The data measurement process for UK GNP: stochastic trends, long memory, and unit roots

Journal of ForecastingJ. Forecast. 21, 245–264 (2002)Published online 14 May 2002 in Wiley InterScience (www.interscience.wiley.com). DOI: 10.1002/for.828

The Data Measurement Process for UKGNP: Stochastic Trends, Long Memory,and Unit Roots

KERRY PATTERSON*Department of Economics, University of Reading, UK

ABSTRACTMuch published data is subject to a process of revision due, for example,to additional source data, which generates multiple vintages of data on thesame generic variable, a process termed the data measurement process orDMP. This article is concerned with several interrelated aspects of the DMPfor UK Gross National Product. Relevant questions include the following. Isthe DMP well behaved in the sense of providing a single stochastic trend inthe vector time series of vintages? Is one of the vintages of data, for examplethe ‘final’, the sole vintage generating the long-memory component? Doesthe multivariate framework proposed here add to the debate on the existenceof a unit root in GNP? The likely implicit assumptions of users (that theDMP is well behaved and the final vintage is ‘best’) can be cast in termsof testable hypotheses; and we show that these ‘standard’ assumptions havenot always been empirically founded. Copyright 2002 John Wiley &Sons, Ltd.

KEY WORDS data measurement process; non-stationarity; long memory;GNP

INTRODUCTION

Much of the macroeconomic data regarded as essential in interpreting the development of the econ-omy is first published in preliminary form and then revised, often quite extensively both in terms ofthe magnitude of the revisions and the time elapse to the ‘final’ data. The data agency usually has tobalance the need for timeliness of publication with the knowledge that preliminary ‘vintages’ of dataare based on incomplete information. This is particularly so for GNP, which is the focus of this study.

The importance of the data revision process has been recognized in a number of articles,1 butthere are still several central questions that have not been answered. To understand the nature andimportance of these questions we first give a brief stylisation of the data measurement process.

* Correspondence to: Kerry Patterson, Department of Economics, University of Reading, Whiteknights Park, Reading, RG66AA, UK. E-mail: [email protected]/grant sponsor: British Academy.1 For example, Holden and Peel (1982a,b), Mankiw and Shapiro (1986), Mork (1987), Patterson (1995a,b), Patterson andHeravi (1991a,b), Young (1987) and Wroe (1993a,b).

Copyright 2002 John Wiley & Sons, Ltd.

246 K. Patterson

The data agency, for example the Office for National Statistics (ONS), or its precursor theCentral Statistical Office (CSO), in the UK, or the Bureau of Economic Analysis in the USA,publishes an initial figure for, say, 1990q1 (generated from the first vintage) of GNP (the genericvariable). Having previously published an initial figure (first vintage) for 1989q4, it also, usuallysimultaneously, publishes a revision of that figure (generated from the second vintage) for GNP,a second revision (third vintage) of the figure for 1989q3, a third revision (fourth vintage) ofthe figure for 1989q2 and so on. This process is referred to as the data measurement process, orDMP, which captures the stochastic relationship amongst the m random variables given by the datavintages—see Patterson (1995a,b). The DMP defines a multivariate distribution for the m randomvariables corresponding to the m vintages of data on the generic variable, in this case GNP. Becausethere are multiple vintages of data, the DMP can be multivariate even though a single variable,such as GNP, is being considered.

With this brief description we can return to the questions raised in the abstract, the answers towhich are interrelated. First, given multiple (m) vintages of data on a generic variable, here GNP,is the DMP well behaved in the sense of providing a single stochastic trend, and hence a singlepermanent or long-memory component, for GNP? It is probably the implicit presumption of mostusers that this is the case. In contrast, we provide evidence that the DMP for GNP has not beenwell behaved with two stochastic trends, which are necessarily not cointegrated.

Second, can a single vintage be taken to represent, in a well-defined sense, the properties ofthe m vintage data set? The implicit assumption of most users is probably that the final vintageshould be used, with all others discarded. The permanent–transitory decomposition due to Stockand Watson (1988) and Gonzalo and Granger (1995), and see also Granger and Haldrup (1997)and Proietti (1997), is developed to provide an answer to this question. We show that, in general,the long-memory component(s) of GNP is (are) a combination of all vintages of data; but that itis possible to formulate a set of testable restrictions to assess whether a single vintage alone isresponsible for the long-memory component of a time series. Also related to this line of analysis iswhether sub-systems of the variables can be separated so that the permanent components of eachsub-system depend only upon variables in the sub-system—see Granger and Haldrup (1997).

Third, can any light be thrown on the question of whether there is a unit root in GNP, byconsidering the complete set of data given by T observations on m vintages? Despite previousresearch2 into this question, none has considered the implications of the process generating thedata for the tests that have been undertaken. The answer to this question arises out of our interestin whether the DMP is well behaved and the dual relationship between cointegration of the mvintages and the number of stochastic trends. We show not just that GNP may have one unit rootbut that it may have multiple unit roots, a possibility that could not be considered with univariateunit root tests. Further, the usual univariate approach to this question is not a valid reduction of themultivariate model with m vintages unless a number of (testable) restrictions are met. One likelybenefit of considering m vintages of data as a system, especially given concerns about the lowpower of conventional ADF tests, is that m ð T observations are used in the analysis, rather than Tas in the conventional case. For example, here the empirical analysis is based on 9 ð 124 D 1116rather than 124 observations. Similar concerns have arisen in other areas, for example, in testingfor a unit root in real exchange rates (Abauf and Jorion, 1990; Macdonald, 1996), and interest

2 The seminal study was Nelson and Plosser (1982), with continuing interest represented by Murray and Nelson (2000);other studies are too numerous to list in detail, but would include, for example, Stock and Watson (1986), Walton (1986),Perron and Phillips (1987), Rudebsuch (1992, 1993), Mocan (1994), Cheung (1996) and Cheung and Chinn (1997).

