Testing for Restricted Stochastic Dominance under Survey Nonresponse with Panel Data: Theory and an Evaluation of Poverty in Australia

TL;DR

This paper develops a new statistical testing method for stochastic dominance in survey data with nonresponse, combining partial identification and design-based inference, and demonstrates its application to poverty analysis in Australia.

Contribution

It introduces a novel pseudo-empirical likelihood based test for restricted stochastic dominance that accounts for nonresponse and complex survey design.

Findings

Method is valid under null hypothesis

Test is consistent against alternatives

Applied to Australian poverty data

Abstract

This paper lays the groundwork for a unifying approach to stochastic dominance testing under survey nonresponse that integrates the partial identification approach to incomplete data and design-based inference for complex survey data. We propose a novel inference procedure for restricted $s$th-order stochastic dominance, tailored to accommodate a broad spectrum of nonresponse assumptions. The method uses pseudo-empirical likelihood to formulate the test statistic and compares it to a critical value from the chi-squared distribution with one degree of freedom. We detail the procedure's asymptotic properties under both null and alternative hypotheses, establishing its uniform validity under the null and consistency against various alternatives. Using the Household, Income and Labour Dynamics in Australia survey, we demonstrate the procedure's utility in a sensitivity analysis of temporal poverty comparisons among Australian households.