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 allow for uncertain group assignment and to recover unobserved heterogeneous effects in cross-sectional and short panel data. We extend the fuzzy C-means approach from the cluster means case to a fully general regression setting and derive asymptotic properties of the corresponding estimators by showing that the problem admits a generalized method of moments (GMM) formulation. We apply the estimator to the 2008 tax rebate and household consumption data, exploiting the randomized timing of disbursements. We find a considerable degree of heterogeneity in MPCs, which varies by consumption good, and provide evidence on their observable determinants, without requiring ex ante assumptions about such relationships. Our aggregated heterogeneous results suggest that the partial equilibrium consumption response to the stimulus was twice as large as what is implied by homogeneous estimates.