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Working Paper 8718

THE NATURE OF GNP REVISIONS

by John Scadding

John Scadding was a v i s i t i n g economist a t
the Federal Reserve Bank o f Cleveland i n 1987.
The author thanks Professor K.W. Mork f o r
p r o v i d i n g a copy o f t h e Parker d a t a and f o r
the f o r e c a s t s e r i e s used i n t h e l a s t s e c t i o n
o f t h i s paper.
Working papers o f t h e Federal Reserve Bank
o f Cleveland are p r e l i m i nary m a t e r i a l s
c i r c u l a t e d t o s t i m u l a t e discussion and
c r i t i c a l comment. The views s t a t e d h e r e i n
are those o f the author and n o t n e c e s s a r i l y
those o f the Federal Reserve Bpnk of
Cleveland o r of t h e Board o f Governors o f
the Federal Reserve .System.

December 1987

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THE NATURE OF GNP REVISIONS

I.

Introduction
Department o f Commerce, Bureau of Economic Analysis (BEA)

The U.S.

issues i t s f i r s t estimate o f q u a r t e r l y GNP two t o three weeks a f t e r t h e
quarter ends.

This 15-day estimate (formerly known as the p r e l i m i n a r y

estimate) i s followed i n r e l a t i v e l y r a p i d succession by the 45-day and 75-day
estimates, which incorporate r e v i s i o n s t o the source data underlying the
15-day estimate and add new data t h a t were not a v a i l a b l e e a r l i e r .
do n o t end w i t h the 75-day estimate.

Revisions

Additional r e v i s i o n s u s u a l l y are

published f o r the succeeding three Julys, and there are f u r t h e r "benchmark"
r e v i s i o n s as data from t h e Census Bureau's economic and population surveys a r e
incorporated.

'

Because t i m e l y data i s needed f o r f o r e c a s t i n g purposes, i t i s a f r e q u e n t
p r a c t i c e t o t r e a t the f i r s t three early, o r p r o v i s i o n a l , estimates o f GNP as
adequate representations o f t h e f i n a l , o r " true," numbers and t o r e v i s e
forecasts on the basis o f t h i s assumption.'

For macropol i c y purposes as

well, i t i s o f t e n tustomary t o t r e a t the i n i t i a l estimates as i f they were
r e l i a b l e i n d i c a t o r s o f what t h e f i n a l numbers w i l l show, again f o r reasons of
time1 iness.
I n both instances, p r a c t i t i o n e r s are very much aware o f the r i s k s
involved i n such assumptions.
substantial.

Revisions o f the e a r l y estimates are o f t e n

For example, t h e y w a n r e v i s i o n w i t h o u t regard t o sign from the

15-day t o the f i n a l estimate over the 1974-1984 sample p e r i o d used i n t h i s
paper i s 1.6 percentage p o i n t s a t an annual r a t e , compared t o a mean growth
r a t e aver the p e r i o d o f 2.9 percent.

I n addition, the e a r l y estimates

sometimes show the wrong d i r e c t i o n f o r r e a l GNP growth (Young, 1987).

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Over the l a s t few years, some research has suggested t h a t t h e
p r o v i s i o n a l estimates o f r e a l GNP growth can be c h a r a c t e r i z e d as r a t i o n a l
forecasts of the f i n a l numbers (Walsh, 1985; Mankiw and Shapiro, 1986).

This,

o f course, provides some j u s t i f i c a t i o n f o r t h e way these p r o v i s i o n a l e s t i m a t e s
a r e t y p i c a l l y used.

However, t h i s paper argues t h a t the t e s t used t o come to

t h i s conclusion has v e r y low power even i f t h e e a r l y GNP estimates a r e
e f f i c i e n t forecasts of t h e f i n a l numbers, which i s one o f t h e i m p l i c i t
conditions o f the t e s t .

Moreover, t h e evidence o f c o r r e l a t i o n between

successive " f i n a l " errors- - the d i f f e r e n c e s between t h e f i n a l numbers and t h e
p r o v i s i o n a l estimates- - suggests t h a t t h e e a r l y numbers, i f they a r e f o r e c a s t s ,
are

not e f f i c i e n t

forecasts.

