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.

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