Monetary Policy and Wealth Effects: Caramp & Silva (2026)

What this is. The paper’s core results, the D-HANK model, and the analytical method (aggregation via a market-implied disaster probability) with the defining equations: enough to understand what was found and how, without reading all 42 pages. To replicate or extend, read the full source at the original.

TL;DR

Caramp and Silva build D-HANK: an analytical heterogeneous-agent New Keynesian model that adds rare aggregate disasters and heterogeneous beliefs about disaster risk to the HANK setting of Kaplan, Moll, and Violante (2018), who find only a minor role for the standard ISE. A contractionary monetary shock redistributes wealth from optimistic to pessimistic savers, raising the market-implied disaster probability and risk premia on stocks and bonds. This time-varying precautionary motive accounts for roughly 60% of the aggregate consumption response on impact; the aggregate wealth effect (via government bond revaluation) accounts for 30%; and the standard intertemporal-substitution effect (ISE) accounts for less than 10%. The model also matches the forward-curve dynamics documented by Hanson and Stein (2015), the equity premium, and the response of corporate spreads, all without requiring a high elasticity of intertemporal substitution. The paper derives conditions (Proposition 4) under which risk premia have no real effects (“risk-premium neutrality”), and shows that belief heterogeneity is necessary to break this neutrality.

Core results

Magnitudes and significance are as reported. Locators point into the source PDF (pages are printed page numbers, beginning at 1011).

#	Result	Locator	Magnitude
R1	Time-varying precautionary motive (TVP) accounts for roughly 60% of the initial output response to a 100 bps monetary shock (estimated fiscal backing solution)	Figure 5, Panel A, p. 1039	Output drops 1.15% on impact; TVP component accounts for ~60%; aggregate wealth effect (GE factor) accounts for ~30%; ISE accounts for less than 10%
R2	Heterogeneous beliefs amplify the consumption response by more than 3x relative to the homogeneous-beliefs economy with disaster risk	Figure 6, Panel B, p. 1040	Homogeneous-beliefs output drop: ~0.35%; heterogeneous-beliefs output drop: ~1.15% (more than three times larger)
R3	Model generates a 100 bps monetary shock that raises the five-year yield by 32 bps and matches the full forward curve estimated by Hanson and Stein (2015)	Figure 3, Panel B, p. 1037	Calibrated psi_lambda = 0.57 (half-life ~4 months); eps_lambda = 315 (33 bps change in disaster probability per 25 bps shock)
R4	Model produces a 4.0% drop in equity prices in response to a 100 bps increase in interest rates, driven primarily by the risk premium rather than the discount-rate channel	Figure 4, Panel C, p. 1038	Stock price decline: 4.0%; consistent with Bernanke and Kuttner (2005) point estimate
R5	Corporate spread rises by 11 bps in response to a 100 bps shock; VAR estimate is 6.5 bps (SE 3.1)	Figure 4, Panel B, p. 1038	Model spread response: 11 bps; excess bond premium (EBP) from VAR: 6.5 bps, SE 3.1
R6	Introducing long-term risky household debt raises the output drop by 48 bps (from ~1.15% to ~1.6%) relative to D-HANK without household debt; the TVP channel accounts for roughly half, the wealth effect for ~40%	Figure 7, Panels A-B, p. 1043	Output drop with HH debt (estimated fiscal): ~1.6%; baseline without HH debt: ~1.15%; additional drop: ~48 bps
R7	Standard RANK model with high EIS (sigma=1) generates a 1.1% output drop via wealth effect amplified by GE, but requires counterfactually large implied fiscal backing (more than 20x the empirical estimate)	Figure 8, Panels A-B, p. 1044	RANK MSV sigma=1: output drops 1.1%; RANK MSV sigma=4: output drops 0.1% (about 11x smaller); D-HANK with estimated fiscal: ~1.15% at sigma=4
R8	Risk-premium neutrality (Proposition 4) holds exactly when fiscal backing is independent of risk premia; heterogeneous beliefs break this condition since belief differences create differential wealth effects even at the same real interest rate	Proposition 4, p. 1027; Figure 1, p. 1028	Two economies with lambda_o < lambda_p: identical [y_t, pi_t, i_t] paths despite larger asset-price drop in the heterogeneous-beliefs economy; output difference = 0 by construction

Overall (paper’s conclusion). In the D-HANK model, the standard intertemporal-substitution channel of textbook New Keynesian models plays only a minor role. Aggregate risk combined with heterogeneous beliefs generates large time-varying precautionary motives that dominate the transmission of monetary shocks. The model can simultaneously match the equity premium, the term premium, the forward-curve dynamics, and the real effects of monetary shocks at a low EIS, a combination that RANK and standard HANK models cannot achieve.