Copyright 2002 John Wiley & Sons, Ltd. J. Forecast. 21, 245–264 (2002)

The Data Measurement Process for UK GNP 247

rates (Balz, 1998). There is evidence that that an increase in power can be obtained by poolingtime series observations into a panel; however, the appropriate panel framework should take intoaccount the possibility of cointegration in the individual time series.

Answers to some other relevant questions of interest are corollaries of these three. For example,(1) are the different vintages of data cointegrated and, if so, (2) are the revisions stationary? (Thesetwo are issues that have been considered before; see Patterson and Heravi (1991a,b) Siklos (1996),but only in a bivariate3 rather than a multivariate framework and, in the case of the UK, for avery limited time span of data.) Despite the likely presumption that the answers to both of thesequestions is yes, there is evidence reported below that the answers for UK GNP are no; and inthis case this implies that an earlier vintage of data does not predict a later vintage to within anon-stationary error. That is GNP does not predict GNP!

The framework developed in this study also has implications for the evaluation of univariatemodelling of processes such as that for GNP. In univariate modelling and forecasting, even thoughthere is a single variable it is important to know which vintage of data is being forecast. A typicalmodel-building procedure is to obtain data for a sample period and, in the modelling procedure,‘hold back’ some of the more recent data for a forecast evaluation. The problem with this procedureis that, even if the estimated model is based on a single vintage of data (which will occur if theforecast period is long enough for the ‘final’ vintage of data to have been published in a singlerun), more recent data is likely to be mixture of vintages. As the characteristics of different vintagesdiffer (initial vintages may be biased as predictors of later vintages, much ‘noisier’ than, and maynot even be cointegrated with, later vintages) the model may not fit the recent data even though itfits the final vintage, when available, perfectly acceptably. The way round this problem is to jointlymodel the m vintages of data, which enables forecasts to be made of all the vintages. This isimportant if forecasts are evaluated on ‘real-time’ data (that is, data available from a single sourceat a real moment in time), which is generally a mixture of vintages; and as increasing use is madeof downloading sources from the Internet, where the transparency of different vintages of data onthe same variable is lost from view.

It may be useful at this stage to draw out some examples from the data to illustrate the scale of therevisions involved in the DMP. The basic data is UK GNP in current prices (which is deflated by aprice index and population to provide real GNP per capita in the third section). To illustrate, the first8 vintages and the final vintage for the two quarters 1976q4 and 1990q3 are graphed in Figures 1(a)and 1(b) (with the final identified as 9), respectively. We concentrate on GNP in current pricesbecause this is where the underlying revisions take place. First, note the scale of the largest revisionsat �3.68% for 1976q4 and �2.22% for 1990q3. On keying in the data for analysis, double-checkinghad continually be made given the magnitude of the changes in the data for given periods. The scaleof these revisions suggests that modelling the DMP may well be important in empirical analysis.

The Office for National Statistics (ONS) has noted that two central reasons for revision arethe receipt of additional data and changes in procedures (Barklem, 2000; Symons, 2001). GNP iscompiled from a multiplicity of sources and methods, which can give rise to revision. For example,several key components are based on surveys, which involve incomplete response at the first passand higher response rates at later passes. The ONS, and its predecessor the Central Statistical

3 Patterson and Heravi (1991a,b) considered whether the revisions to components of the UK national income accountswere stationary and Siklos (1996) considered similar issues for the US National Income and Product Accounts. Gallo andMarcellino (1999) make a useful contribution evaluating efficiency and unbiasedness in a way that explicitly recognizesthe non-stationarity of the data.


248 K. Patterson

28000

28200

28400

28600

28800

29000

29200

29400

29600

29800

1 2 3 4 5 6 7 8 9

Vintage

118000

119000

120000

121000

122000

123000

1 2 3 4 5 6 7 8 9

Vintage

(a)

(b)

Figure 1. (a) First eight vintages and final vintage (9) GNP (current prices) 1976q4 (b) First eight vintagesand final vintage (9) GNP (current prices) 1990q3

Office, have been concerned for some time with the quality of the data produced and publishedin the national accounts, especially the main economic aggregates including GDP and GNP. Thisconcern has led to an extensive range of ONS initiatives; for example, Andrews (2000) describesover twenty projects underway to ‘create some new outputs, improve the quality and coherence ofexisting outputs and strengthen the statistical infrastructure underpinning data collection . . ..’

The remainder of this paper is organized as follows. The next section deals with notation and theframework for analysis. The third section describes the data and results of the empirical analysis.As the empirical results suggest that there are two stochastic trends in the multiple vintages of data,further consideration is given in the fourth section to the reasons for, and the impact of, revisionsto GNP. The final section contains some conclusions.

NOTATION AND ANALYSIS

NotationThe generic variable of interest is denoted y; in the next section this will be the natural logarithmof real per capita GNP. We define m random variables corresponding to m vintages of data fromthe DMP on the generic variable, that is, yv

t for v D 1, . . . , m, where the superscript v indicates the



vintage of data for time period t; m indicates the final vintage. yt without a superscript is the m by1 column vector of different vintages of data, that is, yt D �y1

t , y2t , . . . , ym

t �0 and f�yt� is the jointpdf of yt. A sample of observations and vintages, that is, realizations or outcomes of the processf�yt� for t D 1, . . . , T, can be arranged into a matrix of dimensions T ð m corresponding to thenumber of observations and the number of vintages. A total, or cumulative, revision is defined asyv

t � ymt and a sequential revision is defined as yv

t � yvC1t . Conventional notation of relevance is

that a variable integrated of order 1, denoted I(1), is stationary after differencing once.

