Dsge-Models | Macro Paper Warehouse

Aggregate Implications of Heterogeneous Inflation Expectations: The Role of Individual Experience

Mon, 01 Jan 0001 00:00:00 +0000

Consumers’ inflation expectations are heterogeneous across birth cohorts and history-dependent: using panel data from the Survey of Consumer Expectations (SCE), the paper documents that each cohort’s inflation forecast is anchored to its cumulative inflation history, with the degree of anchoring estimated structurally. The authors model this via an experience-based Kalman filter in which each agent’s forecast combines a common Kalman-filtered signal (derived from food prices) with a cohort-specific reference term built from the cohort’s entire prior sequence of expected inflation. The estimated history-weight parameter θ is negative, confirming that agents positively weight their inflation history rather than overreacting to current news — a pattern that holds not only in US SCE and Michigan Survey of Consumers data but also across six European countries in the ECB Consumer Expectations Survey. Embedded in a Blanchard–Yaari perpetual-youth OLG New Keynesian model — where households hold experience-based expectations but firms set prices under rational Calvo frictions — the mechanism produces qualitatively different aggregate dynamics from full-information rational expectations (FIRE): after inflationary shocks, expectations initially underreact (agents anchor to the low-inflation steady state) and then persist well beyond the shock horizon as high inflation is gradually incorporated into cohort memory, generating hump-shaped expectation dynamics. For monetary policy, the optimal Taylor rule must be more aggressive after cost shocks than under FIRE: an energetic early response prevents the high-inflation episode from entering cohort memories, avoiding a self-reinforcing upward drift in inflation expectations. Applied to the 2021 high-inflation episode, the model predicts that the youngest cohorts — experiencing high inflation for the first time — will exhibit persistently elevated inflation expectations long after the supply shocks that caused the episode have dissipated.

Summary of a forthcoming paper, AI-assisted and human-reviewed. See the linked original for the authoritative claims and full conditions.

In depth

What are the four empirical patterns in the survey data, and do they hold outside the US?

Using the New York Fed’s Survey of Consumer Expectations (a monthly panel from 2013), the paper documents four patterns: (i) inflation expectations differ substantially across birth cohorts; (ii) cohort-specific inflation experience is age-clustered; (iii) individual inflation history is positively correlated with individual inflation expectations; (iv) cohorts do not differ in how they update to current information once their own inflation history is controlled for. These patterns hold in the Michigan Survey of Consumers and, with cohort fixed effects, across the ECB Consumer Expectations Survey covering six European countries — suggesting the mechanism is not US-specific.

How does the experience-based Kalman filter work, and what does estimation yield?

Each consumer’s forecast has two components: a standard Kalman filter signal common to all agents (extracted from food price data) and a cohort-specific reference term that is a weighted average of all past expectations formed by that cohort, governed by the parameter θ. Structurally estimated from SCE data using time fixed effects, θ is negative — meaning consumers positively anchor to their inflation history rather than over-extrapolating from current news. In a goodness-of-fit regression, the experience-based Kalman filter predicts observed cohort-level heterogeneity with a slope coefficient of 1.069, dominating lifetime average inflation and lagged inflation as predictors.

What is the general equilibrium model, and how do heterogeneous expectations enter the IS curve?

The model is a Blanchard–Yaari perpetual-youth OLG New Keynesian economy. Each surviving cohort solves a standard Euler equation using the experience-based expectations operator rather than rational expectations, yielding a history-dependent IS curve in which the effective real rate depends on the weighted average of each cohort’s reference inflation. Intermediate goods producers set prices under Calvo frictions with rational expectations, yielding a standard New Keynesian Phillips curve. The central bank follows a Taylor rule. The IS curve’s history-dependence means that past inflationary episodes — absorbed into cohort memory — affect present aggregate demand.

What do the impulse responses show under experience-based versus FIRE expectations?

Under a taste (demand) shock, experience-based expectations generate lower inflation on impact — agents anchor to the low-inflation steady state — but inflation remains elevated for longer as the shock is incorporated into cohort memory. Under a cost (supply) shock, two forces compete: anchoring to the steady state damps initial price pressure, but rational firms can raise prices by more because the IS curve becomes more inelastic; the net effect requires a stronger interest rate response than under FIRE. In both cases, household expectation dynamics are hump-shaped — initial underreaction followed by gradual build-up — consistent with evidence in Angeletos et al. (2021) and Pfajfar and Roberts (2018).

