Nonparametric estimation and inference about the overlap of two distributions
AbstractThis paper develops methodology for nonparametric estimation of a measure of the overlap of two distributions based on kernel estimation techniques. This quantity has been proposed as a measure of economic polarization between two groups, Anderson (2004) and Anderson et al. (2010). In ecology it has been used to measure the overlap of species. We give the asymptotic distribution theory of our estimator, which in some cases of practical relevance is nonstandard due to a boundary value problem. We also propose a method for conducting inference based on estimation of unknown quantities in the limiting distribution and show that our method yields consistent inference in all cases we consider. We investigate the finite sample properties of our methods by simulation methods. We give an application to the study of polarization within China in recent years using household survey data from two provinces taken in 1987 and 2001. We find a big increase in polarization between 1987 and 2001 according to monetary outcomes but less change in terms of living space.
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Bibliographic InfoArticle provided by Elsevier in its journal Journal of Econometrics.
Volume (Year): 171 (2012)
Issue (Month): 1 ()
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Web page: http://www.elsevier.com/locate/jeconom
Kernel estimation; Inequality; Overlap coefficient; Poissonization; Total variation;
Find related papers by JEL classification:
- C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
- C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
- C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
- D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement
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