# National institute economic forecasts 1968 to 1991: some tests of forecast properties.

Introduction

From time to time the Institute has published in the Review assessments of its economic forecasts based on statistical analysis of their relation with the outturn data. The most recent examples are Savage (1983) for GDP forecasts and NIESR (1984) for inflation. A more extensive analysis has now been carried out covering quarterly forecasts over the period from 1968 to 1991 for a range of economic variables. The full results are reported in Pain and Britton (1992). This note summarises some of the main findings.

At the present time there is particular concern over recent forecasting performance. In common with most other forecasters the Institute substantially underpredicted the strength of the economy in the late 1980s and also failed to foresee the onset and duration of the recent recession. This experience suggests the need to re-evaluate the conclusions of earlier studies of this kind.

In the next section of this note we discuss the Institute's forecasts of some key macroeconomic variables, illustrated with charts of forecast and outturn. The third section reports the main findings of the statistical analysis, which tests the efficiency and bias of the forecasts. It includes tests over the period as a whole and over three sub-samples. The fourth section considers the relationship between forecast errors and data revisions.

The results are consistent with earlier studies in showing that generally Institute forecasts are unbiased and contain information useful for prediction. This can be shown for the period as a whole, including the 1980s, and tests for a deterioration in the forecasts in recent years are not conclusive. Nevertheless the results for some key variables in recent years are disappointing. It would appear that forecasting has become substantially more difficult, probably because of shifts in underlying behavioural relationships which have not yet been fully incorporated into econometric models.

National Institute forecasts

This study focuses on National Institute forecasts of the annual growth in real expenditure, inflation, average earnings, employment and real personal disposable income. We examine both aggregate measures, such as Gross Domestic Product and domestic demand, and individual components of expenditure. The forecasts are all for growth between two particular quarters. This provides a stricter test of forecasting performance than the use of forecasts for growth in a calendar year since the latter contain an important element of estimated outturn.

The forecasts are taken from successive quarterly issues of the National Institute Economic Review over the period from 1968Q1-l990Q2(1). We treat the forecasts as a consistent set even though the structure of the Institute's domestic macroeconometric model has changed considerably over time, with advances in econometric techniques, economic theory, the extent of sectoral disaggregation and the treatment of expectations.

Previous studies of the Institute forecasts have considered a narrower range of variables over a smaller sample period. For example, Holden and Peel (1985) looked at real expenditure and inflation forecasts over the second half of the 1970s alone. Use of a wider range of variables and a larger sample enables us to ask whether forecasting performance has changed over time and whether any observed forecasting difficulties arise from particular variables.

The optimal base point for the annual growth forecasts is determined by the |lnformation lag' - the time between the last available published outturn data and the time at which the forecast is undertaken. In general a forecast for time t can be thought of as being made at time t-i based on information up till t-i-j, where j is the information lag. In the UK the typical information set consists of full information for t-i-2, plus partial information for t- i- 1 and some early (usually financial) information for t-i. Holden and Peel (1985) use t-i-2 as the base point as this reflects the lags in the publication of a full set of National Accounts figures. In this study we have chosen to proceed on the assumption that forecasters have a reasonable picture of activity in the quarter prior to the forecast. For many years the Institute distinguished data for t- i- 1 as an 'estimate' and figures for t-i as being a forecast. Whilst publication lags vary over time, it is generally the case that the forecaster has knowledge of policy settings, retail sales, conditions in the labour market, the balance of payments and retail prices for most, if not all of t-i-1. We therefore concentrate on growth between t-i-1 and t, with i=3.(2)

Whilst the use of forecasts made over the period 1968Q1-l990Q2 yields a sample of 90 observations, it is important to remember that the observations are not fully independent as we focus upon four-quarter growth forecasts. In cases where the sampling interval is smaller than the forecast interval the error term will exhibit serial correlation via a moving average process of order (i+j-1) for a forecast i+j steps ahead. This means that whilst the coefficients obtained using OLS may be unbiased, the covariance matrix will be inconsistent. To overcome this we follow Hansen and Hodrick (1980) in using the Generalised Method of Moments technique to correct the covariance matrix. A similar correction is utilised by Brown and Maital (1981) and Holden and Peel (1985) amongst others. For the forecasts described above the error will follow a MA(3) process.(3)

The NIESR forecasts of selected variables are shown in Charts 1-10 along with the latest available outturn (consistent with the July 1991 issue of Economic Trends). Perhaps the most striking feature of these charts is that for many variables the forecasts have succeeded in anticipating the direction of the short term variation in the growth rate. What the forecasts fail to appreciate is the extent of the variation so that the resulting forecast errors appear to be strongly procyclical.

Five episodes are of interest over this period: the rapid growth in demand in 1973 and 1987/88 (with the subsequent inflationary pressures) and the recessions of 1974/5, 1980/81 and 1991. In some respects the errors associated with the onset of the latest recession may be worse than those of 1980/81 as the downturn in overall activity was not foreseen at all. In contrast the errors in 1980 resulted from a failure to forecast the depth of the recession.

The recent poor performance in forecasting total activity does not appear to be entirely due to errors in forecasting domestic expenditure. Chart 2 shows that the forecasts made for domestic demand did pick up some of the downturn in 1990, although the errors are again positively correlated with the cycle. This is particularly true for 1988, with an error of over 5 per cent in the first quarter of the year. This by itself was not unprecedented; what was unusual was the sustained run of under predictions, last seen to any extent around 1973. Some of the divergence between the GDP and domestic demand forecast errors is accounted for by the export volume forecasts shown in Chart 5, with the errors made towards the end of the 1980s on a par with those made in the early 1980s at a time of a similar appreciation in the real exchange rate. The errors made in the forecasts of import volumes shown in Chart 6 closely reflect those made in the domestic demand forecasts.

