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Forecasting Inflation

Forecasting Inflation. Jon Faust and Jonathan Wright. Forecasting Inflation. A horse-race of forecasting methods for US inflation Conditional forecasts Market-based forecasts Aggregates and disaggregates. Principle 1. Econometric models v. subjective forecasts Econometricians come second.

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Forecasting Inflation

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  1. Forecasting Inflation Jon Faust and Jonathan Wright

  2. Forecasting Inflation • A horse-race of forecasting methods for US inflation • Conditional forecasts • Market-based forecasts • Aggregates and disaggregates

  3. Principle 1 • Econometric models v. subjective forecasts • Econometricians come second

  4. Principle 2 • Good forecasts have time-varying local mean

  5. US Inflation (q/q annualized)

  6. Shifting inflation trends • Considered in many papers • Kozicki and Tinsley (2001, 2005) • Gürkaynak, Sack and Swanson (2005) • Cogley and Sargent (2005) • Cogley and Sbordone (2008) • de Graeve, Emiris and Wouters (2008) • Cogley, Primiceri and Sargent (2010) • Stock and Watson (2010) • Clark (2011) • Dotsey, Fujitsu and Stark (2011)

  7. Inflation forecasting in gap form • Think of inflation as

  8. Shifting inflation trends • Can be modeled econometrically • UCSV (Stock and Watson (2007)) • Exponential smoothing • Blue Chip does a five-to-ten-year-ahead forecast each March and October • Since 1984 • Covers GDP deflator and CPI inflation and other series

  9. Shifting Inflation Trends: Blue Chip Surveys v. Econometrics

  10. Principle 3 • Good forecasts start with good nowcasts • Judgmental forecasts have a particular advantage in predicting the current quarter • Can be used as a “jumping off” point

  11. An amazingly good benchmark Nowcast Steady State

  12. Principle 4 • Heavy Handedness Helps • Best do lots of shrinkage, very informative priors etc.

  13. Lots of Inflation Forecasts • Direct AR in inflation • Iterated AR in inflation (AR(p) for inflation) • Phillips Curve • Random Walk and RW-AO • UCSV • TVP-VAR (Primiceri (2005)) • Fixed ρ forecast (AR(1) with coefficient of 0.46) • Phillips Curve in GAP form • Phillips Curve in GAP form with time-varying NAIRU • Term Structure forecast • VAR in Nelson-Siegel factors, unemployment & inflation gap • EWA, BMA and FAVAR (using 77-variable dataset) • DSGE model (Smets and Wouters (2007)) • Judgmental forecasts (Blue Chip, SPF, Greenbook)

  14. The forecasting exercise • Real-time recursive forecasting in mid month of each quarter • FRB-Philadelphia real-time dataset • Large dataset is not real-time • Judgmental forecasts are “most recent available” • First forecast 1985Q1; last forecast 2010Q4 • Actuals are data observed 2 quarters later

  15. PGDP Inflation RMSPEsRelative to fixed ρ benchmark

  16. …. more relative RMSPEs

  17. Forecasts with quarter t jumping-offRMSPEs Relative to Nowcast + fixed ρ

  18. Correlation matrix of the forecasts

  19. PGDP: forecasts and actuals

  20. Comments on DSGE Models • DSGE Models give competitive forecasts • Often viewed as “validation” • But two caveats: • 1. Don’t use a “real-time” prior. • 2. Maybe DSGE models are just heavy-handed rather than “right” in an economic sense

  21. PGDP: forecasts and actuals

  22. Conditional forecasts • Normally we ask is forecast A better than B on average • Could ask is forecast A better than B • Conditional on something known at time forecast made • Sign of model mis-specification • Conditional on something in the future • Loss function could penalize misses most at some times

  23. Conditional Forecasts • Evaluate RMSPE of inflation forecasts conditional on: • Forecasts made when unemployment is high • Stock and Watson (2010) • Forecasts made when inflation is low • Ball, Mankiw and Romer (1988), Meier (2010) • Forecasts made for periods in 3 years before peaks • Forecasts made for periods in NBER recessions • Forecasts made for periods in 3 years after troughs

  24. Conditional Forecasts • The two circumstances under which inflation is a little more forecastable are: • When unemployment is high • When forecast is made for periods in 3 years after troughs

  25. PGDP Inflation Relative RMSPEs Conditional on high unemployment

  26. PGDP Inflation Relative RMSPEs Conditional on high unemployment

  27. Bottom line • I can beat (or do as well as) best econometric inflation forecasts using • No econometrics • No formalized economics • No information at all directly regarding the forecast period in question • Subjective forecasts still have some incremental predictive power

  28. Is this a surprise? • If CB is doing it’s job, maybe not • Especially at longer horizons

  29. Market based inflation forecasts • Spread between nominal and TIPS bond yields • Widely regarded as inflation “expectations” • Part of the motivation for TIPS issuance (Greenspan (1992)) • But affected by inflation risk premia & liquidity premia

  30. TIPS Inflation Compensation

  31. TIPS Inflation Compensation

  32. Far-Forward Inflation Compensation • Distant-horizon forward inflation compensation is often taken as a measure of long-run inflation expectations • Any measure of long-run inflation expectations must be a martingale • Any martingale has the property that • Testable by a variance ratio test

  33. Volatility of changes in 5-10 year inflation compensation

  34. Comments on CB interpretation of Inflation Compensation • 1. Clearly not literal inflation expectations • 2. Not clear whether CB should care about inflation expectations under P or Q measure • 3. Certain time-inconsistency in Fed interpretation of inflation compensation

  35. Inflation swaps • Bets where parties exchange difference between realized inflation rate and a pre-agreed rate on a notional principle • Under risk-neutrality pre-agreed rate is expected inflation

  36. TIPS and Inflation Swaps

  37. Short-term inflation swaps

  38. Ten-year inflation density June 2010(From inflation floors/caps under Q)

  39. 2-year density forecasts from UCSV model

  40. Predict Aggregates or Disaggregates? • In theory, predicting disaggregates is optimal if parameters are known • But parameter estimation error can wipe out the gains • In practice, the two are about equivalent (Hubrich (2005))

  41. Horse-race for forecasting headline CPI • Fit an AR-GAP to headline CPI • Fit an AR-GAP to core, food and energy CPI • Aggregate using real-time CPI weights • Same but impose that the AR coefficients for food and energy is 0 • Same but impose that the AR coefficient on core is 0.46 • Project headline CPI on disaggregates • Hendry & Hubrich (2010))

  42. RMSPEs for forecasting headline CPI • The Moral: Heavy Handedness Helps

  43. Core v. headline and forecasting • Suppose headline CPI = core CPI plus unforecastable noise • Should fit model to core CPI even if headline is end-objective • Did an exercise of forecasting core CPI • Assessed as a forecast of headline CPI

  44. Relative RMSPEs of “hybrid” forecasts

  45. Conclusions • Inflation forecasting is hard • Judgment is a tough benchmark • Not far from a “glide path” from nowcast to steady state • Almost a “Meese-Rogoff” style result • Heavy shrinkage is needed to have any chance for models to be in the ballpark of judgmental forecasts

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