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http://clevelandfed.org/research/workpaper Best available copy 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 http://clevelandfed.org/research/workpaper Best available copy 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). http://clevelandfed.org/research/workpaper Best available copy 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 http://clevelandfed.org/research/workpaper Best available copy 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 - y p ) y = 0, ( 2 ~ ) E(y 111. Thus: 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 http://clevelandfed.org/research/workpaper Best available copy (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. http://clevelandfed.org/research/workpaper Best available copy 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 . ~By the same token, 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 http://clevelandfed.org/research/workpaper Best available copy 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 http://clevelandfed.org/research/workpaper Best available copy 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 : http://clevelandfed.org/research/workpaper Best available copy 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: http://clevelandfed.org/research/workpaper Best available copy 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 http://clevelandfed.org/research/workpaper Best available copy 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 estimates from the previous q ~ a r t e r . ~These f i n d i n g s are r e p l i c a t e d f o r the 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 GNP growth. 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. http://clevelandfed.org/research/workpaper Best available copy 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 t h a t i s orthogonal t o the fil 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. http://clevelandfed.org/research/workpaper Best available copy 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. http://clevelandfed.org/research/workpaper Best available copy 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. http://clevelandfed.org/research/workpaper Best available copy 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 http://clevelandfed.org/research/workpaper Best available copy 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 . http://clevelandfed.org/research/workpaper Best available copy References Carson, C.S. "GNP: An Overview o f Source Data and E s t i m a t i n g Methods," Survey o f -C u r r e n t Business, v o l . 67 (19871, 103-126. Conrad, W., and C. Corrado. "An A p p l i c a t i o n o f the Kalman F i l t e r t o Revisions i n Monthly R e t a i l Sales Estimates," Journal o f Economic Dynamics and C o n t r o l , v o l . 1 (19791, 177-198. Dhrymes, P.B. I n t r o d u c t o r y Econometrics. New York: Springer- Verlag, 1978. x Howrey, E.P. "Data Revision, Reconstruction and P r e d i c t i o n : An A p p l i c a t i o n t o I n v e n t o r y Investment," Review o f Economics and S t a t i s t i c s , v o l . 61 (19841, 386-393. ky Mankiw, N.G., D.E. Runkle, and M.D. Shapiro. "Are P r e l i m i n a r y Announcements o f t h e Money Stock R a t i o n a l Forecasts?" Journal o f Monetary Economics, V O ~ . 14 (19841, 15-27. Mankiw, N.G., and M.D. Shapiro. "News o r Noise? An A n a l y s i s o f GNP Revisions," Survey o f C u r r e n t Business, v o l . 66 (19861, 20-25. . Mork, K.N. " ' A i n ' t Misbehaving': Forecast E r r o r s and Measurement. E r r o r s i n E a r l y GNP Estimates," Journal o f Business and Economics S t a t i s t i c s , v o l . 5 (1987a1, 165-175. . "Forecastable Money-Growth Revisions: A Closer Look a t t h e Data," Owen Graduate School o f Management, V a n d e r b i l t U n i v e r s i t y , Working Paper NO. 86-108 (1987b1. Scadding, J.L. " G e t t i n g t h e Noise Out: F i l t e r i n g E a r l y GNP Estimates," Federal Reserve Bank o f Cleveland Working Paper (1988- forthcoming). Walsh, C. "Revisions i n the ' F l a s h ' Estimate o f GNP Growth: Measurement E r r o r o r Forecast E r r o r ? " Federal Reserve Bank o f San F r a n c i s c o Economic Review ( F a l l 19851, 5-13. Young, A.H. . V O ~ " Evaluation o f t h e GNP Estimates," Survey o f C u r r e n t Business, 67 (1 987>, 18-42.
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