Some aspects of statistical inference in systems of equations

Abstract: The objective of this thesis is to develop a strategy for statistical/econometric inferences applicable to systemwise testing of econometric models. A common deficiency in many applied econometric studies is the absence of statistical diagnostic testing. A model is only as good as the assumptions being used, and if these assumptions are incorrect then the model can be as good as worthless. In the field of econometrics, available data typically consist of time series data which are not generated under controlled conditions. Hence there arises the need for a well designed misspecification testing strategy. Among other things, the thesis outlines a strategy for how to select an appropriate model. The thesis consists of four papers: Paper I, describes a misspecification testing strategy designed to ensure the appropriateness of the statistical assumptions underlying a system of equations. The strategy is explained and illustrated by means of an empirical example, in which the annual demand for milk in Sweden for the period 1960-1991 is estimated by using an approximation of the AIDS model (LA/AIDS). Paper II, presents an extensive Monte Carlo simulation study to examine the small sample properties of the Breusch-Godfrey test for autocorrelated errors when applied to system of equations. Paper III, presents an extensive Monte Carlo simulation study to examine the small sample properties of the Regression Specification Error Test (RESET) in a system of equations perspective. Paper IV, finally, addresses some problems in a paper by Xepapadeas and Habib (Applied Economics Letters, 1996). It is argued that the authors commit some serious errors when estimating a dynamic almost ideal demand system applied to the Greek data on dairy products.