The consumer price inflation forecasts shown in Chart 7 suggest that forecast errors became considerably smaller in the later half of the 1980s, although this is likely to have been helped by the reduced volatility of inflation. The 1970s were notable for a tendency to underpredict inflation. Similar trends are apparent in the average earnings forecasts shown in Chart 8. The employment forecasts in Chart 9 display a tendency to underestimate the fluctuations in the growth rate,(4) possibly reflecting the errors made in the GDP forecasts. Finally the forecasts made for real personal disposable income are given in Chart 10. Here there does not appear to have been any noticable change in forecasting performance over time.

Regression analysis of outturn and forecast

The main aim of the regression analysis is to examine whether the forecasts described above can be said to satisfy the minimum requirements expected of an optimal (or rational) forecast. A necessary condition for rationality is that the forecast is an unbiased estimate of the realised value so that:

O = E([A.sub.t - t-1][F.sub.t]/[I.sub.t-1]) (1) where A, is the actual outturn [F.sub.t.t-t] is the forecast made at time t-i, [I.sub.t-t] is the information set available at the time of the forecast and E denotes an expectations operator.

The standard test of rationality is to test the joint hypothesis [alpha] = 0 and [beta] = 1 in (2):

[A.sub.t] = [alpha] + [beta.sub.t-t.F.sub.t] + [epsilon.sub.t] (2)

Rejection of the null implies that the forecasts could be improved by knowledge of the [alpha] and [BETA] parameters and therefore provides evidence of inefficiency in the forecast (Mincer and Zarnowitz, 1969). In particular if [BETA] [is not equal to]1, then the forecast and the forecast error must be correlated and therefore it would be possible to improve the forecast by exploiting the correlation.(5) Equation (2) is also often presented as a test of unbiasedness. However Holden and Peel (1990) show the null that [alpha]=O and [BETA] =1 is only a sufficient condition for the absence of bias. A necessary and sufficient condition is given by [alpha]=(1 - [BETA]).E([F.sub.t.t-1]). Thus it is possible to test for bias by testing the null that [alpha]=O in (3):

[A.sub.t] - [F.sub.t.t-1] = [alpha] + [epsilon.sub.t] (3)

It is also useful to amend (2) and (3) so as to investigate whether the results obtained are sensitive to particular unanticipated exogenous shocks such as strikes and major legislative changes. Such unforseen (and arguably unforecastable) events can generate large outliers in the observed forecast errors. Dummies are used below for the dock strikes of 1970, 1972 and 1979, the three-day week of 1974, the VAT shift in 1979 and the introduction of the poll tax in 1990. The impact of the three-day week can be seen in Chart 1 which shows the forecasts for GDP. The amended equations take the form:

[A.sub.t] = [alpha] + [BETA.sub.t] [F.sub.t.-t] + [delta.sub.i] DUM(i) + [epsilon.sub.t] (2a)

[A.sub.t] - [F.sub.t.t-1] = [alpha] + [sigma.sub.i]DUM(i) + [epsilon.sub.t]

(3a)

Dummy variables for all of these events are commonly found in most UK macroeconomic models.

It is also possible to test whether forecast performance has changed significantly over time. This may be done by writing (2) as:

[A.sub.t] = [alpha.sub.O] + [alpha.sub.1] D + [BETA.sub.Ot.t] - [F.sub.t] + [BETA.ub.1.D.sub.t-i.F.sub.t] + [epsilon.sub.t] (4) where D is a dummy variable equal to 1 from the time of the break point onwards. Equation (4) is estimated over the whole sample. The absence of a structural break involves a joint test of [alpha.ub.1] = [BETA.ub.1] = O.

The results of applying (2) and (2a) to the quarterly forecasts made since 1968 are summarised in Table 1. The outturn data used are the most recently available. The respective null hypotheses are tested using Wald [chi.sup.2] statistics obtained from the amended covariance matrix with the covariance matrix derived using the Hansen-Hodrick procedure. Absolute values of the resulting t-statistics are given in parentheses(6). Results are also given for 3 sub-samples of 30 observations each in order to assess changes in performance over time.

[TABULAR DATA OMITTED]

Over the period as a whole the hypothesis of efficiency cannot be rejected with regard to GDP growth, domestic demand, investment, exports, imports, inflation, earnings or employment. In all these cases the intercept terms ([alpha]) are not statistically significant, and the slope coefficients ([BETA]) are not significantly different from unity. The hypothesis of efficiency can be rejected however for the forecasts of consumer spending and real personal disposable income. In both cases there is some evidence of systematic underprediction over the period as a whole.

The correlation coefficients indicate the proportion of the variation in the outturn which is |explained' by the forecast. This is one way of measuring how useful the forecasts have been, or the extent to which they have reduced the subjective uncertainty of future events. For GDP the coefficient is about one-third over the period as a whole (once the dummies are included). For the nominal variables, prices and wages, the coefficients are much higher, but this must be seen in relation to the greater persistance of inflation than real growth.

The results for sub-periods indicate considerable variation in performance in different time periods. The middle sample of 1976-83 is closely related to that used in Holden and Peel (1985) and reveals little evidence of inefficiency, with the null being rejected for the real disposable income forecast alone. The evidence of inefficiency appears greatest in the final sub-sample over the period from 1983Q4 onwards, with the null hypothesis of efficiency being accepted only for GDP, investment, earnings and employment. In the cases of GDP and exports there is no correlation between forecast and outturn over that period at all; for domestic demand and for imports the correlation is relatively high, but the forecasts systematically underpredict the variation in the outturn. Clearly forecasting performance was not as good in the last sub-period as it had been previously. But the question remains whether it was significantly less successful, or whether this is just an example of the variation in performance which is to be expected from time to time.

