Efficiency gains in least squares estimation: a new approach

Posted: September 3, 2020 in Research, Research papers
Tags: , , ,

This paper is a joint effort with prof. Mike Tsionas. It has just been accepted for publication in Econometric Reviews. It really has a new least-squares method to propose that reduces the variance of the estimator in linear regression. And it is very easy to implement.

ABSTRACT. In pursuit of efficiency, we propose a new way to construct least squares estimators, as the minimizers of an augmented objective function that takes explicitly into account the variability of the error term and the resulting uncertainty, as well as the possible existence of heteroskedasticity. We initially derive aninfeasible estimator which we then approximate using Ordinary Least Squares (OLS) residuals from a first-step regression to obtain the feasible “HOLS” estimator. This estimator has negligible bias, is consistent and outperforms OLS in terms of finite-sample Mean Squared Error, but also in terms of asymptotic efficiency, under all skedastic scenarios, including homoskedasticity. Analogous efficiency gains are obtained for the case of Instrumental Variables estimation. Theoretical results are accompanied by simulations that support them.

Download the pre-print and the on-line Appendix.

Comments
  1. anoldmaninthesea says:

    Hello Alecos,

    Have you already read a book entitled DYNAMIC MACROECONOMICS by George Alogoskoufis?

    I’m currently reading a chapter, and I really liked the author’s style. It reminded me of yours, when answering on the Economics SE. The careful ‘answer and reply’ kind of exposition, in a simple clear wording. I may be wrong though… =D

    Anyway, I thought you might wanted to check it out.

    Godspeed!

    • Hello there. You correctly sensed a link here. He was a professor of mine when I was doing my MSc back in the day, and I was his TA (“Tutor Assistant”) when he was teaching the various models that eventually became this book in a graduate Master class in Athens University of Economics and Business, in 2015-2016. George Alogoskoufis is a great teacher, I can assure you for that.

      • anoldmaninthesea says:

        What a nice coincidence!
        I thank you for your opinion.
        Now, I’m seriously thinking of acquiring the book for Christmas… =D

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