DSGE models · Model guide
A lighter heterogeneous-agent structural route that keeps liquid and illiquid balance-sheet channels visible.
How do the wealth distribution and heterogeneous marginal propensities to consume change the transmission of monetary and fiscal policy relative to the representative-agent benchmark?
HANK - heterogeneous-agent New Keynesian - grew from the collision of two traditions. On one side, Bewley (1986), Huggett (1993), and Aiyagari (1994) built incomplete-markets models where agents face idiosyncratic income risk and borrowing constraints, generating endogenous wealth inequality and non-degenerate MPC distributions. On the other side, the New Keynesian DSGE tradition (Woodford 2003, Gali 2015) provided the sticky-price aggregate framework central banks actually use. Kaplan, Moll, and Violante (2018) - 'Monetary Policy According to HANK' - welded the two together, showing that the representative-agent Euler equation is a poor guide to aggregate demand dynamics once you account for realistic wealth heterogeneity. This HANK-lite variant keeps the core balance-sheet channels visible while avoiding the full continuous-time Fokker-Planck machinery of KMV.
The core mechanism is MPC heterogeneity and its interaction with general equilibrium. In the data, households near the borrowing constraint have MPCs of 0.5 - 0.7 out of transitory income, while wealthy unconstrained households have MPCs near 0.05. A representative-agent model forces a single low MPC on everyone. HANK decomposes the aggregate demand response to any shock into direct effects (interest rate exposure, Fisher channel) and indirect effects (changes in labor income, dividends, transfers that redistribute resources across the MPC distribution). Auclert (2019) formalized this into four sufficient statistics: the earnings heterogeneity channel, the Fisher channel, the interest rate exposure channel, and the intertemporal substitution channel. The key finding is that indirect effects through labor income dominate the direct intertemporal substitution effect that drives the entire representative-agent IS curve.
The Federal Reserve Board, the ECB, the Bank of England, and the Riksbank all run HANK-class models in their research divisions. Auclert, Bardoczy, Rognlie, and Straub (2021) developed the sequence-space Jacobian (SSJ) method that makes solving these models computationally tractable - reducing the problem from a high-dimensional state space to a sequence of matrix operations. McKay, Nakamura, and Steinsson (2016) showed that HANK resolves the forward guidance puzzle: incomplete markets discount future rate changes because constrained households cannot borrow against distant rate cuts. Ravn and Sterk (2021) added labor market frictions, showing that unemployment risk amplifies precautionary saving and weakens aggregate demand responses further.
The HANK-lite simplification keeps two asset types (liquid and illiquid), idiosyncratic income risk, and a borrowing constraint, but approximates the wealth distribution dynamics rather than solving the full Kolmogorov forward equation on a fine grid. This retains the economically important channels - MPC heterogeneity, the liquid/illiquid portfolio distinction, and the Auclert decomposition - while being solvable in seconds rather than hours.
The model has two blocks: a household block with incomplete markets and a standard New Keynesian aggregate block with Calvo pricing. On the household side, agents face persistent idiosyncratic income shocks (calibrated to match SCF/PSID wealth distributions), hold two assets - liquid bonds and illiquid capital - and face a borrowing constraint on liquid wealth. The Bellman equation over the two-asset portfolio generates the joint distribution of liquid and illiquid wealth, which pins down the aggregate MPC schedule and the sensitivity of consumption to each type of income or wealth change.
The aggregate block is a standard three-equation NK core: a Phillips curve from Calvo pricing, a Taylor rule, and a goods market clearing condition. The critical difference from representative-agent NK is that the IS curve is replaced by aggregation over heterogeneous household consumption functions. Aggregate demand is the integral of individual consumption policies over the wealth distribution, not a single Euler equation. This means the aggregate consumption response to an interest rate change depends on who holds liquid versus illiquid assets, who is near the constraint, and how labor income and dividends redistribute across the distribution.
The Auclert sufficient statistics decomposition structures the transmission channels. Any aggregate shock's consumption impact is decomposed into: (1) the intertemporal substitution channel (EIS-weighted, as in the representative agent), (2) the income channel (redistribution of labor earnings across the MPC distribution), (3) the Fisher channel (redistribution from debtors to creditors via unexpected inflation), and (4) the interest rate exposure channel (maturity mismatch between assets and liabilities). The sequence-space Jacobian approach (ABRS 2021) computes each channel as a matrix mapping from the path of aggregate variables to the path of aggregate consumption, avoiding the curse of dimensionality.
