Micro Jumps, Macro Humps: Monetary Policy and Business Cycles in an Estimated HANK Model

Household-level data show consumption “jumps” on impact after a transitory income shock – an elevated MPC followed by continued elevated spending – while aggregate output’s response to an identified monetary policy shock is “hump-shaped,” peaking only several quarters after the shock (Introduction, pp. 2-3, Figure 1). The authors state plainly: “as is well-known, representative-agent models feature MPCs that are much too low compared to the data, so models in the macro moments tradition fail to match micro jumps. Similarly, existing heterogeneous-agent models feature an aggregate impulse response to monetary policy that is peaked on impact… so models in the micro moments tradition fail to match macro humps, and are therefore ill-suited for estimation using macro data” (p. 2).

Households update their beliefs about future aggregate variables only with i.i.d. probability 1-θ each period – basing forecasts on information from k periods ago if they have not updated – while always observing and correctly responding to their own current income and interest rate, so borrowing constraints are never violated on stale information (Section 2.3, eq. 4, pp. 9-10). Because “a one-time unanticipated income shock does not change future incomes or interest rates,” intertemporal MPCs themselves are left unchanged by the friction; but “slow adjustment of expectations allows us to model hump-shaped impulse responses to macroeconomic shocks” (p. 10), since households dampen their ex-ante intertemporal substitution and income effects until the shock’s consequences actually show up in their observed income.

The estimated model features sticky prices and wages with indexation, long-term government debt calibrated to the five-year average US duration, and investment subject to adjustment costs (Section 3, throughout; Section 5.3, p. 30, fn. 33: “to our knowledge, this is the first quantitative HANK model to feature long-term debt”). Households hold both a liquid and an illiquid asset, as in Kaplan, Moll and Violante (2018)-style two-asset HANK models, which is why the paper can further decompose consumption responses into contributions from liquid returns, illiquid returns, and labor income (Section 5.2).

The paper uses the sequence-space impulse-matching procedure of Auclert, Bardóczy, Rognlie and Straub (2019), extended with a new methodology for handling non-rational-expectations models, to match (a) a set of macro monetary-policy impulse responses in the tradition of Christiano, Eichenbaum and Evans (2005), and (b) a set of macro aggregate time series in the tradition of Smets and Wouters (2007) (Introduction, p. 4; Section 4). For the full seven-shock model (Section 6), the authors estimate shock AR/MA parameters and standard deviations by computing the log-likelihood directly from sequence-space impulse responses over 1966 Q1-2018 Q4 US data on output, consumption, investment, wages, hours, inflation, and the nominal interest rate, noting the whole procedure “is reliable and fast, even on a laptop computer,” taking about 120 seconds (Section 6.2, pp. 37-38).

Shutting off the investment response to a monetary shock (by setting the adjustment-cost parameter to infinity while holding the real-rate path fixed) reduces the peak output response by 69% and the cumulative 20-quarter output response by 84% – “far larger than investment’s direct share of the output response, which at peak is slightly less than 40%” (Section 5.1, pp. 27-28). The reason is that shutting off investment also sharply weakens the consumption response (peak falls 49%, cumulative falls 72%): “this reflects a powerful investment-consumption feedback that is unique to models with high MPCs: as investment rises, the additional output demand leads to a rise in labor income – much of which is spent on consumption by high-MPC households, leading to even more output demand” (p. 28). In the estimated representative-agent model with habits, by contrast, shutting off investment lowers output only by its direct 38% accounting share, with no change in the consumption impulse at all, “since it is pinned down by the path of real interest rates and intertemporal substitution via the Euler equation” (p. 28).

Even a two-agent model with a 20% hand-to-mouth share, habits, and the same average quarterly MPC, estimated to match the same impulse responses, shows consumption “barely affected when investment is shut off” – “because a two-agent model, even if it has the same average MPC, cannot match the intertemporal MPCs… [and] therefore misses important intertemporal feedbacks from investment to consumption” (Section 5.1, p. 28, and appendix E.1). This is the paper’s central methodological point: matching the average MPC is not enough; matching the full intertemporal MPC profile (how spending responds to income shocks at various future horizons) is what generates the amplification mechanism.

Following Kaplan, Moll and Violante’s (2018) direct/indirect decomposition, the paper finds that “almost the entire consumption response is accounted for by indirect effects” (via illiquid returns and, above all, labor income) while “the direct effect is almost absent” – a finding the authors call “even more extreme” than Kaplan, Moll and Violante (2018) (Section 5.2, eq. 25, Figure 6, p. 29). Switching off inattention while feeding in the same equilibrium price/income paths reveals the direct effect is “alive and well” absent the sticky-expectations friction, showing that inattention specifically dampens intertemporal substitution – “an activity that relies on changes in future expected interest rates” – and is, in the authors’ words, a friction that “must” be present for the model to avoid an implausibly large impact consumption response inconsistent with the micro data (Section 5.2, p. 30).

Two features drive this result: long-term government debt (five-year US-average duration, limiting how much debt must be rolled over at the new interest rate each quarter) and a fiscal rule that adjusts the budget gradually toward a steady-state debt target rather than via a balanced budget every period (Section 5.3, pp. 30-31). Under this baseline, “it still makes minimal difference whether the government adjusts τ, G, or T, nor does it matter much whether the debt itself is short- or long-term” (p. 31); the Kaplan-Moll-Violante-style ranking of fiscal instruments (spending first, then lump-sum transfers, then tax rates) reappears only under the less realistic combination of short-term debt and an immediate balanced-budget rule, where “fiscal policy can play a major role… with a peak output effect that is twice as large as our baseline” (p. 31).

In the estimated representative-agent model, supply shocks (TFP and markups) explain over half of business-cycle-frequency output variation and just under half of consumption variation, with investment shocks explaining only about 15% of output variation and essentially none of consumption variation (Section 6.3, Figure 11, p. 38). In the estimated HA model, by contrast, “investment shocks rise to prominence”: they explain about 65% of output variation and 55% of consumption variation at business-cycle horizons, while supply shocks “become far less important” (Figure 12, p. 38) – a stark difference driven purely by the household side of the model, since the two estimations share the same shock specification.

In the representative-agent model, investment shocks explain “almost none of the covariance of consumption and investment,” reproducing the classic Barro and King (1984) puzzle that investment-driven business-cycle models struggle to generate procyclical consumption without appealing to supply shocks; in the HA model, “investment shocks drive most of the covariance,” a “striking consequence of the model’s investment-consumption complementarity when MPCs are high” (Section 6.3, Figure 13, pp. 38-39). Impulse responses to a pure investment shock make the contrast visible directly: in the HA model consumption and investment “move together and peak at similar times,” whereas in the RA model there is only “a tiny and (due to habit formation) highly backloaded consumption response” (p. 39, Figure 14) – the same investment-consumption feedback responsible for the paper’s monetary-transmission result also resolves this longstanding business-cycle puzzle.