revisions to pce inflation measures: implications for monetary policy

REVISIONS TO PCE INFLATION MEASURES: IMPLICATIONS FOR MONETARY POLICY

Dean CroushoreUniversity of Richmond

Visiting Scholar, Federal Reserve Bank of Philadelphia

October 2007

Motivation

• In 2000, Fed switched main variable for inflation to PCE price index (PCE inflation); in 2004 switched to PCE price index excluding food and energy prices (core PCE inflation)

• Problem: these variables get revised

• Issue: are the revisions large enough to worry about?

Motivating example

• May 2002: FOMC adds line in statement issued after meeting that it fears “an unwelcome decline in inflation”; data show decline in core PCE inflation from 2.0% in 2000Q3 to 1.2% in 2002Q1

• Academic research on deflation and the zero bound are fresh in policymakers’ minds

Figure 1Core PCE Inflation Rate from 1997Q1 to 2002Q1, Vintage May 2002

1.0

1.2

1.4

1.6

1.8

2.0

2.2

2.4

1997 1998 1999 2000 2001 2002

Date

Infl

atio

n R

ate

Fed worries about "an unwelcome fall in inflation"

Motivating example

• Perhaps as a consequence of worry about low inflation, Fed drives real fed funds rate to negative levels for first time since early 1970s

• But: revised data by December 2003 show that inflation wasn’t declining after all

v=May2002 v=Dec20032000Q3 2.0% 1.7%2002Q1 1.2% 1.5%

Figure 2Core PCE Inflation Rate from 1997Q1 to 2002Q1, Vintages May 2002 and December 2003

1.0

1.2

1.4

1.6

1.8

2.0

2.2

2.4

1997 1998 1999 2000 2001 2002

Date

Infl

atio

n R

ate

vintage May 2002

vintage Dec 2003

Motivating example

• The Fed gets rid of the “unwelcome fall” language by May 2004. Revised data by August 2005 show Fed should have worried about an unwelcome rise in inflation

2000Q3 2002Q1v=May 2002 2.0% 1.2%v=Dec2003 1.7% 1.5%V=Aug2005 1.6% 1.8%

Figure 3Core PCE Inflation Rate from 1997Q1 to 2002Q1, Vintages May 2002, Dec. 2003, Aug. 2005

1.0

1.2

1.4

1.6

1.8

2.0

2.2

2.4

1997 1998 1999 2000 2001 2002

Date

Infl

atio

n R

ate

August 2005

May 2002

Dec 2003

Motivation

• Policymakers need to understand revisions to inflation

• This paper:– Determine characteristics of revisions– Investigate forecastability of revisions

Data

• Croushore-Stark real-time data set– Nominal PCE and Real PCE used to create

series on PCE price index (PPCE) • Vintages from 1965Q4 to 2007Q3

– New real-time series collected on PCE price index excluding food and energy prices (PPCEX)

• Vintages from 1996Q1 to 2007Q3• Note that history is limited, as first vintage

appeared in 1996Q1

Data

• Two inflation concepts– One-quarter inflation

– Four-quarter inflation

– v = vintage, t = date to which data refer, t < v

π(1, v, t) = %100}1]))1,(

),({[( 4

tvPPCE

tvPPCE,

π(4, v, t) = %100}1])4,(

),({[

tvPPCE

tvPPCE.

Data

• Concepts of releases– Initial release: first value of inflation reported

at v = t + 1; denoted i– August release: value of inflation reported in

August (usually) of following year; incorporate income-tax return data; denoted A

Data

• Concepts of releases– Pre-benchmark release: last value of inflation

reported before a benchmark revision; occur about every five years; allow us to abstract from redefinitions; denoted b

– Latest available data: the last vintage in the data set; August 2007 in this paper; denoted i

Data

• Concepts of revisions– For both PCE inflation and core PCE inflation, for both

1-quarter inflation and 4-quarter inflation:

i_A: from initial release to August release

i_b: from initial release to pre-benchmark

i_l: from initial release to latest data

A_b: from August release to pre-benchmark

A_l: from August release to latest data

b_l: from pre-benchmark to latest data

Revisions

• Various revision concepts show different patterns over time

• Look at revision from initial to latest for core PCE inflation over 4 quarters: large revisions relative to inflation rate in several years

Figure 4Four Quarter Inflation Rate in PPCEXInitial to Latest Revision and Actuals

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

2.5

3.0

1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005

Date

Act

ual

s an

d R

evis

ion

s (p

erce

nt)

Revision

Initial

Latest

Revisions

• Look at revision from initial to August for core PCE inflation over 4 quarters

• Revisions appear to be positive in most years; averaging about +0.3.

