forecasting inflation
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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. - PowerPoint PPT PresentationTRANSCRIPT
Jon Faust and Jonathan Wright
Forecasting Inflation
A horse-race of forecasting methods for US inflationConditional forecasts
Market-based forecasts
Aggregates and disaggregates
Principle 1Econometric models v. subjective forecasts
Econometricians come second
Principle 2Good forecasts have time-varying local mean
US Inflation (q/q annualized)
Shifting inflation trendsConsidered 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)
Inflation forecasting in gap form
Think of inflation as t t tg
1t t t is inflation gap---stationarytg
Shifting inflation trendsCan be modeled econometrically
UCSV (Stock and Watson (2007))Exponential smoothing
Blue Chip does a five-to-ten-year-ahead forecast each March and OctoberSince 1984Covers GDP deflator and CPI inflation and other series
Shifting Inflation Trends: Blue Chip Surveys v. Econometrics
Principle 3Good forecasts start with good nowcasts
Judgmental forecasts have a particular advantage in predicting the current quarter
Can be used as a “jumping off” point
An amazingly good benchmark
Nowcast
Steady State
Principle 4
Heavy Handedness HelpsBest do lots of shrinkage, very informative priors etc.
Lots of Inflation ForecastsDirect AR in inflationIterated AR in inflation (AR(p) for inflation)Phillips CurveRandom Walk and RW-AOUCSVTVP-VAR (Primiceri (2005))Fixed ρ forecast (AR(1) with coefficient of 0.46)Phillips Curve in GAP formPhillips Curve in GAP form with time-varying NAIRUTerm Structure forecast
VAR in Nelson-Siegel factors, unemployment & inflation gapEWA, BMA and FAVAR (using 77-variable dataset)DSGE model (Smets and Wouters (2007))Judgmental forecasts (Blue Chip, SPF, Greenbook)
The forecasting exerciseReal-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
PGDP Inflation RMSPEsRelative to fixed ρ benchmark
h=0 h=1 h=2 h=3 h=4 h=8
Direct AR 1.05 1.00 0.96 1.04 1.09 1.32
Iterated AR 1.05 1.02 1.01 1.18 1.25 1.52
Phillips Curve 1.06 1.01 0.98 1.07 1.13 1.39
Random Walk 1.19 1.15 1.08 1.03 1.04 1.18
RW-AO 0.95 0.89 0.89 0.91 0.93 1.04
UCSV 0.98 0.96 0.91 0.90 0.93 1.06
AR-GAP 1.03 0.96 0.94 1.01 1.05 1.18
PC-GAP 1.03 1.00 1.00 1.08 1.14 1.33
PCTVN-GAP 1.03 0.99 0.99 1.07 1.13 1.29
Term Structure VAR 1.01 0.93 0.90 0.91 0.93 0.94
…. more relative RMSPEs
h=0 h=1 h=2 h=3 h=4 h=8
TVP-VAR 0.99 0.94 0.93 0.91 0.94 1.08
EWA 1.01 0.93 0.91 0.97 1.01 1.14
BMA 1.00 0.91 0.88 0.96 1.02 1.10
FAVAR 1.01 1.00 1.02 1.06 1.12 1.25
DSGE 1.06 1.02 1.06 1.08 1.06 1.15
DSGE-GAP 1.02 0.95 0.97 0.98 0.96 1.03
Blue Chip 0.81 0.84 0.86 0.90 0.94
SPF 0.82 0.83 0.85 0.87 0.90
Greenbook 0.80 0.80 0.78 0.77 0.79
Nowcast+fixed ρ 0.81 0.94 0.97 1.00 1.00 1.00
Forecasts with quarter t jumping-offRMSPEs Relative to Nowcast + fixed ρ
h=0 h=1 h=2 h=3 h=4 h=8
Random Walk 1.00 0.93 0.86 0.91 0.93 1.04
UCSV 1.00 0.95 0.89 0.89 0.91 1.03
AR-GAP 1.00 0.98 0.96 0.99 1.05 1.18
PC-GAP 1.00 0.99 1.00 1.05 1.12 1.31
PCTVN-GAP 1.00 0.99 1.00 1.04 1.12 1.29
Term Structure VAR 1.00 0.93 0.91 0.91 0.93 0.93
DSGE 1.00 0.88 0.92 1.01 1.01 1.12
DSGE-GAP 1.00 0.88 0.89 0.96 0.96 1.05
BC 1.00 0.90 0.89 0.90 0.94
Correlation matrix of the forecasts
AR-GAP PC-GAP VAR EWA BMA BC SPF
AR-GAP 1.00
PC-GAP 0.88 1.00
TS VAR 0.85 0.94 1.00
EWA 0.99 0.91 0.87 1.00
BMA 0.89 0.91 0.86 0.93 1.00
BC 0.91 0.84 0.88 0.91 0.85 1.00
SPF 0.90 0.84 0.87 0.90 0.84 0.98 1.00
DSGE 0.15 0.22 0.15 0.18 0.17 0.01 0.02
PGDP: forecasts and actuals
1985 1990 1995 2000 2005 2010-1
0
1
2
3
4
5
6
AR-GAP
DSGE
Actuals
Comments on DSGE Models
DSGE Models give competitive forecastsOften 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
PGDP: forecasts and actuals
Conditional forecasts
Normally we ask is forecast A better than B on average
