Multicollinearity in linear economic models - Neeleman, D.

. .

Résumé :
It was R. Frisch, who in his publications 'Correlation and Scatter Analysis in Statistical Variables' (1929) and 'Statistical Confluence Analysis by means of Complete Regression Systems' (1934) first pointed out the complications that arise if one applies regression analysis to variables among which several independent linear relations exist. Should these relationships be exact, then there exist two closely related solutions for this problem, viz. 1. The estimation of 'stable' linear combinations of coefficients, the so-called estimable functions. 2. The dropping of the wen-known condition of unbiasedness of the estimators. This leads to minimum variance minimum bias estimators. This last solution is generalised in this book for the case of a model consisting of several equations. In econometrics however, the relations among variables are nearly always approximately linear so that one cannot apply one of the solutions mentioned above, because in that case the matrices used in these methods are, although ill-conditioned, always of full rank. Approximating these matrices by good-conditioned ones of the desired rank, it is possible to apply these estimation methods. In order to get an insight in the consequences of this approximation a simulation study has been carried out for a two-equation model. Two Stage Least Squares estimators and estimators found with the aid of the above mentioned estimation method have been compared. The results of this study seem to be favourable for this new method.

Sommaire:
I Some Remarks on Linear Economic Models.- I.1 Introduction.- I.2 The economic model.- I.3 The identification problem.- I.4 Multicollinearity.- II. Best Linear P-Unbiased Estimators for a One-Equation Model.- II.1 Introduction.- II.2 The hypotheses.- II.3 The (generalised) least-squares estimators.- II.4 Best linear unbiased estimators of estimable functions.- II.5 Best linear P-unbiased estimators.- II.6 The relation between best linear P-unbiased estimators and estimable functions.- II.7 On the equivalence of best linear P-unbiased estimators.- III. Estimation of a Model Consisting of Several Equations.- III.1 Introduction.- III.2 The hypotheses.- III.3 The estimation of the reduced form.- III.4 The k-class estimators.- III.5 An asymptotic property of k-class estimators.- III.6 Multicollinearity with 2 sls and liml.- III.7 The generalised 2 sls method.- IV. A Monte-Carlo Study.- IV.1 Introduction.- IV.2 Some recent Monte-Carlo studies.- IV.3 Design of the simulation model.- IV.4 Analysis.- Appendix A.- Appendix B.- Literature.