Microeconomic Heterogeneity and Macroeconomic Shocks

Despite nearly three decades of quantitative heterogeneous-agent, incomplete-markets modeling, “representative agent models have remained the benchmark in the study of aggregate fluctuations” (Introduction, p. 2). The authors attribute this “to computational complexity and to some widely held views on the irrelevance of distributions for aggregate outcomes” (p. 2, fn. 1). On computation, solving for the equilibrium law of motion of the entire wealth distribution under rational expectations is intensive, and while Krusell and Smith (1998) pioneered a workable method, “applying their method to the most interesting versions of heterogeneous agent economies remains challenging” even with newer techniques such as projection-perturbation hybrids, sparse grids, and machine learning (Section 2, p. 5). On the “irrelevance” view, the authors argue the field over-generalized Krusell and Smith’s specific approximate-aggregation finding into a belief that heterogeneous- and representative-agent dynamics are interchangeable, which they call an inaccurate reading of the original result (Section 2, p. 5).

The Great Recession tied together portfolio composition, credit access, liquidity, heterogeneous marginal propensities to consume (MPCs), unemployment risk, and rising inequality – “issues that one cannot discuss in a representative agent model (at least not without trivializing them)” (Introduction, pp. 2-3). The house-price collapse “affected households differently, depending on the composition of their balance sheets,” and how much that wealth destruction translated into lower spending “was determined by marginal propensities to consume, which are also very heterogeneous and closely related to households’ access to liquidity” (Mian et al. 2013; Kaplan et al. 2014, cited p. 2); the resulting drop in demand, combined with a breakdown in bank lending to businesses, hit labor demand “unevenly across different occupations and skill levels” (p. 2).

A representative household behaves like a permanent-income consumer: highly sensitive to interest rates and nearly insensitive to transitory income changes, but the empirical literature on marginal propensities to consume finds the opposite pattern. Aggregate time-series evidence finds consumption “not very responsive to changes in interest rates” after controlling for income (Section 3.1, p. 6), and roughly one-third of U.S. households hold “close to zero liquid wealth or are near their borrowing limits” and empirically “do not react to movements in interest rates” (p. 7). Meanwhile the microeconomic MPC literature documents “(i) sizable average MPCs out of small, unanticipated, transitory income changes; (ii) larger MPCs for negative than for positive income shocks; (iii) small MPCs in response to announcements about future income gains; and (iv) substantial heterogeneity in MPCs that is correlated with access to liquidity” (p. 7) – none of which a representative-agent model reproduces. HANK does, because households at a borrowing-constraint kink have high MPCs and low interest-rate sensitivity, while unconstrained households facing uninsurable risk have their intertemporal substitution dampened by the possibility of hitting the kink in the future (p. 7-8, citing Carroll 1997).

A single liquid asset cannot simultaneously match the low average MPC implied by a representative-agent-like discount rate and the observed coexistence of “wealthy hand-to-mouth” and “poor hand-to-mouth” households. In the two-asset model, “the co-existence of a low-return liquid asset and a high-return illiquid asset creates the conditions for the emergence of wealthy hand-to-mouth households (who hold little or no liquid wealth despite owning sizable amounts of illiquid assets) alongside poor hand-to-mouth households,” reproducing the finding that about one-third of U.S. households are hand-to-mouth, two-thirds of those wealthy hand-to-mouth and one-third poor hand-to-mouth (Section 3.5, p. 12). The resulting quarterly MPC out of a $500 windfall is “around 15 to 20 percent” (p. 13), versus about 0.5% in a comparable representative-agent model and only around 4% – “still much lower than empirical estimates” – in a matched one-asset heterogeneous-agent model (p. 13).

Two models are “non-equivalent” when their impulse response functions (IRFs) to a shock differ; “weakly equivalent” when the IRFs coincide but the transmission mechanism differs; and “strongly equivalent” only when both the IRF and the transmission mechanism are the same (Section 4.1, p. 15-16). To assess the transmission mechanism, the authors propose three criteria: whether the IRF decomposition into the contribution of each equilibrium object (wages, interest rates, transfers) is the same; whether the “PE-GE discrepancy” – splitting the IRF gap into a general-equilibrium (different price paths) versus partial-equilibrium (different sensitivity to the same prices) component – is small; and whether the HANK IRF is insensitive to the assumed fiscal closure rule, since “due to Ricardian equivalence, alternative choices for this rule have no effect on the IRF in RANK. However, different rules can potentially have large effects on the IRF in HANK” (p. 16).

A discount-factor demand shock is strongly equivalent: the aggregate consumption IRFs “are almost identical,” and in both models “the driving force for the decline in expenditures is the demand shock itself: households become more patient and so postpone consumption,” with general-equilibrium price and transfer changes playing only a minor role in either model (Section 4.2, p. 17). Both the GE and PE discrepancies are “essentially zero,” and the HANK result is nearly identical whether government debt or lump-sum transfers do the fiscal adjustment, so “both the aggregate response to the shock and its transmission mechanism are very similar in the two models” (p. 17-18).

