Disturbances In The Linear Model Estimation And Hypothesis Testing

1. 1. The general linear model All econometric research is based on a set of numerical data relating to certain economic quantities, and makes infer ences from the data about the ways in which these quanti ties are related (Malinvaud 1970, p. 3). The linear relation is frequently encountered in applied econometrics. Let y and x denote two economic quantities, then the linear relation between y and x is formalized by: where {31 and {32 are constants. When {31 and {32 are known numbers, the value of y can be calculated for every given value of x. Here y is the dependent variable and x is the explanatory variable. In practical situations {31 and {32 are unknown. We assume that a set of n observations on y and x is available. When plotting the ob served pairs (x l' YI)' (x ' Y2)' . . . , (x , Y n) into a diagram with x 2 n measured along the horizontal axis and y along the vertical axis it rarely occurs that all points lie on a straight line. Generally, no b 1 and b exist such that Yi = b + b x for i = 1,2, . . . ,n. Unless 2 l 2 i the diagram clearly suggests another type of relation, for instance quadratic or exponential, it is customary to adopt linearity in order to keep the analysis as simple as possible.

Originally published in 1987. This collection of original papers deals with various issues of specification in the context of the linear statistical model. The volume honours the early econometric work of Donald Cochrane, late Dean of Economics and Politics at Monash University in Australia. The chapters focus on problems associated with autocorrelation of the error term in the linear regression model and include appraisals of early work on this topic by Cochrane and Orcutt. The book includes an extensive survey of autocorrelation tests; some exact finite-sample tests; and some issues in preliminary test estimation. A wide range of other specification issues is discussed, including the implications of random regressors for Bayesian prediction; modelling with joint conditional probability functions; and results from duality theory. There is a major survey chapter dealing with specification tests for non-nested models, and some of the applications discussed by the contributors deal with the British National Accounts and with Australian financial and housing markets.

This work details the statistical inference of linear models including parameter estimation, hypothesis testing, confidence intervals, and prediction. The authors discuss the application of statistical theories and methodologies to various linear models such as the linear regression model, the analysis of variance model, the analysis of covariance model, and the variance components model.

This monograph grew out of joint work with various dedicated colleagues and students at the Vienna Institute for Advanced Studies. We would probably never have begun without the impetus of Johann Maurer, who for some time was the spiritus rector behind the Institute's macromodel of the Austrian economy. Manfred Deistler provided sustained stimulation for our research through many discussions in his econometric research seminar. Similar credits are due to Adrian Pagan, Roberto Mariano and Garry Phillips, the econometrics guest professors at the Institute in the 1982 - 1984 period, who through their lectures and advice have contributed greatly to our effort. Hans SchneeweiB offered helpful comments on an earlier version of the manuscript, and Benedikt Poetscher was always willing to lend a helping . hand when we had trouble with the mathematics of the tests. Needless to say that any errors are our own. Much of the programming for the tests and for the Monte Carlo experiments was done by Petr Havlik, Karl Kontrus and Raimund Alt. Without their assistance, our research project would have been impossible. Petr Havlik and Karl Kontrus in addition. read and criticized portions of the manuscript, and were of great help in reducing our error rate. Many of the more theoretical results in this monograph would never have come to light without the mathematical expertise of Werner Ploberger, who provided most of the statistical background of the chapter on testing for structural change . .

An International Statistical Conference on Linear Inference was held in Poznan, Poland, on June 4-8, 1984. The conference was organized under the auspices of the Polish Section of the Bernoulli Society, the Committee of Mathematical Sciences and the Mathematical Institute of the ,Polish Academy of Sciences. The purpose of the meeting was to bring together scientists from vari ous countries working in the diverse areas of statistical sciences but showing great interest in the advances of research on linear inference taken in its broad sense. Thus, the conference programme included ses sions on Gauss-Markov models, robustness, variance components~ experi mental design, multiple comparisons, multivariate models, computational aspects and on some special topics. 38 papers were read within the vari ous sessions and 5 were presented as posters. At the end of the confer ence a lively general discussion session was held. The conference gathered more than ninety participants from 16 countries, representing both parts of Europe, North America and Asia. Judging from opinions expressed by many participants, the conference was quite suc cessful, well contributing to the dissemination of knowledge and the stimulation of research in different areas linked with statistical li near inference. If the conference was really a success, it was due to all its participants who in various ways were devoting their time and efforts to make the conference fruitful and enjoyable.