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 and find evidence for state dependence in self-reported health.

In the standard missing data model, data are either complete or completely missing. However, applied researchers face situations with an arbitrary number of strata of incompleteness. Examples include unbalanced panels and instrumental variables settings where some observations are missing some instruments. I propose a model for settings where observations may be incomplete, with an arbitrary number of strata of incompleteness. I derive a set of moment conditions that generalizes those in Graham's ( 2011 ) standard missing data setup. I derive the associated efficiency bound and propose efficient estimators. Identification can be achieved even if it fails in each stratum of incompleteness.

This paper introduces a new estimator for the fixed-effects ordered logit model. The proposed method has two advantages over existing estimators. First, it estimates the differences in the cut points along with the regression coefficient, leading to provide bounds on partial effects. Second, the proposed estimator for the regression coefficient is more efficient. I use the fact that the ordered logit model with J outcomes and T observations can be converted to a binary choice logit model in ( J - 1) T ways. As an empirical illustration, I examine the income-health gradient for children using the Medical Expenditure Panel Survey.