## 14. Model generated data implies that the inflation-slack curve is steeper under RE if inflation is driven by exchange rate shock. ## Source details **Canonical URL:** [14. Model generated data implies that the inflation-slack curve is steeper under RE if inflation is driven by exchange rate shock.](https://www.imf.org/-/media/files/publications/wp/2023/english/wpiea2023021-print-pdf.pdf) ## Other formats - [Markdown version](/-/media/files/publications/wp/2023/english/wpiea2023021-print-pdf.pdf.md) - [Structured JSON version](/-/media/files/publications/wp/2023/english/wpiea2023021-print-pdf.pdf.json) --- ### Key empirical patterns and context - After the Great Financial Crisis, low inflation and well-anchored expectations ("the great moderation") were common; the pandemic produced a surge in global inflation not seen since the 1980s. - Cross-country database covers 31 advanced economies and 14 emerging economies going back to the 1960s. - Two empirical objects analyzed: - Degree to which 12-month ahead inflation expectations respond to realized inflation (pass-through measure, focus on coefficient γ1). - Relationship between realized inflation and the unemployment gap (unemployment gap estimated using an HP filter with a parameter of 1,600). - Cross-country correlations: - Countries with higher inflation pass-through to expectations exhibit, on average, more responsiveness of inflation to economic slack. - Countries with more persistent inflation are associated with a steeper inflation-unemployment gap relationship. - Identification algorithm for highly inflationary episodes: 1. Quarters where inflation deviations from the five-year moving average correspond to a z-score above 1.96 of deviations observed during the preceding five years. 2. Among consecutive inflationary quarters, the highest inflation quarter is the local inflation peak. 3. When two or more peaks occur within 8-quarters, the highest quarter is taken as the sole peak. 4. A highly inflationary episode covers 8-quarters before and after a peak. - United States highly inflationary peaks identified: 1966Q4, 1970Q1, 1974Q4, 1980Q2, 2008Q3, and 2021Q4 (US data from 1960). - Stylized within-country finding: - For advanced economies, the inflation-unemployment gap slope appears steeper during highly inflationary episodes. - For emerging market economies, the pattern is heterogeneous; when large exchange-rate depreciations (external shocks) drive inflation, the inflation-unemployment relationship can be flatter during highly inflationary episodes. ### Model environment and estimation details - Structural environment: baseline New Keynesian model (Galí, Smets, and Wouters(2012)) with: - Union that decides wages and household labor supply decisions. - Calvo-style frictions: fraction 1−τ of firms can optimize wages each period; fraction 1−θ of firms can re-optimize prices each period and fraction θ index to past inflation. - IS curve (linearized): ˆy_t = E_t[ˆy_{t+1} − (ˆi_t − ˆπ_{t+1})] + shk^y_t, with shk^y_t = ρ_y shk^y_{t+1} + ε^y_t (AR(1)). - Wage Phillips curve and NK Phillips curve retained in original form. - Monetary policy rule with interest rate smoothing: ˆi_t = ρˆi_{t−1} + (1−ρ)[ρ_π ˆπ_{t+1} + ρ_y y_t] + ε_{i,t}. - Expectation formation variants: - Rational Expectations (RE): full-information conditional expectations. - Adaptive Learning (AL): agents use a Perceived Law of Motion (PLM); best-performing PLM is a univariate AR(2) with constant and two lags. Learning updates use a Kalman filter; PLM leads to time-dependent Actual Law of Motion (ALM): [y_t ω_t]' = α_t + T_t [y_{t−1} ω_{t−1}]' + R_t ε_t. - Estimation sample and variables: - Quarterly data from 2008Q1 to 2019Q4 for Mexico and the US. - Variables: output gap, real wage gap (composition-constant real wage adjustments), annualized quarterly price inflation deviation from target (US: core PCE; Mexico: core CPI), real exchange rate gap, and policy rate. - Filters considered: HP filter (chosen for main results) and linear filter. HP filter parameter for unemployment gap: 1,600. - Estimation method: Bayesian likelihood methods with standard priors as in Smets and Wouters(2007); some parameters calibrated. ### Model