Demand Disagreement: Heyerdahl-Larsen & Illeditsch (2026)

What this is. The paper’s core results, the OLG model it proposes (equilibrium SDF, consumption share dynamics, and bond pricing), and the empirical method (SPF-based demand disagreement proxy and UKF estimation): enough to know what it found and how, without reading all 16 pages. To replicate or extend, read the original at doi.org/10.1016/j.jfineco.2025.104191.

TL;DR

Standard heterogeneous-beliefs models predict that disagreement about asset prices should be tightly linked to disagreement about macroeconomic fundamentals. The data contradict this: a large fraction of yield disagreement remains after conditioning on every macro variable the Survey of Professional Forecasters (SPF) tracks, as documented by Giacoletti, Laursen and Singleton (2021). Albuquerque, Eichenbaum, Luo and Rebelo (2016) highlight a related puzzle for equity returns. Heyerdahl-Larsen and Illeditsch call this the “disagreement correlation puzzle” and resolve it with a model where investors disagree not about fundamentals but about future demand for savings, driven by differing time preferences and a false consensus bias. In equilibrium, this demand disagreement introduces a priced demand shock, generating stochastic yield volatility, time-varying bond risk premia, and an unconditionally upward-sloping yield curve. Using the component of SPF yield disagreement orthogonal to macro disagreement as their proxy, the paper confirms that demand disagreement is positively related to yield volatility and predicts future excess bond returns, consistent with the model.

Core results

Magnitudes are as reported; locators point into the source PDF.

#	Result	Locator	Magnitude
R1	Macro-fundamental disagreement explains only a modest portion of yield disagreement, especially in the changes specification	Table 2, p. 4	Changes R² ranges from 0.22 (3Q ahead, lowest) to 0.32 (1Q ahead, highest); Level R² = 0.72-0.77; substantial residual unexplained by fundamentals
R2	Demand disagreement is strongly positively associated with nominal yield volatility across all maturities (1-5Y), both in model and data	Table 3, p. 12	Standardized coefficients in data: 0.66-0.73 (t-stats 11.5-14.1); model values: 0.99 (near one-for-one)
R3	Demand disagreement is positively associated with model bond risk premia and predicts excess bond returns in data across maturities (2-5Y)	Table 4, p. 12	Standardized data coefficients: 0.38-0.44 (t-stats 4.9-5.8); model instantaneous-premium coefficients: 0.15
R4	Model-implied real yields closely track observed real yields; slope coefficient of one not rejected	Table 5, p. 13	Regression coeff 0.52-0.62, R² = 0.63-0.69 across maturities 2-10Y
R5	Model-implied nominal bond risk premia are positively associated with observed realized premia	Table 5, p. 13	Observed-on-model coefficients 1.28-1.54, R² = 0.08-0.18 across maturities 2-5Y
R6	Baseline calibration generates a positive equity premium and excess bond return that would be essentially zero without demand disagreement	Fig. 3, p. 9	Equity risk premium = 3.6%, stock market volatility = 22.8% at sigma_Delta = 0.8; without disagreement (sigma_Delta = 0) equity premium = 0.11%
R7	Fundamental disagreements also explain only a limited share of logged T-bill disagreement	Table 2, p. 4	Log-disagreement regression R² = 0.497, 0.553, 0.604, and 0.627 for 1Q, 2Q, 3Q, and 4Q ahead, respectively
R8	Long-run correlations between asset outcomes and fundamentals are low, motivating the correlation puzzle	Table 1, p. 3	At 1/5/10-year horizons, stock return correlations with dividends = 0.08/0.46/0.65 and consumption = 0.00/0.28/0.11; trading-volume changes with dividends = 0.21/0.35/0.31 and consumption = 0.29/0.38/0.40; real-yield changes with dividends = 0.26/0.20/0.24 and consumption = -0.16/0.04/0.06
R9	The residual disagreement proxy represents most of the cross-sectional spread in yield forecasts	Fig. 1, p. 4	Demand disagreement is 65% of yield disagreement at one quarter and 76% at four quarters
R10	Demand disagreement lowers patient investors’ long-run consumption share and raises its volatility	Fig. 4, p. 10	Mean share falls from 33.4% at sigma_delta = 0 to 31.7% at 0.4 and 29.0% at 0.8; volatility rises from 10% to 24.5% and 29.4%
R11	The model’s implied real yield curve slope tracks the observed slope with a coefficient statistically indistinguishable from one	Table 5, p. 13	Coefficient = 1.147 (reported Std. Dev. = 0.275), R² = 0.236; coefficient of one is not rejected
R12	The model fits real yield volatility less closely than real yields and bond premia	Table 5, p. 13	Observed-on-model-implied R² = 0.035, 0.086, 0.155, 0.136, and 0.088 for 2-, 3-, 5-, 7-, and 10-year maturities