How does the optimal Taylor rule change under experience-based expectations?

After a cost shock the central bank should be more aggressive than under FIRE. The social cost of tolerating a transitory inflationary episode is much higher under experience-based expectations because it permanently shifts cohort memory upward, creating self-reinforcing dynamics in future periods. An aggressive early response prevents the episode from entering cohort references. After a taste shock the optimal response is similarly strong under both FIRE and experience-based expectations, so the memory channel adds little incremental urgency on the demand side.

What does the model predict about the 2021 high-inflation episode?

Feeding the model with actual monthly data through December 2021, average inflation expectations post-2021 are predicted to be both higher and more persistent under experience-based expectations than under FIRE or diagnostic expectations. Young cohorts, who experienced only low inflation in the 2010s, are updating their memory of inflation upward for the first time, creating a cohort-specific anchoring shift. The model implies that the 2021 episode could have long-lasting effects on consumer price expectations even if the supply shocks that caused it are fully transitory.

Monetary Policy and the Drifting Natural Rate of Interest

Mon, 01 Jan 0001 00:00:00 +0000

This paper analyzes how monetary policy should respond to a long-run natural interest rate that can drift permanently — following a bounded random walk with upper bound 3 percent and lower bound 0 percent — when the zero lower bound (ZLB) on nominal interest rates is a binding constraint. The central result is that the long-run neutral rate (the real policy rate consistent with stable inflation in long-run equilibrium) should fall more than one-for-one with the long-run natural rate as the latter approaches zero, because the mere risk of future ZLB episodes — even when the economy is currently away from the ZLB — imparts a persistent downward bias on inflation expectations that can only be offset by maintaining a pre-emptive expansionary bias. Quantitatively, the model implies that the neutral rate should be zero as soon as the long-run natural rate falls to 75 basis points — well above the near-zero estimates prevailing in the late 2010s — and that the ZLB would bind one-third of the time under optimal policy when the natural rate fluctuates between 0 and 3 percent. Price level targeting with a 10-basis-point upward drift closely approximates optimal commitment policy and has the advantage of not requiring knowledge of the natural rate level.

Summary of a forthcoming paper, AI-assisted and human-reviewed. See the linked original for the authoritative claims and full conditions.

In depth

Q1. What empirical fact motivates the model?

Empirical analyses of the long-run natural rate — the real interest rate prevailing over a long-run equilibrium in which nominal rigidities are absent — consistently find that it is time-varying in a manner best described by a random walk, meaning it can drift without reverting to a constant long-run level. The paper cites Holston, Laubach, and Williams (2017), Fiorentini et al. (2018), and Hamilton et al. (2016) as the main empirical references. Holston et al. (2017) place the long-run natural rate at between 0 and 1 percent in the U.S. and possibly slightly negative in the euro area as of 2016. The paper draws one central lesson: because the natural rate is time-varying and its future level is uncertain, a model with constant natural rate will give unreliable guidance for monetary policy, especially at low natural rate levels near zero.

Q2. What is the model and what are the key equilibrium concepts?

The paper embeds a new Keynesian model in which the long-run natural rate follows a bounded random walk with upper bound 3 percent and lower bound 0 percent, calibrated to post-WWII U.S. TFP data, and studies optimal monetary policy under commitment while imposing the zero lower bound. A critical distinction separates two notions of the long-run equilibrium interest rate: the “long-run natural rate” (denoted ¯r) is the real rate that would prevail in flexible-price equilibrium, determined by fundamentals outside the central bank’s control; the “neutral rate” (r*) is the real policy rate consistent with stable inflation in the long run, which the central bank operationally targets. The two coincide in standard models with constant ¯r, but diverge in this paper because ZLB risk drives a wedge between them.

Q3. What is the main theoretical result?