fit and forecast performance (exact reported figures) - In-sample log marginal likelihood (Table 1): - Linear Filter: RE −391.09 ; AL −341.38 - HP Filter: RE −342.81 ; AL −334.14 - Out-of-sample forecast performance (selected normalized RMSE figures, HP Filter): - 1-quarter ahead RMSE: RE 0.4 ; AL 0.6 - 4-quarter ahead RMSE: RE 2.6 ; AL 2.1 - 8-quarter ahead RMSE: RE 2.6 ; AL 2.2 - Open macro model in-sample log marginal likelihood (Table 3): - REAL Linear Filter: RE −459.24 ; AL −428.20 - Mexican out-of-sample RMSEs (Table 4, exact matrix style entries preserved in source): - 1-quarter ahead RMSE: 0.203 0.380 0.109 0.071 - 4-quarter ahead RMSE: 3.08 2.51 0.256 0.479 - 8-quarter ahead RMSE: 7.07 4.04 1.12 0.434 - Interpretation: - AL model outperforms RE for real wage gap at all horizons and for 4-quarters ahead inflation; RE performs better for near-term (1-quarter ahead) inflation forecasting. - AL does much better forecasting output gap at longer horizons; for inflation, RE has better 4-quarter ahead performance but is worse at the next quarter and substantially worse at the 8-quarter ahead horizon. ### Model simulation results — inflation-slack relationship - Simulation experiment: cost-push inflation shock that takes inflation to levels comparable to recent US experience; simulations run under both RE and AL expectations. - Main simulated pattern: - If an inflationary episode is generated by cost-push shocks, the slope of the inflation-slack curve is steeper under adaptive expectations (AL) than under rational expectations (RE). - When inflation is close to target, the two models have small deviations; as inflation deviates from target, inflation increases faster under AL because inflation expectations deviate more from target under AL. - The steeper inflation-slack curve under AL is driven by expectation formation, not by a change in how slack directly impacts inflation. - Open-economy caveat: - A standard small open-economy model can generate the opposite pattern if the inflationary episode is generated by exchange rate shocks: following a large currency depreciation, the inflation-unemployment relationship can be flatter during a highly inflationary episode (implying a steeper cost of bringing down inflation in such situations). This helps explain heterogeneity in emerging markets. ### Conditional forecasting scenarios and inertia under AL (exact scenario assumptions and outcomes) - Scenario assumptions for US conditional forecasts: 1. Inflation shocks explain most of current inflation and die at a root of 0.8 per quarter with no new shocks to inflation. 2. Interest rates are exogenously at a level consistent with market expectations. - Scenario outcomes (exact reported magnitudes): - Under RE (dashed red lines in source Figure 8): output gap converges to zero and inflation comes down to the Federal Reserve target of 2 percent. - Under fully adaptive expectations (blue lines): near-term acceleration in wage and price inflation; price inflation remains 1.5 percentage points over target even 12 quarters later despite no further shocks assumed. - Under the estimated AL model (black line): inflation, wage growth, and output gap paths lie between RE and fully adaptive cases; after eight quarters inflation is still about a half-percentage point above target. - Analytical expression (NK Phillips curve in expectation form preserved from source): - E_t[π_t] = κ_p E_t[ˆw_t] + (1−β) π_{t−1} + β E_t[π_{t+1}]. - Fully adaptive example: E_t[π_{t+1}] = β_{1,t} π_{t−1} + β_{2,t} π_{t−2}; fully adaptive case β_{1,t}=1, β_{2,t}=0 implies π_t − π_{t−1} = κ_p ˆw_t + ε_{π,t}. - Under RE (β<1) the speed of inflation decline after a shock is influenced by β; ∂Δπ_t / ∂β = E_t[π_{t+1}] − π_{t−1}. ### Optimal monetary policy under adaptive learning (AL) - Welfare loss function minimized by the central bank (equation 27 preserved): minˆit Et Σ′t=0 훽t [0.75(ˆit − ˆit−1) + ˆy2t + ˆπ2t], with equal weights for output gap ˆy and inflation deviation ˆπ and a role for interest rate smoothing. - Three channels through which policy influences inflation: - Demand channel: tighter policy reduces output gap and inflation. - Expectations channel via AR(2): lowering