Overall (paper’s conclusion). Demand disagreement, driven by investors’ incomplete knowledge of the evolving mix of patient and impatient agents in the economy, accounts for a large share of observed yield disagreement and explains stylized facts in bond and equity markets that macro-fundamentals-based models leave unresolved: positive and time-varying risk premia, yield volatility, and an upward-sloping term structure. The single-shock OLG structure is parsimonious but delivers good fits to yields, yield volatilities, and bond risk premia when estimated on SPF and TIPS data.

Theory / model

The economy is a continuous-time OLG model in the tradition of Blanchard (1985) and Garleanu and Panageas (2015). The paper builds on Ehling, Gallmeyer, Heyerdahl-Larsen and Illeditsch (2018a), who study inflation disagreement and the yield curve, shifting the focus to time-preference (demand) disagreement. A continuum of agents is born at rate $\nu > 0$ and dies at the same rate. There are two investor types: patient (type $a$, low discount rate $\rho^a$) and impatient (type $b$, high discount rate $\rho^b > \rho^a$). The fraction of patient newborns is $\alpha_t$, where $\alpha_t = 1/(1+\exp(-l_t))$ and $l_t$ follows a mean-reverting Ornstein-Uhlenbeck process (Section 3.1, p. 5):

$$dl_t = \kappa(\bar{l} - l_t)\,dt + \sigma_l\,dZ_{\alpha,t} \tag{4}$$

This demand shock $Z_{\alpha,t}$ is independent of the output supply shock $Z_{Y,t}$. Aggregate output $Y_t$ follows geometric Brownian motion with drift $\mu_Y$ and volatility $\sigma_Y$. Each agent has log utility over consumption, common endowment, and trades in four securities: the stock, a risk-free bond, and a consol bond (zero-net-supply) driven by $Z_{Y,t}$ and $Z_{\alpha,t}$ respectively.

False consensus bias and belief dynamics. Both types observe $\alpha_t$ and $l_t$, but disagree about the long-run mean $\bar{l}$: patient investors are optimistic ($\bar{l}^a \geq \bar{l}$), impatient investors pessimistic ($\bar{l}^b \leq \bar{l}$) (Section 3.2, p. 5). The likelihood ratio capturing belief disagreement is (Eq. 8, p. 6):

Each agent’s lifetime objective and wealth dynamics are, respectively, Eq. 5 and Eq. 6 (Section 3.1, p. 5):

$$\mathbb{E}_s^i\!\left[\int_s^{\tau^i} e^{-\rho^i(t-s)}\log(c^i_{s,t})\,dt\right] \tag{5}$$ $$dW^i_{s,t} = (r_tW^i_{s,t}-c^i_{s,t})dt + \Phi^i_{s,t}(dR^S_t-r_tdt) + \Psi^i_{s,t}(dR^C_t-r_tdt) + d\mathcal{L}^i_{s,t} \tag{6}$$

Agents of type $i\in\{a,b\}$ perceive the demand process and shock as in Eq. 7 (Section 3.2, p. 5):

$$dl_t = \kappa(\bar{l}^i-l_t)dt + \sigma_l dZ^i_{\alpha,t}, \qquad Z^i_{\alpha,t}=Z_{\alpha,t}-\sigma^i_\Delta t, \qquad \sigma^i_\Delta=(\bar{l}^i-\bar{l})\frac{\kappa}{\sigma_l} \tag{7}$$ $$\eta_t \equiv \frac{\eta_t^b}{\eta_t^a} = \exp\!\left(-\tfrac{1}{2}\sigma_\Delta^2\,t - \sigma_\Delta\,Z_{\alpha,t}\right), \quad \sigma_\Delta = \frac{2\kappa}{\sigma_l}(\bar{l} - \bar{l}^b) \tag{8}$$

The parameter $\sigma_\Delta \geq 0$ measures the degree of demand disagreement between types.

