Identification of Time-Varying Transformation Models with Fixed Effects, with an Application to Unobserved Heterogeneity in Resource Shares

TL;DR

This paper develops new identification results for a class of fixed-T panel models with unknown, time-varying transformations, and applies these to analyze unobserved heterogeneity in household resource shares using Bangladeshi data.

Contribution

It introduces novel identification methods for models with unknown transformations and applies them to uncover unobserved heterogeneity in resource shares.

Findings

Women's resource shares decline with household budgets.

Half of the variation in resource shares is due to unobserved heterogeneity.

The model successfully captures time-varying effects in resource allocation.

Abstract

We provide new results showing identification of a large class of fixed-T panel models, where the response variable is an unknown, weakly monotone, time-varying transformation of a latent linear index of fixed effects, regressors, and an error term drawn from an unknown stationary distribution. Our results identify the transformation, the coefficient on regressors, and features of the distribution of the fixed effects. We then develop a full-commitment intertemporal collective household model, where the implied quantity demand equations are time-varying functions of a linear index. The fixed effects in this index equal logged resource shares, defined as the fractions of household expenditure enjoyed by each household member. Using Bangladeshi data, we show that women's resource shares decline with household budgets and that half of the variation in women's resource shares is due to unobserved household-level heterogeneity.