## CHAPTER 2 MANAGING EXPECTATIONS: INFLATION AND MONETARY POLICY ## Source details **Canonical URL:** [CHAPTER 2 MANAGING EXPECTATIONS: INFLATION AND MONETARY POLICY](https://www.imf.org/-/media/files/publications/weo/2023/october/english/ch2onlineannex.pdf) ## Other formats - [Markdown version](/-/media/files/publications/weo/2023/october/english/ch2onlineannex.pdf.md) - [Structured JSON version](/-/media/files/publications/weo/2023/october/english/ch2onlineannex.pdf.json) --- ### Metrics to Capture Anchoring of Long-Term Inflation Expectations (Online Annex 2.2) - Three complementary metrics (updated to latest available data): - Root-mean-squared deviation of mean inflation expectations from target: - Calculated as: 1/T ∑_{t=1}^T (π^e_{t,h} − π^*)^2, h = 3, ..., 7; w ∈ ω. π^* is the central bank’s inflation target for inflation-targeting economies or the one-year moving average of 10-year-ahead inflation forecasts (π^e_{t,10}) otherwise. The closer to zero this indicator is, the better-anchored expectations are. - Standard deviation of mean inflation expectations: - Calculated as: 1/(T−1) ∑_{t=1}^T (π^e_{t,h} − π̄^e_{h})^2, h = 3, ..., 7; w ∈ ω, where π̄^e_{h} is the average of inflation expectations for horizon h over window ω. - Disagreement in inflation expectations across individual forecasters: - Calculated as: 1/T ∑_{t=1}^T [ 1/(J−1) ∑_{j=1}^J (π^e_{j,t,h} − π^e_{t,h})^2 ], h = 3, ..., 7; w ∈ ω. - Time window and horizons: - Time window: six years (24 quarters). - Horizons: three-, five-, and seven-year-ahead inflation forecasts; the highest value across horizons is taken. - Empirical patterns: - Professional-forecaster series for Brazil, euro area, United Kingdom, and United States: long-term expectations are highly stable; near-term expectations are much more changeable. - Kolmogorov-Smirnov tests: long-term expectations have not significantly shifted across pre-, during-, and post-pandemic periods. - Consistency across metrics: lower values denote better-anchored long-term expectations. ### Historical Episodes of Sustained Rises in Near- and Long-term Expectations (Online Annex 2.3) - Definition and identification: - Episodes selected where both near- and long-term inflation expectations (Consensus Forecasts) jointly rise for a sustained period defined as four sequential quarters. - 32 historical episodes identified: 16 in advanced economies and 16 in emerging market economies. - Underlying sample spans 1989:Q4 to 2023:Q1, with exact coverage varying by economy. - Representative episode end dates (selected): - Advanced Economies: Australia 2005:Q4; Australia 2010:Q2; Germany 1997:Q4; Spain 2006:Q2; Euro Area 2008:Q2; Hong Kong 2004:Q4; Italy 2011:Q2; Japan 2004:Q2; Japan 2011:Q2; Lithuania 2011:Q2; Latvia 2011:Q2; Netherlands 2001:Q2; Norway 2001:Q2; Norway 2008:Q1; New Zealand 2008:Q2; Singapore 2008:Q2. - Emerging Market Economies: Argentina 2010:Q4; Bulgaria 2011:Q1; Brazil 2003:Q1; Brazil 2008:Q2; China 2004:Q1; Indonesia 1998:Q2; Indonesia 2002:Q2; Malaysia 2010:Q2; Malaysia 2013:Q4; Poland 2007:Q2; Russia 2008:Q2; Thailand 2004:Q4; Thailand 2010:Q2; Türkiye 2008:Q4; Venezuela 1994:Q4; Venezuela 1998:Q4. - Empirical outcomes across episodes: - Figure 2.4: plots median outcomes and interquartile ranges across identified episodes and medians for the latest inflationary episode for advanced and emerging market and developing economies. - Online Annex Figure 2.3.1 (advanced-economy sample with full employment coverage): shows an upward skew in the interquartile range for the unemployment rate gap, indicating upside risk to the unemployment gap going forward. - Robustness: alternative episode definition - Alternative criteria: persistently rising near-term expectations for four contiguous quarters while long-term expectations are (1) neither persistently rising nor falling over same period and (2) absolute quarterly changes in long-term expectations no larger than 7 basis points. - Identified episodes under alternative definition: 42 total — 36 advanced economies and 6 emerging market economies. - Patterns under alternative definition: - Long-term expected inflation stayed broadly stable on average in the aftermath. - Near-term expected inflation and headline inflation took about three years to return to pre-episode level (t = -3) on average. - Core inflation declines at about the same pace, somewhat faster than in main-chapter episodes. - Real growth declined on average by about two percentage points about four to five quarters after the end of the episode (t = 0) on average, with risks skewed to the downside. - The real (ex ante) policy rate tended to remain steady on average but came down slowly by about one percentage point on average after three years. - Current episode suggests a sharper slowing on average than these earlier, alternative episodes; comparison shows a drop and then sharp rise similar to main chapter episodes. ### Hybrid Phillips Curve: Specification, Identification, and Robustness (Online Annex 2.4) - Baseline hybrid Phillips curve (associational regression): - Relates annualized quarter-on-quarter, seasonally-adjusted headline CPI inflation π^c_t to: - Lagged inflation π^c_{t−1} - Near-term (next-12-months) inflation expectations E^c_t π^c_{t+h} - Output gap y^c_t - Controls