HERC Seminar: Difference-in-differences estimation when the dependent variable is ordinal

Abstract

This paper proposes an estimator for the treatment effect when using difference-in-differences with ordered data. Ordered data are pervasive in health economics, with examples including self-assessed health and subjective wellbeing, and these data are routinely analysed using non-linear models, such as the ordered probit model. At the same time, the method of difference-in-differences is widely applied in policy evaluation, but while this identification strategy readily applies to continuous outcomes, it is often implausible to assume common trends in models respecting the statistical properties of limited dependent variables. Consequently, ordered outcomes are frequently analysed with linear regression methods when using a difference-in­differences strategy. As an alternative approach, we suggest analysing the treatment effect in terms of the response probability, and assuming common trends at the level of the latent index. An advantage to this approach is the ability to investigate whether the treatment effect materialises across the entire distribution of the outcome variable or is limited to particular sections of it. For example, a reduction in subjective wellbeing (SWB) driven by a shift from high to moderate levels of SWB might warrant a different policy response compared with a shift from low to very low SWB levels. In an application of the estimator to the impact of the 2005 London bombings on the wellbeing of adolescent Muslims we find that linear regression performs relatively well if the goal is to estimate changes in the conditional mean of happiness and depression. However, by retaining the ordinal character of subjective wellbeing, we find strongest evidence that the bombings influenced the lower end of the happiness distribution, with suggestive evidence of an impact across the entire distribution.

Biography

Arne graduated from the University of Bergen in 2000 and gained his MSc from the University of Edinburgh in 2001. After completing his PhD at the University of St Andrews he was appointed to a research fellowship at the University of York´s Centre for Health Economics. He joined the Department of Economics at the University of Sheffield in January 2009 as a Lecturer in Economics, became a Senior Lecturer in 2012 and was promoted to Reader in Economics in 2015 and Professor in 2018. Arne is an Associate Editor of the Journal of Choice Modelling. He is affiliated with the Health, Econometrics and Data Group at the University of York and the International Research Collaborative for Health Economic Experiments.