Latent heterogeneity in the marginal propensity to consume

We estimate the distribution of marginal propensities to consume (MPCs) using a new approach based on the fuzzy C-means algorithm (Dunn (1973), Bezdek (1981)). The algorithm generalizes the K-means methodology of Bonhomme and Manresa (2015) to better accommodate unobserved heterogeneous treatment effects in crosssectional and short panel data by explicitly incorporating a notion of uncertainty over an individual’s group assignment. We extend the fuzzy C-means approach from the cluster means case to a fully-general regression setting, as well as instrumental variables regression, and derive asymptotic properties of the corresponding estimators by showing that the problem admits a GMM formulation. We then apply the estimator to the 2008 tax rebate and household consumption data from the Consumer Expenditure Survey, exploiting the randomized timing of disbursements. We find a considerable degree of heterogeneity in MPCs, which varies by consumption goods. Finally, we provide evidence on the observable determinants of household MPCs, without requiring ex ante assumptions on such relationships, unlike previous studies.

Joint with Daniel Lewis and Davide Melcangi.