X^c_t: changes in global energy prices and nominal effective exchange rates - Economy fixed effects α_c and time fixed effects τ_t - Baseline equation (2.4.1): π^c_t = γ_c π^c_{t−1} + β_c E^c_t π^c_{t+h} + θ_c y^c_t + δ_c X^c_t + α_c + τ_t + ε^c_t - Estimation details: - Quarterly unbalanced panel starting in 1991:Q2 at the earliest through 2023:Q1. - Sample excludes periods of hyperinflation in a small number of EMEs prior to 1997. - Up to 32 advanced economies and 21 emerging market economies included depending on availability. - Coefficients estimated via ordinary least squares (OLS) with Driscoll-Kraay standard errors reported. - Endogeneity concerns and system view: - Expectations formation model (2.4.2): E^c_t π^c_{t+h} = γ_{c,1} π^c_t + γ_{c,2} E^c_{t−1} π^c_{t+h} + e^c_t. - IS-curve formulation for output gap (2.4.3): y^c_t = α_{c,1} y^c_{t−1} + α_{c,2} E^c_t y^c_{t+h} − α_{c,3} ( w^c_t − E^c_t π^c_{t+h} ) + Ω_c X^c_t + u^c_t. - Equations 2.4.1–2.4.3 form a system of simultaneous equations; OLS estimates may be biased under general assumptions. - Instrumental variables (IV) approach: - Instruments: expectation lags, lagged output gap, and current nominal interest rate are used as instruments for current expectations and current output gap under assumption these pre-determined variables do not directly affect current inflation ε^c_t. - First-stage expressions (2.4.4) use only pre-determined and exogenous variables. - IV identification: passthrough estimates β_c and θ_c are unbiased under stated orthogonality assumptions. - Online Annex Table 2.4.1: presents OLS and IV estimates and diagnostic statistics on overidentification and weak identification tests. - Robustness checks: - When multi-period Taylor contracts and indexation are present, include lags of expectations up to the longest contract term. - To guard against exclusion restriction violations, extend lag operator for expectations and instrument current expectations with the first excluded lag (example: include lags 1 to 3 and use lag 4 as excluded instrument). - Baseline IV estimation for advanced economies robust when using 4, 6, and 8 lags as instruments. - Using up to 8 lags provides strong evidence against bias from omitted lagged expectations, noting wage contracts rarely exceed 1 year. ### Heterogeneous Agent Model of Expectations Formation: Structure and Estimation - Agent composition: - Two agent types: backward-looking learners (form expectations from recent/past experience) and forward-looking learners (form expectations rationally, accounting for backward-looking learners). - Model flavor: - Semi-structural New Keynesian variation with wage and price Phillips curves (building on Galí, Smets, and Wouters (2012); Berg, Karam, and Laxton (2006)). - Core linearized country equations: - IS Curve: y_t = α_y y_{t−1} + α_y y_{t+1} + γ(π_{t+1} − r_t) + s_{y,t} - Demand shock: s_{y,t} = ρ_ε s_{y,t−1} + ε_{y,t} - Price Phillips Curve: π_t = α_πy π_{t−1} + α_πy π_{t+1} + k_π w_t + ε_{π,t} - Nominal wage definition: π^w_t = w_t − w_{t−1} + π_t - Wage Phillips Curve: π^w_t = −α^w_y w_{t−1} + α^w_y π^w_{t+1} + K_w y_t + ε_{w,t} - Policy reaction function: r_t = ρ_r r_{t−1} + (1−ρ)(ρ_π π_{t+1} + ρ_y y_t) + ε_{r,t} - Definitions: - y = output gap; π = quarter-on-quarter, annualized core inflation rate; r = nominal monetary policy interest rate; w = constant composition real wage gap; π^w = real wage inflation. - Estimation and data: - Bayesian estimation using quarterly data 2000:Q1 to 2019:Q4 for Brazil and the USA. - Observables: output gap (IMF WEO), annualized quarterly PCE inflation, real wage gap (detrended Employment Cost Index deflated by PCE inflation), one-year and ten-year inflation expectations (Cleveland FED). - Structural parameters estimated include learning speed and fraction of backward-looking agents. - Heterogeneous agent model estimated alongside full-information rational expectations (FIRE) model for comparability. ### Expectations Dynamics, Measurement, and Learning - Near- and long-term expectations: - Modeled so long-term expectations affect current inflation indirectly via near-term expectations (inspired by Blanchard and Bernanke (2023)). - Expectation equations include: π_{t+1} = α_1 π_{t−1} + α_2 π^*_{t+1} + ε_{π,t} and π^*_{t} = α_1^* π^*_{t−1} + α_2^* y^*_{t−1} + ε^*_{t}. - Backward-looking learners: - Use AR(2) forecasting rule: E_t[x_{t+1}] = α_t + β_{t,1} x_t + β_{t,2} x_{t−1}. - Coefficients vary over time and are updated via Kalman filter: - B_{t|t} = B_{t|t−1} + P_{t|t−1} X_{t−1} [Σ_t + X'_{t−1} P_{t|t−1} X_{t−1}]^{−1} * (forecast errors). - B_{t|t} stacks AR(2) coefficients; P_{t|t−1} is covariance matrix; Σ_t is residual variance-covariance. - Forward-looking learners: - Form expectations using full information, accounting for presence and behavior of backward-looking learners; in absence of unanticipated shocks, RE agents’ expectations equal π_{t+1}. ### Historical Decomposition and Scenario Findings - Drivers of post-COVID-19 inflation surge: - Mostly driven by a large cost-push shock persisting from last quarter 2020 to first half 2022 (supply disruptions and Russian invasion of Ukraine). - Inflation expectations initially pushed inflation down for most of the pandemic; only in late 2022 did expectations contribute