Stochastic trends and cointegrationWhen there are multiple vintages of data the appropriate starting point is analysis of the multivariateprocess yt, for example within the Johansen framework4 —see Johansen (1988, 1995a). In order toanswer the questions posed in the Introduction, we first consider the cointegrating rank, r, of the mvintage data set; and also define the number of common stochastic trends s � m � r (see Stock andWatson, 1988). That is, if the cointegrating rank is r in a system of m variables then there are m � rcommon stochastic trends, which provide the random walk components in the system. Equivalently,in an interpretation due to Gonzalo and Granger (1995) and Granger and Haldrup (1997) (and seealso Proietti, 1997), if the cointegrating rank is r < m, then there are s ½ 1 common factors that arelinear combinations of the observable variables. The link between stochastic trends and commonfactors—see Gonzalo and Granger (1995, Proposition 5)—is that they share the same the randomwalk component. A notable feature of the common trends/factors is that they do not cointegrate.

In the Johansen framework we start with the m-variate, pth-order, cointegrating VAR, CVAR,for I(1) variables given by

yt D � C yt�1 Cp�1∑iD1

iyt�i C εt �1�

εt is iid with covariance matrix �. Cointegration implies D ˛ˇ0, with ˛ and ˇ of dimensionm ð r and each of rank r, 1 � r � m; the cointegrating rank is r, and zt D ˇ0yt are the r equilibriumcombinations. The common stochastic trends arise from the dual vector moving average, VMA,representation, given by:

yt D C�t C Ct∑

iD1

εt C CŁ�L��εt C �� 2�

where C D ˇ?�˛0?�I �∑p�1

iD1 i�ˇ?��1˛0?; CŁ�L� D �1 � L��1�C�L� � C�1�� where C�L� is the

matrix lag polynomial of coefficients in the moving average representation of the cointegratedsystem—see Stock and Watson (1988). The symbol ? indicates the orthogonal complement of amatrix; for example, ˛? is an m ð s matrix such that ˛0

?˛ D 0 and ˛˛? is of full rank. While ˇdefines the cointegration space, ˛? defines the space of the common stochastic trends. With thisbackground it is useful to interpret the limits of the cointegrating rank. If r D m, there are no

4 A possible alternative procedure is to use the panel data set-up as, for example, in Abuaf and Jorion (1990) and Jorionand Sweeney (1996) for unit root tests (on the real exchange rate for a panel of countries). In brief this stacks the individualtests into a set of seemingly unrelated regressions. Applied here this would exploit the multivariate nature of the data, thatis, T observations on the m vintages of data, but ignore their interrelatedness except through the covariance structure. Bothmethods use more data by pooling the m regressions on T observations leading to a potentially large increase in power.


250 K. Patterson

unit roots, hence yt is I(0) not I(1), implying a contradiction with the assumption that yt is I(1);therefore, for yt to be I(1) there must be at least one common stochastic trend and r < m. At theother extreme s D m and none of the stochastic trends are common and there is no cointegration;that is, r D 0.

We need to couple this framework with an interpretation of the DMP for a generic variablewith m vintages of data. We define a ‘well-behaved’ DMP as one where the cointegrating rank isr D m � 1, that is, s D m � r D 1 and there is, therefore, a single random walk component (whichprovides the common trend/factor) in the system of m vintages. This is the simplest case andcorresponds to the statement that ‘there is a unit root in GNP’.

Cases other than r D m � 1 are possible and would still be consistent with the general statementthat there is a unit root in GNP, but not with the definition of a well-behaved DMP. For example,if r D m � 2 then s D 2, and there are two unrelated random walk components in GNP. In a sensethis is one unit root too many and points to a ‘poorly behaved’ DMP, with obvious implicationsfor the difficulty of interpreting which trend is GNP. Such a case cannot be ruled out a priori and,as we report below, can occur in practice.5

Identification, stationarity of the (log) revisions and homogeneity of the levelsIt is insufficient simply to estimate the unrestricted version of (1) since the cointegrating vectors willnot be identified without restrictions, which may be either or both exclusion or more general equalityrestrictions—see Johansen (1995a,b). Necessary and sufficient conditions for just identification ofthe r cointegrating vectors are that r � 1 independent restrictions are placed on each cointegratingvector. If the DMP is well behaved then r � 1 D m � 2, so that a total of �m � 1��m � 2� (inde-pendent) restrictions on the r D m � 1 cointegrating vectors are required. No testable restrictionson identification result otherwise. Restrictions in excess of this number are over-identifying andcan be tested with a likelihood ratio test statistic asymptotically distributed as 2�q�, where q is thenumber of over-identifying restrictions—see Johansen and Juselius (1992) and Johansen (1995b).

In the case of a well-behaved DMP an interesting set of just-identifying restrictions arises fromthe argument that all pairs of vintages should cointegrate. One could, for convenience, regard allvintages as pairwise cointegrating with the final vintage, which gives m � 2 zero restrictions oneach cointegrating vector; equivalently, the sequential vintages could be regarded as cointegrating.Whichever, this then implies that vintage i pairwise cointegrates with vintage j. Stationarity of the(log) revisions, implying homogeneity of degree one in the levels, then additionally implies that thecoefficients in each cointegrating vector are equal but opposite in sign. This results in q D r � 1over-identifying restrictions, which can be tested in the standard way.

For example, with m D 4, r D m � 1 D 3, and where ˇij is the ith coefficient in the jth cointe-grating vector, the restrictions parameterized in indirect form are:

[ 1 1 0 00 0 1 00 0 0 1

]ˇ11

ˇ21

ˇ31

ˇ41

D

( 000

) [ 0 1 1 01 0 0 00 0 0 1

]ˇ12

ˇ22

ˇ32

ˇ42

D

( 000

)

5 There is a suggestion in the CSO’s own evaluation, of possible worries about the DMP for GNP. For example, someconcern was expressed by the UK’s Central Statistical Office (the precursor of the Office for National Statistics) followingthe Pickford Review—see Wroe (1993a)—about the quality of some of its macroeconomic data and some general concernsabout the balance of payments data were documented in Patterson (1992).



