Why you should also use OLS estimation of tail exponents

Thiago Trafane Oliveira Santos () and Daniel Oliveira Cajueiro
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Daniel Oliveira Cajueiro: Department of Economics, University of Brasilia, Brazil. National Institute of Science and Technology for Complex Systems

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Abstract: Even though practitioners often estimate Pareto exponents running OLS rank-size regressions, the usual recommendation is to use the Hill MLE with a small-sample correction instead, due to its unbiasedness and efficiency. In this paper, we advocate that you should also apply OLS in empirical applications. On the one hand, we demonstrate that, with a small-sample correction, the OLS estimator is also unbiased. On the other hand, we show that the MLE assigns significantly greater weight to smaller observations. This suggests that the OLS estimator may outperform the MLE in cases where the distribution is (i) strictly Pareto but only in the upper tail or (ii) regularly varying rather than strictly Pareto. We substantiate our theoretical findings with Monte Carlo simulations and real-world applications, demonstrating the practical relevance of the OLS method in estimating tail exponents.

Date: 2024-09, Revised 2024-09
New Economics Papers: this item is included in nep-ecm and nep-rmg
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