Overcoming Weak Identification in the Estimation of Household Resource Shares

Dunbar et al. (2013) develop a collective model of the household that allows to identify resource shares, that is, how total household resources are divided up among household members. We show why, especially when the data exhibit relatively flat Engel curves, the model is weakly identified and induces high variability and an implausible pattern in least squares estimates. We propose an estimation strategy nested in their framework that greatly reduces this practical impediment to recovery of individual resource shares. To achieve this, we follow an empirical Bayes method that incorporates additional (or out-of-sample) information on singles and relies on mild assumptions on preferences. We show the practical usefulness of this strategy through a series of Monte Carlo simulations and by applying it to Mexican data. The results show that our approach is robust, gives a plausible picture of the household decision process, and is particularly beneficial for the practitioner who wishes to apply the DLP framework. Our welfare analysis of the PROGRESA program in Mexico is the first to include separate poverty rates for men and women in a CCT program.