A bivariate finite mixture growth model with selection

A model is proposed to analyze longitudinal data where two response variables are available, one of which is a binary indicator of selection and the other is continuous and observed only if the first is equal to 1. The model also accounts for individual covariates and may be considered as a bivariate finite mixture growth model as it is based on three submodels: (i) a probit model for the selection variable; (ii) a linear model for the continuous variable; and (iii) a multinomial logit model for the class membership. To suitably address endogeneity, the first two components rely on correlated errors as in a standard selection model. The proposed approach is applied to the analysis of the dynamics of household portfolio choices based on an unbalanced panel dataset of Italian households over the 1998–2014 period. For this dataset, we identify three latent classes of households with specific investment behaviors and we assess the effect of individual characteristics on households’ portfolio choices. Our empirical findings also confirm the need to jointly model risky asset market participation and the conditional portfolio share to properly analyze investment behaviors over the life-cycle.