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High correlation among errors and the efficiency of ordinary least squares in linear models

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Abstract

This note compares ordinary least squares (OLS) and Gauss-Markov (GM) estimates of regression parameters in linear models when errors are homoscedastic but otherwise arbitrary. It is shown that the efficiency of OLS relative to GM depends crucially on the underlying regressor matrix. This extends and qualifies previous results (Krämer 1980), where errors were confined to be first-order autoregressive. In particular, whenever there is a constant in the regression, it is shown that OLS has limiting efficiency of 1 as correlation increases also in the general case.

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  1. Institut für Höhere Studien, Stumpergasse 56, A-1060, Wien

    Walter Krämer

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  1. Walter Krämer
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Krämer, W. High correlation among errors and the efficiency of ordinary least squares in linear models. Statistische Hefte 25, 135–142 (1983). https://doi.org/10.1007/BF02932396

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  • DOI: https://doi.org/10.1007/BF02932396

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