Heterogeneity in MPCs and unexplained variation in consumption expenditures

Quantile regression is a popular method to estimate the dispersion in MPCs in the population. We discuss the challenges that this method faces given the large unexplained variation in consumption expenditures in survey data. We highlight that quantile regression estimates do not recover the distribution of MPCs if either unexplained variation is due to measurement error or if differences in MPCs are partly driven by ex ante heterogeneity across households. To quantify the likely extent of the bias, we propose a simulation-based approach where we back out the underlying distribution of MPCs for a range of calibrations that attribute the unexplained variation to a split between unobserved factors and measurement noise. All results point in the same direction: the true distribution of MPCs is significantly more dispersed than what is estimated by quantile regression.