DSGE models · Model guide
Two-agent New Keynesian structure that separates hand-to-mouth from asset-holding households.
How do heterogeneous consumption responses - some households saving optimally, others spending hand-to-mouth - change the transmission of monetary and fiscal policy?
The TANK model descends from the rule-of-thumb consumer literature that Campbell and Mankiw (1989) launched with a simple empirical observation: aggregate consumption tracks current income far more closely than the permanent income hypothesis predicts. Gali, Lopez-Salido, and Valles (2007) embedded that idea in a New Keynesian DSGE by splitting the population into optimizing (Ricardian) households and hand-to-mouth (HtM) consumers who spend their entire after-tax labor income each period. Bilbiie (2008) formalized the analytics in "Limited Asset Market Participation, Monetary Policy, and Inverted Aggregate Demand Logic," showing that the HtM share can qualitatively change the sign of aggregate demand's response to interest rates rather than merely rescale the standard NK model.
The mechanism is transparent. A fraction lambda of households are hand-to-mouth: they hold no assets, cannot borrow, and consume exactly their current disposable income (wages plus transfers minus taxes). The remaining (1 - lambda) are Ricardian: they have access to a full menu of assets and smooth consumption intertemporally via the standard Euler equation. Aggregate consumption is the population-weighted sum C = lambda * (1 - lambda) * . Because HtM households have a marginal propensity to consume of one out of current income, any policy that shifts current income - wage changes from demand fluctuations, targeted transfers, tax rebates - has a direct, amplified effect on aggregate demand that the representative-agent model misses entirely. The aggregate MPC is no longer near zero; it is lambda * 1 + (1 - lambda) * MPC_r, which can be substantial.
Central banks and fiscal authorities use TANK-style models operationally. The IMF's Flexible System of Global Models (FSGM) includes a rule-of-thumb consumer share to generate realistic fiscal multipliers for Article IV consultations. The Federal Reserve Board's SIGMA model and the ECB's EAGLE model both feature a hand-to-mouth household sector. Debortoli and Gali (2018) showed that TANK captures a surprising fraction of the aggregate dynamics produced by fully heterogeneous-agent (HANK) models at a fraction of the computational cost, making it the workhorse for policy shops that need distributional realism without solving Bewley-Huggett-Aiyagari on a grid.
Bilbiie (2020) extended the analysis in "The New Keynesian Cross," deriving a discounted Euler equation for the Ricardian household that interacts with the HtM share to produce what he calls the TANK IS curve. When lambda exceeds a critical threshold (roughly the reciprocal of the markup), aggregate demand logic inverts: a rate cut can be contractionary because the indirect income effects on HtM households dominate the direct intertemporal substitution of Ricardian households. This inverted aggregate demand result is the sharpest analytical finding unique to TANK and has no analogue in representative-agent NK or standard HANK models.
The model has two household blocks, one firm block, and one policy block. On the demand side, Ricardian households maximize expected discounted utility subject to a standard intertemporal budget constraint with access to bonds (and possibly capital). Hand-to-mouth households face a static budget constraint: consumption equals after-tax labor income plus any government transfers. Aggregate demand is the lambda-weighted sum of the two consumption plans. The supply side is the standard NK Calvo pricing block - monopolistically competitive firms face random price-adjustment opportunities, generating the New Keynesian Phillips Curve. The central bank follows a Taylor-type interest rate rule.
The TANK IS curve differs structurally from the standard NK IS curve. In the representative-agent model, the IS curve is [ (1/sigma) * ([pi_{t+1}] - r_n_t). In TANK, the aggregation of the two consumption Euler equations (one dynamic, one static) produces a modified IS curve where the coefficient on the real rate gap depends on lambda. Bilbiie (2008) showed that the effective intertemporal elasticity becomes (1 - lambda * chi) / sigma, where chi captures the general-equilibrium feedback of output on HtM income. When lambda * chi > 1, the aggregate demand curve slopes the wrong way - the inverted demand logic.
Equilibrium determination in TANK inherits the Blanchard-Kahn structure from the NK core but with modified stability conditions. The Taylor principle must now be evaluated against the TANK IS curve coefficients, not the standard ones. Bilbiie (2008) derived the modified determinacy region: when aggregate demand is inverted, the Taylor principle flips - the central bank must respond less than one-for-one to inflation for determinacy. This has implications for the design of monetary policy rules in economies with large HtM populations.