Equivalent regressions using (3) and (3a) are reported in Pain and Britton (1992). The results largely confirm the findings in Table 1, with many of the inefficient forecasts also being biased. An additional point of interest is the change in the direction of bias in the GDP forecasts in the various subsamples, with a consistent underprediction of growth in the final period. This is also reflected in the domestic demand errors and appears to largely stem from the investment forecasts. For consumers' expenditure there is evidence of significant underprediction throughout the entire sample. This is also true of the disposable income forecasts.

Tests for a structural break

The question as to whether performance could be said to have changed significantly in the final sub-sample was addressed by using (4) with D equal to 1 from 1983Q4 onwards. The resulting regressions are given in Table 2, along with Wald tests for a structural break. (Dummy variables were included, but are not reported.)

The test statistics are best interpreted as asking whether any inefficiencies in the forecasts from 1983Q4 onwards differ from those in earlier forecasts. Somewhat surprisingly there only appears to be evidence of structural breaks in the relationships for investment and disposable income when the latest outturns are used, although the statistics for GDP, domestic demand and inflation are significant at the 10 per cent level. The most likely explanation is that many coefficients are poorly determined in the final subsample and therefore consistent with a number of different hypotheses. If the initial outturns are used, the null is rejected for four variables, GDP, inflation, employment and disposable income.

Overall, the evidence presented thus far is suggestive of some deterioration in forecast performance since the mid-1980s, although the experience of forecasting different variables is by no means uniform. Indeed for some variables such as investment it is not possible to reject the null that the most recent forecasts are collectively unbiased and efficient, even though the relationship between the forecast and the outcome appears to have changed significantly.

Was the information set used efficiently?

The absence of bias and inefficiency in (2) and (3) is only a necessary condition for rationality. A further requirement is that forecasts should fully reflect the information in the past history of the variable concerned as well as previous forecast errors. Figlewski and Wachtel (1981) test for efficiency using a regression of the forecast error (defined using the first outturn denoted by i) on the most recent forecast error perceived at the time of the forecast:

[A.sub.t] - [F.sub.t-i.t] = [alpha] + [BETA] ([A.sub.t-i-1] - [F.sub.t-21-1.t-i]) (5)

If the forecast is efficient and takes into account any lessons learnt from the past then it should be possible to impose [alpha] = [BETA] = O.

An alternative approach is to use an equation of the form

[A.sub.t] = [alpha] + [BETA.sub.t-i.F.sub.t] + [gamma] [A.sub.t-i-1] + [epsilon.sub.t] (6)

This equation allows us to compare the information in the NIESR forecasts with that from a simple time series model that projects growth at the last observed rate at the time of the forecast. The t-statistic on [BETA] provides a test of whether the forecast itself adds any relevant information (Fair and Shiller, 1990). The t-statistic on [gamma] indicates whether the forecast has omitted any relevant information (allowing for possible bias).

The relationship between the forecast errors in (5) is reported in Table 3. Over the period as a whole there appears to be relatively little relationship between the errors, with the null only being rejected for investment, employment and disposable income. For investment, the departure from rationality largely stems from a failure to make full use of the information contained in past errors during the second sub-sample.

[TABULAR DATA OMITTED]

As with the previous tests, the evidence of inefficiency is greatest in the final sub-sample, with the null being rejected for consumption, inflation, earnings, employment and disposable income. In most cases this is associated with a significant intercept term, which simply confirms the bias found in some earlier tests. In the cases of inflation and earnings (and also GDP) the coefficient on the latest error terms is significant. This suggests that forecasters could have done better over this period if they had adjusted their initial projections to take account of the errors observed in previous forecasts. In an informal way forecasters always try to learn from their mistakes. The results in Table 3 suggest that there was considerable scope for doing so during the 1980s.

The results from the forecast encompassing test (6) augmented by dummy variables) are reported in Table 4. Over the sample as a whole, all the forecasts contain significant information, even though some are inefficient. The domestic demand, exports and earnings regressions are the only ones in which the lagged own growth rates are close to being significant at conventional levels. The corollary to this is that there is relatively little in the lagged information set of the variables alone that can account for the forecast errors.

[TABULAR DATA OMITTED]

Again the results differ across the sub-samples, with the investment forecasts in the first period and the import forecasts in both the first and second periods containing little useful information. In the most recent period this is true of the GDP, export and inflation forecasts. The problems with GDP may arise from exports since the domestic demand forecast seems to contain more useful information. The results for earnings are also of interest, since in both the first and third sub-samples the forecast and the lagged growth rate are significant, suggesting a greater degree of inertia in wages than the forecasts allowed for.

The relationship between data revisions and forecast

errors

This final section addresses the hypothesis that the observed forecast errors arise from the false signals that forecasters have received about the position of the economic cycle as a result of errors in the National Accounts. One common explanation for recent forecast errors is that there has been a deterioration in the quality of official statistics, see for example Hibberd (1990). This concern mainly relates to the apparent failure of initial estimates to fully capture the extent of the variation in the growth rate rather than its direction of movement. Underlying the problem of data revisions is the feeling that if forecasters knew where the economy was they would be able to provide a better picture of where it was going. This argument can be assessed in two ways. First, it is possible to examine individual forecasts to see how important data errors were. One example of such a study is Blake and Pain (1991). Alternatively, it is possible to test the importance of data revisions across the cycle as a whole. This provides some indication of whether data revisions have a consistent adverse effect on forecasts. For example, whilst data errors may have contributed to errors made in 1987/88, it is less clear how they influenced the failure to spot the recession in 1990/1.