positively to inflation. - Demand and monetary policy had a positive but small contribution to inflation in 2021 and 2022. - Near-term expectations deviations from target: - Cost-push and wage cost shocks initially drove increases in expectations in 2021; monetary policy became more important in 2022. - Own inflation expectations shocks first maintained expectations below target early in the pandemic, then turned positive as above-target inflation fed into expectations and increased inflation inertia. - Shock responses (heterogeneous agents vs FIRE): - Pure demand shock: heterogeneous agents’ model yields a larger hump-shaped output gap response due to larger estimated shock persistency and more inertial expectations, producing larger and more persistent inflation and inflation expectations despite stronger monetary tightening. - Wage cost shock: heterogeneous agents’ model produces higher initial inflation that feeds into expectations and prolongs the inflationary spell. ### Monetary Policy Frameworks, Communication, and Rationality Tests - Policy framework quality: - IAPOC index (Unsal, Papageorgiou, and Garbers 2022) captures monetary policy framework quality as average of Communication, Independence and Accountability, and Policy and Operational Strategy; ranges from 0 to 1. - Advanced economies have higher mean IAPOC indicators than emerging market and developing economies. - Rationality test (Lovell 1986): - Regression: π_{i,t} = α_i ⋅ π_{t|i,t−4}^e + β_i ⋅ π_{i,t−5} + ε_{i,t}; under rational expectations β_i = 0. - Scenario calibration for improving frameworks: - Improvement modeled by increasing share of forward-looking agents by difference between estimated forward-looking shares in representative advanced and emerging market economies. - Optimal policy definition and channels: - Optimal interest rate path {w_t} for t = 1 to ∞ minimizes welfare loss Σ_{t=j}^{∞} β^t (0.9(w_t − w_{t−1})^2 + (y_t − 0)^2 + (π^~_t − 0)^2), where first term captures interest rate smoothing and equal weights on output gap and inflation deviations are benchmarked. - Central bank influences inflation via three channels in estimated adaptive-learning model: 1. Direct demand channel: tighter policy cools demand → lowers y_t → lowers inflation. 2. Expectations channel: lowering current inflation reduces next-period expectations. 3. Learning channel: agents update forecasting coefficients when realized inflation differs from expectations; observing less inflation than expected alters how past inflation matters for future inflation. ### Firms’ Inflation Expectations: ECFIE Construction, Validation, and Predictive Power - ECFIE addresses scarcity of firm surveys with criteria: high frequency (monthly or quarterly), more than 350 firms, representativeness. - Construction steps: - Step 1: identify two keyword sets (inflation-related and expectations-related) via GPT and human judgment. - Step 2: “bag-of-words” computes frequency of sentences containing any keywords from both sets in earnings calls transcripts. - Validation and predictive power: - Correlation of ECFIE with Federal Reserve Bank of Cleveland’s survey-based index of non-financial business expectations: 0.97. - Similar high correlations for other advanced and emerging market economies. - Predictive effect: a one-unit increase in the index is associated with a 2 percentage points increase in inflation on impact, which then lasts for three quarters. ### Near-Term Expectations, Monetary Policy Frameworks, and Empirical Association - Hypothesis: better monetary policy frameworks (higher IAPOC) associated with smaller deviations of actual inflation and near-term expectations from targets and less time away from targets. - Distance-from-target measures used: - Δπ^a_{i,t} = |(π_{w,t} − C_{i})|^2 (actual inflation deviation) - Δπ^e_{i,t} = |(E_w[π_{i,t}] − C_{i})|^2 (expected near-term deviation) - Regression (sample 2007:Q1 to 2019:Q4, IAPOC available pre-COVID): - Δπ^k_t = β_k ⋅ MPF_{i,t} + ν_{i,k} + ε_{i,t,k}, where k ∈ {C,e} and MPF = IAPOC (0 to 1); dependent variables winsorized at the 2.5 percent level. - Main empirical findings: - Negative association between MPF quality and deviations from target for actual inflation and near-term expectations. - When observations equally weighted (Online Annex Table 2.7.1): - Relationship strongly statistically significant for actual inflation deviations. - On borderline of almost statistical significance for expected inflation deviations. - Estimated coefficient range: −4.78 (actual deviations for emerging market economies) to −0.94 (near-term expected deviations for advanced economies). - Policy-relevant magnitudes: - A rise in IAPOC of about 0.2 (roughly the difference between the median emerging market economy and the median advanced economy) implies, using emerging market estimates, an almost one percentage point lower deviation of actual inflation from target. - Median actual deviation of inflation from target is about a percentage point, making the estimated effect economically sizable. - Note: estimates exclude 2020 onward; including 2020+ increases standard errors and removes statistical significance because of large shocks. *Source: IMF staff compilation (Online annex material from CHAPTER 2 MANAGING EXPECTATIONS: INFLATION AND MONETARY POLICY).