The IMF uses TANK-style models in its Flexible System of Global Models (FSGM) and the Global Integrated Monetary and Fiscal Model (GIMF) for fiscal multiplier analysis in Article IV reports. The HtM share lambda is calibrated country-by-country - typically 0.2-0.4 for advanced economies, 0.4-0.7 for emerging markets - and directly determines the model's fiscal multiplier predictions. Without the HtM block, these models would predict government spending multipliers near zero in a Ricardian world, contradicting empirical evidence.
TANK is the standard framework for analyzing targeted fiscal transfers. During the COVID-19 pandemic, central bank research departments used TANK models to assess the macroeconomic impact of stimulus checks and enhanced unemployment benefits. The key prediction: transfers targeted at HtM households have multipliers well above one because the full transfer is spent immediately, while transfers to Ricardian households are largely saved. Coenen et al. (2012) used this framework for the European fiscal consolidation debate.
TANK fails when the question requires the full wealth distribution. HANK (Kaplan-Moll-Violante 2018) shows that the interaction between liquid and illiquid wealth creates a much richer set of MPCs than the binary 0-or-1 split in TANK. TANK also cannot speak to the endogenous entry and exit from the HtM state - households that are temporarily constrained behave differently from those that are permanently excluded from asset markets. For questions about wealth inequality dynamics, portfolio rebalancing channels, or the distributional consequences of asset price changes, HANK is the minimum viable model.
Bilbiie's (2020) "New Keynesian Cross" analysis established TANK as the analytical bridge between the NK and HANK literatures. The discounted Euler equation framework he developed shows exactly which HANK features can be captured by a two-agent approximation and which cannot. This makes TANK the natural starting point for any researcher who wants distributional realism without committing to a full Bewley-Huggett-Aiyagari computational apparatus.
Fraction of households that consume their entire current disposable income each period; the key parameter governing aggregate MPC and policy transmission heterogeneity.
Consumption of optimizing households who smooth intertemporally via the Euler equation; responds to expected future income and real interest rates.
Consumption of constrained households; equals current after-tax labor income plus transfers, , with MPC = 1 out of disposable income.
Population-weighted aggregate consumption lambda * (1 - lambda) * ; the composition shifts the aggregate MPC and policy multipliers.
The population is split into exactly two types: Ricardian (fraction 1 - lambda) with full asset market access and hand-to-mouth (fraction lambda) with zero asset holdings.
If violated: If the wealth distribution is continuous (as in HANK), the effective MPC schedule is nonlinear in income and the two-type approximation misses the intensive margin of wealth accumulation. Kaplan, Moll, and Violante (2018) show HANK can produce different aggregate dynamics than TANK for certain shocks.
HtM households consume exactly C_h_t = w_t * N_h_t + T_h_t each period with no saving or borrowing.
If violated: If constrained households can partially save or borrow (e.g., through informal credit or durable goods), their MPC falls below 1 and the amplification mechanism weakens. The strict MPC = 1 assumption overstates the TANK channel.
Firms face random price-adjustment opportunities with fixed probability (1 - theta) per period, generating the standard NKPC.
If violated: State-dependent pricing (Dotsey-King-Wolman 1999, Golosov-Lucas 2007) makes the Phillips curve slope endogenous to the inflation rate. The interaction between state-dependent pricing and household heterogeneity is largely unexplored.
Utility is separable in consumption and labor: U(C, N) = C^{1-sigma}/(1-sigma) - N^{1+varphi}/(1+varphi).
If violated: Non-separable preferences (GHH, Jaimovich-Rebelo) change the mapping from output to HtM consumption by altering the income effect on labor supply. The inverted demand threshold shifts.
Lambda is a fixed parameter, not an endogenous outcome of the wealth distribution.
If violated: In HANK, the fraction of effectively hand-to-mouth households is endogenous - it rises in recessions as households deplete buffer stocks. TANK cannot capture this procyclical amplification of the HtM channel.
The monetary policy rule satisfies the TANK-modified determinacy conditions, which depend on lambda and the general-equilibrium income feedback parameter chi.
If violated: When aggregate demand is inverted (lambda * chi > 1), standard aggressive Taylor rules destabilize the economy. The central bank must satisfy the flipped Taylor principle: phi_pi < 1 in the inverted region.
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