Theory / model

The D-HANK model is a continuous-time heterogeneous-agent New Keynesian model. The economy is populated by three types: workers $w$, optimistic savers $o$, and pessimistic savers $p$, with masses $\mu_w$, $\mu_o$, $\mu_p$ summing to 1. Savers invest in short-term bonds, long-term government bonds, and corporate equity. They have heterogeneous subjective beliefs $\lambda_j$ ($j \in \{o,p\}$) about the Poisson arrival rate of aggregate disasters, with $\lambda_o \leq \lambda_p$. The aggregation uses the heterogeneous-beliefs framework of the risk-centric model of demand recessions in Caballero and Simsek (2020).

Savers’ problem. Each saver $j$ maximizes (p. 1017):

$$V_{j,t}(B_{j,t}) = \max E_j \!\left[ \int_t^{t^*} e^{-\int_t^z \rho_{j,u}\,du} \frac{C_{j,z}^{1-\sigma}}{1-\sigma}\, dz + e^{-\int_t^{t^*} \rho_{j,u}\,du} V^*_{j,t^*}(B^*_{j,t^*}) \right]$$

subject to the flow budget constraint:

$$dB_{j,t} = \left[(i_t - \pi_t)B_{j,t} + r_{L,t}B^L_{j,t} + r_{E,t}B^E_{j,t} + T_{j,t} - C_{j,t}\right]dt + \left[B^*_{j,t} - B_{j,t}\right]dN_t$$

where $i_t$ is the nominal rate, $\pi_t$ is inflation, $r_{L,t}$ and $r_{E,t}$ are excess returns on long-term bonds and equities conditional on no disaster, $T_{j,t}$ are transfers, and $N_t$ is the Poisson disaster process with arrival rate $\bar{\lambda}$.

Euler equations. The Euler equation for short-term bonds (eq. 1, p. 1018):

$$\dot{C}_{j,t} / C_{j,t} = \sigma^{-1}(i_t - \pi_t - \rho_{j,t}) + (\lambda_j / \sigma) \left[(C_{j,t}/C^*_{j,t})^{\sigma} - 1\right]$$

The first term is the standard ISE; the second captures the precautionary savings motive from disaster risk. The Euler equations for long-term bonds and equities (eqs. 2-3, p. 1018):

$$r_{L,t} = \lambda_j (C_{j,t}/C^*_{j,t})^{\sigma} \cdot (Q_{L,t} - Q^*_{L,t})/Q_{L,t}$$ $$r_{E,t} = \lambda_j (C_{j,t}/C^*_{j,t})^{\sigma} \cdot (Q_{E,t} - Q^*_{E,t})/Q_{E,t}$$

where the risk premium equals the price of disaster risk times the quantity of risk (the relative loss in asset value in the disaster state).

Market-implied disaster probability (Proposition 1, p. 1019). With heterogeneous beliefs, the economy aggregates as if a representative saver holds a CES-weighted belief:

$$\lambda_t = \left[ \frac{\mu_o C_{o,t}}{\mu_o C_{o,t} + \mu_p C_{p,t}} \lambda_o^{1/\sigma} + \frac{\mu_p C_{p,t}}{\mu_o C_{o,t} + \mu_p C_{p,t}} \lambda_p^{1/\sigma} \right]^{\sigma}$$

and $\eta_t = e^{-\int_0^t \rho_{s,z}\,dz} C_{s,t}^{-\sigma}$ is a valid SDF. This aggregation result is the key: the heterogeneous economy behaves as a representative-agent model with an endogenous, time-varying disaster probability that responds to monetary shocks via wealth redistribution. This extends the redistribution-via-risk-premia channel of Kekre and Lenel (2022) into a full New Keynesian model with analytical aggregation.