* ### CHAPTER 2 MANAGING EXPECTATIONS: INFLATION AND MONETARY POLICY ### CHAPTER 2 MANAGING EXPECTATIONS: INFLATION AND MONETARY POLICY ### Online Annex 2.2 — Metrics to Capture Anchoring of Long-Term Inflation Expectations - Three complementary metrics are calculated and updated to the latest available data: - Root-mean-squared deviation of mean inflation expectations from target: - Calculated as: 1/T ∑_{t=1}^T (π^e_{t,h} − π^*)^2, h = 3, ..., 7; w ∈ ω, where π^* is the central bank’s inflation target for inflation-targeting economies or the one-year moving average of 10-year-ahead inflation forecasts (π^e_{t,10}) otherwise. The closer to zero this indicator is, the better-anchored expectations are. - Standard deviation of mean inflation expectations: - Calculated as: 1/(T−1) ∑_{t=1}^T (π^e_{t,h} − π̄^e_{h})^2, h = 3, ..., 7; w ∈ ω, where π̄^e_{h} is the average of inflation expectations for horizon h over window ω. - Disagreement in inflation expectations across individual forecasters: - Calculated as: 1/T ∑_{t=1}^T [ 1/(J−1) ∑_{j=1}^J (π^e_{j,t,h} − π^e_{t,h})^2 ], h = 3, ..., 7; w ∈ ω, where π^e_{j,t,h} is agent j’s expectation and π^e_{t,h} is the average across forecasters. - Time window and horizons: - The time window used for the calculation of the three metrics is six years (24 quarters). - Measures are computed using three-, five-, and seven-year-ahead inflation forecasts, with the highest value across horizons taken. - Empirical patterns: - Online Annex Figure 2.2.1: near-term and long-term inflation expectations from professional forecasters for Brazil, euro area, United Kingdom, and United States — long-term expectations are highly stable, near-term expectations are much more changeable. - Kolmogorov-Smirnov tests indicate long-term expectations have not significantly shifted across pre-, during-, and post-pandemic periods. - Although the three metrics capture distinctive characteristics, the overall picture is consistent across metrics: lower values denote better-anchored long-term expectations. ### Online Annex 2.3 — Historical Episodes of Sustained Rises in Near- and Long-term Inflation Expectations - Definition and identification: - Historical episodes chosen based on a joint rise in both near- and long-term inflation expectations (from professional forecasters; Consensus Forecasts) for a sustained period defined as four sequential quarters. - 32 historical episodes identified (16 in advanced economies and 16 in emerging market economies). Underlying sample spans 1989:Q4 to 2023:Q1, with exact time coverage varying by economy according to data availability. - Online Annex Table 2.3.1 lists identified episodes and their end-episode quarterly dates. - Representative listed episodes (end-episode quarterly date shown): - Advanced Economies: Australia 2005:Q4; Australia 2010:Q2; Germany 1997:Q4; Spain 2006:Q2; Euro Area 2008:Q2; Hong Kong 2004:Q4; Italy 2011:Q2; Japan 2004:Q2; Japan 2011:Q2; Lithuania 2011:Q2; Latvia 2011:Q2; Netherlands 2001:Q2; Norway 2001:Q2; Norway 2008:Q1; New Zealand 2008:Q2; Singapore 2008:Q2. - Emerging Market Economies: Argentina 2010:Q4; Bulgaria 2011:Q1; Brazil 2003:Q1; Brazil 2008:Q2; China 2004:Q1; Indonesia 1998:Q2; Indonesia 2002:Q2; Malaysia 2010:Q2; Malaysia 2013:Q4; Poland 2007:Q2; Russia 2008:Q2; Thailand 2004:Q4; Thailand 2010:Q2; Türkiye 2008:Q4; Venezuela 1994:Q4; Venezuela 1998:Q4. - Empirical outcomes across identified episodes: - Figure 2.4 plots median outcomes and interquartile ranges across identified episodes and medians for the latest inflationary episode for advanced and emerging market and developing economies respectively. - Online Annex Figure 2.3.1 (advanced economy sample with full employment coverage) shows an upward skew in the interquartile range for the unemployment rate gap, suggesting upside risk to the unemployment gap going forward. - Alternative definition of historical episodes (robustness check): - Alternative episodes require persistently rising near-term expectations for four contiguous quarters, while long-term expectations are: (1) neither persistently rising nor falling over same period; and (2) absolute quarterly changes in long-term expectations no larger than 7 basis points (the maximum absolute quarterly change in long-term expectations observed for the median advanced economy over 2022). - These criteria identify 42 historical episodes: 36 from advanced economies and 6 from emerging market economies. - Patterns under the alternative definition: - Long-term expected inflation stayed broadly stable on average in the aftermath, with balanced risks. - Near-term expected inflation and headline inflation took about three years to return to pre-episode level (t = -3) on average. - Core inflation comes down at about the same pace, somewhat faster than in the main chapter episodes. - Real growth declined on average by about two percentage points about four to five quarters after the end of the episode (t = 0) on average, with risks skewed to the downside. - The real (ex ante) policy rate tended to remain steady on average but came down slowly by about one percentage point on average after three years. - The current episode suggests a sharper slowing on average than these earlier, alternative episodes; comparison suggests