Monetary Policy with Opinionated Markets

The paper studies how persistent belief disagreements between the Federal Reserve and financial markets about future aggregate demand shape optimal monetary policy and market outcomes. Empirically, forward interest rates and Fed projections often diverge, reflecting differing views on future economic activity. The authors develop a New Keynesian framework where the market anticipates policy "mistakes" (under the market’s belief), which in turn influence current demand through expectations of future rates. Central questions: How should the Fed set policy when markets hold opinionated, persistent beliefs? How do policy announcements transmit when they reveal the Fed’s beliefs? What are the implications for gradualism, communication, and inflation-output trade-offs? The study is important for interpreting Fed-market divergences, understanding the nature of monetary policy shocks, and designing communication to avoid tantrum-style overreactions.

The paper connects to several strands: (1) Gradualism in monetary policy (Woodford 2003; Bernanke 2004; Stein and Sunderam 2018), adding a novel expected-gradualism mechanism driven by disagreement and a Brainard-type (1967) prudence under tantrum risk. (2) Central bank communication literature (Blinder et al. 2008), rationalizing transparency as a tool to reveal beliefs and reduce market overreactions (e.g., forward guidance beyond ELB concerns). (3) Optimal policy with departures from rational expectations or imperfect knowledge (Evans-Honkapohja; Eusepi-Preston; García-Schmidt & Woodford; Gabaix), differing here because neither side is assumed correct ex ante; both are fully rational conditional on their dogmatic beliefs. (4) Empirical monetary shocks literature using high-frequency identification (Bernanke-Kuttner; Gürkaynak-Sack-Swanson), reframed as "Fed belief surprises" that behave like policy shocks for markets but are optimal under the Fed’s belief. (5) Fed information effect literature; here, announcements signal the Fed’s belief rather than fundamentals per se. (6) New Keynesian policy with cost-push shocks (Clarida-Gali-Gertler; Galí): disagreements act like cost-push shocks from the Fed’s perspective. (7) Disagreement and expectations literature using surveys and asset prices (e.g., Andrade et al.; Coibion-Gorodnichenko; Bauer-Chernov), tying interest rate and inflation disagreement patterns to the model.

Framework: A variant of the New Keynesian model with Calvo price stickiness. The representative household ("the market") makes consumption-savings and labor decisions; the Fed sets the nominal policy rate before the within-period aggregate demand shock realizes, capturing transmission lags. Baseline assumes fully sticky prices (zero inflation), extended to partial flexibility (NK Phillips Curve). Key equations (in log-linear terms): IS equation linking output gap to expected real rates, current demand shock, and expected future gap; NKPC when κ>0. Beliefs and disagreements: Aggregate demand g_t has a persistent component plus transitory noise. At the start of each period, both Fed and market observe the same public signal but apply heterogeneous, idiosyncratic interpretations. Each updates beliefs via Kalman filtering. Belief disagreements are persistent (AR(1) with persistence φ) and agents "agree to disagree" while expecting the other to learn toward their own view. Timing: agents interpret signals; the Fed sets i_t; the demand shock realizes; allocations and outcomes are determined. Policy problem: The Fed minimizes a standard quadratic loss over output gap and inflation, without commitment, and—under the equilibria considered—solves a static problem each period because continuation values are exogenous to current i_t. With fully sticky prices (κ=0), the Fed targets zero expected output gap under its own belief. With κ>0, the Fed trades off expected output and inflation. Shock identification within the model: When the market does not observe the Fed’s interpretation, the Fed’s rate announcement reveals the Fed’s belief—generating microfounded "Fed belief surprises." A further extension allows uncertainty about how the market interprets the Fed’s move (short-term vs long-term belief change), generating "tantrum" dynamics when markets overinterpret the move as long-term. Empirics (motivating facts): Using Greenbook/Tealbook (Fed staff) vs Blue Chip consensus (market), the authors document that: (i) rate disagreements co-move with inflation (demand) disagreements; (ii) disagreements are persistent. Robustness uses forward rates and TIPS breakevens (with caveats during the GFC due to liquidity premia).