[ 0 0 1 11 0 0 00 1 0 0

]ˇ13

ˇ23

ˇ33

ˇ43

D

( 000

)

This is a total of 9 restrictions, whereas just-identification requires 6 restrictions. The restrictionsare independent across equations and can be tested in the standard way, with the LR test statisticdistributed as 2(3) under the null.

The long-memory componentOne of the central questions noted in the Introduction was concerned with identifying the long-memory components in the m-vintage data set for GNP. If, for example, the DMP is well behaved,there is a single long-memory component and it is of interest to know whether this can be related toa particular vintage. It makes sense, therefore, to use the permanent–transitory (P–T) decompositiondue to Gonzalo and Granger (1995) and Granger and Haldrup (1997), in which observable commonfactors are extracted from the vector time series yt. Even if there are multiple stochastic trends, sothat the DMP is not well behaved, it may be possible to relate the several permanent componentsto observable variables.

First, the P–T decomposition is summarized in the following equations.

yt D yPt C yT

t P–T decomposition of yt (3a)

yPt D ˇ?�˛0

?ˇ?��1Ft Permanent (long-memory) component (3b)

yTt D ˛�ˇ0˛��1zt Transitory (short-memory) component (3c)

yt D A1Ft C Qyt Common factor interpretation (4a)

Ft D B1yt D ˛0?yt Linear combination of observables (4b)

A1 is an m ð s matrix of loadings on the s common factors in Ft D �f1t, . . . , fst�0, and is any basisof the null space of ˇ0. Equation (3a) simple states that there is an exhaustive permanent–transitory(P–T) decomposition. The permanent, I(1), component is yP

t � 1Ft, where 1 � ˇ?�˛0?ˇ?��1 and

Ft are the observable common factors. The transitory, I(0), component is yTt � 2zt where 2 �

˛�ˇ0˛��1 and zt � ˇ0yt. Note that yt D [ˇ?�˛0?ˇ?��1˛0

? C ˛�ˇ0˛��1ˇ0]yt D yt, so that, as expected,the P–T decomposition is exhaustive—see also Johansen (1995a, p. 40). Qyt are I(0) components,which are functions of the r cointegrating combinations ˇ0yt. Gonzalo and Granger (1995) showthat the s ð m matrix B1 D ˛0

?. In the common factor approach, the complementary interpretationof a cointegrating rank of r is that the system is driven by s common factors that do not cointegrate.

If r D m � 1 then s D 1 so there is just one common factor, f1t, and this is the case referred toearlier as a well-behaved DMP. B1 is then a 1 ð m row vector of weightings on the m vintages ofdata in yt, say f1t D ∑m

vD1 b1vyvt , where b1v is the vth element of B1; this relates the single common

factor (or equivalently the single common stochastic trend) in this case to the observable variablescomprising the m vintages of data. The permanent component is yP

t � ˇ?�˛0?ˇ?��1˛0

?yt D 1f1t,where 1 D �11, . . . , m1�0; hence for the vth vintage the permanent component is v1

∑mvD1 b1vyv

t ,that is, the common factor scaled by v1. Note that even in the well-behaved case the common factor,and the permanent component, is not generally a single vintage but a linear combination of vintages.Certain special cases arise from restricting the space of common trends. For example, when is the


252 K. Patterson

permanent component just a single vintage? It turns out that to answer this question it is convenientto first consider the dual relationship between weak exogeneity and the common trends space.

Weak exogeneityWeak exogeneity is a useful concept in this context because we can develop its link to commonfactors. For example, consider the well-behaved case with r D m � 1, then there is a single commonfactor given by ˛0

?yt where ˛0? is a 1 ð m row vector. The hypothesis that the final vintage is weakly

exogenous corresponds to the last row of ˛ comprises 0 elements, thus ˛0? is (proportional to) the

vector i D �0, . . . , 0, 1�; equivalently this corresponds to the formulation in Gonzalo and Granger(1995, Theorem 3) on testing hypotheses on ˛?, that is, H: ˛? D G� where, in this case, G D i 0and � is a scalar, with the interpretation that the common factor is driven by the final vintage.This formulation generalizes quite simply for the case when s > 1. Consider the case where thehypothesis is that the last two vintages are weakly exogenous, for which we must have r � m � 2.Then the last two rows of ˛ comprise 0 elements, thus ˛0

? can be constructed as (proportional to)the 2 ð m matrix [Q0, I2] where Q0 is a 2 ð �m � 2� matrix of 0s. The equivalent hypothesis on ˛?is ˛? D G� where G D [Q0, I2]0 and � is 2 ð 1, with the interpretation that the last two vintages aredriving the whole system.

DATA AND EMPIRICAL RESULTS

Data and characteristicsThe data for the United Kingdom is obtained and constructed as follows. The GNP measure isbased on the expenditure estimate of GDP from successive issues of the Monthly Digest of Statistics(MDS). The average estimate is not published before the December 1988 issue of MDS. GNP isGDP plus net property income from abroad (NPY), and the GNP data is seasonally adjusted incurrent prices. Seasonally adjusted data are used partly because of the preference of the ONS topublish seasonally adjusted data, with non-seasonally adjusted data now the exception in EconomicTrends, the quarterly version of the MDS; and because the publication of non-seasonally adjustedNPY in MDS ceased with effect from the March 1989 issue. In order to focus on revisions tothe basic underlying series, that is, GNP in current prices, the deflator to obtain real values is theRetail Price Index (RPI all items and then seasonally adjusted). The RPI is not revised, so that therevision structure in GNP is unaltered by this choice6. Finally, the data is expressed on a per capitabasis by dividing by the total UK population. There have been some relatively minor revisions tothe UK population data, but in order to focus on the revisions to GNP this data is obtained from asingle source, that is, the Annual Supplement to Economic Trends (ONS, 2000).

