Estimation of Censored Panel‐data Models With Slope Heterogeneity

Abstract

This paper considers estimation of censored panel-data models with individual-specific slope heterogeneity. The slope heterogeneity may be random (random slopes model) or related to covariates (correlated random slopes model). Maximum likelihood and censored least-absolute 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 (Econometrica 2000; 68: 399-405) 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.1 Wooldridge (2005) provides conditions under which standard fixed-effects estimators consistently estimate the population average of the fixed-effects slopes. See also Arellano and Bonhomme (2012), which extends Chamberlain's set-up for the purposes of identifying distributional characteristics of the heterogeneous slopes. 2 In the case of additive fixed effects, Honoré (2008) considers a partial-effect quantity that is unaffected by the incidentalparameters problem. 3 Under the additional assumption of normally distributed errors, Honoré (1998) proposes an instrumental-variables estimator that allows for fixed effects in slopes.

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