In assessing the importance of data revisions it is very important to specify the period to which forecasts relate. A forecast of output growth between year i- 1 and year i made in year i will necessarily as a matter of arithmetic depend heavily on early estimates of the level of output in year i-1. If the provisional estimates are incorrect then the growth forecast could well prove inaccurate. Alternatively if we are concerned only with forecasts of growth over periods which are genuinely in the future the effect of data revisions will be ambiguous. If the estimates of activity in the pre-forecast period were to be revised up, this could lead forecasters either to raise or lower their forecasts for growth in the future depending on the model and methods they are using.

The general relationship between the latest data for growth and the initial estimate(7) is typified by the domestic demand figures in Chart 11, with the initial estimates providing a reasonable estimate of the true growth rate and capturing a number of turning points in the respective series. Whilst there was a period between 1986-88 when growth in domestic demand was continually underestimated, the errors were not noticeably larger than in earlier periods, with a string of similar errors being made in the early 1970s at the time of the |Barber boom'.(8)

The results from a test of whether there is a significant relationship between forecast errors and data revisions are reported in Pain and Britton (1992). We find significant effects for both the trade volumes and for real disposable income in the full sample and domestic demand and investment in the first two sub-samples, although (as yet) there does not appear to be a firmly established relationship in the final sub-sample. The null is rejected for consumption in the final sample, but this largely reflects the consistently positive forecast error.

Overall the results are mixed. This suggests that there is relatively little firm evidence that data inaccuracies have a significant influence on forecast errors. Indeed the evidence we present may simply reflect the known effects on growth rates associated with rebasing. However this conclusion is necessarily tentative. In particular it does not imply that preliminary data have not been a source of error in individual forecasts.

Conclusions

The positive finding from this study is that over the period from 1969 to the present day the Institute forecasts are generally unbiased and weakly efficient and clearly contain information significant for prediction. Previous studies had suggested that this was true of forecasts up till 1980, but we did not know beforehand that the results would hold up when the forecasts made over the last decade were included. On this basis it is still possible to conclude that economic forecasting is a worthwhile activity, although the evidence for this is not as strong as it was ten years ago and the experience of forecasting different variables is far from uniform.

NOTES

(1) In the case of the Institute, the forecast is typically begun at the end of the first month in the quarter, with the Review published at the end of the second month. (2) Thus for 1968Q1 we take the forecast for growth between 1967Q4 and 1968Q4. (3) It is also possible to correct for possible heteroskedasticity in the estimation of the standard errors of the coefficients. We have not done this at present. Evidence in Mishkin (1990) suggests that such corrections, in contrast to the serial correlation ones, do not help to produce better statistical inference. (4) This may simply indicate that the forecasts are optimal, see Mincer and Zarnowitz (1969). (5) We interpret evidence of inefficiency as a departure from rationality, although, as Zellner (1986) illustrates, if loss functions are asymmetric then biased predictors may be optimal. (6) The reported t-statistics indicate whether [alpha] and [BETA] are significantly different from zero. (7) The initial estimate of annual growth up to a particular quarter consists of the growth rate perceived at the time of the forecast undertaken in the following quarter. It thus consists of 3 quarters worth of official data plus an estimate made by the forecaster. (8) This is less true of some of the components of expenditure. For example, the initial investment estimates for 1988 underpredicted the true growth rate by as much as 8 to 9 per cent.

REFERENCES

Blake A.P. and N.C. Pain (1991), |Data adjustment and forecast performance', National Institute Economic Review, 135, 66-78. Brown B.W. and S. Maital (1981), |What do economists know? An empirical study of experts' expectations', Econometrica, 49, 491-504. Fair R.C. and R.J. Shiller (1990), |Comparing information in forecasts from econometric models', American Economic Review, 80,375-389. Figlewski S. and P.Wachtel (1981), |The formation of inflationary expectations', Review of Economics and statistics, LXIII, 1-10. Hansen L.P. and R.J. Hodrick (1980), |Forward exchange rates as optimal predictors of future spot rates: An econometric analysis', journal of Political economy, 88, 829-853. Hibberd J. (1990), |Official statistics in the late 1980s', Treasury Bulletin, Summer 1990, 2-13. Holden K. and D.A. Peel (1985), |An evaluation of quarterly National Institute forecasts', Journal of Forecasting, 4,227-234. Holden K. and D.A. Peel (1990), |On testing for unbiasedness and efficiency of forecasts', The Manchester School, LVIII, 120-127. Mincer J. and V. Zarnowitz (1969), |The evaluation of economic forecasts', in Economic Forecasts and Expectations, ed. J. Mincer, Columbia University Press. Mishkin F.S. (1990), 'Does correcting for heteroscedasticity help?', Economics Letters, 34, 351-356. NIESR (1984)' The National Institute's forecasts of inflation 1964-82', National Institute Economic Review 107,47-49. Pain, N. and A. Britton, (1992), |The recent experience of economic forecasting in Britain: some lessons from National Institute forecasts', National Institute Discussion Paper (New Series) No. 20. Savage D. (1983), |The assessment of the National Institute's forecasts of GDP, 1959-82', National Institute Economic Review, 105,29-35. Zellner A. (1986), |Biased predictors, rationality and the evaluation of forecasts', Economics Letters, 21, 45-48.