The evidence o f s e q u e n t i a l l y c o r r e l a t e d f i n a l e r r o r s i s e q u a l l y
c o n s i s t e n t w i t h t h e hypothesis t h a t t h e p r o v i s i o n a l estimates a r e measurements
o f the f i n a l numbers contaminated w i t h e r r o r , o r "noise."

This paper proposes

and implements a t e s t t h a t suggests t h a t t h e p r o v i s i o n a l estimates o f r e a l GNP
growth are contaminated w i t h noise.

One. i m p l i c a t i o n of t h i s c o n c l u s i o n i s

t h a t i t should be p o s s i b l e t o f i l t e r the e a r l y GNP estimates t o o b t a i n b e t t e r
estimates o f the f i n a l GNP numbers.

Section V I o f t h i s paper i l l u s t r a t e s one

a p p l i c a t i o n o f f i l t e r i n g the p r o v i s i o n a l estimates o f r e a l GNP growth.

In

p a r t i c u l a r , the evidence o f b i a s and i n e f f i c i e n c y t h a t Mork (1987a) f i n d s i n
the p r o v i s i o n a l estimates i s absent f r o m the f i l t e r e d estimates.

11. Forecasts Versus Observatiens
The p r a c t i c e of t r e a t i n g new GNP estimates as t h e f i n a l numbers would be
on a more secure foundation i f , a t a minimum, these e a r l y numbers were
unbiased e s t i m a t o r s and i f they provided no i n f o r m a t i o n about t h e subsequent
" f i n a l r e v i s i o n u - - t h a t i s , the d i f f e r e n c e between t h e f i n k 1 number and t h e

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e a r l y estimate i t s e l f .

I n o t h e r words, using the 15-day estimate, y P , as an

example, and l e t t i n g y denote t h e f i n a l value of r e a l GNP growth:

-

(la)

E(y

(lb)

E(Y - y')yP

y P ) = 0,
= 0,

where E i s the expectations operator c o n d i t i o n a l on y P .
Under these conditions, there would be no information i n t h e p r o v i s i o n a l
estimate i t s e l f t h a t would a l l o w one t o estimate the subsequent r e v i s i o n .

In

t h a t sense yP (and i t s companion 45-day and 75-day estimates, y r ' and y r 2 )
could be considered r a t i o n a l forecasts o f t h e f i n a l number (Walsh, p. 7 ) .
As noted e a r l i e r , c u r r e n t p r a c t i c e i s somewhat schizophrenic.
Forecasters and policymakers f r e q u e n t l y use the p r o v i s i o n a l estimates as i f
they were r a t i o n a l forecasts.

But o f t e n the e a r l y numbers are described as i f

they had information about subsequent r e v i s i o n s .

Thus, very l a r g e o r very

small i n i t i a l estimates are o f t e n viewed w i t h suspicion.

This view o f t h e

numbers i s consistent w i t h a c h a r a c t e r i z a t i o n o f them as observations o f t h e
f i n a l number measured w i t h e r r o r .

I f t h i s c h a r a c t e r i z a t i o n i s expressed i n

terms o f a classical-errors-in-variables model, the p r o v i s i o n a l estimates w i l l
be unbiased estimates o f the f i n a l number, and the f i n a l r e v i s i o n w i 11 be
uncorrelated w i t h the f i n a l number i t s e l f .

On the other hand, as noted above,

the f i n a l r e v i s i o n w i l l be c o r r e l a t e d w i t h the p r o v i s i o n a l estimate.
(2a)

E(y

-

y P ) = 0,

(2b)

E(y

-

Thus:

y p ) y = 0,

( 2 ~ ) E(y

111.

y P ) y P f 0.

Previous Studies
P r i o r work on the p r o p e r t i e s o f the GNP estimates goes back a t l e a s t t o

Zellner (1958).

A good summary o f work i n t h i s area can be found i n Young

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(1987).

The s p e c i f i c issue o f whether the, r e v i s i o n s behave more l i k e f o r e c a s t

e r r o r s o r observation e r r o r s has been e x p l i c i t l y addressed o n l y r e c e n t l y .
Manki w and Shapiro (1986), drawing on a methodology they and Runkle had
devi sed e a r l i e r t o examine the n a t u r e of money-supply announcements (Manki w,
e t al.,

19841, concluded t h a t t h e e a r l y GNP estimates behaved more l i k e

forecasts.

