A dynamic ordered logit model with fixed effects

TL;DR

This paper introduces a fixed-T panel data ordered logit model with fixed effects and state dependence, providing identification and estimation methods, and applies it to analyze health determinants across European countries.

Contribution

It develops a novel dynamic ordered logit model with fixed effects, offering identification results and a consistent estimator for panel data with ordered outcomes.

Findings

Health status shows persistence with an AR(1) coefficient of about 0.25.

Income's effect on health becomes insignificant after controlling for unobserved heterogeneity.

The model requires only four observations per individual for identification.

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 autoregressive 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) the autoregressive parameter is positive and analogous to a linear AR(1) coefficient of about 0.25, indicating persistence in health status; (ii) the association between income and health becomes insignificant once we control for unobserved heterogeneity and persistence.