From time to time the Institute has published in the Review assessments of its economic forecasts based on statistical analysis of their relation with the outturn data. The most recent examples are Savage (1983) for GDP forecasts and NIESR (1984) for inflation. A more extensive analysis has now been carried out covering quarterly forecasts over the period from 1968 to 1991 for a range of economic variables. The full results are reported in Pain and Britton (1992). This note summarises some of the main findings.

At the present time there is particular concern over recent forecasting performance. In common with most other forecasters the Institute substantially underpredicted the strength of the economy in the late 1980s and also failed to foresee the onset and duration of the recent recession. This experience suggests the need to re-evaluate the conclusions of earlier studies of this kind.

In the next section of this note we discuss the Institute's forecasts of some key macroeconomic variables, illustrated with charts of forecast and outturn. The third section reports the main findings of the statistical analysis, which tests the efficiency and bias of the forecasts. It includes tests over the period as a whole and over three sub-samples. The fourth section considers the relationship between forecast errors and data revisions.

The results are consistent with earlier studies in showing that generally Institute forecasts are unbiased and contain information useful for prediction. This can be shown for the period as a whole, including the 1980s, and tests for a deterioration in the forecasts in recent years are not conclusive. Nevertheless the results for some key variables in recent years are disappointing. It would appear that forecasting has become substantially more difficult, probably because of shifts in underlying behavioural relationships which have not yet been fully incorporated into econometric models.

National Institute forecasts

This study focuses on National Institute forecasts of the annual growth in real expenditure, inflation, average earnings, employment and real personal disposable income. We examine both aggregate measures, such as Gross Domestic Product and domestic demand, and individual components of expenditure. The forecasts are all for growth between two particular quarters. This provides a stricter test of forecasting performance than the use of forecasts for growth in a calendar year since the latter contain an important element of estimated outturn.

The forecasts are taken from successive quarterly issues of the National Institute Economic Review over the period from 1968Q1-l990Q2(1). We treat the forecasts as a consistent set even though the structure of the Institute's domestic macroeconometric model has changed considerably over time, with advances in econometric techniques, economic theory, the extent of sectoral disaggregation and the treatment of expectations.

Previous studies of the Institute forecasts have considered a narrower range of variables over a smaller sample period. For example, Holden and Peel (1985) looked at real expenditure and inflation forecasts over the second half of the 1970s alone. Use of a wider range of variables and a larger sample enables us to ask whether forecasting performance has changed over time and whether any observed forecasting difficulties arise from particular variables.

The optimal base point for the annual growth forecasts is determined by the |lnformation lag' - the time between the last available published outturn data and the time at which the forecast is undertaken. In general a forecast for time t can be thought of as being made at time t-i based on information up till t-i-j, where j is the information lag. In the UK the typical information set consists of full information for t-i-2, plus partial information for t- i- 1 and some early (usually financial) information for t-i. Holden and Peel (1985) use t-i-2 as the base point as this reflects the lags in the publication of a full set of National Accounts figures. In this study we have chosen to proceed on the assumption that forecasters have a reasonable picture of activity in the quarter prior to the forecast. For many years the Institute distinguished data for t- i- 1 as an 'estimate' and figures for t-i as being a forecast. Whilst publication lags vary over time, it is generally the case that the forecaster has knowledge of policy settings, retail sales, conditions in the labour market, the balance of payments and retail prices for most, if not all of t-i-1. We therefore concentrate on growth between t-i-1 and t, with i=3.(2)

Whilst the use of forecasts made over the period 1968Q1-l990Q2 yields a sample of 90 observations, it is important to remember that the observations are not fully independent as we focus upon four-quarter growth forecasts. In cases where the sampling interval is smaller than the forecast interval the error term will exhibit serial correlation via a moving average process of order (i+j-1) for a forecast i+j steps ahead. This means that whilst the coefficients obtained using OLS may be unbiased, the covariance matrix will be inconsistent. To overcome this we follow Hansen and Hodrick (1980) in using the Generalised Method of Moments technique to correct the covariance matrix. A similar correction is utilised by Brown and Maital (1981) and Holden and Peel (1985) amongst others. For the forecasts described above the error will follow a MA(3) process.(3)

The NIESR forecasts of selected variables are shown in Charts 1-10 along with the latest available outturn (consistent with the July 1991 issue of Economic Trends). Perhaps the most striking feature of these charts is that for many variables the forecasts have succeeded in anticipating the direction of the short term variation in the growth rate. What the forecasts fail to appreciate is the extent of the variation so that the resulting forecast errors appear to be strongly procyclical.

Five episodes are of interest over this period: the rapid growth in demand in 1973 and 1987/88 (with the subsequent inflationary pressures) and the recessions of 1974/5, 1980/81 and 1991. In some respects the errors associated with the onset of the latest recession may be worse than those of 1980/81 as the downturn in overall activity was not foreseen at all. In contrast the errors in 1980 resulted from a failure to forecast the depth of the recession.

The recent poor performance in forecasting total activity does not appear to be entirely due to errors in forecasting domestic expenditure. Chart 2 shows that the forecasts made for domestic demand did pick up some of the downturn in 1990, although the errors are again positively correlated with the cycle. This is particularly true for 1988, with an error of over 5 per cent in the first quarter of the year. This by itself was not unprecedented; what was unusual was the sustained run of under predictions, last seen to any extent around 1973. Some of the divergence between the GDP and domestic demand forecast errors is accounted for by the export volume forecasts shown in Chart 5, with the errors made towards the end of the 1980s on a par with those made in the early 1980s at a time of a similar appreciation in the real exchange rate. The errors made in the forecasts of import volumes shown in Chart 6 closely reflect those made in the domestic demand forecasts.