New Keynesian Phillips Curve and interest rate rule (eq. 11, p. 1023; eq. 6, p. 1020):

$$\dot{\pi}_t = (\rho_s + \lambda) \pi_t - \kappa y_t, \qquad \kappa = \phi^{-1}(\varepsilon-1)\phi Y$$ $$i_t = r_n + \phi_{\pi} \pi_t + u_t$$

Aggregate Euler equation (Proposition 2, eq. 10, p. 1023):

$$\dot{y}_t = -\bar{\sigma}^{-1}(i_t - \pi_t - r_n) + \chi_{p_d} p_{d,t}$$ $$\bar{\sigma}^{-1} = \frac{1 - \mu_w}{1 - \mu_w \chi_y} \sigma^{-1}$$ $$\chi_{p_d} = (\lambda/\bar{\sigma}) (C_s/C^*_s)^{\sigma}$$ $$p_{d,t} = \sigma(c_{s,t} - c^*_{s,t}) + \hat{\lambda}_t \qquad \text{(price of disaster risk)}$$

The aggregate EIS is amplified by the cyclicality of income inequality $\chi_y$. The extra term $\chi_{p_d} p_{d,t}$ connects aggregate risk and asset prices to real output.

Wealth effect decomposition (Proposition 6, eq. 26, p. 1033). The prior paper by the same authors, Caramp and Silva (2023), decomposes output into the ISE and the wealth effect; the D-HANK adds aggregate risk and heterogeneity to that framework. Output decomposes into three components:

$$y_t = \bar{\sigma}^{-1} \hat{y}_{m,t} \quad \text{(ISE)} + \chi_{\lambda} \hat{y}_{\lambda,t} \quad \text{(time-varying precautionary motive)} + (\rho - \omega) e^{\omega t} \Omega_0 \quad \text{(GE factor} \times \text{aggregate wealth effect)}$$

where $\Omega_0$ is the aggregate wealth effect at impact, $\chi_{\lambda} = \chi_{p_d} \varepsilon_{\lambda}$, and the GE factor $(\rho - \omega)$ ensures that $\int_0^{\infty} e^{-\rho t}(\rho-\omega)e^{\omega t}\,dt = 1$, so the wealth effect shifts output in all periods by $\rho \Omega_0$, amplified in general equilibrium.

Method

The paper contributes two methodological innovations that allow analytical aggregation in a setting with heterogeneous portfolios.

Approximate block-recursivity (Proposition 3, p. 1025). The market-implied disaster probability $\hat{\lambda}_t$ and relative net worth $b_{p,t} - b_{o,t}$ can be solved independently of output and inflation if the effect of savers’ aggregate consumption $c_{s,t}$ on risk premia is second-order (the term $r_k \sigma c_{s,t}$ is $O(\|i_t - r_n\|^2)$). Under this approximation:

$$\hat{\lambda}_t = e^{-\psi_{\lambda} t} \hat{\lambda}_0$$ $$\hat{\lambda}_0 = \varepsilon_{\lambda} (i_0 - r_n)$$

where $\varepsilon_{\lambda} \geq 0$ and is strictly positive if and only if $\lambda_p > \lambda_o$. The persistence parameter $\psi_{\lambda} = \xi$ (the speed of reversion in Uzawa preferences). The initial price of risk depends linearly on the initial monetary shock, with coefficient $\varepsilon_{\lambda}$ that captures the pass-through of nominal rates to the disaster probability via wealth redistribution.

Four-equation system. Combining the aggregate Euler equation (10), the NKPC (11), the Taylor rule (6), and the price of risk equation (19):

$$p_{d,t} = \bar{\sigma} y_t + e^{-\psi_{\lambda} t} \hat{\lambda}_0$$

the system has the same structure as the textbook three-equation NK model but with an additional term connecting asset prices to aggregate dynamics. The system is solved analogously to buildsFrom: value-function-iteration (matrix eigendecomposition of the $2 \times 2$ system in $[y_t, \pi_t]$), with the unstable root solved forward and the stable root backward.

Wealth effect formula (eq. 29, p. 1035). The aggregate wealth effect can be written entirely in terms of policy variables:

$$\Omega_0 = \frac{\rho - \omega}{(\rho - \omega)\chi_{\tau} + \bar{d}_G \kappa} \left[ \int_0^{\infty} e^{-\rho t} \Delta B^L_t (i_t - r_n + r_L \hat{\lambda}_t)\,dt - \bar{d}_G \int_0^{\infty} e^{-\rho t} \hat{\pi}_t\, dt - \int_0^{\infty} e^{-\rho t} \tau_t\, dt \right]$$

where $\Delta B^L_t = (1 - e^{-\psi_L t})\bar{d}_G$ is the portfolio exposure to long-term bonds, and $\tau_t$ is the fiscal backing (taxes on savers). This expression shows that equity revaluations do not affect $\Omega_0$ (the term $r_E$ drops out), only government bond revaluations do.

