This paper uses an estimated Heterogeneous Agent New Keynesian (HANK) model to evaluate the quantitative importance of two channels in driving aggregate consumption fluctuations in the US: (i) precautionary savings against unemployment risk and (ii) MPC heterogeneity. I find that MPC heterogeneity is the dominant channel because a large fraction of households are close to the borrowing limit. The empirical average MPC target in HANK generates counterfactually volatile aggregate consumption, and thus makes it more difficult for the estimated model to match the persistence of the aggregate data, indicating an MPC puzzle. This is because the likelihood‐based estimation favors a low degree of nominal rigidity and responsive monetary policy in the HANK model to reduce the discrepancy between consumption volatility in the model and in the data. The low degree of nominal rigidity and responsive monetary policy reduce the persistence of endogenous variables in the model.