current inflation reduces next period inflation expectations. - Learning channel: policy influences households’ learning process (coefficients in AR(2)) by generating surprises that update belief formation. - Optimal policy prescription with adaptive learning: - Front-load tightening and then ease. - Quantified deviations from previous path (exact reported magnitudes): - Policy tighter by 150 basis points in 2022Q3. - Policy tighter by 30 basis points in 2022Q4. - By end-2024, policy rate is 40 basis points lower in the optimal path compared to the previous path. - Assumptions behind these quantifications: central bank has full knowledge of current and future shocks and full knowledge of how actions impact expectations; the inflation shock dissipates with a half-life of 2.5 quarters. - Implication: AL expectations are more inertial and take longer to return to target once they drift away; more aggressive policy actions (respond sooner, more strongly, then ease) are needed to re-anchor inflation expectations. ### Open-economy extension and exchange rate shocks - Uncovered interest parity introduced for de-trended real exchange rate z (equation 28 preserved): zt = Et[zt+1] − [ˆit − ˆπt+1 − (ˆiFt − ˆπFt+1)] + εzt; an increase in z means depreciation. - Domestic IS curve for small open economy includes foreign spillovers (equation 29 preserved): ˆxt = φx(Et[ˆxt+1]) − φr(ˆit − ˆπt+1) + φz zt + φXFEt[ˆxFt+1] + shkx. - Domestic Phillips curve expanded to include exchange rate (equation 30 preserved): πt = κp ˆwt + (1−β)πt−1 + βπt+1 + λzt + εpi,t. - Re-estimation using US and Mexico data 2008Q1 to 2019Q4: - US open-economy shock decomposition: inflation shock decomposition almost identical to closed economy; interest rate decomposition similar except for positive contribution of inflation in 2021Q4. - US inflation and monetary policy shocks are the largest contributors to recent real exchange rate movements of the Mexican Peso. - Mexico households' expectations are more backward-looking than US households: Mexico households put twice as much weight on past inflation to explain future inflation compared to US households. - Coefficient reflecting mean expected inflation was zero (households expected inflation at central bank target). - Exchange rate depreciation experiment: - Simulated shock: exchange rate depreciates the Peso by 50% in one quarter. - Model-generated data produces an inflation-slack curve with a higher slope in the RE model under an exchange rate shock. - The relative slope of the inflation-slack curve depends on which shock generates inflation; a shift in expectation formation (RE vs AL) is sufficient to change the observed slope without assuming non-linearity in how slack affects inflation. ### Policy implications and conclusions - Expectations formation matters for inflation dynamics, the slope of the inflation-slack curve, and the cost of disinflation. - Shifts from rational expectations toward more adaptive learning can rationalize steeper inflation-slack curves observed during high-inflation episodes. - When expectations are adaptive, disinflation can be less costly than implied by Phillips curves estimated during normal times that ignore expectation-formation differences. - In environments with adaptive learning and a positive output gap plus rising inflation, optimal policy should tighten sooner and more strongly (front-load tightening) and then ease to re-anchor expectations and lower disinflation costs. - In small open economies experiencing exchange-rate-driven inflationary episodes, the inflation-slack trade-off can be less steep during the episode (implying higher costs of disinflation) because exchange-rate shocks transmit directly to prices. *Source — text and figures extracted from the supplied IMF working paper content unit.* ### References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 ### References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 ### Appendices - A. Open economy model fit. . . . . . . . . . . . . . . . . . . . . . . . . . 34 ### Tables - 1. In-Sample Forecast Performance for RE and AL Models. . . . . . . . . . . . . . . 18 - 2. Out-of-Sample Forecast Performance for RE and AL Models. . . . . . . . . . . 