Calibration method. Parameters are disciplined by four moments: (i) natural interest rate $r_n = 1\%$; (ii) equity premium of 7.0% in stationary equilibrium (implies $\sigma = 4$); (iii) initial five-year yield response of 32 bps per 100 bps monetary shock (from a four-lag VAR on 1962-2007 US data); (iv) the entire forward curve estimated by Hanson and Stein (2015), used to pin $\varepsilon_{\lambda}$ and $\psi_{\lambda}$. The fiscal backing $\tau_t$ is estimated from the VAR impulse responses for government revenues and expenditures.

Empirical specifications

The paper is primarily a structural theory paper; the empirical content consists of VAR-based calibration moments and model-vs-data comparisons, not standalone reduced-form regressions.

VAR for fiscal and interest-rate dynamics (Section III.A, p. 1036). A four-lag VAR is estimated on quarterly US data 1962:Q1 to 2007:Q3. Variables (in order): real GDP per capita, CPI inflation, real consumption per capita, real investment per capita, capacity utilization, hours worked per capita, real wages, tax revenues/GDP, government expenditures/GDP, federal funds rate, five-year constant maturity rate, real value of government debt/GDP. The recursiveness assumption identifies the monetary shock: the federal funds rate is ordered third to last, five-year rate and government debt last. Bootstrapped 68% confidence bands are reported (Figure 2). The VAR is used to estimate the fiscal backing $\tau_t$ and the interest-rate impulse response that the model then matches.

Forward-curve calibration (Figures 3-4, pp. 1037-1038). The response of forward rates to a 25 bps change in the two-year yield around FOMC meetings is taken from Hanson and Stein (2015). The model forward curve is derived by solving the partial differential equation (PDE) for bond prices (Appendix S1, Internet Appendix Section III) and compared to the data-based forward rates. The model matches the long-horizon forward-rate response that standard models cannot explain.

Model-vs-data checks (Figures 4-7, pp. 1038-1043):

• Corporate spread: model predicts 11 bps rise per 100 bps shock, matching the VAR-based estimate of Gertler and Karadi (2015) of 6.5 bps (SE 3.1 bps) for the excess bond premium. Untargeted.
• Equity price: model predicts 4.0% drop; point estimate from Bernanke and Kuttner (2005) is the comparison benchmark. Untargeted.
• Output decomposition: model output drop (~1.15%, estimated fiscal) is compared against Miranda-Agrippino and Ricco (2021) estimate of ~1.15%.

Datasets used

Dataset	Role in paper	Wiki page
US macroeconomic VAR data (FRED/BEA/BLS)	Calibration of fiscal backing and interest-rate dynamics via VAR; variables include real GDP, CPI, consumption, investment, capacity utilization, hours, wages, tax revenues, govt expenditures, federal funds rate, five-year CMT rate, real govt debt (1962:Q1-2007:Q3)	FRED
Hanson & Stein (2015) forward-rate estimates	Calibration targets for the forward curve and persistence of risk premia	No page yet
Bernanke & Kuttner (2005) equity-price estimates	Untargeted model comparison for equity price response	No page yet
Gilchrist & Zakrajsek (2012) excess bond premium	Untargeted model comparison for corporate spread response	No page yet

Sample for VAR: quarterly, 1962:Q1 to 2007:Q3. Model calibration uses stationary equilibrium moments (equity premium 7.0%, credit spread 200 bps, debt-to-income ratio 10%, duration 5 years).

When to read the full paper

Use the original if you are: building or extending HANK models with aggregate risk; studying the transmission mechanism of monetary policy through asset prices; seeking the proofs of the eight propositions and lemma (Appendix, pp. 1045-1049); calibrating the term premium or credit spread to monetary shocks; or extending the model to richer capital structures or full quantitative HANK settings. The Internet Appendix contains the forward-curve PDE, additional robustness (sticky wages, investment, wealthy hand-to-mouth households), and the mapping between $\varepsilon_{\lambda}$ and underlying belief parameters.

Attribution and rights

Source: peer-reviewed, The Journal of Finance 81(2), April 2026. This distillation was extracted by an LLM on 2026-06-01 and is not human-verified or independently reproduced. The CC BY 4.0 licence permits mirroring; the verbatim PDF is not hosted in this batch.

Attribution (CC BY 4.0). Caramp, Nicolas, and Dejanir H. Silva. “Monetary Policy and Wealth Effects: The Role of Risk and Heterogeneity.” The Journal of Finance 81, no. 2 (April 2026): 1011-1052. DOI: 10.1111/jofi.70021. (c) 2026 The Author(s). Licensed under CC BY 4.0. This page is an adaptation by the Institute for Automated Research: core results extracted and re-expressed; changes were made.