The Federal Reserve Board and ECB research departments use HANK models to evaluate fiscal transfer programs (stimulus checks, expanded UI) where the distributional incidence determines the aggregate demand impact. The 2020 - 2021 COVID stimulus evaluations were a high-profile use case: HANK models predicted that transfers targeted at liquidity-constrained households would have fiscal multipliers 3 - 5x larger than transfers to wealthy households, matching the observed spending patterns in JPMorgan Chase Institute and Census Pulse data.
HANK-lite is the standard framework for analyzing the forward guidance puzzle. McKay, Nakamura, and Steinsson (2016) showed that incomplete markets discount the effect of future rate commitments because constrained households cannot borrow against distant rate cuts. The quantitative resolution depends on the fraction of constrained agents and the persistence of the income process - parameters that HANK-lite calibrates to microdata while remaining computationally tractable enough for rapid policy experiments.
The model fails when the question requires tracking the full nonlinear dynamics of the wealth distribution - for example, analyzing the transition after a large structural reform that permanently shifts the stationary distribution. It also fails when the two-asset approximation is too coarse: if the question involves housing markets with leverage constraints, mortgage refinancing, or collateral-dependent credit access, a richer asset structure is needed. For these, the full Kaplan-Moll-Violante continuous-time formulation or the Bayer-Luetticke (2020) discrete-time approach is more appropriate.
Auclert's sufficient statistics decomposition makes HANK-lite a natural bridge between structural modeling and empirical work. Researchers can estimate the four redistribution elasticities from micro data (SCF, PSID, administrative records) and feed them into the aggregate model without solving the full heterogeneous-agent problem. This 'sufficient statistics HANK' approach is increasingly used at policy institutions that need distributional analysis but lack the computational infrastructure for full-scale HANK.
Risk-free bonds subject to a borrowing constraint >= b_min; the binding constraint generates high-MPC households at the bottom of the liquid wealth distribution.
Capital or housing that earns a higher return but cannot be instantly liquidated; the liquid-illiquid split generates 'wealthy hand-to-mouth' households with high MPCs despite positive net worth.
The marginal propensity to consume as a function of position in the joint liquid-illiquid wealth distribution; ranges from near-zero for unconstrained wealthy to 0.5+ for constrained households.
Variance of the idiosyncratic income process; higher risk increases precautionary saving, shifts the wealth distribution leftward, and raises the average MPC.
Total consumption change decomposed into Auclert's four channels: intertemporal substitution, income heterogeneity, Fisher redistribution, and interest rate exposure.
Households face idiosyncratic income risk and cannot fully insure against it. Liquid wealth is bounded below by b_min, generating a positive measure of constrained agents.
If violated: With complete markets, the wealth distribution is degenerate and the model collapses to the representative-agent NK. The entire MPC heterogeneity mechanism disappears.
Households hold liquid bonds and illiquid capital with different returns and liquidity properties. The illiquidity friction is modeled as an adjustment cost or a probabilistic access event.
If violated: With a single asset, there are no 'wealthy hand-to-mouth' households. The model loses the empirically important distinction between net worth and liquid wealth, and the MPC distribution becomes too compressed relative to data.
Firms face the standard Calvo lottery for price adjustment, generating a forward-looking Phillips curve identical to the representative-agent NK model.
If violated: With flexible prices, monetary policy is neutral regardless of the wealth distribution. The HANK channels only matter because sticky prices allow real effects of nominal shocks.
The ergodic distribution of wealth exists and the economy fluctuates around it. The linearization is taken around this stationary distribution.
If violated: If the wealth distribution has a unit root or trending moments, the linearization point drifts and the sequence-space Jacobian approach breaks down. Non-stationary wealth dynamics require global methods.
Aggregate dynamics are approximated by first-order perturbation around the stationary equilibrium. Individual policy functions are solved nonlinearly, but aggregate responses are linear in the shock.
If violated: Large shocks that move many households across the borrowing constraint simultaneously generate nonlinear aggregate responses. The linear approximation misses threshold effects and asymmetric responses to positive vs. negative shocks.
Households do not internalize the effect of aggregate shocks on the wealth distribution when making portfolio decisions (MIT shock approach).
If violated: With aggregate risk priced into individual decisions, precautionary saving against aggregate states generates additional dampening. Krusell-Smith (1998) style solutions are needed, adding substantial computational cost.
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