19 - 3. In-Sample Model Performance for RE and AL in Open Macro Model. . . . . . 34 - 4. Out-of-Sample Forecast Performance for RE and AL Models. . . . . . . 34 ### Figures - 1. Relationship between inflation pass-through and the inflation-unemployment gap slope. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 - 2. Highly inflationary cases: United States. . . . . . . . . . . . . . . . . . . . . . 11 - 3. Highly inflationary cases vs other: United States. . . . . . . . . . . . . . . . . 12 - 4. Highly inflationary cases: Advanced Economies vs Emerging Markets. . . . . . 12 - 5. Highly inflationary cases: Mexico and Brazil. . . . . . . . . . . . . . . . . . . 13 - 6. Highly inflationary cases vs other: Mexico and Brazil. . . . . . . . . . . . . . 13 - 7. Model generated data implies that the inflation-slack curve is steeper under adaptive expectations. . . . . . . . . . . . . . . . . . . . . . . . . . 21 - 8. Inflation is stickier when expectations are adaptive learning. . . . . . . . . . . . . . . . . . . . . . . 22 - 9. Inflation converges more quickly to target with more forward-looking inflation in the RE model. . . . . . . . . . . . . . . . . . . . . . . . . 24 - 10. The central bank should front-load tightening and then ease. . . . . . . . . . . . . . . . . . . . . . 26 - 11. US Shock decomposition in open macro model. . . . . . . . . . . . . . . . . . . 28 - 12. Real exchange rate shock decomposition in open macro model. . . . . . . . . . . . . 28 - 13. Expectations in Mexico appear more backward-looking than in the US. . . . . . . . . . . . . . . . . 28 *Source: wpiea2023021-print-pdf - References. . . . . . . . . . . . . . . . . . . . . . 32* ### 14. Model generated data implies that the inflation-slack curve is steeper under RE if ### 14. Model generated data implies that the inflation-slack curve is steeper under RE if inflation is driven by exchange rate shock. ### Key empirical patterns and context - After the Great Financial Crisis, low inflation and well-anchored expectations ("the great moderation") were common; the pandemic produced a surge in global inflation not seen since the 1980s. - Cross-country database covers 31 advanced economies and 14 emerging economies going back to the 1960s (advanced and emerging economy ISO lists provided in source). - Two empirical objects analyzed: - Degree to which 12-month ahead inflation expectations respond to realized inflation (pass-through measure, focus on coefficient γ1). - Relationship between realized inflation and the unemployment gap (unemployment gap estimated using an HP filter with a parameter of 1,600). - Cross-country correlations: - Countries with higher inflation pass-through to expectations exhibit, on average, more responsiveness of inflation to economic slack. - Countries with more persistent inflation are associated with a steeper inflation-unemployment gap relationship. - Identification of highly inflationary episodes (algorithm): 1. Quarters where inflation deviations from the five-year moving average correspond to a z-score above 1.96 of deviations observed during the preceding five years. 2. Among consecutive inflationary quarters, the highest inflation quarter is the local inflation peak. 3. When two or more peaks occur within 8-quarters, the highest quarter is taken as the sole peak. 4. A highly inflationary episode covers 8-quarters before and after a peak. - United States highly inflationary peaks identified: 1966Q4, 1970Q1, 1974Q4, 1980Q2, 2008Q3, and 2021Q4 (US data from 1960). - Stylized within-country finding: - For advanced economies, the inflation-unemployment gap slope appears steeper during highly inflationary episodes. - For emerging market economies, the pattern is heterogeneous; when large exchange-rate depreciations (external shocks) drive inflation, the inflation-unemployment relationship can be flatter during highly inflationary episodes. ### Model environment and estimation details - Model based on Galí, Smets, and Wouters(2012) with: - Union that decides wages and household labor supply decisions. - Calvo-style frictions for wage and price setting: fraction 1−τ of firms can optimize wages each period; fraction 1−θ of firms