Thiago Trafane Oliveira SantosCentral Bank of Brazil, Brasília, Brazil. Department of %Economics, University of Brasilia, Brazil, Daniel Oliveira CajueiroDepartment of Economics, University of Brasilia, Brazil. National Institute of Science and Technology for Complex Systems
{"title":"Why you should also use OLS estimation of tail exponents","authors":"Thiago Trafane Oliveira SantosCentral Bank of Brazil, Brasília, Brazil. Department of %Economics, University of Brasilia, Brazil, Daniel Oliveira CajueiroDepartment of Economics, University of Brasilia, Brazil. National Institute of Science and Technology for Complex Systems","doi":"arxiv-2409.10448","DOIUrl":null,"url":null,"abstract":"Even though practitioners often estimate Pareto exponents running OLS\nrank-size regressions, the usual recommendation is to use the Hill MLE with a\nsmall-sample correction instead, due to its unbiasedness and efficiency. In\nthis paper, we advocate that you should also apply OLS in empirical\napplications. On the one hand, we demonstrate that, with a small-sample\ncorrection, the OLS estimator is also unbiased. On the other hand, we show that\nthe MLE assigns significantly greater weight to smaller observations. This\nsuggests that the OLS estimator may outperform the MLE in cases where the\ndistribution is (i) strictly Pareto but only in the upper tail or (ii)\nregularly varying rather than strictly Pareto. We substantiate our theoretical\nfindings with Monte Carlo simulations and real-world applications,\ndemonstrating the practical relevance of the OLS method in estimating tail\nexponents.","PeriodicalId":501293,"journal":{"name":"arXiv - ECON - Econometrics","volume":"29 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - ECON - Econometrics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.10448","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
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.