The aggregate consumption paths again “lie almost on top of each other,” but the transmission mechanism differs sharply: in RANK, the entire consumption fall is driven by intertemporal substitution in response to the higher liquid interest rate that the central bank engineers in response to rising inflation, whereas in HANK “the change in interest rates accounts for less than half of the fall in consumption,” with the rest coming from the direct fall in disposable household income interacting with HANK’s high MPCs (Section 4.3, p. 18). Both the GE and PE discrepancies are non-zero and large in this case – households respond less to the interest-rate rise but more to the income fall in HANK than in RANK, which is why the case is classified as weak rather than strong equivalence (p. 18-19).

For a contractionary monetary shock, consumption drops “by almost 50% more in RANK than in HANK” in the first quarter, and the transmission mechanisms diverge sharply: in RANK, direct intertemporal substitution from the higher real rate accounts for virtually the whole effect, while in HANK the fall in disposable income “plays a role that is at least as important as the substitution channel” (Section 4.4, p. 19). For fiscal shocks, the divergence is starker still: a deficit-financed government spending increase crowds out much less private consumption in HANK than RANK because higher MPC households spend more of the induced rise in labor income (Section 4.5, p. 21), and because of Ricardian equivalence, “RA models are particularly ill-suited for analyzing the effects of fiscal stimulus that takes the form of a change in the timing of transfers” – such policies have zero effect on consumption or output in RANK by construction, whereas in HANK a temporary transfer increase produces a first-quarter aggregate MPC of roughly 15-25%, amplified further by general-equilibrium aggregate-demand effects under sticky prices (Section 4.5, pp. 21-23).

The authors suggest adding a direct preference for holding liquid government bonds to the representative household’s utility function, u(C,H,B) = log C - ψH^(1+1/ε)/(1+1/ε) + φ(B^(1-σ) - 1)/(1-σ), as a reduced-form stand-in for HANK’s precautionary savings motive (Section 4.6, eq. 7, p. 25). The curvature parameter σ governs both the sensitivity of consumption to income and to interest rates: “higher values of σ lead to a larger aggregate MPC and lower sensitivity to changes in the interest rate,” and the authors report that setting σ = 2.5 “yields an aggregate MPC of similar magnitude as in HANK and an IRF decomposition in response to a TFP shock that is very similar to the decomposition in HANK” (p. 25). This modified RANK, unlike the baseline, also shares HANK’s wider class of policy rules compatible with equilibrium determinacy (p. 25-26, citing Hagedorn 2018).

The paper gives three examples: microfounding a fall in aggregate demand through channels other than an ad hoc discount-factor shock, using cross-sectional transmission patterns to help identify the source of a shock, and studying how aggregate shocks and policy reshape inequality. On the first, HANK can generate a demand-driven downturn through “tighter credit limits…that reduce borrowing capacity” or “increased uninsurable labor market risk…that exacerbates the desire for precautionary saving” (Section 5.1, p. 26-27), mechanisms with no representative-agent analogue. On the second, because “weakly equivalent models differ in terms of their transmission mechanism, but not in terms of their aggregate response to a shock,” and time-series data alone struggle to identify mechanisms, the model’s prediction that a monetary shock’s consumption effect is concentrated among hand-to-mouth households via the income channel, while wealthier households respond more through the interest-rate channel, offers a testable cross-sectional signature (Section 5.2, pp. 28-29). On the third, the model shows a contractionary monetary shock modestly raises consumption inequality, with wealthy households’ consumption sheltered or helped by the interest-rate rise while poorer households bear the brunt of the induced fall in labor income (Section 5.3, pp. 29-30).

The authors highlight real frictions in product markets – search frictions that make household “shopping” behavior endogenous – as “a promising alternative approach to generating real effects of changes in aggregate demand, that does not rely on price stickiness” (Section 6, p. 32-33), citing Huo and Ríos-Rull (2016), where the friction shows up as endogenous aggregate productivity movements, and Kaplan and Menzio (2016), where it shows up as endogenous markups. They note such models “fit particularly well with HA models because household shopping behavior is intimately linked to consumption decisions” (p. 33), in contrast to the standard New Keynesian channel, for which “there is much less microeconomic evidence for the large movements in quantities implied by price stickiness” (p. 32).

“The asset pricing implications of this first generation of HANK models are disconcerting”: equity prices barely move in response to aggregate shocks, and when they do it is often in the wrong direction – for instance, an expansionary monetary shock raises marginal costs and lowers profits, pushing equity prices down, when the (mixed but mostly opposite-signed) evidence points toward stock and house prices rising after expansionary policy (Section 6, “Time-varying risk premia,” p. 34). This matters because “heterogeneity in household balance sheets means that some households are much more exposed to movements in asset prices than others,” so current HANK models “miss the potentially large wealth effects on consumption for wealthy households that can arise from changes in asset prices” (p. 34) – the literature’s leading proposed fix is incorporating time-varying risk premia, following the logic that “market participants’ willingness to bear risk is greater in booms than in recessions” (p. 34, citing Cochrane 2017).