Maximal Correlation Techniques in Constructing Non-Linear Econometric Models

Abstract

Abstract Constructing non-linear stochastic econometric models is considered, from the point of view of revealing and proper reflecting quantitatively stochastic dependencies between input and output variables involved in the models. The dependencies are investigated by applying a corresponding measure of dependence, the maximal correlation. The approach enables one both to obtain corresponding non-linear transformations describing relationships between the input and output variables and to assure the existence of the model parameters estimates. As well, the approach provides obtaining the model identifiability conditions and quantitative description of the model non-linearity. The presentation is preceded with an analysis of a close approach available in the tutorial literature, with emphasizing certain delusions involved.