Two-part fractional regression model for the demand for risky assets†

Abstract

Empirical studies of household portfolio choices are often interested in quantifying the effects of various covariates on the fraction of a household's wealth invested in risky assets such as common stocks. The preferred econometric specification in these studies is the two-limit Tobit model, which can accommodate the fractional nature of the dependent variable. However, it is restrictive, because it assumes that the same data generating process determines both whether households participate in the stock market and the fraction of wealth invested in stocks. This article demonstrates that, in this setting, a two-part version of the fractional response model of Papke and Wooldridge (1996) constitutes an attractive alternative to Tobit by comparing the performance of the two models using data on portfolio choices of Australian households. We find that (1) the Tobit model is rejected by our data in favour of a two-part specification; and (2) marginal effects of covariates on the share of risky assets conditional on participation estimated from Tobit are confounded by the effects of these covariates on the participation decision.

Notes

¹ Another two-part model for fractional response is a zero-inflated beta model proposed recently by Cook et al. (2008). However, this model relies on beta distribution for modelling share among participants and hence, does not account for possible clustering at one in the portfolio share data.

² We construct risk attitude indicators from household heads’ response when asked to state the amount of financial risk that they were willing to take with funds used for savings or investment (high, average or low). We also construct the indicator variable for not having any spare cash, which was one of the possible answers to the risk taking question.

³ The result of the Lin and Schmidt (1984) test is also consistent with this conclusion: the value of the Lagrange Multiplier (LM) test statistic, which under the null hypothesis has a chi-squared distribution with 22 degrees of freedom, is equal to 114; this implies that one can reject the Tobit model in favour of a two-part specification.