This r e s u l t c o n t r a s t e d s h a r p l y w i t h t h e i r e a r l i e r f j n d i n g t h a t

p r e l i m i n a r y money-supply announcements appeared t o behave more l i k e
observations than f o r e c a s t s .

Walsh (19851, u s i n g a d i f f e r e n t sample, a l s o

concluded t h a t the e a r l y GNP estimates appeared t o behave l i k e f o r e c a s t s .
However, Walsh found evidence t h a t the e a r l y GNP estimates were
i n e f f i c i e n t , because they d i d n o t i n c o r p o r a t e i n f o r m a t i o n f r o m p r i o r r e v i s i o n s
t h a t was h e l p f u l i n p r e d i c t i n g f i n a l GNP.

I n t h e same vein, Mork (1987a)

found evidence o f b i a s and i n e f f i c i e n c y i n t h e p r o v i s i o n a l GNP estimates.

As

he explains, t h i s makes t h e Mankiw- Shapiro t e s t s problematic, s i n c e t h e y a r e
t e s t s o f the j o i n t hypothesis t h a t e a r l y GNP estimates are e f f i c i e n t f o r e c a s t s
o f t h e f i n a l number.
The evidence o f i n e f f i c i e n c y i s e q u a l l y c o n s i s t e n t w i t h t h e o b s e r v a t i o n s
model being t r u e and t h e e r r o r s i n successive estimates being s e r i a l l y
correlated.

This framework o f s e q u e n t i a l l y c o r r e l a t e d r e v i s i o n e r r o r s has

been s u c c e s s f u l l y a p p l i e d t o t h e a n a l y s i s o f r e t a i l sales (Conrad and Corrado,
1979) and i n v e n t o r y investment (Howrey, 1984).

R e t a i l sales d a t a a r e an

important component o f the e a r l y GNP numbers, w h i l e the i n v e n t o r y numbers a r e
o f t e n an important source o f ' t ~ e variance i n the GNP numbers.

Thus, evidence

t h a t the o v e r a l l GNP numbers behave i n t h e same way as two o f t h e i r i m p o r t a n t
components would remove one obvious anomaly between the two s e t s of result^.^
Under circumstances o f c o r r e l a t e d r e v i s i o n s , the Mankiw- Shapiro t e s t s
cannot d i s c r i m i n a t e between the f o r e c a s t s and observations hypotheses.

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However, t h e c o r r e l a t i o n s t r u c t u r e between successive GNP r e v i s i o n s w i l l be
q u i t e d i f f e r e n t under the two hypotheses, and t h i s d i f f e r e n c e can be e x p l o i t e d
t o d i s c r i m i n a t e between the two c h a r a c t e r i z a t i o n s o f the data.

First,

however, we examine why the Mankiw-Shapiro t e s t i s n o t l i k e l y t o be o f much
help i n d i s c r i m i n a t i n g between the two explanations even when a l l o f i t s
maintained conditions are met.

IV.

Testinq the Two Explanations
The t e s t devised by Mankiw, e t a t . t o d i s c r i m i n a t e between t h e forecasts

and observations models was simple and ingenious.

I f the observations model

were c o r r e c t , then according t o equation (2b) a regression o f yp on t h e f i n a l
revision y

-

y P should y i e l d a nonzero ~ o e f f i c i e n t . ~ the same token,
By

the regression o f y on the r e v i s i o n should be zero.

The d i f f i c u l t y w i t h t h i s

t e s t i s t h a t asymptotic r e s u l t s suggest t h a t i t has low power.

To i l l u s t r a t e ,

the o r d i n a r y l e a s t squares estimate o f the slope c o e f f i c i e n t o f r e g r e s s i n g
yP on y-y P i s :

(3)

bo = E(y

-

yP)yP

I f the observations model i s c o r r e c t , so t h a t y P = y

+

u, where u has zero

mean and i s uncorrelated w i t h y, then (3) can be r e w r i t t e n :

where b , i s the regression c o e f f j c i e n t from the a l t e r n a t i v e t e s t , t h a t i s ,
from the regression o f y

-

y P on y.

