Jon Faust and Jonathan Wright. Forecasting Inflation A horse-race of forecasting methods for US inflation Conditional forecasts Market-based forecasts

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


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


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

Documents

Jon Faust and Jonathan Wright. Forecasting Inflation A horse-race of forecasting methods for US inflation Conditional forecasts Market-based forecasts