The consumer price inflation forecasts shown in Chart 7 suggest that forecast errors became considerably smaller in the later half of the 1980s, although this is likely to have been helped by the reduced volatility of inflation. The 1970s were notable for a tendency to underpredict inflation. Similar trends are apparent in the average earnings forecasts shown in Chart 8. The employment forecasts in Chart 9 display a tendency to underestimate the fluctuations in the growth rate,(4) possibly reflecting the errors made in the GDP forecasts. Finally the forecasts made for real personal disposable income are given in Chart 10. Here there does not appear to have been any noticable change in forecasting performance over time.

Regression analysis of outturn and forecast

The main aim of the regression analysis is to examine whether the forecasts described above can be said to satisfy the minimum requirements expected of an optimal (or rational) forecast. A necessary condition for rationality is that the forecast is an unbiased estimate of the realised value so that:

O = E([A.sub.t - t-1][F.sub.t]/[I.sub.t-1]) (1) where A, is the actual outturn [F.sub.t.t-t] is the forecast made at time t-i, [I.sub.t-t] is the information set available at the time of the forecast and E denotes an expectations operator.

The standard test of rationality is to test the joint hypothesis [alpha] = 0 and [beta] = 1 in (2):

[A.sub.t] = [alpha] + [beta.sub.t-t.F.sub.t] + [epsilon.sub.t] (2)

Rejection of the null implies that the forecasts could be improved by knowledge of the [alpha] and [BETA] parameters and therefore provides evidence of inefficiency in the forecast (Mincer and Zarnowitz, 1969). In particular if [BETA] [is not equal to]1, then the forecast and the forecast error must be correlated and therefore it would be possible to improve the forecast by exploiting the correlation.(5) Equation (2) is also often presented as a test of unbiasedness. However Holden and Peel (1990) show the null that [alpha]=O and [BETA] =1 is only a sufficient condition for the absence of bias. A necessary and sufficient condition is given by [alpha]=(1 - [BETA]).E([F.sub.t.t-1]). Thus it is possible to test for bias by testing the null that [alpha]=O in (3):

[A.sub.t] - [F.sub.t.t-1] = [alpha] + [epsilon.sub.t] (3)

It is also useful to amend (2) and (3) so as to investigate whether the results obtained are sensitive to particular unanticipated exogenous shocks such as strikes and major legislative changes. Such unforseen (and arguably unforecastable) events can generate large outliers in the observed forecast errors. Dummies are used below for the dock strikes of 1970, 1972 and 1979, the three-day week of 1974, the VAT shift in 1979 and the introduction of the poll tax in 1990. The impact of the three-day week can be seen in Chart 1 which shows the forecasts for GDP. The amended equations take the form:

[A.sub.t] = [alpha] + [BETA.sub.t] [F.sub.t.-t] + [delta.sub.i] DUM(i) + [epsilon.sub.t] (2a)

[A.sub.t] - [F.sub.t.t-1] = [alpha] + [sigma.sub.i]DUM(i) + [epsilon.sub.t]

(3a)

Dummy variables for all of these events are commonly found in most UK macroeconomic models.

It is also possible to test whether forecast performance has changed significantly over time. This may be done by writing (2) as:

[A.sub.t] = [alpha.sub.O] + [alpha.sub.1] D + [BETA.sub.Ot.t] - [F.sub.t] + [BETA.ub.1.D.sub.t-i.F.sub.t] + [epsilon.sub.t] (4) where D is a dummy variable equal to 1 from the time of the break point onwards. Equation (4) is estimated over the whole sample. The absence of a structural break involves a joint test of [alpha.ub.1] = [BETA.ub.1] = O.

The results of applying (2) and (2a) to the quarterly forecasts made since 1968 are summarised in Table 1. The outturn data used are the most recently available. The respective null hypotheses are tested using Wald [chi.sup.2] statistics obtained from the amended covariance matrix with the covariance matrix derived using the Hansen-Hodrick procedure. Absolute values of the resulting t-statistics are given in parentheses(6). Results are also given for 3 sub-samples of 30 observations each in order to assess changes in performance over time.

[TABULAR DATA OMITTED]

Over the period as a whole the hypothesis of efficiency cannot be rejected with regard to GDP growth, domestic demand, investment, exports, imports, inflation, earnings or employment. In all these cases the intercept terms ([alpha]) are not statistically significant, and the slope coefficients ([BETA]) are not significantly different from unity. The hypothesis of efficiency can be rejected however for the forecasts of consumer spending and real personal disposable income. In both cases there is some evidence of systematic underprediction over the period as a whole.

The correlation coefficients indicate the proportion of the variation in the outturn which is |explained' by the forecast. This is one way of measuring how useful the forecasts have been, or the extent to which they have reduced the subjective uncertainty of future events. For GDP the coefficient is about one-third over the period as a whole (once the dummies are included). For the nominal variables, prices and wages, the coefficients are much higher, but this must be seen in relation to the greater persistance of inflation than real growth.

The results for sub-periods indicate considerable variation in performance in different time periods. The middle sample of 1976-83 is closely related to that used in Holden and Peel (1985) and reveals little evidence of inefficiency, with the null being rejected for the real disposable income forecast alone. The evidence of inefficiency appears greatest in the final sub-sample over the period from 1983Q4 onwards, with the null hypothesis of efficiency being accepted only for GDP, investment, earnings and employment. In the cases of GDP and exports there is no correlation between forecast and outturn over that period at all; for domestic demand and for imports the correlation is relatively high, but the forecasts systematically underpredict the variation in the outturn. Clearly forecasting performance was not as good in the last sub-period as it had been previously. But the question remains whether it was significantly less successful, or whether this is just an example of the variation in performance which is to be expected from time to time.

