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Balancing the national accounts: comments on papers by Andy Blake and Nigel Pain (NIESR) and Peter Kenny (CSO).

The idea of balancing the national accounts can be traced back to the start of national accounting in its modern form. Estimates of national income had been produced in the years before the Second World War, but the first attempt to cast economic data in an accounting framework was that of Meade and Stone (1941). A year later the first paper on balancing the national accounts (Stone, Champernowne and Meade, 1942) appeared. Had the least squares approach, which Peter Kenny at the CSO has worked on, been computationally feasible at the time, balanced accounts would probably be taken as a matter of course, and would not be seen as a slightly confusing adjunct to the conventional ways of presenting the data. While Stone had maintained an interest in balancing after the war, and other work was done in the area (for example, Arkhipoff, 1969) the renewed interest in the topic in the 1980s owes its origins to Byron (1978) who pointed out that a combination of improved computing power and better algorithms removed the difficulties faced in 1942. Dick Stone then encouraged work on the topic in the Cambridge Growth Project. This led to a number of papers in the area, and the Department of Applied Economics in Cambridge is at present home to a successor project funded by the ESRC which aims both to develop balancing methods and to apply the techniques to long runs of historical data. This project is joint with the Oxford Institute of Economics and Statistics, where Charles Feinstein is revising his estimates of national income and expenditure (Feinstein, 1972), and the output of the whole operation will be a long series of balanced estimates of national income for the United Kingdom. Our hope is that the user of historical data will become the user of balanced data.

At the same time I should report that the Bank of England have devoted resources to data reconciliation. Dunn and Egginton (1990) studied a method of data reconciliation for use when data reliabilities are unknown, and Egginton (1990) presents a useful investigation of the robustness of different methods of data reconciliation. He finds, on the basis of a Monte Carlo study, that the results of the least squares method are not very sensitive to underlying assumptions about data reliability. The article by Blake and Pain points to a helpful extension of the approach. The balancing model is based on an uncontroversial restriction on the national accounting data. The restriction that the accounting constraints should be satisfied is not going to excite much controversy. Indeed it is often, and in my view quite unfairly, regarded as a shortcoming of statisticians if the constraints are not satisfied more or less. The idea that the problems may lie somewhere else is given rather less attention. But it is not difficult to see that '1992' and the winding down of frontier controls will make the collection of trade statistics harder and the results less reliable-the reduced accuracy should not be blamed on the statisticians. There may be other models which it is expected that the data should satisfy. For example, the Treasury have a much publicised model of the economy which is constructed around the national accounting aggregates and aims to model them. The estimated equations have reliabilities attached to them. and one might think that this view of the world could be used together with the Central Statistical Office's view of the data to construct estimates of national accounting aggregates which reflect not only the CSO's views of the world, but also the Treasury's thoughts on the underlying regularities in the data.

To my knowledge the Treasury have not done this, but Blake and Pain's paper presents the first stage of such an exercise performed on the National Institute Model. They demonstrate how the accounting constraints of the national accounts can be combined with the behavioral constraints of a macroeconomic model in order to produce more reliable estimates of national income. CSO data are trusted unless 1) accounting constraints are violated or 2) they imply rather large residuals in equations which have relatively small standard errors.

Obviously we cannot say to what extent this approach will help to anticipate future revisions, but one has a general impression that the modellers have often been as good as the CSO at pinning down the very recent past. A combination of the two should therefore result in a marked gain in reliability.(1) (1) Department of Applied Economics and Clare College, Cambridge. Financial support from the ESRC under grant no. R00023 1814 is gratefully acknowledged. Furthermore, there are of course a number of models of the economy in the public domain. The study which Blake and Pain have done is reasonably straightforward, and perhaps we can hope that the Treasury will aim to replicate it on the other models which are mounted with the Warwick bureau.

The use of balanced data on their own, for the period 198702-198902 seems to worsen the performance of the forecast which was produced in November 1989. However, the use of these data combined with the early estimate of manufacturing output led to a large residual in the manufacturing output equation, and was taken as evidence that manufacturing output was overstated. Adjustment of these manufacturing estimates to bring the equation residual to its mean value for the previous eight quarters led to a forecast which proved to be a rather better prediction than was the original forecast.

It is not clear how far the improvement comes f rom the correction to the manufacturing output data (and thus to GDP(O)) rather than from the balancing of the data in the period leading up to the forecast. Since the use of balanced data on their own worsens the forecast performance slightly it might seem that the main gain is to be had from the correction of the manufacturing data. But it would be a mistake to distinguish the two adjustments too much. Both are needed in order to revise the estimated data sensibly.

There is, however, a real problem in assessing the efficacy of this approach. Are there other equations in the NIESR model which give rise to similar large residuals, but whose data are not revised promptly? The benefits of the example shown here might be due to luck.