Under optimal commitment, the neutral rate r should fall more than one-for-one with the long-run natural rate ¯r — that is, the central bank should maintain a negative gap (r < ¯r) that widens as ¯r falls toward zero — because permanent downward movements in ¯r make future ZLB binding episodes permanently more likely, creating a persistent downward bias on inflation expectations that requires pre-emptive accommodation even in periods when the ZLB is not currently binding.** This result contrasts with the existing literature on optimal commitment at the ZLB, which has emphasized forward guidance — the promise to maintain low rates even after the economy recovers from a ZLB episode — as the primary stabilization tool. The paper shows that forward guidance alone is not sufficient when ¯r can permanently drift lower, because each downward drift permanently raises the probability of future ZLB episodes, reducing the central bank’s scope for fulfilling future inflation promises.

Q4. What are the quantitative implications?

The model implies that the neutral rate r reaches zero when the long-run natural rate ¯r is at 75 basis points — a level that was well above the near-zero estimates of ¯r prevailing at the end of the 2010s — and that the ZLB binds one-third of the time under optimal policy when ¯r fluctuates between 0 and 3 percent.* The 75 basis-point threshold means that a central bank operating in an environment where ¯r has declined to its estimated late-2010s levels would already be constrained to a neutral rate of zero under optimal policy. The one-third ZLB frequency is higher than what would be predicted by models with constant ¯r at typical calibrations, reflecting the permanent nature of ¯r shocks and their cumulative effect on the neutral rate.

Q5. What do the adjustment dynamics look like after a negative ¯r shock?

Following a permanent reduction in ¯r, the real policy rate adjusts gradually rather than immediately — remaining temporarily above the new long-run neutral rate during the transition — implying that monetary policy is contractionary along the adjustment path and that a permanent decline in ¯r is followed by a temporary disinflation before the economy settles at the new r.* This history-dependence of optimal commitment policy means the central bank does not immediately jump to the new, lower r* after a ¯r shock; it moves gradually, making the short-run policy stance more contractionary than the long-run position. The temporary disinflation is consistent with the general principle of history-dependence of optimal policy under commitment.

Q6. What role does price level targeting play?

Price level targeting variants — particularly a rule with an optimally chosen upward drift of 10 basis points — closely approximate the economic outcomes achieved under optimal commitment policy in the model, with the practical advantage that such rules do not require the central bank to know or estimate the current level of the long-run natural rate ¯r. The Eggertsson-Woodford (2003) price level target works well in models with constant ¯r by generating positive inflation expectations in the wake of deflationary ZLB episodes. Adding a small upward drift of 10 basis points strengthens this property under a drifting ¯r, because it provides additional buffer against the downward expectations bias that permanent ¯r drift generates. Under price level targeting rules, the neutral rate reaches the ZLB as soon as ¯r falls below 1 percent.

Key concepts

long-run natural rate (¯r) : the real interest rate prevailing over a long-run equilibrium in which nominal rigidities are absent; in this paper modelled as a bounded random walk with upper bound 3 percent and lower bound 0 percent, calibrated to post-WWII TFP data.

neutral rate (r)* : the real policy rate consistent with stable inflation in the long run; distinct from ¯r in this paper because ZLB risk drives a negative gap (r* < ¯r) that widens as ¯r approaches zero.

zero lower bound (ZLB) : the constraint that nominal policy rates cannot fall below zero; in this model the reason that permanent reductions in ¯r create a persistent downward bias on inflation expectations even when the ZLB is not currently binding.

expansionary bias : the paper’s finding that optimal commitment policy should maintain r* < ¯r — a pre-emptive accommodation away from the ZLB — to offset the downward bias on inflation expectations created by the risk of future ZLB episodes.

price level targeting : a monetary policy rule in which the central bank targets the price level rather than the inflation rate; shown in this paper to approximate optimal commitment policy and to have the practical advantage of not requiring knowledge of ¯r.