Figure 5Four Quarter Inflation Rate in PPCEXInitial to August Revision and Actuals

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

2.5

3.0

1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005

Date

Act

ual

s an

d R

evis

ion

s (p

erce

nt)

Revision

Initial

August

Revisions

• Revisions to PCE inflation and core PCE inflation are similar

• We have longer sample for PCE inflation (1965Q3 to 2006Q4) than core PCE inflation (1996Q1 to 2006Q4), so use the former for more comprehensive view of revisions

Figure 6

Revisions to Four Quarter Inflation Rate in PPCE and PPCEXInitial to August Revision

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005

Date

Rev

isio

ns

(per

cen

t)

PPCEX

PPCE

Characteristics of Revisions

• First, get a feel for the size of revisions to different concepts (Table 1)

Table 1Statistics on Revisions

One-Quarter Inflation Rate

PPCEX PPCE

standard 90% standard 90%Revision error interval error interval

i_A 0.41 −0.48, 0.79 0.65 −1.02, 1.08

i_b 0.39 −0.48, 0.64 0.54 −0.79, 1.08

i_l 0.46 −0.59, 0.91 0.89 −1.37, 1.48

A_b 0.33 −0.58, 0.38 0.53 −0.98, 0.70

A_l 0.40 −0.71, 0.69 0.84 −1.31, 1.36

b_l 0.31 −0.39, 0.51 0.85 −1.36, 1.41

Table 1 (cont.)Statistics on Revisions

Four-Quarter Inflation Rate

PPCEX PPCE

standard 90% standard 90%Revision error interval error interval

i_A 0.23 −0.19, 0.56 0.32 −0.38, 0.57

i_b 0.26 −0.25, 0.58 0.26 −0.34, 0.56

i_l 0.32 −0.38, 0.65 0.44 −0.59, 0.95

A_b 0.21 −0.50, 0.17 0.29 −0.47, 0.36

A_l 0.24 −0.38, 0.30 0.43 −0.73, 0.83

b_l 0.16 −0.28, 0.30 0.44 −0.91, 0.71

Characteristics of Revisions

• Size of revisions (Table 1)• Generally, revisions over longer spans

have potential to be revised more, so standard error rises, 90% interval rises in size

• Exception is revision from August release to pre-benchmark release; probably because of some August releases coming after benchmark revisions

Test for Zero Mean Revisions

• Simple test: is the mean revision zero?

• Results in Table 2

Table 2Zero-Mean Test

PPCEX PPCE

Revision p-value p-value

i_l 0.09 0.20 0.11 0.12

i_b 0.05 0.42 0.06 0.20

i_A 0.14 0.03* 0.10 0.06

A_b −0.09 0.08 −0.04 0.31

A_l −0.05 0.42 0.01 0.85

b_l 0.04 0.37 0.06 0.41

xx

Test for Zero Mean Revisions

• Simple test: is the mean revision zero?

• Results in Table 2

• Revisions after initial release tend to be positive, but in only one case do we reject the null hypothesis that the mean differs from zero

Test for Zero Median Revisions

• Simple test: are positive and negative revisions equally likely?

• Sign test (Table 3)

Table 3Sign Test

PPCEX PPCE

Revision s p-value s p-value

i_l 0.60 0.22 0.57 0.07

i_b 0.52 0.76 0.52 0.62

i_A 0.67 0.03* 0.57 0.07

A_b 0.45 0.54 0.37 0.00*

A_l 0.43 0.35 0.47 0.41

b_l 0.43 0.35 0.54 0.33

Test for Zero Median Revisions

• Simple test: are positive and negative revisions equally likely?

