When do Endogenous Portfolios Matter for HANK?

Most heterogeneous-agent New Keynesian (HANK) models assume households hold a fixed, exogenously given mix of assets – a simplification that is natural because standard first-order or “MIT shock” solution methods leave portfolio choice genuinely indeterminate, but one that sidesteps the fact that agents who perceive aggregate risk and can invest in several assets have a well-defined optimal portfolio near the steady state. This paper develops a new sequence-space method for solving jointly for these “zeroth-order” endogenous portfolios and for the model’s impulse responses, extending the fake-news-algorithm machinery of Auclert, Bardóczy, Rognlie and Straub (2021) with a second-order perturbation of the household portfolio problem evaluated just before shocks realize. When there are at least as many assets as aggregate shocks, optimal portfolios reduce to a simple risk-sharing test – marginal utility must respond proportionally across households to any aggregate shock – and the correction this implies for the model’s sequence-space Jacobians uses the same objects as the ordinary, exogenous-portfolio computation. Applying the method to a simple HANK model with a stock and a bond, the authors find that endogenous portfolios leave the aggregate effects of balanced-budget government spending shocks and of monetary policy shocks unchanged relative to the standard exogenous-portfolio (100%-stock) benchmark, because in both cases the exogenous portfolio already happens to satisfy (or trivially bypass) the risk-sharing condition. Deficit-financed fiscal transfers are different: because such transfers disproportionately raise the consumption – and lower the marginal utility – of poor, high-marginal-propensity-to-consume (high-MPC) households, optimal hedging induces poor agents to take large short positions in the booming stock market, cutting the baseline calibration’s impact transfer multiplier from 0.2 to 0.08 and its cumulative multiplier from 0.77 to 0.53. This result is sensitive to how much gross portfolio exposure is allowed: realistic short-sale and leverage constraints (stocks between -100% and 200% of net worth) bring the multiplier back close to the exogenous-portfolio benchmark, and adding more shocks than assets (incomplete markets) likewise pulls results back toward the exogenous-portfolio case when the additional shocks are hard to hedge. A parallel exercise with nominal assets shows the same logic working in the opposite direction: when households start out highly exposed to a Fisher (debt-deflation) channel, optimal portfolios shrink that exposure toward empirically plausible levels and substantially dampen the response to monetary shocks. The authors conclude that endogenous portfolios can matter a great deal for HANK results, but only when high-MPC agents are permitted to take large gross positions to hedge aggregate risk – a scope condition the paper is explicit about throughout.

Tomáš Ťapák | Macro Paper Warehouse

When do Endogenous Portfolios Matter for HANK?