Equilibrium SDF. Proposition 1 (p. 6) establishes the equilibrium SDF:

$$\xi_t = \frac{X_t}{Y_t}, \qquad X_t = \int_{-\infty}^t \nu e^{-\nu(t-s)}\!\left(\alpha_s\beta_s^a e^{-\rho^a(t-s)}\frac{\eta_t^a}{\eta_s^a} + (1-\alpha_s)\beta_s^b e^{-\rho^b(t-s)}\frac{\eta_t^b}{\eta_s^b}\right)X_s\,ds$$

The SDF is inversely proportional to aggregate output $Y_t$ and depends on the process $X_t$, which captures heterogeneity in time discount rates and beliefs. The key state variable that fully describes all asset prices is the consumption share of patient investors, $f_t$.

The equilibrium follows from each type’s static consumption choice subject to its state-price budget constraint, Eq. 9, and the resulting optimal consumption and newborn consumption share, Eqs. 10-11 (Section 4, pp. 5-6):

$$\max_{\{c^i_{s,t}:s\leq t\}} \mathbb{E}_s^i\!\left[\int_s^\infty e^{-(\rho^i+\nu)(t-s)}\log(c^i_{s,t})dt\right], \qquad \text{s.t. }\mathbb{E}_s^i\!\left[\int_s^\infty e^{-\nu(t-s)}\frac{\xi^i_t}{\xi^i_s}(c^i_{s,t}-Y_t)dt\right]=0 \tag{9}$$ $$c^i_{s,t}=c^i_{s,s}e^{-\rho^i(t-s)}\frac{\xi^i_s}{\xi^i_t}, \qquad c^i_{s,s}=\frac{1}{\kappa^i_s}, \qquad i\in\{a,b\} \tag{10}$$ $$\beta^i_t \equiv \frac{c^i_{t,t}}{Y_t}=(\rho^i+\nu)\phi_t, \qquad i\in\{a,b\}, \qquad \phi_t=\frac{W_t}{Y_t} \tag{11}$$

Risk-free rate and market price of demand risk. Proposition 3 (p. 6) gives the equilibrium short rate and market prices of risk (Eqs. 12-13):

$$r_t = \mathcal{E}_f[\rho] + \mu_Y - \sigma_Y^2 + \nu\bigl(1 - \alpha_t\beta_t^a - (1-\alpha_t)\beta_t^b\bigr) \tag{12}$$ $$\theta_{\alpha,t} = \sigma_\Delta\!\left(\tfrac{1}{2} - f_t\right) \tag{13}$$

where $\mathcal{E}_f[\rho] = f_t\rho^a + (1-f_t)\rho^b$ is the consumption-share-weighted discount rate and $\beta_s^i = (\rho^i + \nu)\phi_t$ is the initial consumption-wealth ratio. The market price of demand shock risk $\theta_{\alpha,t}$ is strictly decreasing in $f_t$: when patient investors dominate (high $f_t$), the consol appears overpriced and $\theta_\alpha < 0$; when impatient investors dominate (low $f_t$), the market price of demand risk is positive.

Consumption share dynamics. Proposition 5 (p. 9) gives the stochastic differential equation for $f_t$ (Eq. 15):

$$df_t = \mu_{f,t}\,dt + \sigma_{f,t}\,dZ_{\alpha,t} \tag{15}$$ $$\mu_{f,t} = \nu\bigl(\alpha_t\beta_t^a(1-f_t) - (1-\alpha_t)\beta_t^b f_t\bigr) + (\rho^b - \rho^a)f_t(1-f_t) + \sigma_\Delta^2\!\left(\tfrac{1}{2} - f_t\right)f_t(1-f_t)$$ $$\sigma_{f,t} = f_t(1-f_t)\sigma_\Delta$$

The diffusion $\sigma_{f,t}$ is maximized at $f_t = 0.5$ and vanishes at the extinction boundaries, so demand shocks have the largest impact when the economy is balanced between types.

Consol price and stock return. Corollary 2 (p. 7) establishes that the consol price equals the wealth-consumption ratio $\phi_t$, and its return is exposed only to the demand shock $Z_{\alpha,t}$. The stock price $P_{s,t} = Y_t\phi_t$ and its return dynamics are (Eq. 14):

$$d\log P_{s,t} = d\log Y_{s,t} + d\log B_t^C \tag{14}$$

separating cash-flow exposure from exposure to the consol. Both the stock and the consol inherit stochastic risk premia through their exposure to the demand shock price $\theta_{\alpha,t}$.

