Intertemporal collective household models: Identification in short panels with unobserved heterogeneity in resource shares

We provide a new full-commitment intertemporal collective household model to estimate resource shares, defined as the fraction of household expenditure enjoyed by household members. Our model implies nonlinear time-varying household quantity demand functions that depend on fixed effects. We provide new econometric results showing identification of a large class of models that includes our household model. We cover fixed-T panel models where the response variable is an unknown monotonic function of a linear latent variable with fixed effects, regressors, and a nonparametric error term. The function may be weakly monotonic and time-varying, and the fixed effects are unrestricted. We identify the structural parameters and features of the distribution of fixed effects. In our household model, these correspond to features of the distribution of resource shares. Using Bangladeshi data, we show: women's resource shares decline with household budgets; and, half the variation in women's resource shares is due to unobserved heterogeneity.