45A setup without the shocks Ļˆ and šœƒ 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 diļ¬€erences from KS-Hetero are the speciļ¬cation of aggregate shocks and the nature of Ī² heterogeneity. As columnsĀ 4 and 6 in TableĀ 3 show that the aggregate MPC is similar under the FBS or KS aggregate process (0.21 vs.Ā 0.23), we believe the residual diļ¬€erence in MPCs is mostly or entirely accounted for by the vastly diļ¬€erent assumptions about the distribution of Ī². While the lowest, middle, and highest discrete values of Ī² in our Ī²-Dist speciļ¬cation are very close to the three KS Ī² values, (0.9858,0.9894,0.9930), about 29% of our simulated agents have an intermediate Ī² between the lowest and central types; the corresponding percentiles of Ī² in the KS-Hetero model (as well as the 4% below that) all have Ī² = 0.9894. As the average MPC is convex in Ī², this relative dispersion of the central mass results in an increased MPC in Ī²-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.