## Disturbances in the Linear Model: Estimation and Hypothesis Testing1. 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. |

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### Contents

A Appendix | 17 |

BLUF disturbance estimation | 50 |

An empirical SI | 64 |

Copyright | |

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adapted hyp alternative applied arbitrary autocorrelation BLU disturbance BLUF BLUS estimator BLUS vector bounds test calculated Chapter column vectors consider consisting covariance matrix criterion critical region defined denoted diagonal elements diagonal matrix Durbin and Watson economic time series eigenvectors exact Durbin-Watson test follows given Hence heterovariance test hypothesis idempotent implies instance ith column Koerts and Abrahamse least-squares Lemma linear combination linear model linearly independent LU disturbance estimator matrix F matrix satisfying matrix with rank maximal minimal mixed tests nonnegative definite nonsingular nonzero eigenvalues orthogonal orthonormal orthonormal basis P-matrix parameters percent powers of test(Q principal components probability distribution procedure rank n-k regression residual vector regressors respect scalar selection device significance level significance points specification square matrix stochastically independent streamlined Table test statistic Theil tion UMPS unique values variance X k matrix X-matrices zero