The first data set to be analysed comprises vintages 1 to 8 on the natural logarithm of real GNPper capita. The first vintage for the first observation was obtained from the July 1964 issue of MDSand the last vintage on the last observation from the July 1998 issue of MDS. The effective sampleperiod is 1964q1 to 1995q2. The number of vintages published by the ONS (CSO) has varied overthe sample period with a maximum of 26 and, thus, the vintage of the ‘final’ data is variable.Nevertheless, since the ‘final’ data is often thought to be best, and it is this that is published inlong runs, we also consider the initial data set augmented by the final vintage.

6 Using ‘real’ GNP as published by the ONS (CSO) was considered but, because of the scale of revisions, it provedimpossible to link the m vintages across the changes of base year without fundamentally altering the properties of theseries.



We first consider some characteristics of the data. The revisions relative to the eighth and finalvintages are graphed in Figures 2(a) and 2(b), with some summary characteristic in Table I.

Figure 2 and Table I indicate that the revisions are generally quite substantial. Taking the 8thvintage as the reference, the mar for the first vintage is 1.80% and relative to the final vintagethis increases to just under 3%. Most of the revisions are negative, that is, ym

t > yvt , so the mean

revision and the mar do not differ by much—for example, the mean revision relative to the 8thvintage is �1.72%. The 3rd row shows that there are still substantial revisions before the finalseries is achieved.

1963 1965 1967 1969 1971 1973 1975 1977 1979 1981 1983 1985 1987 1989 1991 1993 1995800

900

1000

1100

1200

1300

1400

1500

1600

1700Vintage 8

Vintage 1

Cumulative revision

1963 1965 1967 1969 1971 1973 1975 1977 1979 1981 1983 1985 1987 1989 1991 1993 1995-96

-80

-64

-48

-32

-16

0

16

(a)

Figure 2. (a) First and eighth vintages of GNP (real per capita) (b) First and final vintages of GNP (real percapita)


254 K. Patterson

1963 1965 1967 1969 1971 1973 1975 1977 1979 1981 1983 1985 1987 1989 1991 1993 1995800

900

1000

1100

1200

1300

1400

1500

1600

1700Final Vintage

Vintage 1

Total revision

1963 1965 1967 1969 1971 1973 1975 1977 1979 1981 1983 1985 1987 1989 1991 1993 1995-125

-100

-75

-50

-25

0

25

(b)

Figure 2. (Continued )

Table I. Percentage mean absolute revisions of GNP relative to the 8th vintage and relative tothe final vintage

v D 1 2 3 4 5 6 7 8

%mar 8th 1.80 1.40 1.11 0.87 0.58 0.41 0.17 —s.d 1.31 1.25 1.09 1.13 0.75 0.71 0.50 —%mar final 2.96 2.56 2.26 2.02 1.73 1.55 1.31 1.14s.d 2.08 2.02 1.89 1.89 1.59 1.53 1.38 1.28

Notes: %mar is the mean absolute %revision, where the proportionate revision is 100�yvt � ym

t �/yvt ; m D 8 for

the first row and m D final for the 3rd row; s.d is the standard deviation of the %revisions.



Data analysisA second-order CVAR was selected on the basis of standard selection and reduction criteria—see,for example, Patterson (2000). The trace and maximum eigenvalue, �max, test statistics for cointe-grating rank with the 8 vintage data set are reported in Table II.

The test statistics strongly support the view that there are 7 cointegrating vectors, and henceone stochastic trend. For example, the trace statistic for the null of r � 7 against the alternative ofr D 8 is 0.33 compared to the 5% and 10% critical values (cv) of 3.76 and 2.69, respectively. Thetrace statistic is 19.42 (5% cv D 15.41 and 10% cv D 13.33) for the null of r � 6 against r ½ 7.The �max statistics confirm this view, and small-sample adjustments to either the test statistics orcritical values would not alter this conclusion. (On small-sample adjustments see Ahn and Reinsel,1988 and Reimers, 1992, and for consistency of rank selection using the trace statistic see Nielsenand Rahbeck, 2000.) Thus, using the first 8 vintages of data the DMP is well behaved in thesense defined earlier: there is one common trend/factor driving the system. The existence of onecommon trend means that the unit root hypothesis in GNP is not rejected, although we cannot yetsay whether there is a single vintage at the basis of the permanent component of the vector timeseries comprising the first 8 vintages.

With r D 7, just identification (see Johansen, 1995b; Davidson, 1994) can be achieved by inter-preting the cointegrating vectors as providing pairwise cointegration between the vth vintage, forv D 1, . . . , 7, and the 8th vintage. Thus the jth cointegrating vector, j D 1, . . . r, comprises zeroentries apart from a normalization on the (j, j)th element and the unrestricted coefficient ˇ8j. Theextent that the coefficients on the 8th vintage, that is, ˇ8j for j D 1, . . . , r D m � 1, differ from unitycan be interpreted as the extent of departures from homogeneity, and hence from stationarity of the(log) revisions. These estimates are shown in Table III. Although the estimates are uniformly above1, the relatively large standard errors rescue the view that at least individually the null hypothesisof stationarity of revisions cannot be rejected. The joint hypothesis that the coefficients are eachunity, and hence the revisions are stationary, is testable imposing 7 over-identifying restrictions.The resulting test statistic is 9.45 [0.22], with p-value in [.], distributed as 2(7) under the null,

Table II. Test statistics for cointegrating rank (8 vintages)

Rank O� Trace 95% 90% �max 95% 90%null

r D 0 0.527 411.62 156.00 150.53 92.76 51.42 48.33r � 1 0.459 318.87 124.24 118.50 76.18 45.28 42.32r � 2 0.442 242.68 94.15 89.48 72.32 39.37 36.76r � 3 0.382 170.36 68.52 64.84 59.74 33.46 30.90r � 4 0.326 110.62 47.21 43.95 48.91 27.07 24.73r � 5 0.289 61.71 29.68 26.79 42.29 20.97 18.60r � 6 0.143 19.42 15.41 13.33 19.08 14.07 12.07r � 7 0.003 0.34 3.76 2.69 0.34 3.76 2.69

Table III. Estimates of inhomogeneity, O 8j for j D 1, . . . , 7

v D 1 2 3 4 5 6 7

Coefficient �1.005 �1.010 �1.009 �1.010 �1.009 �1.007 �1.003Std. error 0.013 0.011 0.009 0.008 0.006 0.004 0.002


256 K. Patterson

which does not lead to rejection at conventional significance levels. Imposing stationarity impliesthat each cointegrating vector comprises the pair 1, �1 with zeros elsewhere, such that overall theyprovide a basis for the cointegration space.

