Testing for Restricted Stochastic Dominance

Abstract

Asymptotic and bootstrap tests are studied for testing whether there is a relation of stochastic dominance between two distributions. These tests have a null hypothesis of nondominance, with the advantage that, if this null is rejected, then all that is left is dominance. This also leads us to define and focus on restricted stochastic dominance, the only empirically useful form of dominance relation that we can seek to infer in many settings. One testing procedure that we consider is based on an empirical likelihood ratio. The computations necessary for obtaining a test statistic also provide estimates of the distributions under study that satisfy the null hypothesis, on the frontier between dominance and nondominance. These estimates can be used to perform dominance tests that can turn out to provide much improved reliability of inference compared with the asymptotic tests so far proposed in the literature.

Keywords:

• Bootstrap test
• Empirical likelihood
• Stochastic dominance

JEL Classification:

• C100
• C120
• C150
• I320

ACKNOWLEDGMENTS

This research was supported by the Canada Research Chair program (Chair in Economics, McGill University) and by grants from the Social Sciences and Humanities Research Council of Canada, the Fonds Québécois de Recherche sur la Société et la Culture, and the PEP Network of the International Development Research Centre. We are grateful to Abdelkrim Araar and Marie-Hélène Godbout for their research assistance and to Olga Cantó, Bernard Salanié, Bram Thuysbaert and two anonymous referees for helpful comments.

Notes

See Levy (1992) for a review of the breadth of these Hadar and William (1969) and Hanoch and Levy (1969) for early developments.

See, for instance, Beach and Richmond (1985), McFadden (1989), Klecan et al. (1991), Bishop et al. (1992), Anderson (1996), Davidson and Duclos (2000), Barrett and Donald (2003), Linton et al. (2005), and Maasoumi and Heshmati (2005).

See for instance Foster and Shorrocks (1988a).

See for instance Foster and Shorrocks (1988b).

See inter alia Holton (2003) and Jorion (2001).

See http://lissy.ceps.lu for detailed information on the structure of these data.

See Summers and Heston (1991) for the methodology underlying the computation of these parities, and \texttthttp://pwt.econ.upenn.edu/ for access to the 1999-2000 figures.