Optimal monetary policy with uncertain private sector foresight

Mon, 01 Jan 0001 00:00:00 +0000

Central banks must set policy under uncertainty about how private-sector expectations form, which changes how monetary policy transmits to output and inflation. This paper studies optimal time-consistent monetary policy using a New Keynesian finite-horizon planning (NK-FHP) model in which households and firms have limited foresight: they solve structural problems only up to a finite horizon, and update their beliefs about longer-run inflation by averaging over past data. In this setting—unlike in standard New Keynesian models—an “inflation scares” problem can arise: agents’ longer-run inflation expectations can deviate persistently from the central bank’s target, generating costly and prolonged disinflations. The authors formally characterize optimal policy when the planning horizons of private-sector agents are uncertain and a risk of inflation scares is present, showing that risk-management considerations modify the standard “leaning against the wind” principle with a novel preemptive motive: the optimal policy responds more aggressively to the risk of unanchoring to prevent inflation scares from materializing. An estimated version of the model is used to quantify how much this preemptive motive mattered during the post-pandemic inflation surge.

Summary of a forthcoming paper, AI-assisted and human-reviewed. See the linked original for the authoritative claims and full conditions.

In depth

Q1. What is the NK-FHP model and how does it differ from standard New Keynesian models?

In the NK-FHP model, households and firms are boundedly rational because they evaluate state-contingent paths only up to a finite horizon; beyond that horizon they extrapolate longer-run beliefs by averaging over past data, making those beliefs adaptive rather than anchored at the target. When agents have long planning horizons, the model approximates rational expectations: inflation expectations are well anchored, disinflations are relatively costless, and policy transmits quickly. When planning horizons are short, longer-run inflation expectations can become unanchored, disinflations are costly, and policy transmission lags lengthen. The NK-FHP model thus nests both extremes and provides micro-foundations for the “inflation scares” discussed by Goodfriend (1993).

Q2. What is the “inflation scares problem” and why does it matter for optimal policy?

An inflation scare occurs when agents’ longer-run inflation expectations deviate persistently from the central bank’s target because agents with short planning horizons update beliefs adaptively, and past high inflation feeds forward into current expectations. This creates a welfare-relevant asymmetry: once expectations become unanchored, a disinflation is costly in output because the central bank must build credibility against backward-looking expectations. The standard NK model with rational expectations does not generate this problem—rational agents’ inflation expectations are pinned to the target irrespective of history—so it cannot address the design of policy specifically to prevent scares from materializing.

Q3. What is the “preemptive motive” and how does it modify the leaning-against-the-wind principle?

Optimal time-consistent policy under uncertain private-sector foresight adds a preemptive motive to the standard leaning-against-the-wind (LATW) principle: the central bank contracts demand not just in response to current output-gap and inflation deviations, but also to prevent expectations from becoming unanchored. Under the standard NK LATW result (Clarida, Galí, and Gertler 1999), the policymaker responds to the means of output and inflation. Under uncertain and potentially short-horizon foresight, optimal policy also depends on the distribution of output and inflation, as well as agents’ beliefs about future inflation—specifically, whether those beliefs risk drifting away from target. The preemptive motive implies a more aggressive policy response to the risk of an inflation scare even before the scare has fully materialized.

Q4. How does the paper relate to the post-pandemic inflation experience?

Using parameter estimates from an estimated version of the NK-FHP model, the paper applies the optimal policy framework to quantify how much the preemptive motive matters during the recent post-pandemic inflation surge. The model—which has been shown in related work (Gust, Herbst, and López-Salido 2022, 2024) to fit macroeconomic time series substantially better than hybrid NK models and to account for initial underreaction and subsequent overreaction of inflation forecasts—is well suited to analyze an episode where longer-run inflation expectations initially remained anchored but later showed signs of drift. The paper’s quantification indicates that risk-management considerations, including the preemptive motive, significantly affect the optimal policy path.

Key concepts

finite-horizon planning (NK-FHP) : a bounded-rationality framework (Woodford 2018) in which agents evaluate only those state-contingent paths within a finite planning horizon, updating beliefs about events beyond the horizon adaptively from past data.

inflation scares : episodes (Goodfriend 1993) in which agents’ longer-run inflation expectations deviate persistently from the central bank’s target, making disinflation costly; the NK-FHP model provides micro-foundations for such scares.

preemptive motive : the additional incentive for a policymaker to tighten beyond what current output-gap and inflation deviations alone would prescribe, specifically to prevent longer-run inflation expectations from becoming unanchored.

time-consistent policy under uncertainty : optimal policy that does not rely on commitment and hence accounts for future re-optimization; in this model it must also account for the non-additive uncertainty arising from a distribution of planning horizons.