None of the statistics on the error-correction coefficients, ˛, for the final vintage are significant,which suggests that it would be worth considering whether this vintage is weakly exogenous.The joint test of stationarity and weak exogeneity of the 8th vintage gives a test statistic of10.57[0.72] distributed as 2(14) under the null. Testing weak exogeneity alone gives a test statis-tic of 1.06[0.99] distributed as 2(7) under the null. These test statistics suggest non-rejectionboth jointly and separately. Following the discussion above, weak exogeneity of the 8th vintageimplies that it is the common factor. Coupled with non-rejection of stationarity, some algebrashows that ˇ?�˛0

?ˇ?��1˛0? D I8, the identity matrix of order 8. Hence, the permanent, I(1), com-

ponent is yPt � ˇ?�˛0

?ˇ?��1˛0?yt D �y8

t , . . . , y8t �0; thus, we do not reject the hypothesis that the

8th vintage provides the unit root driving the system comprising the first 8 vintages of data. Thetransitory components, which are I(0) by definition, are now easily derived by the exhaustivedecomposition into permanent and transitory components and are the cumulative revisions, that is,yT

t D ˛�ˇ0˛��1zt D �y1t � y8

t , y2t � y8

t , . . . , 0�0.The hypothesis that the 8th vintage is strongly exogenous is also of interest. In addition to weak

exogeneity, strong exogeneity requires that none of yvt�i, i D 1, . . . , p � 1 and v D 1, . . . , m � 1,

are significant in the equation for ymt (that is, the mth row of (1) may only contain lags of ym

t ).As p D 2, in this case, the terms in the equation are yv

t�1, and of these the t-statistics on y1t�1

and y2t�1 are significant with p-values of 2.5% and 1.82%, respectively. Hence, strong exogeneity

is rejected, with the implication that a univariate unit root test on the 8th vintage would be invalid.We now consider whether these results are changed if the ‘final’ vintage is added to the data set,

with the cointegration test statistics reported in Table IV.It is now evidently difficult to sustain the hypothesis that r D m � 1; equivalently there are

multiple stochastic trends/common factors. Consider the trace test, then the null hypothesis r � 8is not rejected at any reasonable level of significance, and the null hypothesis r � 7 is not rejectedat the 5% or 10% levels whilst there is rejection of r � 6. The small-sample adjustment suggestedby Ahn and Reinsel (1988) implies that the test statistics are multiplied by 0.855, and with thisadjustment the p-value increases further above 10%. This is clearly an uncomfortable finding, sincean implication is that if there are two stochastic trends/common factors they are necessarily notcointegrated. The joint null hypothesis that the successive vintages, or equivalently each vintageand the final vintage, are cointegrated is implicitly rejected by the finding that s D 2. To illustrate

Table IV. Test statistics for cointegrating rank (including the final vintage)

Rank O� Trace 95% 90% �max 95% 90%null

r D 0 0.532 449.94 192.89 186.39 94.24 57.12 53.98r � 1 0.462 355.70 156.00 150.53 76.82 51.42 48.33r � 2 0.450 278.88 124.24 118.50 74.18 45.28 42.32r � 3 0.386 204.70 94.15 89.48 60.51 39.37 36.76r � 4 0.363 144.20 68.52 64.84 56.03 33.46 30.90r � 5 0.315 88.17 47.21 43.95 46.93 27.07 24.73r � 6 0.208 41.24 29.68 26.79 28.86 20.97 18.60r � 7 0.092 12.38 15.41 13.33 12.38 14.07 12.07r � 8 0.003 0.35 3.76 2.69 0.35 3.76 2.69



Table V. Excluding one vintage at a time

Excludev D

1 2 3 4 5 6 7 8 Final

Trace 13.59 12.87 12.70 12.24 12.47 12.32 12.46 12.57 19.42Adjusted 11.84 11.21 11.06 10.66 10.86 10.73 10.85 10.95 16.91

Notes: 95% critical value D 15.41; the small-sample adjustment is [(T–mp)/T]Trace D 0.871(Trace).

this point we exclude one vintage at a time for v D 1, . . . , m, with the results reported in Table V.Using the trace test statistic to illustrate whether r � 6 (hence s ½ 2) can be rejected, we see thatthis is only the case when the final vintage is excluded; rejecting the other vintages barely altersthe test statistic.