Taking p r o b a b i l i t y l i m i t s , we have:

where, under the observations model, the expected value o f b, i s zero, and

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a and a a r e the variances o f t h e f i n a l estimate o f GNP growth and t h e
:
:
observations e r r o r .

Two items are worth n o t i n g about t h i s r e s u l t .

F i r s t , as

a p r a c t i c a l matter, the term on the right- hand side of ( 3 ' ) i s l i k e l y t o be
small.

Thus;the

p r e c i s i o n o f bo i s l i k e l y t o be c r i t i c a l .

This w i l l be a

problem, however, because the regressor i s measured w i t h e r r o r .
p r o p e r t i e s o f bo are not a v a i l a b l e .

Small sample

However, Dhrymes (1978) has shown t h a t

o r d i n a r y l e a s t squares estimates o f the goodness o f f i t w i l l be biased
downward asymptotically, leading t o a tendency, i n t h i s case, t o accept t h e
nu1 1 hypothesis even when i t i s false (Dhrymes, p. 263).
The p r a c t i c a l r e s u l t i s t h a t OLS estimates of the two slope
c o e f f i c i e n t s , bo and b,, may i n d i c a t e t h a t

both are

zero.

The r e s u l t s i n

t a b l e 1 suggest t h a t t h i s i s n o t simply a t h e o r e t i c a l c u r i o s i t y .

Table 1

shows t h e r e s u l t s o f performing t h e Mankiw, e t a l . t e s t s on the same body o f
data f o r the three d i f f e r e n t samples used by Mankiw-Shapiro, Walsh, and t h i s
study.

For two o f the three sample periods, the r e s u l t s , i n t e r p r e t e d

l i t e r a l l y , would mean r e j e c t i n g n e i t h e r the forecasts nor observations
hypothesis.

The one exception i s the s e t o f estimates from the Walsh sample.

But t h e s e n s i t i v i t y o f the estimates t o small v a r i a t i o n s i n the sample p e r i o d
c l e a r l y shown by t a b l e 1 r a i s e s a serious question about the robustness o f
t h i s one s e t o f r e s u l t s .

V.

Correlated GNP Revisions
Walsh's evidence o f i n e f f j c i e n c y suggests t h a t t h e Mankiw, e t a l . t e s t s

have even l e s s power than when the i m p l i c i t conditions o f the t e s t are met.
To i 1l u s t r a t e , a sty1i z e d representation o f Walsh's f i n d i n g i s :
(4)

yt

-

y:'

= a,(y;

-

y:')

+ e2rr

a, nonzero.

This evidence o f " i n e f f i c i e n c y " could j u s t as e a s i l y be c o n s i s t e n t w i t h

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the observations model.

Equation (4) i s o b s e r v a t i o n a l l y e q u i v a l e n t t o an

observations model i n which successive e r r o r s o f measurement are s e r i a l l y
correlated w i t h each other.

To see t h i s , define a, = ao/l-ao, and use

t h i s t o r e w r i t e (4) as:
(4'

yt

- y:'

= ao(yt

-

y!)

+ e'2t.

Performing p r i o r regressions o f the form (41, ( 4 ' ) and then c a r r y i n g o u t
the Mankiw, e t a l . t e s t s on the r e s i d u a l s c l e a r l y w i l l n o t work, because t h e
regressions estimates o f e2 and e l 2 by construction w i l l be orthogonal t o
yr ' and y, r e s p e c t i v e l y .

However, t h e r e l a t i o n s h i p between successive

errors i s q u i t e d i f f e r e n t under the two hypotheses, and t h i s d i f f e r e n c e can be
used to d i s c r i m i n a t e between the two models.

To i l l u s t r a t e , consider t h e

structure o f r e v i s i o n s t o GNP i f t h e f o r e c a s t i n g model i s c o r r e c t .

It i s

easiest t o t h i n k o f t h i s r e l a t i o n s h i p as being between successive i n t e r i m
revisions, t h a t i s , r l = yrl-yP, r 2 = y r 2 - y r l , and r 3 = y-yr2.'
I f e a r l i e r r e v i s i o n s provide i n f o r m a t i o n about l a t e r ones, t h e most general

structure of the r e v i s i o n s w i l l be:

with the e i s being mutually uncorrelated white noise.