For the heterogeneous-risk-aversion extension, Eq. 16 defines the effective relative risk aversion and weighted demand-disagreement volatility (Section 6.1, p. 14):

$$\mathcal{R}_t=\frac{1}{f_t\gamma^a_1+(1-f_t)\gamma^b_1}, \qquad \bar{\sigma}_{\Delta,t}=\frac{f_t\gamma^a_1\sigma^a_\Delta+(1-f_t)\gamma^b_1\sigma^b_\Delta}{f_t\gamma^a_1+(1-f_t)\gamma^b_1} \tag{16}$$

Method

The empirical motivation starts from the common pricing functional and the forecast equation for investors who disagree about fundamentals (Eq. 1, Section 2.2, p. 3):

$$p_t=\mathbb{E}^i_t[m^i_{t+1}x_{t+1}]=p(X^F_t), \qquad \hat{p}^{i}_{t,t+\Delta t}=\mathbb{E}^i_t[p_{t+\Delta t}]=\mathbb{E}^i_t[p(X^F_{t+\Delta t})], \quad 0<\Delta t\leq 1 \tag{1}$$

Demand disagreement proxy (Eq. 2-3). Because demand disagreement is not directly observable, the paper constructs a proxy from SPF data (Section 2.3, p. 4). Every forecaster $i$ in the SPF reports a forecast for the three-month T-bill rate $\hat{y}^i_{t,t+\Delta t}$ and for macro fundamentals $\hat{X}^{i,LF}_{t,t+\Delta t}$ for horizons $\Delta t \in \{1Q,2Q,3Q,4Q\}$. The paper first regresses the yield forecast on macro forecasts in a pooled cross-section:

$$\hat{y}^i_{t,t+\Delta t} = \beta_0 + \beta'_X \hat{X}^{i,F}_{t,t+\Delta t} + \beta_y \hat{y}^i_{t,t} + \varepsilon^i_{t,t+\Delta t}, \qquad \Delta t\in\{1Q,2Q,3Q,4Q\} \tag{2}$$

The residual $\varepsilon^i_{t,t+\Delta t}$ captures yield disagreement unrelated to macro fundamentals. The demand disagreement proxy for period $t$ is the cross-sectional standard deviation of this residual:

$$DD_{t,t+\Delta t} = \text{SD}_t(\varepsilon^i_{t,t+\Delta t}) \tag{3}$$

This proxy accounts for 65% of total yield disagreement at the one-quarter horizon and 76% at the four-quarter horizon (Fig. 1, p. 4).

UKF state estimation. To estimate the two latent state variables $(f_t, \alpha_t)$, the paper uses the Unscented Kalman Filter (UKF) (Section 5.7, p. 12; Fig. 6, p. 13). The two observables used for filtering are the demand disagreement proxy $DD_t$ and the two-year TIPS yield, covering Q1 1999 to Q2 2024. The observation equations are:

$$y_t = h(l_t, f_t) + e_{y,t}, \qquad DD_t = g(l_t, f_t) + e_{DD,t}$$

with $\alpha_t = 1/(1+\exp(-l_t))$ and diagonal noise covariances. The UKF is preferred over the EKF because it avoids linearization: instead of approximating the nonlinear observation equations, the UKF propagates the state distribution through them directly using a set of deterministic sigma points.

Empirical tests. Yield volatility regressions (Table 3) use an AR(1)-GARCH(1,1) model to estimate nominal yield volatility, then regress standardized volatility on the demand disagreement proxy with Newey-West standard errors (4 lags). Bond risk premium regressions (Table 4) define the excess return of a $T$-maturity bond (T in quarters) as $rx^{(T)}_{t,t+4} = Ty^{(T)}_t - (T-4)y^{(T-4)}_{t+4} - y^{(1)}_t$ and regress on $DD_t$. Both use the SPF sample Q3 1981-Q2 2024 and the paper reports no fixed effects for these time-series regressions. Table 5 uses filtered states over Q1 1999-Q2 2024 and compares observed series with model-implied series.