• Optimal policy under disagreement (κ=0): The policy rate is a weighted average of beliefs: i_t = ρ + (1−φ) g^F_t + φ g^M_t. The Fed partially accommodates the market’s view; the weight on the market rises with belief persistence φ. The equilibrium output gap equals the disagreement (under the market’s belief), y_t = g^M_t − g^F_t.
• Expected rates and expected gradualism: The market and Fed have different expected paths of future rates. Each expects the other to learn toward their own belief over time, so forward-rate paths diverge but converge toward each agent’s current belief at long horizons. When the Fed becomes more optimistic, it raises the policy rate less than its own belief change because the market’s expected forward rates also rise (perceived "mistakes"), which dampens current demand; the Fed expects continued hikes as the market learns—expected gradualism. When the market becomes more optimistic than the Fed, the Fed initially overshoots relative to its own belief to offset market-induced demand, expecting to unwind as the market learns.
• Microfounded monetary policy shocks (Fed belief surprises): When the market does not observe the Fed’s interpretation, policy announcements reveal the Fed’s belief. Positive belief surprises raise current and forward rates and lower the market’s expected output gaps, similar to textbook contractionary shocks for financial markets. However, subsequent real effects depend on which belief is closer to the true data-generating process (DGP): if the Fed’s residual interpretation is unbiased (on average) under the DGP, average output gaps following such shocks are zero; if the Fed is on average "too optimistic" under the DGP, then shocks are followed by negative output gaps.
• Tantrum shocks and prudential gradualism: If the Fed is uncertain about how markets will parse its announcement (short-term vs long-term belief change), markets may overinterpret a move as long-term, leading to an overreaction of forward rates and a miss of the Fed’s target even under its own belief. Anticipation of tantrums induces more cautious (gradual) policy adjustments than certainty-equivalent. Clear communication that reveals the Fed’s belief can neutralize tantrum risk.
• Partial price flexibility (κ>0): Disagreements influence expected inflation via the NKPC, creating an inflation-output trade-off akin to cost-push shocks from the Fed’s perspective. The Fed’s optimal real rate places even more weight on the market’s belief than under full stickiness. Disagreements break divine coincidence and act like persistent cost-push shocks (AR(1) with persistence φ), mapping to Clarida-Gali-Gertler optimal policy results.
• Empirical motivation: Fed-market disagreements on 4-quarter-ahead rates are strongly correlated with inflation disagreements; disagreements are persistent. Appendix regressions show: (i) FFR disagreement vs inflation disagreement coefficient ≈ 0.87 (SE 0.16); (ii) inflation disagreement persistence coefficient ≈ 0.70 (SE 0.06). Robustness using forward rates and TIPS breakevens yields similar patterns outside the GFC, when TIPS liquidity premia distort breakevens.

The model answers how a policymaker should set rates when markets hold entrenched, differing beliefs about future demand. Anticipated policy "mistakes" under the market’s view shift forward rates and current demand, so the Fed’s optimal reaction function must incorporate market beliefs. This explains observed gaps between forward rates and official projections and rationalizes expected gradualism and occasional initial overshooting in response to shifts in beliefs. By distinguishing between belief revelation and fundamental shocks, the paper provides a structural interpretation for event-study "policy shocks," clarifying why financial market responses can be conventional while real effects hinge on whose belief aligns with the DGP. Allowing for misinterpretation risk (tantrums) yields a prudential rationale for slower adjustment and for communication (forward guidance, dots) that reveals beliefs to align expectations and limit overreactions. With partial price flexibility, disagreements create an inflation-output trade-off, so optimal policy further tilts toward market beliefs to offset induced inflation or disinflation pressures, making disagreements observationally similar to cost-push shocks. These mechanisms connect belief-driven disagreement to practical policy tools and observed market dynamics.

The paper contributes a coherent framework where Fed-market belief disagreements shape optimal policy, forward rates, and macro-financial responses. Main contributions: (1) A weighted-average policy rule that internalizes market beliefs, implying expected gradualism and occasional initial overshooting; (2) A microfoundation for monetary policy shocks as belief revelations (Fed belief surprises), reconciling financial responses with potentially muted average real effects when the Fed’s beliefs are accurate; (3) A theory of tantrum shocks from belief misinterpretation that justifies prudential gradualism and targeted communication to reveal policy beliefs; (4) With partial price flexibility, disagreements act like cost-push shocks that break divine coincidence and raise the optimal weight on market beliefs. Future research directions include: embedding richer dynamics and commitment to study intertemporal trade-offs; testing the model’s quantitative implications for accommodation weights and gradualism; distinguishing beliefs across heterogeneous agents (financial markets vs price setters); and investigating belief-driven policy uncertainty and risk premia in nonlinear settings.

• Stylized, log-linear New Keynesian environment with a representative household/market and Calvo pricing; results are mostly qualitative rather than calibrated quantitatively.
• Belief disagreements arise via heterogeneous interpretations of a public signal with learning in a steady state; other forms of information frictions or heterogeneity may alter dynamics.
• Baseline assumes fully sticky prices; NKPC results rely on partial flexibility extension and treat financial market expectations as if aligned with price-setter expectations.
• The model abstracts from risk premia in forward rates and TIPS liquidity premia; empirical comparisons can be confounded (e.g., GFC period).
• No explicit commitment problem is modeled; policy is set period-by-period, potentially understating commitment benefits.
• Identification of belief surprises vs other information effects in data remains challenging; the DGP alignment (Fed vs market) is unobserved and time-varying.