To f a c i l i t a t e

comparison w i t h the observationq model s p e c i f i c a t i o n , r e w r i t e ( 5 ) i n terms o f
the f i n a l e r r o r s , u l = y-y P, u2 = y- y r l , u3 = y- y r 2 , by n o t i n g t h a t :

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Combining ( 5 ) and (6) yields:

or, in matrix notation,

where D is the triangular matrix in ( 6 ) .
The comparable representation for the observations model with
sequentially correlated measurement errors is:

or, in matrix notation,

F *
The test strategy pursued here is a simple one.

If (9) is correct, then

the off-diagonal elements in the estimated variance-covariance matrix of g
should be zero.

By the same token. estimating (7) should yield nonzero

off-diagonal elements because:

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The r e g r e s s i o n estimates o f equations (7) and (9) are r e p o r t e d i n t a b l e
2.

The r e s t r i c t i o n s on t h e c o e f f i c i e n t s imposed by the f o r e c a s t s model ( p a r t

a) y i e l d a much poorer f i t t o the data, w i t h the exception, o f course, o f
equation (3a).

But t h i s exception has no s i g n i f i c a n c e because e q u a t i o n (3a),

l i k e i t s c o u n t e r p a r t (3b),

i s simply a n o r m a l i z a t i o n c o n d i t i o n d e f i n i n g t h e

base f o r t h e s t r u c t u r e o f succeeding e r r o r s .
The numbers i n p a r t c o f t a b l e 2 p r o v i d e the t e l l i n g evidence.

Here t h e

estimated variance- covariance m a t r i c e s c l e a r l y i n d i c a t e t h a t the d a t a do n o t
support the r e s t r i c t i o n s i m p l i e d by t h e f o r e c a s t i n g model.

The off- diagonal

elements i n t h e m a t r i x f o r t h e o b s e r v a t i o n equations a r e e i t h e r z e r o o r
t r i v i a l l y d i f f e r e n t f r o m zero.

The covariances from t h e f o r e c a s t s model, on

the o t h e r hand, a r e u n i f o r m l y l a r g e r , and i n one instance- - the covariance
between e l and e2- -the i m p l i e d c o r r e l a t i o n i s c l o s e t o u n i t y .

Thus, on

balance, t h e evidence s t r o n g l y suggests t h a t the f i n a l r e v i s i o n s do n o t behave
l i k e pure f o r e c a s t e r r o r s and c o n t a i n s i g n i f i c a n t elements o f measurement
errors.

VI.

F i 1t e r i n g GNP Estimates
As noted a t the b e g i n n i n g p f r t h i s paper, acknowledging elements o f

observation e r r o r i n the p r e l i m i n a r y d a t a suggests f i l t e r i n g t h e p r o v i s i o n a l
numbers t o o b t a i n b e t t e r estimates o f what t h e f i n a l GNP numbers w i l l show.
companion paper (Scadding,

1988) c o n s t r u c t s f i l t e r e d estimates o f GNP f o r t h e

same p e r i o d used i n t h i s a n a l y s i s .

A

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F i l t e r i n g the data allows estimates o f the f i n a l revisions, y- y P ,
etc.,

t o be made as the p r o v i s i o n a l estimates o f GNP become a v a i l a b l e .

Thus,

i f y l i s the f i l t e r e d value o f t h e 15-day estimate o f GNP, the estimated

f i n a l r e v i s i o n error, y-y P, i s y,-yP.