Equivalent regressions using (3) and (3a) are reported in Pain and Britton (1992). The results largely confirm the findings in Table 1, with many of the inefficient forecasts also being biased. An additional point of interest is the change in the direction of bias in the GDP forecasts in the various subsamples, with a consistent underprediction of growth in the final period. This is also reflected in the domestic demand errors and appears to largely stem from the investment forecasts. For consumers' expenditure there is evidence of significant underprediction throughout the entire sample. This is also true of the disposable income forecasts.

Tests for a structural break

The question as to whether performance could be said to have changed significantly in the final sub-sample was addressed by using (4) with D equal to 1 from 1983Q4 onwards. The resulting regressions are given in Table 2, along with Wald tests for a structural break. (Dummy variables were included, but are not reported.)

The test statistics are best interpreted as asking whether any inefficiencies in the forecasts from 1983Q4 onwards differ from those in earlier forecasts. Somewhat surprisingly there only appears to be evidence of structural breaks in the relationships for investment and disposable income when the latest outturns are used, although the statistics for GDP, domestic demand and inflation are significant at the 10 per cent level. The most likely explanation is that many coefficients are poorly determined in the final subsample and therefore consistent with a number of different hypotheses. If the initial outturns are used, the null is rejected for four variables, GDP, inflation, employment and disposable income.

Overall, the evidence presented thus far is suggestive of some deterioration in forecast performance since the mid-1980s, although the experience of forecasting different variables is by no means uniform. Indeed for some variables such as investment it is not possible to reject the null that the most recent forecasts are collectively unbiased and efficient, even though the relationship between the forecast and the outcome appears to have changed significantly.

Was the information set used efficiently?

The absence of bias and inefficiency in (2) and (3) is only a necessary condition for rationality. A further requirement is that forecasts should fully reflect the information in the past history of the variable concerned as well as previous forecast errors. Figlewski and Wachtel (1981) test for efficiency using a regression of the forecast error (defined using the first outturn denoted by i) on the most recent forecast error perceived at the time of the forecast:

[A.sub.t] - [F.sub.t-i.t] = [alpha] + [BETA] ([A.sub.t-i-1] - [F.sub.t-21-1.t-i]) (5)

If the forecast is efficient and takes into account any lessons learnt from the past then it should be possible to impose [alpha] = [BETA] = O.

An alternative approach is to use an equation of the form

[A.sub.t] = [alpha] + [BETA.sub.t-i.F.sub.t] + [gamma] [A.sub.t-i-1] + [epsilon.sub.t] (6)

This equation allows us to compare the information in the NIESR forecasts with that from a simple time series model that projects growth at the last observed rate at the time of the forecast. The t-statistic on [BETA] provides a test of whether the forecast itself adds any relevant information (Fair and Shiller, 1990). The t-statistic on [gamma] indicates whether the forecast has omitted any relevant information (allowing for possible bias).

The relationship between the forecast errors in (5) is reported in Table 3. Over the period as a whole there appears to be relatively little relationship between the errors, with the null only being rejected for investment, employment and disposable income. For investment, the departure from rationality largely stems from a failure to make full use of the information contained in past errors during the second sub-sample.

[TABULAR DATA OMITTED]

As with the previous tests, the evidence of inefficiency is greatest in the final sub-sample, with the null being rejected for consumption, inflation, earnings, employment and disposable income. In most cases this is associated with a significant intercept term, which simply confirms the bias found in some earlier tests. In the cases of inflation and earnings (and also GDP) the coefficient on the latest error terms is significant. This suggests that forecasters could have done better over this period if they had adjusted their initial projections to take account of the errors observed in previous forecasts. In an informal way forecasters always try to learn from their mistakes. The results in Table 3 suggest that there was considerable scope for doing so during the 1980s.

The results from the forecast encompassing test (6) augmented by dummy variables) are reported in Table 4. Over the sample as a whole, all the forecasts contain significant information, even though some are inefficient. The domestic demand, exports and earnings regressions are the only ones in which the lagged own growth rates are close to being significant at conventional levels. The corollary to this is that there is relatively little in the lagged information set of the variables alone that can account for the forecast errors.

[TABULAR DATA OMITTED]

Again the results differ across the sub-samples, with the investment forecasts in the first period and the import forecasts in both the first and second periods containing little useful information. In the most recent period this is true of the GDP, export and inflation forecasts. The problems with GDP may arise from exports since the domestic demand forecast seems to contain more useful information. The results for earnings are also of interest, since in both the first and third sub-samples the forecast and the lagged growth rate are significant, suggesting a greater degree of inertia in wages than the forecasts allowed for.

The relationship between data revisions and forecast

errors

This final section addresses the hypothesis that the observed forecast errors arise from the false signals that forecasters have received about the position of the economic cycle as a result of errors in the National Accounts. One common explanation for recent forecast errors is that there has been a deterioration in the quality of official statistics, see for example Hibberd (1990). This concern mainly relates to the apparent failure of initial estimates to fully capture the extent of the variation in the growth rate rather than its direction of movement. Underlying the problem of data revisions is the feeling that if forecasters knew where the economy was they would be able to provide a better picture of where it was going. This argument can be assessed in two ways. First, it is possible to examine individual forecasts to see how important data errors were. One example of such a study is Blake and Pain (1991). Alternatively, it is possible to test the importance of data revisions across the cycle as a whole. This provides some indication of whether data revisions have a consistent adverse effect on forecasts. For example, whilst data errors may have contributed to errors made in 1987/88, it is less clear how they influenced the failure to spot the recession in 1990/1.

