Bayesian Analysis of the Two-Part Model with Fractional Response: Application to Household Portfolio Choice

This paper studies determinants of household stock marker participation and proportion of risky assets in household financial wealth using recent data from Australia. The methodological novelty of the paper consists in addressing in a systematic fashion the two prominent features of the data: fractional nature of the proportion of financial wealth invested in stocks and prevalence of zeros which stems from the fact that many households do not participate in the stock market. The dependent variable in this case is a mixture of discrete and continuous outcomes, with continuous outcome bounded between zero and one. To study participation and share decisions jointly the paper proposes a two-part model which combines a probit model for participation decision and a linear regression model for the logistic transformation of the fraction of financial wealth invested in stocks. To accommodate possible deviations from normality in the share of risky assets conditional on participation, the transformed share is modelled as having a discrete mixture of normals distribution. The paper then compares posterior distributions of marginal effects of the covariates on participation and share decisions across competing models which include tobit, two-part normal model for untransformed share, two-part normal model for logistically transformed share and two-part mixture of normals model for transformed share. We find that for variables which have a larger explanatory power for participation than for share, the tobit model tends to overpredict marginal effects on share among participants. On the other hand, there seems to be little difference in the marginal effects of covariates on share conditional on participation implied by different versions of the two-part model. Empirical results suggest that education, age, net worth, planning horizon and risk attitudes are the main factors which affect households’ exposure to risky assets in Australia.