a drop and then sharp rise similar to the main chapter episodes’ comparison. ### Online Annex 2.4 — Hybrid Phillips Curve Analysis: Specification and Identification - Baseline hybrid Phillips curve specification (associational regression): - Relates annualized quarter-on-quarter, seasonally-adjusted headline CPI inflation (π^c_t) to: - Lagged inflation π^c_{t−1} - Near-term (next-12-months) inflation expectations from Consensus Forecasts E^c_t π^c_{t+h} - Output gap y^c_t - Controls: changes in global energy prices and nominal effective exchange rates X^c_t - Economy and time fixed effects - Baseline equation (2.4.1): π^c_t = γ_c π^c_{t−1} + β_c E^c_t π^c_{t+h} + θ_c y^c_t + δ_c X^c_t + α_c + τ_t + ε^c_t - Estimation details: - Quarterly frequency using an unbalanced panel starting in 1991:Q2 at the earliest through 2023:Q1. - Sample excludes periods of hyperinflation in a small number of EMEs prior to 1997. - Up to 32 advanced economies and 21 emerging market economies included depending on data availability. - Coefficients estimated via ordinary least squares (OLS) with Driscoll-Kraay standard errors shown. - Endogeneity concerns and causal estimation strategy: - OLS treats inflation expectations as exogenous; this relies on strong timing and measurement assumptions. - Expectations formation model (Equation 2.4.2): - E^c_t π^c_{t+h} = γ_{c,1} π^c_t + γ_{c,2} E^c_{t−1} π^c_{t+h} + e^c_t - First term allows expectations to respond to current inflation; second term captures persistence; e^c_t assumed white noise. - Output gap endogeneity addressed via IS-curve formulation (Equation 2.4.3): - y^c_t = α_{c,1} y^c_{t−1} + α_{c,2} E^c_t y^c_{t+h} − α_{c,3} ( w^c_t − E^c_t π^c_{t+h} ) + Ω_c X^c_t + u^c_t - Relates current output gap to lagged output gap, expected future output gap, real rate of interest (w^c_t − E^c_t π^c_{t+h}), other cost-push factors X^c_t. - System view: - Equations 2.4.1–2.4.3 form a system of simultaneous equations for current inflation, inflation expectations, and the output gap; OLS estimates of the hybrid Phillips curve will be biased under more general assumptions. - Instrumental variables (IV) approach and first stages: - Motivation: expectations lags for inflation and output, lagged output gap, and current nominal interest rate do not directly affect current inflation, motivating their use as instruments for current expectations and current output gap. - First-stage expressions (Equation 2.4.4) express expected future inflation and the output gap as functions of pre-determined and exogenous variables only; these serve as first stages for IV estimation. - IV identification and inference: - Passthrough estimates for inflation expectations β_c and the output gap θ_c using IV are unbiased under the assumption that the lags of expectations for inflation and the output gap, the lagged output gap, and the current nominal interest rate are uncorrelated with ε^c_t in Equation 2.4.1. - Online Annex Table 2.4.1 shows both the OLS and IV coefficient estimates for Equation 2.4.1, along with diagnostic statistics on overidentification and weak identification tests. - Methodological context and literature links (as cited): - Builds on October 2018 WEO Chapter 3 and subsequent WEO chapters. - References to approaches and justifications: Mavroeidis, Plagborg-Møller, and Stock (2014); Coibion and Gorodnichenko (2015); Adam and Padula (2011); Fuhrer (2017); Alvarez and Dizioli (2023); McLeay and Tenreyro (2020); Barnichon and Mesters (2021); and other literature on expectations formation alternatives. *Source: IMF staff compilation (Online annex material from CHAPTER 2 MANAGING EXPECTATIONS: INFLATION AND MONETARY POLICY).* ### CHAPTER 2 MANAGING EXPECTATIONS: INFLATION AND MONETARY POLICY ### CHAPTER 2 MANAGING EXPECTATIONS: INFLATION AND MONETARY POLICY ### Robustness Checks - Hybrid Phillips curves may require inclusion of lags of expectations up to the longest contract term when multi-period Taylor contracts and indexation are present. - To guard against exclusion restriction violations on lagged expectations, the lag operator for expectations in Equation 2.4.1 is extended and current expectations are instrumented with the first excluded lag (example: lags 1 to 3 included and lag 4 used as excluded instrument). - Baseline IV estimation for advanced economies is shown to be robust when using 4, 6, and 8 lags as instruments. - Using up to 8 lags provides strong evidence against bias from omitted lagged expectations, given that wage contracts rarely exceed 1 year (and even less for prices). ### Heterogeneous Agent Model of Expectations Formation: Model Structure - Economy populated by two agent types: - Backward-looking learners: form expectations based on recent and past experience. - Forward-looking learners: form expectations rationally based on full information, including knowledge about backward-looking learners. - Model is a semi-structural New Keynesian variation (Galí, Smets, and Wouters (2012); Berg, Karam, and Laxton (2006)) including wage and price Phillips curves (PC). - Core equilibrium equations (linearized, per country) include: - IS Curve: y_t = α_y y_{t−1} + α_y y_{t+1} + γ(π_{t+1} − r_t) + s_{y,t} - Demand shock process: s_{y,t} = ρ_ε s_{y,t−1} + ε_{y,t} - Price PC: π_t = α_πy