Further research is needed. I hope that this is just the first part of a more detailed study of the use of a macroeconomic model in assessing data reliability and refining early estimates of data. The method described in Appendix A of Blake and Pain's paper seems to me to be the way forward. It could be used in conjunction with a simplified linear representation of the NIESR model derived using the methods of Weale et al. (1989) in order to provide better estimates of current data. The observed data are x, and the true data are x*. The true data satisfy the accounting constraints Ax*=0. The constraints imposed by the model are stochastic, so that, if C represents the properties of the model, then the model implies Cx* = r where r is the vector of residuals. We do not expect r to be zero because it is known that the model does not fit perfectly.(2) Least squares minimization then implies the minimization of: [Mathematical Expression Omitted] subject to the constraints that Ax*=0 and Cx*=r. The solution to this exercise means that large adjustments will be made to estimates either because they are known to be unreliable or because they lead to large residuals. Confidence in the model is traded off against confidence in the data. I do not think that rationality of expectations poses a problem to setting out the model in this way because serially uncorrelated shocks, like observational errors, typically have rather little impact on jumping variables. In other words C may be calculated taking expectations as constant.

While I very much hope that work will proceed in the direction of finding ways in which the macroeconomic models can help the statisticians with their task, it would not be sensible to anticipate a rapid shift to this approach of estimating data. As Peter Kenny reports, many of the statisticians find it difficult to accept the idea of accounts reconciled to meet the requirements of accounting consistency; it is clear that they will not be happy with data prepared using Blake and Pain's approach. The use of a behavioural model must be more controversial than reliance purely on accounting constraints.

The CSO has begun the practice of making adjustments to their estimates of the national accounts (see Economic Trends, October 1990, p.82 for example). They take the view that the output measure is the best indicator of short-term movements in output (although their very latest estimates described in he press release of December 1990 do incorporate a small alignment adjustment to the output data), and that the deflators are reliable. As a consequence movements in the residual between the expenditure and reflated output estimate imply a fault with the expenditure data, while movements in the residual between income and reflated output point to a problem with the income data. These observations are not very controversial. Taking the data for the period 1986Q1 to 1990Q2 as published in Economic Trends (October 1990) and deducting the CSO's adjustments, one finds a variance in the quarter-on-quarter percentage growth rate of nominal GDP of 2.08 for the expenditure estimate, .83 for the income estimate and .49 for the reflated output estimate. If the measurement errors are independent of the true value of the data, then it follows immediately that the expenditure estimate is much the most unreliable. On the basis of an F-test at a 5 per cent level one could accept the hypothesis that the income and output estimates have equal variance (and therefore that their measurement errors have equal variance), but this is not a reason for quarrelling with the CSO's assessment. In any case the expenditure estimate is clearly worse. After making adjustments to the expenditure and income sides the variances of the growth rates in these two estimates falls to .57 and 0.51 respectively. The adjustments have the effect of reducing the variances of the two more noisy estimates. However, since the adjustments are somewhat arbitrary, the question must arise whether they are in fact appropriate. Fortunately, the issue can be investigated more formally. A statistical test of the CSO's assumptions can be carried out. Consider the expenditure data in current prices. As noted above, these have much more noise in them than do the income data, and so there is, in some sense, more to look at. The statistical adjustments made by the CSO are applied to all the main categories of demand except government spending. There is no adjustment to the factor cost adjustment, which might seem slightly surprising given that one is made to consumer's expenditure. The underlying assumption seems to be that it is tax-free expenditure which is under-recorded. Perhaps this is not too unreasonable, since indirect tax records presumably help collect data on those items on which taxes are paid. However, for the purposes of this exercise, I propose to look simply at two components of expenditure, stockbuilding and everything else. I also look at the adjustment which the CSO make to stockbuilding and the sum of those which they make to everything else. The CSO make adjustments in the light of the residual error and with the aim of reducing it almost to zero. The question I am addressing then, is whether errors are attributed to stockbuilding which belong elsewhere, or vice versa.

Suppose that there are difficulties in measuring stockbuilding which are attributable to the way in which the stockbuilding data are collected. Then these errors should be uncorrelated with the estimates of everything else. Kenny's paper certainly suggests that those collecting the data did not identify important correlations which would make these errors correlated with the measurement errors in the other expenditure items and there is no hint that they are correlated with the true values of the other expenditure items. A fortiori the correlations between the adjustments to stockbuilding and the corrected values of other expenditure should be zero.

in the same way, the measurement errors in the other items of expenditure should be independent of those in stockbuilding and of the corrected value of stockbuilding. These observations mean that the correlations between the adjustment to stockbuilding, and the value of the other expenditure items corrected by their expenditure adjustment should be zero. The adjustment to the other components should be uncorrelated with the corrected value of stockbuilding.(3)