Could ask is forecast A better than BConditional 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
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
Conditional Forecasts
The two circumstances under which inflation is a little more forecastable are:When unemployment is highWhen forecast is made for periods in 3 years after troughs
PGDP Inflation Relative RMSPEs Conditional on high unemployment
h=0 h=1 h=2 h=3 h=4 h=8
Direct AR 1.10 1.04 1.02 1.11 1.18 1.21
Iterated AR 1.10 1.07 1.10 1.28 1.34 1.42
Random Walk 1.25 1.26 1.25 1.06 1.14 1.18
RW-AO 0.95 0.95 0.98 0.96 0.93 1.04
UCSV 0.98 1.05 0.98 0.93 0.96 1.03
Fixed ρ 1.07 0.99 0.97 1.03 1.07 1.15
PC-GAP 1.05 0.94 0.92 0.98 0.97 1.05
PC-GAP TV-NAIRU 1.04 0.93 0.89 0.93 0.91 1.02
Term Structure VAR 1.09 0.97 0.91 0.80 0.78 0.92
PGDP Inflation Relative RMSPEs Conditional on high unemployment
h=0 h=1 h=2 h=3 h=4 h=8
TVP-VAR 0.96 0.94 1.05 0.99 0.95 1.08
EWA 1.04 0.89 0.85 0.92 0.96 1.06
BMA 1.01 0.83 0.80 0.91 0.95 0.95
FAVAR 1.04 1.00 0.99 0.90 0.99 1.20
DSGE 1.07 1.12 1.02 0.87 0.75 0.66
DSGE-GAP 1.05 1.05 0.96 0.84 0.71 0.84
Blue Chip 0.75 0.76 0.79 0.83 0.87
SPF 0.76 0.73 0.73 0.78 0.81
Greenbook 0.61 0.74 0.81 0.77 0.70
Nowcast+fixed ρ 0.75 0.90 0.96 1.00 1.00 1.00
Bottom lineI can beat (or do as well as) best econometric inflation
forecasts usingNo econometricsNo formalized economicsNo information at all directly regarding the forecast period
in question
Subjective forecasts still have some incremental predictive power
Is this a surprise?
If CB is doing it’s job, maybe notEspecially at longer horizons
Market based inflation forecastsSpread 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
TIPS Inflation Compensation
TIPS Inflation Compensation
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
( )t t h tE y y
2( )t h tVar y y h
Volatility of changes in 5-10 year inflation compensation
Horizon Standard Deviation (bps) Variance Ratio Test
One Day 5.0
One Month 21.3 -1.26
Three Months 27.3 -2.22**
Six Months 33.6 -2.01**
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
Inflation swapsBets 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
TIPS and Inflation Swaps
Short-term inflation swaps
Ten-year inflation density June 2010(From inflation floors/caps under Q)
-2 -1 0 1 2 3 4 5 60
5
10
15
20
25
30
35
40
45
2-year density forecasts from UCSV model
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))
Horse-race for forecasting headline CPI
Fit an AR-GAP to headline CPI
Fit an AR-GAP to core, food and energy CPIAggregate 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))
RMSPEs for forecasting headline CPI
h=0 h=1 h=2 h=3 h=4 h=8
AR on Aggregates 2.70 2.71 2.75 2.86 2.82 2.89
AR on disaggregates 2.56 2.60 2.63 2.75 2.81 2.85
-Impose Zeros on Food & Energy 2.50 2.54 2.59 2.68 2.70 2.71
-Impose All Params 2.47 2.48 2.49 2.52 2.53 2.47
Hendry & Hubrich 2.75 2.88 2.71 2.76 2.77 2.80
The Moral: Heavy Handedness Helps
Core v. headline and forecastingSuppose 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 CPIAssessed as a forecast of headline CPI
Relative RMSPEs of “hybrid” forecasts
h=0 h=1 h=2 h=3 h=4 h=8
Direct AR 0.89 0.89 0.87 0.87 0.95 0.95
Recursive AR 0.89 0.86 0.96 0.95 0.97 0.99
PC 0.87 0.87 0.86 0.86 0.94 0.96
Random Walk 0.73 0.70 0.76 0.73 0.75 0.82
AR-GAP 0.93 0.94 0.95 0.96 1.01 0.99
PC-GAP 0.92 0.94 0.95 0.97 1.00 0.98
PCTVN-GAP 0.91 0.93 0.95 0.97 1.00 0.99
Term Structure VAR
0.93 0.96 0.97 0.97 0.99 1.01
EWA 0.92 0.93 0.94 0.96 1.00 0.99
BMA 0.91 0.89 0.92 0.95 1.00 0.99
FAVAR 0.92 0.92 0.98 0.98 0.98 0.99
Conclusions
Inflation forecasting is hard
Judgment is a tough benchmarkNot far from a “glide path” from nowcast to steady stateAlmost a “Meese-Rogoff” style result
Heavy shrinkage is needed to have any chance for models to be in the ballpark of judgmental forecasts