We consider the class of fixed-Tpanel models where the response variable is an unknown function of a linear latent variable with fixed effects, regressors, and an error term. We call this class Fixed Effects Linear Transformation, or FELT. The key distinction from existing models in FELT is that the unknown function may be weakly monotonic and time-varying. This distinction accommodates outcomes and regressors that are discrete or continuous, and allows the unknown function to differ arbitrarily across periods. We provide new identification results for the structural parameters in FELT, as well as for specific features of the conditional distribution of the fixed effects. Our results allow for serial correlation and require only two time periods.
We estimate the structural parameters of a full-commitment intertemporal collective household model whose implied observable demand equations fit into the FELT class. The model requires time-varying response functions and has a direct interpretation for fixed effects: they are the resource shares of household members. Using consumption data from Bangladesh, we show that women’s resource shares are correlated with household budgets and not fully explained by observed covariates.

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