirdly, the study is then able to provide some identifiability results in conjunction with a consistent estimator on the basis of the characteristic function. The estimator thus obtained by minimizing the squared Euclidean distance between the empirical and the theoretical joint moment generating functions of quantity and price conditional on predetermined variables is shown to have the large-sample properties of strong consistency and normality. Since the functional form involves a full information representation and is endowed with convenient regularity properties for the purpose of numerical optimization, this approach is suggested either to complement maximum likelihood estimation or to provide a framework for consistent specification tests for models of markets in disequilibrium.;Monte Carlo experiments on the small sample properties of the proposed moment generating function estimator are investigated; and their results are promising. Moreover, the results seem better than those reported in the literature of exogenous switching regression models.;The contributions of this work are as follows: First, in the context of disequilibrium models, properties of the least-squares estimator resulting from the improper premise that market is in equilibrium are analyzed. The asymptotic bias of the ordinary least-squares estimator resulting from quantity-price regression is found to have two components, due to disequilibrium (sample selection bias) and price endogeneity (simultaneous equations bias). The consequence of using the two-stage least-squares estimator to purge the latter component is also analyzed.