Complementarity, Heterogeneity, and Multipliers: Utility for HANK

Complementarity between consumption and work is essential for heterogeneous-agent models' ability to generate realistic multiplier effects from aggregate demand shocks, while avoiding puzzling predictions. We show how parameterizing complementarity - in the spirit of Frisch's utility acceleration"- separately from income effects is necessary to achieve both. HANK models equipped with such complementarity deliver plausible fiscal multipliers and simultaneously resolve two key challenges in the literature: a "trilemma" of matching marginal propensities to earn (MPEs) and to consume (MPCs), and a Catch-22 "dilemmac of resolving the forward guidance puzzle. We establish these results analytically in a tractable HANK framework and confirm them in a calibrated quantitative HANK model. Standard utility functions, however, constrain either complementarity or income effects - or both - thereby forcing multipliers to depend exclusively on one or the other. We introduce two flexible parametric forms that allow arbitrary, independent calibration of complementarity and income effects: a quasi-separable "GHH-CRRA" utility and a "CCRRA" (constant complementarity and relative risk aversion) specification.