Abstract
Asymptotic and bootstrap inference methods for inequality indices are for the most part unreliable due to the complex empirical features of the underlying distributions. In this paper, we introduce a Fieller-type method for the Theil Index and assess its finite-sample properties by a Monte Carlo simulation study. The fact that almost all inequality indices can be written as a ratio of functions of moments and that a Fieller-type method does not suffer from weak identification as the denominator approaches zero, makes it an appealing alternative to the available inference methods. Our simulation results exhibit several cases where a Fieller-type method improves coverage. This occurs in particular when the Data Generating Process (DGP) follows a finite mixture of distributions, which reflects irregularities arising from low observations (close to zero) as opposed to large (right-tail) observations. Designs that forgo the interconnected effects of both boundaries provide possibly misleading finite-sample evidence. This suggests a useful prescription for simulation studies in this literature.
This work was supported by the William Dow Chair of Political Economy (McGill University), the Bank of Canada (Research Fellowship), the Toulouse School of Economics (Pierre-de-Fermat Chair of excellence), the Universitad Carlos III de Madrid (Banco Santander de Madrid Chair of excellence), the Natural Sciences and Engineering Research Council of Canada, the Social Sciences and Humanities Research Council of Canada, the Fonds de recherche sur la société et la culture (Québec), and by project ANR-16-CE41-0005 managed by the French National Research Agency (ANR).
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Notes
- 1.
See Scheffé (1970) for a modified version of Fieller’s method that avoid the confidence set \(\mathbb {R}\).
- 2.
Note that the variance of \(\hat {\mu }\), the variance of \(\hat {\nu }\) and covariance of the \((\hat {\mu },\,\hat {\nu })\) are equal to \(\hat {\sigma }_{\mu }^{2}/n\), \(\hat {\sigma }_{\nu {}}^{2}/n\;\)and \(\hat {\sigma }_{\mu {\nu }}/n\).
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Dufour, JM., Flachaire, E., Khalaf, L., Zalghout, A. (2018). Confidence Sets for Inequality Measures: Fieller-Type Methods. In: Greene, W., Khalaf, L., Makdissi, P., Sickles, R., Veall, M., Voia, MC. (eds) Productivity and Inequality. NAPW 2016. Springer Proceedings in Business and Economics. Springer, Cham. https://doi.org/10.1007/978-3-319-68678-3_6
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