Consider what would happen if the whole of the residual error were attributed to stockbuilding, when in fact some of it belonged elsewhere. The stockbuilding adjustment would then include a part of the other expenditure data, and so one would expect to see a correlation between the two. Since other expenditure is also adjusted, the picture is not as simple as this, but my test is based on the same principle. The position is complicated by the fact that before 1988 no adjustments were made to any of the expenditure variables apart from stockbuilding. I propose to look at the period from 1986Q1 to 1990Q2, taking the data from Economic Trends, October 1990, splitting the sample at 1988Q1, so as to investigate whether this change of practice makes any difference. The following table shows the relevant values of R[sup.2] from the relevant regressions. These results suggest clearly a correlation between the adjustment which is made to stockbuilding and the corrected estimates of the other items of expenditure, although there is no perceptible correlation between the correction to the other expenditure items and the estimate of stockbuilding. The most obvious conclusion from the correlation between the stockbuilding adjustment and the corrected sum of the other expenditure aggregates is that a correction is being made to stockbuilding which should be made to some of the other components of GDP(E), and that would be my maintained hypothesis at the moment.

On its own, this argument does not provide a cast iron case against the CSO approach. The CSO may have good reasons for believing that stockbuilding is mismeasured when the other components of expenditure are high relative to output, although that is not obvious from their account of the adjustments in Economic Trends. But I hope it at least demonstrates the sort of question which can be raised by the application of simple statistical methods to the study of measurement residuals.

These two papers have made a valuable contribution to the issue of balancing. The first represents a step towards the use of an econometric model in the process of data estimation, and I hope this will be developed to the point where data users such as the Treasury regard it as routine to assess early estimates in the light of their model.

The second paper draws attention to the problems faced in setting up a system of balanced accounts and in convincing practitioners of their utility. Kenny questions whether the necessary resources will be available for more than occasional exercises. I would have thought that a cost-benefit analysis of the gains in accuracy from balancing compared with those that could be procured elsewhere would suggest that balancing, far from being a costly way of improving the accounts, is one of the cheapest available. Many of the costs are likely to be overhead costs. A working system need not take much time to maintain. And I hope that my simple calculations have suggested some objective evidence which might indicate why the present approach leaves something to be desired.

There is, however, a more general point which should be drawn from both papers. Data construction is susceptible to the same sort of treatment as the estimation of model parameters. Parametric estimation has made a great deal of progress since the days of ordinary least squares. On the other hand the use of econometric techniques for data estimation is at an early stage, and there is a great deal of ground to cover.

REFERENCES Arkhipoff, O. (1969), 'Essai de mise sur ordinateur des comptes nationaux', Comptabilite Nationale 1966/67: Etude Speciale

No 1, Direction de la Statistique et de la Comptabilite Nationale, Yaounde. Byron, R. (1978), 'The estimation of large social account matrices', Journal of the Royal Statistical Society, Series A, pp.

359-67. Dunn, G, and D.M. Egginton, (1990), 'Balancing the National Accounts: An asymptotically maximum-likelihood approach

using trends', Bank of England Technical Paper No. 27. Egginton, D.M (1990), 'A Monte Carlo study of alternative approaches to balancing the National Accounts', Bank of England

Technical Paper No.35. Feinstein, C.H. (1972), National Income, Expenditure and Output of the United Kingdom.- 1855-1965, Cambridge University

Press. Meade, J.E and J.R.N. Stone. (1941), 'The construction of tables of national income, expenditure, savings and investment',

Economic Journal, Vol. 51, pp. 216-33. Stone, J.R.N, D.G. Champernowne and J.E. Meade, (1942), 'The precision of national income estimates', Review of

Economic Studies, Vol. 9, pp. 111-35. Weale, M.R., A.P. Blake, N. Christodoulakis, J.E. Meade and D.A. Vines, (1989), Macroeconomic Policy: Inflation Wealth

and the Exchange Rate, Unwin Hyman. Weale, M.R. (1989),'Asymptotic maximum likelihood estimation of national income and expenditure', Department of Applied

Economics Discussion Paper No. 8913.

NOTES (1) It is sometimes suggested that forecasters perform less well at turning points of the economy. This may be true, but it is not a good reason for giving models no role in data estimation. (2) An unimportant modification is needed if there is bias in the residuals-see Appendix A of Blake and Pain's paper. (3) The results offered by Weale (1989) imply that the correlations should be insignificant provided that the correct reliabilities are used. The present exercise could be regarded as an investigation of whether correct reliabilities are used in balancing. TABULAR DATA OMITTED
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Title Annotation:"Data Adjustment and Forecast Performance" by Andy Blake and Nigel Pain, and "Work on Balanced Accounts in the CSO: History and Prospects" by P.B. Kenny
Author:Weale, Martin
Publication:National Institute Economic Review
Date:Feb 1, 1991
Previous Article:Work on balanced accounts in the CSO: history and prospects.
Next Article:The home economy.

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