can re-optimize prices each period and fraction θ index to past inflation. - IS curve after linearization: ˆy_t = E_t[ˆy_{t+1} − (ˆi_t − ˆπ_{t+1})] + shk^y_t, with shk^y_t following an AR(1): shk^y_t = ρ_y shk^y_{t+1} + ε^y_t. - Wage Phillips curve and NK Phillips curve specified (equations retained in original form in source). - Monetary policy reaction function with interest rate smoothing: ˆi_t = ρˆi_{t−1} + (1−ρ)[ρ_π ˆπ_{t+1} + ρ_y y_t] + ε_{i,t}. - Expectation formation variants: - Rational Expectations (RE): agents use full-information conditional expectations. - Adaptive Learning (AL): agents use a simple statistical model / Perceived Law of Motion (PLM); best-performing PLM is a univariate AR(2) with constant and two lags. Learning updates use a Kalman filter; PLM leads to time-dependent Actual Law of Motion (ALM): [y_t ω_t]' = α_t + T_t [y_{t−1} ω_{t−1}]' + R_t ε_t. - Estimation: - Quarterly data from 2008Q1 to 2019Q4 for Mexico and the US. - Variables: output gap, real wage gap (composition-constant real wage adjustments used following Howard, Rich, and Tracy(2022)), annualized quarterly price inflation deviation from target (US: core PCE; Mexico: core CPI), real exchange rate gap, and policy rate. - Filters considered: HP filter and linear filter; HP filter chosen for main results because better in-sample fit and out-of-sample forecast performance. - Estimation method: Bayesian likelihood methods with standard priors as in Smets and Wouters(2007); some parameters calibrated. ### Model fit and forecast performance (selected exact values from source) - HP filter parameter used for unemployment gap: 1,600. - In-sample log marginal likelihood (Table 1): - Linear Filter: RE −391.09 ; AL −341.38 - HP Filter: RE −342.81 ; AL −334.14 - Out-of-sample forecast performance (normalized RMSE comparisons reported in Table 2; selected figures shown in source): - HP Filter, 1-quarter ahead RMSE: RE 0.4 ; AL 0.6 (inflation and wage gap panels as in source tables) - HP Filter, 4-quarter ahead RMSE: RE 2.6 ; AL 2.1 - HP Filter, 8-quarter ahead RMSE: RE 2.6 ; AL 2.2 - Overall: AL model outperforms RE for real wage gap at all horizons and for 4-quarters ahead inflation; RE performs better for near-term (1-quarter ahead) inflation forecasting. ### Model simulation results — inflation-slack relationship - Simulation experiment: cost-push inflation shock that takes inflation to levels comparable to recent US experience; simulations run under both RE and AL expectations. - Main simulated pattern: - If an inflationary episode is generated by cost-push shocks, the slope of the inflation-slack curve is steeper under adaptive expectations (AL) than under rational expectations (RE). - The two models have small deviations when inflation is close to target; as inflation deviates from target, inflation increases faster under AL because inflation expectations deviate more from target under AL. - The steeper inflation-slack curve under AL is driven by how inflation expectations are formed, not by a change in how slack directly impacts inflation. - Open-economy caveat: - A standard small open-economy model can generate the opposite pattern if the inflationary episode is generated by exchange rate shocks: following a large currency depreciation, the inflation-unemployment relationship can be flatter during a highly inflationary episode (implying a steeper cost of bringing down inflation in such situations). This helps explain heterogeneity in emerging markets (e.g., Brazil vs Mexico examples in 2000s). ### Conditional forecasting scenarios and inertia under AL - Scenario assumptions for US conditional forecasts: 1. Inflation shocks explain most of current inflation and die at a root of 0.8 per quarter with no new shocks to inflation. 