Addressing attrition in nonlinear dynamic panel data models with an application to health

We present a general framework for nonlinear dynamic panel data models subject to missing outcomes due to endogenous attrition. We consider non-ignorable attrition, where the distribution of the outcome depends on missingness conditional on the unobserved heterogeneity. A major challenge posed by the dynamic specification is the inherent correlation between the lagged dependent variable and unobserved individual heterogeneity. Our key assumption is that the distribution of the unobserved effect does not depend on attrition conditional on observed covariates and initial condition. The resulting estimator is a joint maximum likelihood estimator (MLE) that accommodates a dynamic specification, correlated unobserved heterogeneity, and endogenous attrition. We discuss the binary response model as an example. Finite sample properties are studied using Monte Carlo simulations. In the empirical application, the proposed method is applied to estimating a dynamic health model for older women. After accounting for unobserved heterogeneity and nonrandom attrition, having health problems that limit work in the previous period is associated with a significantly higher probability of having health problems that limit work in the current period (18.4 percentage points increase for White women, 22.9 percentage points increase for Black women, and 16.1 percentage points increase for women of other races and ethnicities).