Given that we do not reject s D 2, an interesting question is what drives the two stochastictrends/common factors. A possibility, suggested by bringing together the results in Tables II, IVand V, is as follows. The results in Table II showed that r D 7 and hence s D 1 in the first 8vintages, and that the hypothesis of weak exogeneity of the 8th vintage could not be rejected. Then,from Table IV, adding the final vintage did not increase the cointegrating rank. This suggests that ahypothesis of interest is that the 8th and final vintages are weakly exogenous in the larger system.If so then ˛? D G� where G D [Q0, I2]0 as above The likelihood ratio test statistic, distributed as2(14) under the null, is 12.60 with a p-value of 0.56, hence the null hypothesis in not rejected. Thisimplies that we cannot reject the hypothesis that the permanent, I(1), component of each vintageis a function of the last two vintages, with the exception of the weakly exogenous vintages wherethe permanent component is just the corresponding weakly exogenous vintage. Although ˛? onlydefines the space of the common trends, the permanent and transitory components are unique andof interest. The permanent component and transitory components are:

I(1) component of real GNP I(0) component of real GNPyP

t � ˇ?�˛0?ˇ?��1˛0

?yt yTt D ˛�ˇ0˛��1ˇ0yt

y1t

y2t

y3t

y4t

y5t

y6t

y7t

y8t

yft

P

D

1.597 �0.5921.501 �0.4971.475 �0.4661.393 �0.3831.211 �0.2021.156 �0.1491.038 �0.0341 00 1

(y8

t

yft

)

y1t

y2t

y3t

y4t

y5t

y6t

y7t

y8t

yft

T

D

1 0 0 0 0 0 0 �1.597 0.5920 1 0 0 0 0 0 �1.501 0.4970 0 1 0 0 0 0 �1.475 0.4660 0 0 1 0 0 0 �1.393 0.3830 0 0 0 1 0 0 �1.211 0.2020 0 0 0 0 1 0 �1.156 0.1490 0 0 0 0 0 1 �1.038 0.0340 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0

y1t

y2t

y3t

y4t

y5t

y6t

y7t

y8t

yft

The weight on y8t in the permanent component for vintages v D 1, . . . , 7 is always greater than the

weight on yft ; and the weight on the final vintage declines as v approaches the 7th vintage.

One question of interest, given the structure of revisions, has already been implicitly answered bythe above representation of the permanent components. Consider the two sub-systems comprisingthe first eight vintages and the final vintage, then the question is whether the subsystems are separatein the sense of Konishi and Granger (1992) and Granger and Haldrup (1997). Separation occurs ifthe permanent components of each sub-system are a function of just the variables in the sub-system.


258 K. Patterson

That is not the case here, because the permanent component of the first sub-system depends uponthe second sub-system. Thus, whilst the final vintage does not cointegrate with the preliminaryvintages it does contribute to their common stochastic trends.

WHY DO REVISIONS OCCUR?

Given the findings of the previous section, some further consideration is given in this section tothe nature and possible reasons for revisions that induced multiple stochastic trends in GNP overthe sample period.

Note that the means of the sequential revisions to GNP are uniformly positive, indicating thatthe first (and more generally the preliminary vintages) tend to underestimate the later vintages.This is a feature of the data that is evident from Figures 2(a) and 2(b) for the comparison with the8th and final vintages, respectively. Concentrating on and comparing the upper panel in each ofthese figures it is evident that the gap that opens up in passing from the first to the final vintageis more substantial than the gap between the first and 8th vintage. This appears to be an importantfactor in explaining why we find more than one stochastic trend in the multiple vintages of datawhen the final vintage is included in the data set. As the formal analysis suggests, one trend isthen insufficient to represent the different tendencies in the data. This can be seen more clearlyif we select part of the sample and enlarge the relevant part of Figure 2(b), which is shown inFigure 3 for the 1st and final vintages for the two periods 1977–1981 and 1985–1990. It is clearthat revisions leading to the final vintage change the nature of the series in respect to the timing oflocal peaks and troughs and the local slope of the series.

Revisions to GNP data occur for a number of reasons. Generally, regular revisions occur becausemore comprehensive data becomes available and judgmental adjustments are replaced with moresource data (Barklem, 2000; Symons, 2001). In their definitive Sources and Methods (ONS, 1998)the ONS comment: ‘Estimates of GDP are built from numerous sources of information: businesssurveys, household and other social surveys, administrative information and survey data from theInland Revenue and many other sources. Data are collected monthly, quarterly, annually or insome cases from ad hoc surveys. Some of the resulting estimates which feed into GDP are firmlybased whilst others may be weak.’ Also, Penneck and Mahajan (1999) note: ‘All data sources aresubject to statistical error. Surveys are subject to sampling error . . .. In addition, statistical surveysand administrative sources are both subject to non-sampling error due to incomplete coverage,non-response, measurement error, etc.’

Thus, there is potential for revision from the many sources, and different methods, that feedinto the calculation of GDP and hence GNP. Further, the different components of GDP vary inthe extent to which they are revised. In terms of mean revisions to growth rates over the period1970–1998, Symons (2001) identifies the most revised series as gross operating surplus and thengross fixed capital formation (GFCF), followed by exports of services and imports of services. Asto GFCF, which is relevant for the expenditure estimate of GDP, Symons notes ‘The past 29 yearshave been characterized by a tendency for the initial estimate to constantly underestimate the finalestimate of growth in this series . . ..’

In principle and practice, preliminary estimates, especially from survey sources, are usually basedon less than full information. For example, estimates of household consumption are based on theONS Family Expenditure Survey, the International Passenger Survey and the National Food Survey.Although initial and final response rates for these surveys are not published some indication of why



data gets revised can be given from the Monthly Production Inquiry (MPI). The MPI is a surveyof about 9000 companies collecting data on business output and employment, and is a key inputto the Index of Production and the output measure of GDP. The initial response rate from theMPI is of the order of 81–83%, but this increases to over 90% with later estimates. In generalwith incomplete preliminary responses, imputations are made for non-response and outliers aretrimmed; for a discussion of outlier treatment in the ONS see Kokic and Cruddas (1996). In time,some non-responding units respond, outliers are corrected, processing errors may be discovered andcorrected, all giving rise to revisions to GDP and GNP.