In assessing the importance of data revisions it is very important to specify the period to which forecasts relate. A forecast of output growth between year i- 1 and year i made in year i will necessarily as a matter of arithmetic depend heavily on early estimates of the level of output in year i-1. If the provisional estimates are incorrect then the growth forecast could well prove inaccurate. Alternatively if we are concerned only with forecasts of growth over periods which are genuinely in the future the effect of data revisions will be ambiguous. If the estimates of activity in the pre-forecast period were to be revised up, this could lead forecasters either to raise or lower their forecasts for growth in the future depending on the model and methods they are using.

The general relationship between the latest data for growth and the initial estimate(7) is typified by the domestic demand figures in Chart 11, with the initial estimates providing a reasonable estimate of the true growth rate and capturing a number of turning points in the respective series. Whilst there was a period between 1986-88 when growth in domestic demand was continually underestimated, the errors were not noticeably larger than in earlier periods, with a string of similar errors being made in the early 1970s at the time of the |Barber boom'.(8)

The results from a test of whether there is a significant relationship between forecast errors and data revisions are reported in Pain and Britton (1992). We find significant effects for both the trade volumes and for real disposable income in the full sample and domestic demand and investment in the first two sub-samples, although (as yet) there does not appear to be a firmly established relationship in the final sub-sample. The null is rejected for consumption in the final sample, but this largely reflects the consistently positive forecast error.

Overall the results are mixed. This suggests that there is relatively little firm evidence that data inaccuracies have a significant influence on forecast errors. Indeed the evidence we present may simply reflect the known effects on growth rates associated with rebasing. However this conclusion is necessarily tentative. In particular it does not imply that preliminary data have not been a source of error in individual forecasts.

Conclusions

The positive finding from this study is that over the period from 1969 to the present day the Institute forecasts are generally unbiased and weakly efficient and clearly contain information significant for prediction. Previous studies had suggested that this was true of forecasts up till 1980, but we did not know beforehand that the results would hold up when the forecasts made over the last decade were included. On this basis it is still possible to conclude that economic forecasting is a worthwhile activity, although the evidence for this is not as strong as it was ten years ago and the experience of forecasting different variables is far from uniform.

NOTES

(1) In the case of the Institute, the forecast is typically begun at the end of the first month in the quarter, with the Review published at the end of the second month. (2) Thus for 1968Q1 we take the forecast for growth between 1967Q4 and 1968Q4. (3) It is also possible to correct for possible heteroskedasticity in the estimation of the standard errors of the coefficients. We have not done this at present. Evidence in Mishkin (1990) suggests that such corrections, in contrast to the serial correlation ones, do not help to produce better statistical inference. (4) This may simply indicate that the forecasts are optimal, see Mincer and Zarnowitz (1969). (5) We interpret evidence of inefficiency as a departure from rationality, although, as Zellner (1986) illustrates, if loss functions are asymmetric then biased predictors may be optimal. (6) The reported t-statistics indicate whether [alpha] and [BETA] are significantly different from zero. (7) The initial estimate of annual growth up to a particular quarter consists of the growth rate perceived at the time of the forecast undertaken in the following quarter. It thus consists of 3 quarters worth of official data plus an estimate made by the forecaster. (8) This is less true of some of the components of expenditure. For example, the initial investment estimates for 1988 underpredicted the true growth rate by as much as 8 to 9 per cent.

REFERENCES

Blake A.P. and N.C. Pain (1991), |Data adjustment and forecast performance', National Institute Economic Review, 135, 66-78. Brown B.W. and S. Maital (1981), |What do economists know? An empirical study of experts' expectations', Econometrica, 49, 491-504. Fair R.C. and R.J. Shiller (1990), |Comparing information in forecasts from econometric models', American Economic Review, 80,375-389. Figlewski S. and P.Wachtel (1981), |The formation of inflationary expectations', Review of Economics and statistics, LXIII, 1-10. Hansen L.P. and R.J. Hodrick (1980), |Forward exchange rates as optimal predictors of future spot rates: An econometric analysis', journal of Political economy, 88, 829-853. Hibberd J. (1990), |Official statistics in the late 1980s', Treasury Bulletin, Summer 1990, 2-13. Holden K. and D.A. Peel (1985), |An evaluation of quarterly National Institute forecasts', Journal of Forecasting, 4,227-234. Holden K. and D.A. Peel (1990), |On testing for unbiasedness and efficiency of forecasts', The Manchester School, LVIII, 120-127. Mincer J. and V. Zarnowitz (1969), |The evaluation of economic forecasts', in Economic Forecasts and Expectations, ed. J. Mincer, Columbia University Press. Mishkin F.S. (1990), 'Does correcting for heteroscedasticity help?', Economics Letters, 34, 351-356. NIESR (1984)' The National Institute's forecasts of inflation 1964-82', National Institute Economic Review 107,47-49. Pain, N. and A. Britton, (1992), |The recent experience of economic forecasting in Britain: some lessons from National Institute forecasts', National Institute Discussion Paper (New Series) No. 20. Savage D. (1983), |The assessment of the National Institute's forecasts of GDP, 1959-82', National Institute Economic Review, 105,29-35. Zellner A. (1986), |Biased predictors, rationality and the evaluation of forecasts', Economics Letters, 21, 45-48.

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Author: | Pain, Nigel; Britton, Andrew |
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Publication: | National Institute Economic Review |

Date: | Aug 1, 1992 |

Words: | 4457 |

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