2. Interest rates are exogenously at a level consistent with market expectations. - Scenario outcomes (exact reported magnitudes): - Under RE (dashed red lines in source Figure 8): output gap converges to zero and inflation comes down to the Federal Reserve target of 2 percent. - Under fully adaptive expectations (blue lines): near-term acceleration in wage and price inflation; price inflation remains 1.5 percentage points over target even 12 quarters later despite no further shocks assumed. - Under the estimated AL model (black line): inflation, wage growth, and output gap paths lie between RE and fully adaptive cases; after eight quarters inflation is still about a half-percentage point above target. - Analytical insight (exact expressions from source): - NK Phillips curve in expectation form: E_t[π_t] = κ_p E_t[ˆw_t] + (1−β) π_{t−1} + β E_t[π_{t+1}]. (Equation numbers preserved in source.) - Fully adaptive specification example: E_t[π_{t+1}] = β_{1,t} π_{t−1} + β_{2,t} π_{t−2}; fully adaptive case β_{1,t}=1, β_{2,t}=0 implies π_t − π_{t−1} = κ_p ˆw_t + ε_{π,t}. - Under RE (β<1) the speed of inflation decline after a shock is influenced by β; ∂Δπ_t / ∂β = E_t[π_{t+1}] − π_{t−1}. ### Policy implications and optimal policy under learning - With adaptive learning and positive output gap plus rising inflation, optimal monetary policy implies an interest rate path that is steeper under AL than under RE: - AL expectations are more inertial and take longer to return to target once they drift away; more aggressive policy actions (respond sooner, more strongly, then ease) are needed to re-anchor inflation expectations. - If inflation increases substantially above target and expectations remain anchored, the disinflation cost would be substantially higher (i.e., a central bank that keeps credibility could face higher output costs), but if expectations are de-anchored the observed high inflation with modest output gap changes could reflect de-anchoring (and re-anchoring expectations can reduce disinflation costs). - In small open economies experiencing exchange-rate-driven inflationary episodes, the inflation-slack trade-off can be less steep during the episode (implying higher costs of disinflation) because exchange-rate shocks transmit directly to prices. *Italic: Source — text and figures extracted from the supplied IMF working paper content unit.* ### 0. That is, in the RE setting, the larger the coefficient on expected inflation, the faster infla- ### How Costly Will Reining in Inflation be? It Depends on How Rational We Are ### Expectations, inflation dynamics, and the role of real wages - In the RE setting, larger coefficient on expected inflation implies faster inflation decline compared to the AL model; when 훽=1 (pure forward looking expectations) the NK PC (equation 12) can be rewritten as a forward sum of the real wage gap (equation 26): 휋t = 휅p Σ′j=0 훽j Et[ˆwt+j] + 휀휋t. - Monetary policy is more powerful under forward-looking expectations because it can control future deviations of the wage gap and thus affect changes in inflation. - Real wage dynamics are critical to wage and price inflation evolution since wages determine marginal costs in the model; this modeling choice allows assessment of wage-price spiral likelihood and illustrates that wages can anchor inflation when cost-push shocks occur. - A negative real wage gap can help anchor inflation even with fully adaptive expectations; this contrasts with models where the Phillips curve includes only the output gap (e.g., Cochrane (2022)), which require a negative output gap to lower inflation. The model shows that a positive output gap and a negative real wage gap can coexist, allowing the central bank to anchor inflation. ### Optimal monetary policy under adaptive learning (AL) - Welfare loss function minimized by the central bank (equation 27): minˆit Et Σ′t=0 훽t [0.75(ˆit − ˆit−1) + ˆy2t + ˆπ2t], with equal weights for output gap ˆy and inflation deviation ˆπ and a role for interest rate smoothing. - Assumptions in simulations: central bank has full knowledge of current and future shocks and full knowledge of how actions impact expectations. - Three channels for monetary policy to influence inflation: - Standard demand channel: tighter policy reduces output gap and inflation. - Expectations channel via AR(2): lowering current inflation reduces next period inflation expectations. - Learning channel: policy influences households’ learning process (coefficients in AR(2)) by generating surprises that update belief formation. - Optimal policy prescription (with adaptive learning expectations): front-load tightening and