The Double Power Law in Consumption and Implications for Testing Euler Equations

We provide evidence suggesting that the cross-sectional distributions of U.S. consumption and its growth rate obey the power law in both the upper and lower tails, with exponents approximately equal to 4. Consequently, high order moments are unlikely to exist, and the GMM estimation of Euler equations that employs cross-sectional moments may be inconsistent. Through bootstrap studies, we find that the power law appears to generate spurious non-rejection of heterogeneous-agent asset pricing models in explaining the equity premium. Dividing households into age groups, we propose an estimation approach which appears less susceptible to fat tail issues