A Dynamic Ordered Logit Model With Fixed Effects

Abstract

We study a fixed-T panel data logit model for ordered outcomes that accommodates fixed effects and state dependence. We provide identification results for the auto-regressive parameter, regression coefficients, and the threshold parameters in this model. Our results require only four observations on the outcome variable. We provide conditions under which a composite conditional maximum likelihood estimator is consistent and asymptotically normal. We use our estimator to explore the determinants of self-reported health in a panel of European countries over the period 2003-2016. We find that: (i) that the auto-regressive parameter is positive and analogous to a linear AR(1) coefficient of about 0.25, indicating persistence in health status (ii) that the association between income and health becomes insignificant once we control for unobserved heterogeneity and persistence.