45A setup without the shocks ψ  and θ  is similar to the KS-Hetero model in that it replicates their idiosyncratic income process. Such setup with a less strict borrowing constraint (like in KS-Hetero) implies an aggregate MPC of 0.14. The remaining differences from KS-Hetero are the specification of aggregate shocks and the nature of β  heterogeneity. As columns 4 and 6 in Table 3 show that the aggregate MPC is similar under the FBS or KS aggregate process (0.21 vs. 0.23), we believe the residual difference in MPCs is mostly or entirely accounted for by the vastly different assumptions about the distribution of β  . While the lowest, middle, and highest discrete values of β  in our β  -Dist specification are very close to the three KS β  values, (0.9858,0.9894,0.9930)  , about 29% of our simulated agents have an intermediate β  between the lowest and central types; the corresponding percentiles of β  in the KS-Hetero model (as well as the 4% below that) all have β = 0.9894  . As the average MPC is convex in β  , this relative dispersion of the central mass results in an increased MPC in β  -Dist relative to KS-Hetero even when idiosyncratic income shocks are shut down and borrowing is allowed. These results are reported in our online appendix.