III - Linear expected value models

Abstract

This chapter discusses the linear expected value models. It describes various models with this common thread, bearing such names as the general linear hypothesis, linear regression, multiple regression, linear functional relationship, and linear structural relationship, are considered. The chapter explains that there is no explicit introduction of a so-called error term into the standard models. It deals with the errors-in-variables model, and in the study of the structural relation when it is not treated conditionally on X, explicitly examines the stochastic nature of the error term and its relation to X. Otherwise, the stochastic nature of the error term is directly reflected in the stochastic nature of the primary variable of interest, Y, so that one might study Y directly. The chapter also presents an analysis of a special model where the errors in the linear relation are an autoregressive sequence. It discusses linear stochastic difference equations model, a more special model than that involving correlated dependent variables.