π_{t−1} + α_πy π_{t+1} + k_π w_t + ε_{π,t} - Nominal wage definition: π^w_t = w_t − w_{t−1} + π_t - Wage PC: π^w_t = −α^w_y w_{t−1} + α^w_y π^w_{t+1} + K_w y_t + ε_{w,t} - Policy reaction function: r_t = ρ_r r_{t−1} + (1−ρ)(ρ_π π_{t+1} + ρ_y y_t) + ε_{r,t} - Definitions: y = output gap; π = quarter-on-quarter, annualized core inflation rate; r = nominal monetary policy interest rate; w = constant composition real wage gap; π^w = real wage inflation. ### Expectations Dynamics and Measurement - Near- and long-term expectations modeled (inspired by Blanchard and Bernanke (2023)); long-term expectations affect current inflation indirectly via near-term expectations. - Expectation equations include: - π_{t+1} = α_1 π_{t−1} + α_2 π^*_{t+1} + ε_{π,t} (expectation equation) - π^*_{t} = α_1^* π^*_{t−1} + α_2^* y^*_{t−1} + ε^*_{t} (long-run expectation equation) - Observable measures of near- and long-term expectations tracked through measurement equations. - Backward-looking learners use AR(2) forecasting rule: - E_t[x_{t+1}] = α_t + β_{t,1} x_t + β_{t,2} x_{t−1} - Coefficients vary over time and are updated via a Kalman filter (Slobodyan and Wouters (2012a; 2012b)): - B_{t|t} = B_{t|t−1} + P_{t|t−1} X_{t−1} [Σ_t + X'_{t−1} P_{t|t−1} X_{t−1}]^{−1} * (forecast errors) - B_{t|t} stacks AR(2) coefficients; P_{t|t−1} is the covariance matrix; Σ_t is the variance-covariance matrix of AR(2) residuals. - Forward-looking learners form expectations using full information, accounting for the presence and behavior of backward-looking learners; in absence of unanticipated shocks the RE agents’ expectations equal π_{t+1}. ### Model Estimation and Data - Estimated with Bayesian methods using quarterly data 2000:Q1 to 2019:Q4 for Brazil and the USA. - Observable variables used: output gap (IMF WEO), annualized quarterly PCE inflation, real wage gap (quarterly and annualized detrended Employment Cost Index (ECI) deflated by PCE inflation), and one-year and ten-year inflation expectations (Cleveland FED). - Estimated structural parameters include learning speed and fraction of backward-looking agents. - The heterogenous agent model and the full-information rational expectations (FIRE) model are estimated on the same data for comparability. ### Historical Decomposition and Scenario Analysis: Key Findings - Post-COVID-19 inflation increase was mostly driven by a large cost-push shock persisting from last quarter 2020 to first half 2022 (supply disruptions and Russian invasion of Ukraine). - Inflation expectations initially pushed inflation down for most of the pandemic; only in late 2022 did expectations contribute positively to inflation. - Demand and monetary policy had a positive but small contribution to inflation in 2021 and 2022. - Near-term inflation expectations deviations from target: - Cost-push and wage cost shocks initially drove increases in expectations in 2021; monetary policy became more important in 2022. - Own inflation expectations shocks initially maintained expectations below target early in the pandemic, then turned positive as above-target inflation fed into expectations, increasing inflation inertia. - Shock responses: - Pure demand shock: output gap has a larger hump-shaped response in heterogeneous agents’ model due to larger estimated shock persistency and more inertial expectations; leads to larger and more persistent inflation and inflation expectations despite stronger monetary tightening. - Wage cost shock: higher initial inflation in heterogeneous agents’ model that feeds into expectations and prolongs the inflationary spell. ### Monetary Policy Framework, Communication, and Rationality Tests - Better monetary policy frameworks and communication strategies can reduce inflation faster by shaping expectations, making agents more forward-looking. - Rationality test concept: regress future inflation on inflation expectations and lagged inflation; under rational expectations lagged inflation should be insignificant (Lovell 1986). - Regression used to test mean rationality: - π_{i,t} = α_i ⋅ π_{t|i,t−4}^e + β_i ⋅ π_{i,t−5} + ε_{i,t} - If expectations are rational, β_i = 0. - IAPOC index (Unsal, Papageorgiou, and Garbers 2022) captures monetary policy framework quality (average of Communication, Independence and Accountability, and Policy and Operational Strategy), ranges from 0 to 1. - Advanced economies have higher mean IAPOC indicators than emerging market and developing economies. - Scenario calibration: improvement in framework is modeled by increasing the share of forward-looking agents by the difference between estimated forward-looking shares in representative advanced and emerging market economies. ### Optimal Monetary Policy Decisions (Definition and Channels) - Optimal interest rate path {w_t} for t = 1 to ∞ minimizes welfare loss: - Σ_{t=j}^{∞} β^t (0.9(w_t − w_{t−1})^2 + (y_t − 0)^2 + (π^~_t − 0)^2) - Benchmark assumes equal weights for output gap and inflation deviations; first term captures interest rate smoothing. - Implicit assumptions: central bank knows current and future shocks and how its actions impact expectations. - In the estimated adaptive-learning (AL) model, the central bank influences inflation via three channels: 1. Direct demand channel: tighter policy cools demand → lowers output gap → lowers inflation. 