Omitted variable tests and dynamic specification. An application to demand homogeneity (Q1577044)

In the book, omitted variable tests for a dynamic multivariate regression model are studied analytically and applied to the Rotterdam model of demand. Chapter 1 is introductory. In Chapter 2, the linear regression model \(y_t=\beta x_t+u_t\) is considered, where \(x_t\) are random regressors that follow an \(AR(1)\) stationary Gaussian process and \(u_t\) are random errors following another stationary \(AR(1)\) process. Consistency results for ordinal least squares estimator of parameter \(\beta\) and for usual residual variance estimator are proved and the asymptotic distribution of a quasi \(t\)-statistic for testing hypothesis \(\beta=0\) is developed. Results of a simulation experiment are presented here, too. In Chapter 3, basic definitions of the consumer theory are presented and the Rotterdam model of demand is described and transformed into a linear regression model. In Chapter 4, quasi-maximum likelihood estimator of the regression coefficient of the Rotterdam model is presented and robust estimators of its covariance matrix are considered. Chapter 5, which is of the main importance, deals with testing homogeneity in the Rotterdam model. It is shown that testing of homogeneity can be considered as testing the omission of a variable in a multivariate regression model. Various tests for homogeneity are defined and discussed both for correctly and wrongly specified error processes and consequences of misspecification of the error process are studied. In Chapter 6 results of simulation experiments are presented, where population parameters are based on the Rotterdam model estimated from annual and seasonal consumers nominal and real expenditure data from the UK economy. Chapter 7 is concluding.