The ONS, and its predecessor the CSO, has been keenly aware of the difficulties caused bysubstantial revisions to national accounts data. Towards the end of the 1980s there was considerable

1977 1978 1979 1980 19811100

1125

1150

1175

1200

1225

1250

1275

1300

1325Final VintageVintage 1

Total revision

1977 1978 1979 1980 1981-128

-112

-96

-80

-64

-48

-32

-16

(a)

Figure 3. (a) First and final vintages of GNP (real per capita) 1977–1981, (b) First and final vintages of GNP(real per capita) 1985–1990


260 K. Patterson

1985 1986 1987 1988 1989 19901300

1350

1400

1450

1500

1550

1600Final VintageVintage 1

Total revision

1985 1986 1987 1988 1989 1990-112

-96

-80

-64

-48

-32

-16

0

16

(b)

Figure 3. (Continued )

concern in government and key user agencies (for example, the Bank of England) about the scaleof some of the revisions to GDP and GNP and their components. One measure of the discordancybetween sources is the residual error, that is, the algebraic difference between the expenditure andincome measures of GDP. In a broad way this indicates the scope for revision as later estimatesmay bring the different measures of GDP closer together. The large magnitude of the residual erroris not just a recent phenomenon. It has been of the order of 4% or 5% of GDP on a number ofoccasions in our sample period (for example: 1965q1: �5.10%; 1973q3, 3.66%; 1979q3, �5.89%;1985q2, �4.51%; 1988q2, �5.53%).

As a result of the difficulty in interpreting key economic statistics, an efficiency scrutiny was setup to examine deficiencies in the national accounts (resulting in the Pickford Report—for somedetails see Wroe, 1993a). Also of relevance to the quality of GDP data were the ‘Chancellor’s



Initiatives’ in 1990 and 1991, which were concerned with improving the quality of national accountsdata—see Caplan and Daniel (1992), Cook (1994) and Jenkinson and Brand (2000). Buckingham(1992) recommended a number of changes to the sources and methods used to compile the balanceof payments statistics. In the mid-1990s there was also an external constraint in the form of theEuropean System of Accounts and its quality criteria. One of the impacts of this was to place‘reservations’ on the UK national accounts, which have now been removed.

The problems that the ONS has sought to address concerning data revisions have been pervasiverather than focused on one or two components of GNP/GDP; and there has been a conscious attemptto improve the quality of macroeconomic statistics throughout the range of series compiled in thenational accounts. To illustrate, in the area of capital spending the capital expenditure sample wasdoubled to 32,000 in 1999, the inventory sample was increased from 16,000 to 21,500 in 2000 anda new survey on business spending patterns, which feeds into industry specific deflators, was intro-duced in 1999 (Andrews, 2000). The changes due to these initiatives will primarily have an impacton data relating to the later part of the 1990s; because several years are needed before the final vin-tage is available, it is too early to say whether they have had the desired effect, although that is likely.

CONCLUSIONS

As noted in the Introduction, the rule with most macroeconomic time series is that the data repre-senting observations on those variables is revised a number of times, often with a long time elapsebefore there are no further revisions. This feature of the DMP leads to a number of pertinent ques-tions for users of such data. Three such questions with corollaries were raised and then answeredin this paper. The first concerned whether the DMP for real GNP was well behaved, with a singlestochastic trend, which, in turn, would cause no ambiguity in interpreting ‘the trend in GNP’. Theanswer to this question was that this is only the case in our data set if the analysis was confinedto the first eight vintages. Extending the data set to include the final vintage broke the bond ofcointegration to the previous vintages.

Second, we considered the question of whether there was a single long-memory or permanentcomponent in the vector time series of different data vintages, which could be identified with asingle vintage of data. The existence of a single stochastic trend was necessary but not sufficient forthis to be the case. The further conditions required were only satisfied if the data set did not includethe final vintage. When the final vintage was included there was evidence of two stochastic trendsand, therefore, two long-memory components. Separating the data vintages into two sub-systemscomprising the first eight and the final vintage did not result in separation as the long-memorycomponent of the first sub-system depended in part on the final vintage.

Third, we also considered the question of whether GNP contains a unit root. However, whenthe DMP results in multiple vintages, the appropriate question is not whether there is a unitroot but whether the system comprising m vintages of data on the generic variable, GNP, has acointegrating rank r < m. The difference s D m � r is the number of stochastic trends, or randomwalk components in the vector time series. The Johansen framework in this context is effectively amethod of pooling the ‘panel’ of vintages to get a multivariate unit root test. We found one randomwalk component if the final vintage of data was excluded, but two non-cointegrated random walkswhen the final vintage was included. This was confirmation in terms of the question of whetherthere is there a unit root in GNP, but there was one unit root too many in terms of the behaviourof the DMP.


262 K. Patterson

It is clear from the ONS’s own concerns and initiatives (Andrews, 2000) to improve data qualitythat they are aware of some of the difficulties that have arisen with large revisions to the macroeco-nomic aggregates in the national accounts, and to GDP and GNP in particular. A series of initiativeshas led to a large number of projects across a range of areas, covering, for example, inventoriesand fixed capital, expenditure of local and central government, various price indices, expenditureon goods and services by non-households and so on. These initiatives should lead, in due course,to greater concordance between the preliminary and final vintages of data on key aggregates suchas GDP and GNP.

ACKNOWLEDGEMENTS

Constructive comments from the editor and a referee are gratefully acknowledged. Helpful com-ments from Jesus Gonzalo and Tommaso Proietti, concerning the permanent–transitory decompo-sition, are also acknowledged. The author also benefited from discussions with staff at the Officefor National Statistics. Partial financial support from a British Academy grant and research supportat an early stage in the project from Saeed Heravi are acknowledged.

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Author’s biography:Kerry Patterson, Professor of Econometrics at the University of Reading, England, was an economic adviserat the Bank of England for 15 years and has published extensively on applied econometrics, including a recenttextbook. It was his experience in ‘real-time’ forecasting that alerted him to the problems arising from datarevisions.

Author’s address:Kerry Patterson, Department of Economics, Whiteknights Park, University of Reading, RG6 6AA, UK.


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The data measurement process for UK GNP: stochastic trends, long memory, and unit roots