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