Fiscal and Monetary Policy with Heterogeneous Agents

The authors build a HANK model with sticky nominal wages and flexible prices, rather than the sticky-price/flexible-wage setup used in many early HANK models, because sticky prices with flexible wages generate implausibly countercyclical profits that interact with heterogeneity to drive results, and require an endogenous labor-supply margin that tends to produce excessively large marginal propensities to earn (Introduction, pp. 1-2). As the authors put it, the sticky-price approach “leads to implausibly countercyclical profits in response to demand shocks… It also requires modifying the standard incomplete market model to incorporate an endogenous labor supply choice… [which] typically implies marginal propensities to earn that are too large relative to the data.” Their alternative preserves “the core structure of the standard incomplete market model, with endogenous choice only between consumption and savings,” with unions setting wages and allocating hours uniformly across agents (pp. 1-2, 5-6).

The model is calibrated at a quarterly frequency to a 500% wealth-to-GDP ratio, 100% government debt-to-GDP, a 2% real interest rate, and a 20% government-spending share, with two-point discount-factor heterogeneity used to jointly hit an income-weighted quarterly MPC of 0.2 and match the 2019 Survey of Consumer Finances wealth Lorenz curve (Section 2, Table 1, pp. 7-8). The resulting fit “to the overall Lorenz curve is very good,” though the model “slightly understates the mass in the middle of the distribution… and understates inequality in the far right tail” (p. 8).

iMPCs – the derivatives of aggregate consumption with respect to labor income, interest rates, and capital gains at each horizon – are “sufficient statistics for household behavior in general equilibrium,” letting the authors connect microeconomic consumption evidence directly to macro policy responses (Section 2, pp. 7-10). The calibrated model’s iMPCs out of labor income are “large on impact and remain elevated for some time,” consistent with empirical estimates of roughly 0.15 to 0.25 at a quarterly level, while iMPCs out of capital gains are “low and flat” – a joint pattern the authors show neither the representative-agent nor two-agent model, nor other tractable heterogeneous-agent models in the literature, can simultaneously reproduce (pp. 8-9).

A government-spending increase financed entirely by contemporaneous taxes (zero deficit) raises output one-for-one, dY = dG, “irrespective of all household heterogeneity” (Proposition 1, p. 10). This holds identically in the RA, TA, and HA versions of the model, echoing a classical balanced-budget multiplier result (Gelting 1941, Haavelmo 1945), and establishes the baseline against which deficit-financed fiscal policy is then compared.

In the representative-agent model a deficit-financed tax cut has no output effect at all (Ricardian equivalence), in the two-agent model its effect is proportional to, and dies out with, the tax cut itself, but in the heterogeneous-agent model it generates prolonged, hump-shaped output effects because households partially save the cut, building “excess savings” that they then draw down as buffer-stock savers even after taxes start rising to pay off the debt (Section 3, pp. 10-12). Quantitatively, under a fiscal rule that retires the extra debt over roughly ten years, the HA model’s output response stays well above the RA and TA responses across the impulse-response horizon (Figure 2(a)), and the associated private wealth gains “trickle up” over time toward wealthier, lower-MPC households as poorer households spend theirs down first (p. 12, citing Auclert, Rognlie and Straub 2023c).

When steady-state government debt is zero, an interest-rate shock produces an output response that is identical across the RA, HA, and TA models, for any given monetary policy rule (Proposition 2, p. 13, generalizing Werning 2015 and an earlier two-agent-model result in Bilbiie 2008). The authors show this is not a coincidence but follows from an exact offsetting relationship: “when agents have larger MPCs, they are also less sensitive to interest rates,” because high-MPC agents have shorter effective horizons over which to substitute intertemporally, so amplification from higher consumption responsiveness is exactly cancelled by attenuation from lower interest-rate sensitivity (p. 13).

Heterogeneity changes the transmission mechanism, not necessarily the total aggregate effect: decomposing the consumption response to a rate cut shows that “indirect” effects (from labor income, tax cuts, and capital gains) are substantially larger than the “direct” interest-rate effect on household saving decisions (Section 4, “Direct vs indirect effects,” pp. 14-15, attributing the finding to Kaplan, Moll and Violante 2018 and Auclert 2019). In the decomposition, the labor-income channel is “large on impact and then declines relatively slowly,” while capital gains from the stock-market boom generated by lower rates provide a smaller but persistent boost, reflecting households’ low marginal propensity to consume out of capital gains (p. 15).

Longer-duration government debt weakens the aggregate effect of monetary policy, because less debt needs to be rolled over at the new rate each period, reducing the fiscal-channel tax response that amplifies HA transmission – though bondholders do gain from the resulting capital gain on longer bonds (Section 4, “Maturity structure,” pp. 15-16, citing Auclert 2019 and cross-country evidence in Calza, Monacelli and Stracca 2013). By contrast, when government debt and household nominal liabilities (such as mortgages) are nominal rather than real, a demand-driven rise in inflation redistributes from nominal creditors to nominal debtors – the “Fisher channel” – which “tends to go in the direction of amplifying the effects of monetary policy,” since debtors typically have higher MPCs than creditors, although “the exact empirical magnitude of this effect… remains open to debate” (p. 16).

When labor-market risk is countercyclical, the expectation of a future downturn raises precautionary savings today and amplifies demand shocks; the authors’ calibrated example shows this channel can become powerful enough to generate equilibrium indeterminacy at more extreme parameter values (Section 4, “Cyclical income risk,” pp. 16-18). On forward guidance specifically, the authors show that McKay, Nakamura and Steinsson’s (2016) proposal that heterogeneous-agent models resolve the “forward guidance puzzle” (implausibly powerful effects of announcements about future monetary accommodation) works in their model only because it also assumes procyclical income risk – in general, “what is true in partial equilibrium need not be true in general equilibrium,” since the equilibrium consumption effect of a future rate cut can, under monetary equivalence, be just as independent of its horizon as in the representative-agent model (p. 18).

Sequence-space methods let the authors incorporate behavioral frictions “naturally,” as long as those frictions leave the aggregate steady state unchanged (Section 5, “Behavioral frictions,” pp. 18-19, citing Auclert, Rognlie and Straub 2020). Illustrating with a case in which households never anticipate future aggregate labor income or tax changes but remain fully rational about individual income risk, the paper shows the deficit-financed fiscal shock’s output response becomes hump-shaped rather than immediately peaking, “as households do not immediately realize that their income will be persistently higher” (p. 19).

The HANK literature “has not yet reached a comparable level of maturity” to the representative-agent New Keynesian literature’s quadratic-loss characterization of optimal policy, partly because most tractable results come from simplified special cases (two-agent, zero-liquidity, CARA, or flexible-price models) or from assuming an exogenous, ad hoc loss function that “sidesteps the equity-efficiency tradeoff” central to heterogeneous-agent economies (Section 5, “Optimal policy,” pp. 20-21). A further obstacle they highlight is that “an unrestricted HA model, with standard preferences and both monetary and fiscal instruments, typically lacks a well-defined Ramsey steady state,” which is usually the necessary starting point for analyzing optimal responses to shocks (p. 21, citing Chien and Wen 2022 and Auclert, Cai, Rognlie and Straub 2024d).