S i m i l a r l y , y z and y, are the

f i l t e r e d estimates o f the 45- and 75-day p r o v i s i o n a l GNP numbers, and t h e
estimated f i n a l r e v i s i o n e r r o r s c o n d i t i o n a l on these values are yz-yr

'

and

y3-yr2, respectively.
These r e s u l t s o f f i l t e r i n g the data can be used t o reexamine Mork's
findings t h a t the e a r l y GNP estimates were " ill- behaved" (Mork, 1987a).
S p e c i f i c a l l y , Mork found t h a t the f i n a l r e v i s i o n s had a nonzero mean and were
correlated w i t h a p u b l i c l y a v a i l a b l e o u t s i d e f o r e c a s t and w i t h p r o v i s i o n a l
These f i n d i n g s are r e p l i c a t e d f o r the
estimates from the previous q ~ a r t e r . ~
sample period used i n t h i s p e r i o d and are shown i n the f i r s t two l i n e s o f
table 3.
If f i l t e r i n g i s possible, Mork's question becomes whether the f i n a l

revisions r e l a t i v e t o the estimates made of those r e v i s i o n s from t h e f i l t e r e d
data
-show the

signs o f i l l - b e h a v i o r he described.

The t h i r d and f o u r t h

equations i n t a b l e 3 address t h i s question by adding the f i l t e r e d estimates o f
the f i n a l revisions, yI-yP, etc.,
dramatically d i f f e r e n t .

t o the regressions.

The r e s u l t s are

The constants and t h e c o e f f i c i e n t s on t h e lagged

values o f y r ' become t r i v i a l l y d i f f e r e n t from zero, and the accompanying F
s t a t i s t i c s show t h a t the data cannot r e j e c t the hypothesis t h a t these
coefficients are zero.

O f coupse, these r e s u l t s do not i n any way c o n t r a d i c t

Mork's f i n d i n g s ; the problems he notes do appear t o be u n a t t r a c t i v e features
o f the p r o v i s i o n a l estimates o f r e a l G P growth.
N

However, a t the same time,

the r e s u l t s i n t a b l e 3 i n d i c a t e t h a t these problems are e a s i l y corrected by
filtering.

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VII.

Conclusion
Recent work has i n d i c a t e d t h a t revisions t o e a r l y estimates o f GNP can

be regarded as f o r e c a s t e r r o r s .

The evidence presented here suggests t h a t if

one has t o choose between two p o l a r characterizations- - the forecast versus t h e
observation e r r o r representations- - the observations model appears b e t t e r
suited t o the data.

I n r e a l i t y , o f course, the estimates are most l i k e l y a

mixture o f both, since t h e Bureau o f Economic Analysis draws upon both sample
data and e x t r a p o l a t i o n s when sample data are n o t a v a i l a b l e .

Research by Mork

(1987b1, which reexamines Mankiw, Runkle, and Shapiro's e a r l i e r work on t h e
nature o f money-supply announcements, suggests they are a mixture o f
observations and forecasts, w i t h observations accounting f o r a l i t t l e over 50
percent o f the published f i g u r e .
The companion paper by Scadding t h a t examines t h e usefulness o f
f i l t e r i n g the e a r l y GNP estimates provides i n d i r e c t r e s u l t s t h a t are
q u a l i t a t i v e l y the same.

The procedure used i n t h a t paper decomposes t h e f i n a l

r e v i s i o n i n t o an estimate of t h e observation e r r o r , and a r e s i d u a l element

l
t h a t i s orthogonal t o the fi t e r e d GNP estimate- - in o t h e r words, an element
t h a t behaves l i k e a forecast e r r o r .

Although the r e s u l t s c l e a r l y i n d i c a t e

t h a t some o f the f i n a l r e v i s i o n t o r e a l GNP growth i s observation e r r o r and
can be removed by f i 1t e r i n g , they a1 so suggest t h a t t h e r e s i d u a l f o r e c a s t - li ke
e r r o r remains substantial.

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Footnotes
1.
An e x c e l l e n t , comprehensive d e s c r i p t i o n o f t h e methods and d a t a used i n
computing t h e d i f f e r e n t estimates o f GNP i s contained i n Carson (1987).
C l e a r l y no " f i n a l " estimate i s i n f a c t ever f i n a l . This a r t i c l e f o l l o w s
the usual p r a c t i c e and t r e a t s the l a t e s t a v a i l a b l e f i g u r e a f t e r t h e 75-day
estimate as t h e f i n a l f i g u r e . The d a t a a r e from t h e BEA's GNP r e v i s i o n s t u d y
prepared before the 1985 rebenchmarking; these data were s p e c i a l l y prepared by
the BEA s t a f f t o a b s t r a c t d e f i n i t i o n a l changes and r e c l a s s i f i c a t i o n s . The
data f o r t h e 15- and 45-day estimates go back t o t h e second q u a r t e r of 1968.
However, r e g u l a r releases o f t h e 75-day estimate began i n t h e second q u a r t e r
o f 1974, and f o r t h i s series P a r k e r ' s d a t a have no corresponding " f i n a l "
estimates a f t e r the f i r s t q u a r t e r of 1984. These two c o n s t r a i n t s d e f i n e t h e
sample used i n t h i s study.