then ease. Quantified deviations from previous path: - Policy tighter by 150 basis points in 2022Q3. - Policy tighter by 30 basis points in 2022Q4. - By end-2024, policy rate is 40 basis points lower in the optimal path compared to the previous path. - These results depend on full information by the central bank and that the inflation shock dissipates with a half-life of 2.5 quarters. - With the optimal policy, output gap and inflation converge faster to zero and target, respectively; monetary policy deviations influence inflation with effects growing over time. ### Open-economy extension and exchange rate shocks - Uncovered interest parity introduced for de-trended real exchange rate z (equation 28): zt = Et[zt+1] − [ˆit − ˆπt+1 − (ˆiFt − ˆπFt+1)] + εzt; an increase in z means depreciation. - Domestic IS curve for small open economy includes foreign spillovers (equation 29): ˆxt = φx(Et[ˆxt+1]) − φr(ˆit − ˆπt+1) + φz zt + φXFEt[ˆxFt+1] + shkx. - Domestic Phillips curve expanded to include exchange rate (equation 30): πt = κp ˆwt + (1−β)πt−1 + βπt+1 + λzt + εpi,t. - Re-estimation using US and Mexico data 2008Q1 to 2019Q4: - US open-economy shock decomposition: inflation shock decomposition almost identical to closed economy; interest rate decomposition similar except for positive contribution of inflation in 2021Q4. - US inflation and monetary policy shocks are the largest contributors to recent real exchange rate movements of the Mexican Peso. - Expectation formation differences across countries: - Mexico households' expectations are more backward-looking than US households: Mexico households put twice as much weight on past inflation to explain future inflation compared to US households. - Coefficient reflecting mean expected inflation was zero (households expected inflation at central bank target). - With backward-looking expectations in Mexico, a stronger monetary policy response is necessary following cost-push shocks. - Exchange rate depreciation experiment: - Simulated shock: exchange rate depreciates the Peso by 50% in one quarter. - Model-generated data produces an inflation-slack curve with a higher slope in the RE model under an exchange rate shock. - The relative slope of the inflation-slack curve depends on which shock generates inflation; a shift in expectation formation (RE vs AL) is sufficient to change the observed slope without assuming non-linearity in how slack affects inflation. ### Model fit and forecast performance - Appendix A reports improved model performance of AL relative to RE in the open macro model: - Table 3 (In-Sample Model Performance for RE and AL in Open Macro Model): Log marginal likelihoodREAL Linear Filter-459.24-428.20 - Out-of-sample forecast performance for Mexican variables (Table 4): AL generally better than RE, with specifics preserved as reported: - Output Gap / Inflation / Linear FilterREALREAL - 1-quarter ahead RMSE 0.203 0.380 0.109 0.071 - 4-quarter ahead RMSE 3.08 2.51 0.256 0.479 - 8-quarter ahead RMSE 7.07 4.04 1.12 0.434 - Interpretation: - AL model does much better forecasting output gap at longer horizons. - For inflation, RE has better 4-quarter ahead performance, but is worse at the next quarter and substantially worse at the 8-quarter ahead horizon. ### Policy implications and conclusions - Expectations formation matters for inflation dynamics, the slope of the inflation-slack curve, and the cost of disinflation. - Shifts from rational expectations toward more adaptive learning can rationalize steeper inflation-slack curves observed during high-inflation episodes. - When expectations are adaptive, disinflation can be less costly than implied by Phillips curves estimated during normal times that ignore expectation-formation differences. - Optimal monetary policy in environments with high inflation and a positive output gap under adaptive learning: tighten sooner and more strongly to influence the learning process and avoid high-inflation beliefs that raise disinflation costs. *How Costly Will Reining in Inflation be? It Depends on How Rational We Are — Working Paper No. WP/23/21* --- _Source: https://www.imf.org/-/media/files/publications/wp/2023/english/wpiea2023021-print-pdf.pdf_