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Maximum likelihood and censored least\u2010absolute deviations estimators are proposed for both models. The estimators are simple to implement and, in the case of maximum likelihood, lead to straightforward estimation of partial effects. The rescaled bootstrap suggested by Andrews (<jats:italic>Econometrica<\/jats:italic>2000;<jats:bold>68<\/jats:bold>: 399\u2013405) is used to deal with the possibility of variance parameters being equal to zero. The methodology is applied to an empirical study of Dutch household portfolio choice, where the outcome variable (portfolio share in safe assets) has corner solutions at zero and one. As predicted by economic theory, there is strong evidence of correlated random slopes for the age profiles, indicating a heterogeneous age profile of portfolio adjustment that varies significantly with other household characteristics. 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