• Sign test (Table 3)

• Results: two cases that reject null hypothesis that proportion of positive revisions is one-half– Core PCE inflation: initial to August– PCE inflation: August to pre-benchmark

News versus Noise

• Revisions that incorporate news increase the standard deviation of later releases; revisions correlated with later releases; consistent with early releases being optimal forecasts of later releases

• Revisions that reduce noise reduce the standard deviation of later releases; revisions correlated with earlier releases; consistent with early releases being inefficient forecast of later releases

News versus Noise

• News-noise test 1:– If standard deviation of releases rise for later

release concepts → news– If standard deviation falls → noise– Results in Table 6

Table 6Standard Deviations of Inflation Rates

Data Set PPCEX PPCE

Initial Release 0.582 2.757

August 0.578 2.680

Pre-Benchmark 0.536 2.817

Latest 0.478 2.697

News versus Noise

• News-noise test 1:– If standard deviation of releases rise for later

release concepts → news• True for PPCE for August to pre-benchmark

revision

– If standard deviation falls → noise• True for all revisions of PPCEX• True for PPCE for initial to August revision, pre-

benchmark to final revision

News versus Noise

• News-noise test 2: look at correlation between revisions and earlier or later releases– Revision correlated with later release: news– Revision correlated with earlier release: noise

• Results in Table 7

News versus Noise

• Table 7 results

• PPCEX– 10 noise revision tests: 9 are significant

• Implies that all revisions reduce noise

– 4 news revision tests: 0 are significant• Implies that no revisions provide news

News versus Noise

• Table 7 results• PPCE (much longer sample)

– 10 noise revision tests: 7 are significant• Implies that some revisions reduce noise

– 4 news revision tests: 1 is significant• Implies that August to pre-benchmark revision

provides news

– Most likely candidates for forecasting revisions: initial to August and pre-benchmark to latest

Forecasting Revisions

• Given these full sample results, can we forecast revisions in real time out of sample?

• First, try forecasting August release given initial release– Roll through sample starting in 1985Q1– Run regression of revision on actual:

r(i, A, 1, t) = α + β i(1, t) + ε(t). (1)

Forecasting Revisions

• Forecasting August release given initial release– Use regression coefficients to estimate

revision, then apply to initial release:

– Calculate RMSE of this forecast of the actual, compare with RMSE assuming that initial release is optimal forecast of August release

),1,,(ˆ),1(),1(ˆ tAirtitA

Table 8

RMSEs for Forecast-Improvement Exercises

Panel A: Actuals = August Release RMSE

Forecast based on initial release, eq. (2) 0.452

Assume no revision from initial 0.490

Forecast Improvement Exercise Ratio 0.922

Forecasting Revisions

• Forecasting revisions from initial to August release appears promising, reduces RMSE in this sample

Forecasting Revisions

• Try same thing for revision from pre-benchmark to latest data

• Big problem in implementing in real time: when new benchmark revision occurs, run regression based on latest available data, but latest available data will change over time

• So procedure seems less likely to forecast revisions well

Forecasting Revisions

• Forecasting revision from pre-benchmark to latest data

• Typical regression: r(b, v1985Q4, 1, t) = α + β i(1, t) + ε(t). (3)

• Forecast of latest data:

• Results in Table 8B

),1,,(ˆ),1(),1(ˆ tlbrtbtl

Table 8 (cont.)RMSEs for Forecast-Improvement Exercises

RMSE

Panel B: Actuals = Latest Available ReleaseForecast based on pre-benchmark release, eq. (4) 0.940

Assume no revision from pre-benchmark 0.681

Forecast Improvement Exercise Ratio 1.380

Forecasting Revisions

• Forecasting revision from pre-benchmark to latest data

• Results show revisions not forecasted well; better to use pre-benchmark values as optimal forecast of latest-available data

Forecasting Revisions

• What if you want to forecast the revision from pre-benchmark to latest data just before a new benchmark revision comes out?

• Example: Just before December 2003 benchmark revision: can we predict the revised values for data from 1985Q1 to 2003Q3?

Table 8 (cont.)RMSEs for Forecast-Improvement Exercises

RMSE

Panel C: Actuals = vintage 2004:Q1Forecast based on pre-benchmark release, eq. (4) 0.713

Assume no revision from pre-benchmark 0.686

Forecast Improvement Exercise Ratio 1.039

Forecasting Revisions

• Results (Table 8C) not as bad as 8B, but better off assuming no revision

• Overall: Revision from initial release to August appears forecastable; nothing else does

Forecasting Revisions

• 2007 data: my forecasts of revisions

PCE Inflation Initial Forecast

Release Aug2008Date2007:Q1 3.35% 3.50%2007:Q2 4.31% 4.40%

CONCLUSIONS AND IMPLICATIONS FOR POLICYMAKERS

• PCE inflation rates may be revised significantly

• Policymakers may wish to down-weight their response to inflation data because of uncertainty

• Analysts can easily forecast revisions to PCE inflation