Optimal Policy Rules in HANK

The paper asks “should household inequality affect the conduct of cyclical stabilization policy?” and distinguishes two conceptually separate channels: household inequality could change transmission (how policy instruments map into any given targets, like inflation and output), or it could change the targets themselves (e.g., if policymakers also want to dampen the distributional effects of shocks) (Introduction). The paper studies both channels in turn within a single quantitative HANK model with two policy instruments – the nominal interest rate and lump-sum stimulus payments – allowing it to hold constant which channel is being examined.

The model is a rich business-cycle economy with nominal wage rigidities (intermediated by labor unions) and household heterogeneity, in which households self-insure against idiosyncratic income risk by trading capital, short-term bonds, and long-term bonds with different durations and inflation exposures. Labor-supply and price-setting frictions are kept simple enough that the aggregate supply side still collapses to a standard New Keynesian Phillips curve, “focusing our analysis on the demand-side and inequality implications of household heterogeneity” (Section 2). The calibration is explicitly disciplined by “evidence on monetary shock propagation”: the model is built to generate “fairly evenly distributed effects of monetary policy, with consumption responding by broadly similar percentage amounts across the wealth and income distributions,” while also featuring “an elevated average marginal propensity to consume (MPC)” and meaningful cross-sectional dispersion in the response to lump-sum transfers, so that fiscal and monetary channels are calibrated separately and realistically (Introduction).

No: Proposition 1 shows that, under a mild regularity condition ensuring interest-rate policy can freely manipulate aggregate demand, the optimal forecast target criterion for a dual-mandate policymaker is “exactly the same in our economy as it is in standard representative-agent models, and thus invariant to household heterogeneity.” The key step is that “household heterogeneity only affects the demand side of the economy (i.e., the ‘IS’ curve)… this demand block is a slack constraint: the policymaker can pick an output-inflation allocation subject to the model’s Phillips curve, and then simply set nominal rates as necessary to generate demand consistent with the desired allocation” (Section 5.2). Because the paper’s Phillips curve is, by construction, independent of household heterogeneity, “it follows that the optimal target criterion – and so also the optimal output-inflation allocation – is exactly as in RANK.” The paper further argues that even the path of interest rates needed to implement this optimum is likely to be very close between empirically disciplined RANK and HANK models, since both must match the same evidence on monetary transmission (Section 5.2).

The planner is built to insure households against business-cycle-induced fluctuations in their relative consumption shares, without wanting to alter the long-run steady state or provide extra insurance against idiosyncratic risk beyond what self-insurance already achieves – achieved formally through time-varying planner weights chosen so the deterministic steady state is efficient. This construction serves two purposes: it ensures “the policymaker does not seek to intervene in the absence of cyclical shocks,” and it keeps the problem tractable in linear-quadratic form, as in Woodford (2003) (Section 6.1). A second-order approximation of this objective (Proposition 2) yields a quadratic loss containing the usual inflation and output-gap terms plus a new term penalizing the cross-sectional dispersion of consumption shares around their steady-state values – “household heterogeneity then simply adds a third, inequality-related term, with the planner wishing to stabilize the consumption shares of everyone in the economy” (Section 6.1).

The paper’s central qualifying result is that “optimal policy deviates from the dual-mandate case – i.e., is shaped by household heterogeneity – if and only if the policy instruments can affect cross-sectional consumption inequality.” If interest-rate changes are distributionally neutral (as in the special case of Werning, 2015), the extra distributional term in the optimal rule is exactly zero and “the optimal rule continues to take a standard dual-mandate form” (Section 6.2, equation 34); conversely, “if interest rate cuts are strongly progressive (as is the case in Bhandari et al., 2021; Dávila & Schaab, 2022), then the concerns about inequality… may materially change optimal monetary policy conduct.” The paper’s calibrated model sits much closer to the neutral end of this spectrum.

Very little: when the model is hit by a distributional shock that redistributes income from low- to high-income households (a demand shock resembling the Covid-19 recession), the optimal monetary policy response under distributional objectives is “very similar to the dual-mandate policy,” with interest rates “cut somewhat more on impact” but output and inflation still “continue to be stabilized almost perfectly.” The reason is that monetary policy in this model “can only raise the consumption of all households more or less uniformly,” so “a policy that stabilizes consumption at the bottom at the same time over-stimulates consumption at the top, leading to substantial aggregate overheating” (Section 6.3) – the distributional gain from more aggressive rate cuts is not worth the aggregate cost. A similar result holds for a cost-push shock, where the incidence of monetary policy is close to uniform so “a central banker with distributional objectives thus sees no need to deviate from the dual-mandate outcomes” (Section 6.4).

Stimulus checks are shown to be far better suited to distributional stabilization: because of both elevated marginal propensities to consume among low-income households and the fact that a fixed dollar transfer is a larger share of income at the bottom of the distribution, “fiscal stimulus payments are much more progressive,” and in response to the distributional shock, “the policymaker can use the checks to almost perfectly stabilize aggregate output, inflation, and consumption inequality” simultaneously – with little need to adjust interest rates at all (Section 6.3). The paper frames interest-rate policy and stimulus checks as complementary rather than substitute tools precisely because they have “very different cross-sectional incidence profiles”: “for shocks with uniform incidence, the policymaker may instead want to mostly rely on monetary policy; and for other shocks, a mixture of the two instruments may be desirable” (Section 6.3, Discussion).

The authors are explicit that their conclusions are conditional on the model’s implied transmission channels, not a general feature of heterogeneous-agent economies: when they instead simulate a variant with a “counterfactually strong effect of policy on the labor share” (a sticky-price rather than sticky-wage variant), monetary policy becomes progressive rather than distributionally neutral, and “this model implies that distributional concerns have an important impact on policy.” Contrasting this alternative specification with their baseline, the authors write that “distributional concerns in principle can shape optimal policy design – it is just a feature of our model environment that they do not” in the baseline calibration (Section 6.4). They explicitly connect this to reconciling conflicting findings in the literature: “some analyses conclud[e] that inequality strongly shapes optimal monetary policy design (e.g., Bhandari et al., 2021; Dávila & Schaab, 2022; Smirnov, 2023) and others conclud[e] that it does not (Le Grand et al., 2025, and here),” arguing the difference traces to assumptions about the size of monetary policy’s distributional effects, not to a disagreement about the underlying logic (Introduction).

First, for dual-mandate central banks, household inequality “is likely to only have modest effects” on interest-rate policy, since empirically disciplined HANK and RANK models yield similar prescriptions for rates. Second, whether distributional objectives should shape monetary policy “depends crucially on the causal effects of nominal interest rate changes on consumption inequality,” which the paper’s evidence-disciplined model finds to be modest. Third, stimulus checks “may be a more useful tool for distributional purposes,” since they “achieve stabilization through insurance at the bottom” (Conclusion). The authors close by noting that these fiscal advantages must still be weighed “against the classic challenges in using fiscal policy as a stabilization tool described by Friedman (1968)” – explicitly the practical, non-model limitations of using discretionary fiscal transfers for stabilization.