2. Expectations channel (forecast equation): lowering current inflation reduces next-period expectations. 3. Learning channel: agents update forecasting-coefficients when realized inflation differs from their expectations; seeing less inflation than expected alters how past inflation matters for future inflation. ### Firms’ Inflation Expectations: ECFIE Construction and Validation - Firms’ surveys are scarce; ECFIE (Albrizio, Dizioli, and Simon (2023)) addresses frequency, sample size, and representativeness constraints. - Desirable criteria: 1) high frequency (monthly or quarterly); 2) more than 350 firms; 3) representative of the economy. - ECFIE construction: - Step 1: identify two keyword sets (inflation-related and expectations-related) via GPT and human judgment. - Step 2: “bag-of-words” approach computes frequency of sentences that contain any keywords from both sets in earnings calls transcripts. - Validation and predictive power: - Correlation of ECFIE with Federal Reserve Bank of Cleveland’s survey-based index of non-financial business expectations: 0.97. - Similar high correlations obtained for other advanced and emerging market economies. - Predictive effect: a one-unit increase in the index is associated with a 2 percentage points increase in inflation on impact, which then lasts for three quarters. ### Near-Term Inflation Expectations and Monetary Policy Frameworks: Empirical Association - Hypothesis: better monetary policy frameworks (higher IAPOC) associated with smaller deviations of actual inflation and near-term expectations from targets and less time away from targets. - Distance-from-target measures: - Δπ^a_{i,t} = |(π_{w,t} − C_{i})|^2 (actual inflation deviation definition as specified) - Δπ^e_{i,t} = |(E_w[π_{i,t}] − C_{i})|^2 (expected near-term deviation definition as specified) - Regression estimated over sample 2007:Q1 to 2019:Q4 (IAPOC available pre-COVID): - Δπ^k_t = β_k ⋅ MPF_{i,t} + ν_{i,k} + ε_{i,t,k}, where k ∈ {C,e}; MPF = IAPOC (0 to 1); dependent variables winsorized at the 2.5 percent level. - Main empirical findings: - Estimates indicate a negative association between MPF quality and deviations from target for actual inflation and near-term expectations. - When observations are equally weighted (Online Annex Table 2.7.1): - Relationship is strongly statistically significant for actual inflation deviations. - On the borderline of almost statistical significance for expected inflation deviations. - Estimated coefficient range: −4.78 (actual deviations for emerging market economies) to −0.94 (near-term expected deviations for advanced economies). - A rise in IAPOC of about 0.2 (roughly the difference between the median emerging market economy and the median advanced economy) implies, using emerging market estimates, an almost one percentage point lower deviation of actual inflation from target. - Median actual deviation of inflation from target is about a percentage point, making the estimated effect economically sizable. - Note: estimates exclude 2020 onward; including 2020+ increases standard errors and removes statistical significance due to large shocks. *Source: CHAPTER 2 MANAGING EXPECTATIONS: INFLATION AND MONETARY POLICY (online annex).* ### CHAPTER 2 MANAGING EXPECTATIONS: INFLATION AND MONETARY POLICY ### CHAPTER 2 MANAGING EXPECTATIONS: INFLATION AND MONETARY POLICY ### References - Adam, Klaus, and Mario Padula. 2011. “Inflation Dynamics and Subjective Expectations in the United States.” Economic Inquiry 49 (1): 13–25. - Albrizio, Silvia, Allan Dizioli, and Pedro Vitale Simon. 2023. “Mining the Gap: Extracting Firms’ Inflation Expectations from Earning Calls.” IMF Working Paper 23/202, International Monetary Fund, Washington, DC. - Alvarez, Jorge, and Allan Dizioli. 2023. “How Costly Will Reining in Inflation Be? It Depends on How Rational We Are.” IMF Working Paper 2023/021, International Monetary Fund, Washington DC. - Angeletos, George-Marios, and Jennifer La’O. 2009. “Incomplete Information, Higher-Order Beliefs and Price Inertia.” Journal of Monetary Economics 56: S19–S37. - Angeletos, George-Marios, and Chen Lian. 2023. “Dampening General Equilibrium: Incomplete Information and Bounded Rationality.” Handbook of Economic Expectations, eds. Rudiger Bachmann, Giorgio Topa, and Wilbert van der Klaaw, Chapter 20. Elsevier: London. - Baba, Chikako, Romain Duval, Ting Lan, and Petia Topalova. 2023. “The 2020–2022 Inflation Surge across Europe: A Phillips-Curve-Based Dissection.” IMF Working Paper 2023/30, International Monetary Fund, Washington DC. - Barnichon, Regis, and Geert Mesters. 2021. “The Phillips Multiplier.” Journal of Monetary Economics 117: 689–705. - Bems, Rudolfs, Francesca Caselli, Francesco Grigoli, and Bertrand Gruss. 2021. “Expectations’ Anchoring and Inflation Persistence.” Journal of International Economics 132: 103516. - Berg, Andrew, Philippe D. Karam, and Douglas Laxton. 2006. “A Practical Model-Based Approach to Monetary Policy Analysis: Overview.” IMF Working Paper 06/80, International Monetary Fund, Washington, DC. - Blanchard, Olivier J., and Ben S. Bernanke. 2023. “What Caused the US Pandemic-Era Inflation?” NBER Working Paper 31417, National Bureau of Economic Research, Cambridge, MA. - Buono, Ines, and Sara Formai. 