2.

3.
Mankiw and Shapiro r e c o n c i l e t h e d i f f e r e n c e by arguing t h a t t h e e r r o r s
i n GNP components wash o u t i n t h e aggregate. A t the same time, t h e y
acknowledge t h a t t h e i r f i n d i n g s may be "due t o a l a c k o f s t a t i s t i c a l power"
(Mankiw and Shapiro, p . 25).
4.
The o r i g i n a l l y formulated t e s t regressed y on y P , and y P on y, b u t
the ones used here are obviously e q u i v a l e n t .

5.
I n p r i n c i p l e , t h e l a g g e d v a l u e o f r l , etc., c o u l d b e i n c l u d e d i n the
information s e t used f o r f o r e c a s t i n g , b u t i n f a c t , i n t e r q u a r t e r r e v i s i o n s
appear t o be uncorrelated.

6.
The f o r e c a s t used by Mork, and denoted by y F i n t a b l e 3, i s the median
forecast from the National Bureau o f Economic ResearchIAmerican S t a t i s t i c a l
Association q u a r t e r l y survey. Mork examined the performance of a1 1 t h r e e
p r o v i s i o n a l estimates, b u t found t h a t t h e 15-day and 45-day estimates had t h e
major problems, and they t h e r e f o r e a r e t h e ones examined here. Mork a l s o
examined the estimates' performances over a longer sample p e r i o d than
considered here, as we1 1 as over two subsamples, the l a t t e r of which r o u g h l y
corresponds t o the one used here. The r e s u l t s r e p o r t e d i n p a r t a of t a b l e 3
correspond c l o s e l y t o Mork's r e s u l t s f o r h i s l a t e r subsample, even though he
used general i zed method o f moments e s t i m a t i o n r a t h e r than t h e o r d i n a r y 1e a s t
squares estimation used i n t h i s paper.

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Table 1:
Walsh sample:

1976:IQ

Dep. var.

yp
-0.010

-

Estimates of Slope Coefficients

1983:IVQ

Mankiw-Shapiro sample:

1976:IIQ-1982:IVQ
Regressors
-

Regressors

Y - yp

Y
0.185*

Dep. var.
Y - Y'

Sample used i n this paper:

1974:IIQ - 1984:IQ
Regressors

Dep. var.

Y

-

yp

yp

-0.055

Y
0.116

*Statistically different from zero at the 5-percent level.

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Table 2: Estimates of Error Structure

a.

Forecasts model

(la) u3

b.

=

0.110 + 0.192(u3-u2) - 0.591(u2-ul)
(0.45)
(0.48)
. (-1.93)

s.e.e.

=

1.517

Observations model

c. Variance-covariance of estimated residuals
e3
e2
e1

e3
e2
e1

2.210
-0.281
-0.251
e3

2.408
2.149
e2

0.510
e1

Forecasts model

0.298
0.000 0.353
0.056 -0.043
e3
e2

0.298
e1

Observations model

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Table 3:

a.
(la)

b.

p r e d i c t i o n s o f F i n a l Revisions

Without f i l t e r i n g
Yt

-

Y!

0.839
(2.29)

-

0.173y:f
(-1 - 9 6 )

I

+

0.128yt
(1.01)

F = 2.887*

With f i l t e r i n q

*Test t h a t a l l c o e f f i c i e n t s a r e zero; s i g n i f i c a n t a t 5- percent confidence
level.
**Test t h a t a l l c o e f f i c i e n t s except p r o v i s i o n a l estimate of f i n a l r e v i s i o n a r e
zero; n o t s i g n i f i c a n t a t 5- percent l e v e l .

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.

V O ~

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