Health, Children, and Elderly Living Arrangements: A Multiperiod-Multinomial Probit Model with Unobserved Heterogeneity and Autocorrelated Errors

This paper develops a general multiperiod-multinomial probit model for panel data to estimate the living arrangements of the elderly. The model has the following features:
(a) In each period choices do not necessarily obey the assumption of independence of irrelevant alternatives.
(b) Unobserved person-specific attributes are treated as random effects. These random effects may also be correlated across alternatives.
(c) In addition, unobserved choice-specific utility components may persist over some time, creating an autoregressive and/or heteroscedastic error structure.
The model is estimated by simulating the choice probabilities in the likelihood function. We examine several variants of the specification of the correlation structure and investigate the extent the biases created by ignoring intertemporal correlations.