2018. “New Evidence on the Evolution of the Anchoring of Inflation Expectations.” Journal of Macroeconomics 57: 39–54. - Candia, Bernardo, Olivier Coibion, and Yuriy Gorodnichenko. 2023. “The Macroeconomic Expectations of Firms.” Handbook of Economic Expectations, eds. Rudiger Bachmann, Giorgio Topa, and Wilbert van der Klaaw, Chapter 11. Elsevier: London. - Capistrán, Carlos, and Manuel Ramos-Francia. 2010. “Does Inflation Targeting Affect the Dispersion of Inflation Expectations?” Journal of Money, Credit and Banking 42 (1): 113–34. - Coibion, Olivier, and Yuriy Gorodnichenko. 2012. “What Can Survey Forecasts Tell Us About Informational Rigidities?” Journal of Political Economy 120 (1): 116–59. - Coibion, Olivier, and Yuriy Gorodnichenko. 2015. “Information rigidity and the expectations formation process: A simple framework and new facts.” American Economic Review 105 (8): 2644–78. - Coibion, Olivier, Yuriy Gorodnichenko, and Rupal Kamdar. 2018. “The Formation of Expectations, Inflation, and the Phillips Curve.” Journal of Economic Literature 56 (4): 1447–91. - Coibion, Oliver, Yuriy Gorodnichenko, Saten Kumar, and Mathieu Pedemonte. 2020. “Inflation Expectations as a Policy Tool?” Journal of International Economics 124: 103297. - Demertzis, Maria, Massimiliano Marcellino, and Nicola Viegi. 2012. “A Credibility Proxy: Tracking US Monetary Developments.” The B.E. Journal of Macroeconomics 12 (1): 1–36. - Dizioli, Allan, and Hou Wang. 2023. “How Do Adaptive Learning Expectations Rationalize Stronger Monetary Policy Response in Brazil?” IMF Working Paper 2023/19, International Monetary Fund, Washington, DC. - Dovern, Jonas, Ulrich Fritsche, and Jiri Slacalek. 2012. “Disagreement among Forecasters in G7 Countries.” Review of Economics and Statistics 94 (4): 1081–96. - Ehrmann, Michael. 2015. “Targeting Inflation from Below: How Do Inflation Expectations Behave?” International Journal of Central Banking 11 (4): 213–49. - Erceg, Andrew T., and Christopher J. Levine. 2003. "Imperfect Credibility and Inflation Persistence." Journal of Monetary Economics, 50 (4): 915–44. - Farhi, Emmanuel, and Iván Werning. 2019. “Monetary Policy, Bounded Rationality, and Incomplete Markets.” American Economic Review 109 (11): 3887–928. - Fuhrer, Jeffrey. 2017. “Expectations as a Source of Macroeconomic Persistence: Evidence from Survey Expectations in a Dynamic Macro Model.” Journal of Monetary Economics 86: 22–35. - Galí, Jordi, Frank Smets, and Rafael Wouters. 2012. “Unemployment in an Estimated New Keynesian Model.” NBER Macroeconomics Annual 26: 329–360. - Hassan, Tarek A., Stephan Hollander, Laurence van Lent, Ahmed Tahoun. 2019. “Firm-Level Political Risk: Measurement and Effects.” Quarterly Journal of Economics 134 (4): 2135–202. - Hassan, Tarek A., Stephan Hollander, Laurence van Lent, Markus Schwedeler, Ahmed Tahoun. 2022. “Firm-Level Exposure to Epidemic Diseases: Covid-19, SARS, and H1N1.” NBER Working Paper 26971, National Bureau of Economic Research, Cambridge, MA. - Kumar, Saten, Hassan Afrouzi, Olivier Coibion, and Yuriy Gorodnichenko. 2015. “Inflation Targeting Does Not Anchor Inflation Expectations: Evidence from Firms in New Zealand.” Brookings Papers on Economic Activity 46: 151–225. - Lovell, Michael C. 1986. “Tests of the Rational Expectations Hypothesis.” American Economic Review 76 (1): 110–24. - Mankiw, N. Gregory, and Ricardo Reis. 2002. “Sticky Information versus Sticky Prices: A Proposal to Replace the New Keynesian Phillips Curve.” Quarterly Journal of Economics, 117 (4): 1295–328. - Mavroeidis, Sophocles, Mikkel Plagborg-Møller, and James H. Stock. 2014. “Empirical Evidence on Inflation Expectations in the New Keynesian Phillips Curve.” Journal of Economic Literature 52 (1): 124–88. - McLeay, Michael, and Silvana Tenreyro. 2020. “Optimal Inflation and the Identification of the Phillips Curve.” NBER Macroeconomics Annual vol. 34, edited by Martin S. Eichenbaum, Erik Hurst, and Jonathan Parker, Chapter 4. University of Chicago Press: Chicago, IL. - Musy, Olivier. 2021. “A New Keynesian Phillips Curve with Staggered Contracts and Indexation.” Economics Bulletin 41 (1): 60–65. - Sims, Christopher A. 2003. “Implications of Rational Inattention.” Journal of Monetary Economics 50 (3): 665–90. - Slobodyan, Sergey, and Raf Wouters. 2012a. “Learning in a Medium-Scale DSGE Model with Expectations Based on Small Forecasting Models.” American Economic Journal: Macroeconomics 4 (2): 65–101. - Slobodyan, Sergey, and Raf Wouters. 2012b. “Learning in an Estimated Medium-Scale DSGE Model.” Journal of Economic Dynamics and Control 36: 22–46. - Unsal, Filiz D., Chris Papageorgiou, and Hendre Garbers. 2022. “Monetary Policy Framework: An Index and New Evidence.” IMF Working Paper 2022/022, International Monetary Fund, Washington, DC. - Woodford, Michael. 2003. “Imperfect Common Knowledge and the Effects of Monetary Policy.” In Knowledge, Information, and Expectations in Modern Macroeconomics: In Honor of Edmund S. Phelps, edited by Philippe Aghion, Roman Frydman, Joseph Stiglitz, and Michael Woodford, 25–58. Princeton University Press: Princeton, NJ. *Source: CHAPTER 2 MANAGING EXPECTATIONS: INFLATION AND MONETARY POLICY (PDF).* --- _Source: https://www.imf.org/-/media/files/publications/weo/2023/october/english/ch2onlineannex.pdf_