Estimating Endogenous Effects on Ordinal Outcomes

Abstract

Recent research underscores the sensitivity of conclusions drawn from the application of econometric methods devised for quantitative outcome variables to data featuring ordinal outcomes. The issue is particularly acute in the analysis of happiness data, for which no natural cardinal scale exists, and which is thus routinely collected by ordinal response. With ordinal responses, comparisons of means across different populations and the signs of OLS regression coefficients have been shown to be sensitive to monotonic transformations of the cardinal scale onto which ordinal responses are mapped. In many applications featuring ordered outcomes, including responses to happiness surveys, researchers may wish to study the impact of a ceteris paribus change in certain variables induced by a policy shift. Insofar as some of these variables may be manipulated by the individuals involved, they may be endogenous. This paper examines the use of instrumental variable (IV) methods to measure the effect of such changes. While linear IV estimators suffer from the same pitfalls as averages and OLS coefficient estimates when outcome variables are ordinal, nonlinear models that explicitly respect the ordered nature of the response variable can be used. This is demonstrated with an application to the study of the effect of neighborhood characteristics on subjective well-being among participants in the Moving to Opportunity housing voucher experiment. In this context, the application of nonlinear IV models can be used to estimate marginal effects and counterfactual probabilities of categorical responses induced by changes in neighborhood characteristics such as the level of neighborhood poverty. * We have benefitted from comments from participants at research seminars given at Erasmus University Rotterdam, Duke, Simon Fraser, Leicester, and a 2018 joint CeMMAP/Northwestern conference on incomplete models. Adam Rosen and Andrew Chesher gratefully acknowledge financial support from the UK Economic and Social Research Council through a grant (RES-589-28-0001) to the ESRC Centre for Microdata Methods and Practice (CeMMAP). Adam Rosen gratefully acknowledges financial support from a British Academy mid-career Fellowship. The usual disclaimer applies.