Empirical specifications

Yield volatility regression (R2, Table 3). For each maturity $T \in \{1,2,3,4,5\}$ years, the paper estimates:

$$\sigma^{(T)}_{y,t} = \gamma_0 + \gamma_1\,DD_t + \epsilon_t$$

where $\sigma^{(T)}_{y,t}$ is the conditional standard deviation of the $T$-year yield from an AR(1)-GARCH(1,1) fitted to actual quarterly yields. Coefficients are standardized (both variables normalized) and standard errors are Newey-West with 4 lags. Standardized coefficients range from 0.66 to 0.73 in the data (t-stats 11.5-14.1), and the model produces standardized coefficients of 0.99, consistent with the empirical magnitudes.

Bond risk premium regression (R3, Table 4). For each maturity $T \in \{2,3,4,5\}$ years (equivalently $T \in \{8,12,16,20\}$ quarters), the one-year holding period excess bond return is:

$$rx^{(T)}_{t,t+4} = \gamma_0 + \gamma_1\,DD_t + \epsilon_t$$

where $rx^{(T)}_{t,t+4} = Ty^{(T)}_t - (T-4)y^{(T-4)}_{t+4} - y^{(1)}_t$ (T in quarters; positive when bonds appreciate). Standardized coefficients range from 0.38 to 0.44 in the data (t-stats 4.9-5.8). The model’s Table 4 coefficient is from a regression of its instantaneous bond risk premium on demand disagreement and is smaller but same-sign (0.15). The data predictive relationship is robust to controlling for yield levels and macroeconomic disagreement (Tables 12-15, Internet Appendix).

Goodness-of-fit (R4-R5, R11-R12, Table 5). Using filtered state variables $(f_t, \alpha_t)$, the paper generates model-implied time series for real yields (maturities 2, 3, 5, 7, 10Y and slope), real yield volatilities, and nominal bond risk premia. It estimates the following observed-on-model regression separately for each series:

$$y^{\text{Data}}_t = a + b y^{\text{Model}}_t + u_t$$

The sample is Q1 1999-Q2 2024. Table 5 reports a “Std. Dev.” column alongside coefficients; it does not report fixed effects or a Newey-West correction for these regressions. Real yields have $b=0.52-0.62$ and $R^2=0.63-0.69$; the real yield slope has $b=1.147$ (reported Std. Dev. $=0.275$, $R^2=0.236$), and the coefficient of one is not rejected. Nominal bond risk premia have $b=1.28-1.54$ and $R^2=0.08-0.18$, with one not rejected. Real yield volatility has weaker fit, with $R^2=0.035-0.155$.

Datasets used

Dataset	Role in paper	Wiki page
Survey of Professional Forecasters (SPF), Philadelphia Fed	Yield and macro forecasts; source of the demand disagreement proxy DD (Q3 1981-Q2 2024, quarterly)	no page yet
TIPS yields (2-year, Federal Reserve/FRED)	Observable for UKF state estimation (Q1 1999-Q2 2024)	FRED
Shiller long-run U.S. stock market and macro data	Correlation puzzle motivation (Table 1): annual stock returns, dividends, consumption, one-year yield (1891-2009)	Shiller data

Sample: SPF quarterly data from Q3 1981 to Q2 2024 (172 quarters) for the main empirical results; Shiller annual data from 1891 to 2009 for the motivating correlation puzzle in Table 1. Replication data and code are deposited at Mendeley Data and Zenodo (links on the article landing page).

When to read the full paper

Use the original if you are: building or calibrating a heterogeneous-beliefs OLG model for bond markets; constructing a survey-based measure of disagreement orthogonal to macro fundamentals; extending the framework to recursive preferences, production, or learning from experience (Section 6 outlines these; the Internet Appendix contains the full derivations); or evaluating the UKF filtering approach for latent state estimation in a nonlinear OLG model. Table 3 (yield volatility) and Table 4 (bond return predictability) are the main empirical entry points; Fig. 3 (unconditional moments vs. sigma_Delta) is the key calibration diagnostic.

Attribution and rights

Source: peer-reviewed, Journal of Financial Economics 175 (2026) 104191. This distillation was extracted by an LLM on 2026-06-24 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). Heyerdahl-Larsen, Christian, and Philipp Illeditsch. “Demand disagreement.” Journal of Financial Economics 175 (2026) 104191. DOI: 10.1016/j.jfineco.2025.104191. © 2025 The Authors. Published by Elsevier B.V. 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.