^{page 8 note (1)} These figures are drawn from C. H. Feinstein ‘Statistical Tables of National Income, Expenditure and Output of the UK 1855-1965’, Cambridge University Press, 1976 and include both insured and uninsured unemployed. If only insured unemployed are included the numbers for 1929 and 1932 are 1 1/4 million and 2 3/4 million respectively (‘The British Economy Key Statistics 1900-1970’, London and Cambridge Economic Service, 1971).

^{page 9 note (1)} ‘Financial Statement and Budget Report 1980/81’, HC500, HMSO, 25 March 1980.

^{page 9 note (2)} Savage, D. ‘Monetary targets and the control of the money supply’, National Institute Economic Review, no. 89, August 1979.

^{page 13 note (1)} In a regression of the change in output in 1980 on past productivity performance in the industry orders, the correlation coefficient was 0.45.

^{page 14 note (1)} This figure was derived from OPCS population projections EG activity rate forecasts and current data on registered employment. The figure for the 20-24 age group is 12 per cent. If people on Youth Opportunity Programmes are included among the unemployed, the percentage for those under 20 would rise to 30 per cent. Comparable figures for October 1979 were 12 per cent of the under-20s registered as unemployed, and 8 per cent of the 20-24 age group. Inclusion of the gross YOP numbers would raise the under-20s rate to about 17 per cent.

^{page 16 note (1)} C.f. the figure of 13.7 per cent for 1979 quoted in table A of ‘Equipment Leasing’ in the Bank of England Quarterly Bulletin, September 1980. This figure is the volume of leasing expressed not as a percentage of investment, but as a per centage of purchased assets.

^{page 16 note (1)} See Appendix tables 14-17 for further details.

^{page 17 note (1)} See National Institute Economic Review, No. 93, August 1980, pp. 30-2 for a discussion of alternative measures of competitiveness.

^{page 19 note (1)} For further details see Appendix table 17.

^{page 21 note (1)} This article is a condensed version of the work set out in S. Brooks and K. Cuthbertson ‘Economic Models and Econ omic Forecasts’ which is being published separately as a National Institute Discussion Paper. That discussion paper contains a full description and definition of the methods used and has an Appendix which sets out detailed information on the errors and their analysis.

^{page 22 note (1)} Report from the House of Commons Treasury and Civil Service Committee, HC 720, HMSO, 1980.

^{page 24 note (1)} See, for example, D. R. Osborn, ‘National Institute gross output forecasts: a comparison with US performance’, National Institute Economic Review, No. 88, May 1979.

^{page 24 note (2)} Examples of this form of model validation and its draw backs are given in K. Cuthbertson, ‘The determination of expenditure on consumer durables’, National Institute Econ omic Review, November 1980, pp. 62-72, and K. Cuthbertson, B. Henry, D. G. Mayes, and D. Savage, ‘The money supply and the PSBR’, National Institute Economic Review, No. 94, November 1980, pp. 19-22. Ex-post ‘forecasts’ may be made either ‘outside’ or ‘within’ the sample period used to estimate the equations.

^{page 24 note (3)} See F. Teal and D. R. Osborn, ‘An assessment and com parison of two NIESR econometric model forecasts’, National Institute Economic Review, No. 88, May 1979 for an example of this in detail.

^{page 25 note (1)} Some variables may be treated as either endogenous or exogenous according to circumstances. Two important examples of this at the present time in our own model are average earnings and the exchange rate. In both cases there are equations available for the determination of these variables in the same way as other endogenous variables, and when simulating the model, for example to examine the effects of alternative monetary policies, these equations would be included. However, in the preparation of forecasts it may be decided to set aside the equations and instead to write in an exogenous future path, for example that the effective exchange rate will stay constant throughout the forecast period. It is also possible to iterate between ‘exogenous’ paths for an important variable and the rest of the model. After an initial path has been chosen, the model is run and in the light of the results the initial path of the ‘exogenous’ variable may be modified.

^{page 25 note (2)} See P. Ormerod, and M. J. C. Surrey, ‘Formal and informal aspects of forecasting with an econometric model’, National Institute Economic Review, No. 81, August 1977.

^{page 25 note (3)} See Cuthbertson, op. cit.

^{page 27 note (1)} One possibility might be to use an ARIMA time series model to give a ‘base run’ projection for ‘financial trans actions’.

^{page 27 note (2)} A new wage equation has now been incorporated in the NIESR model based on the work of S. G. B. Henry, M. C. Sawyer, and P. Smith, ‘Models of inflation in the United Kingdom’, National Institute Economic Review, No. 77, August 1976, and preliminary work has been done on modelling the exchange rate (see, K. Cuthbertson, S. G. B. Henry, D. G. Mayes, and D. Savage. ‘Modelling and forecasting the capital account of the balance of payments: a critique of the ‘reduced form’ approach’, National Institute Discussion Paper no. 37, February 1980.

^{page 27 note (3)} Thus ‘system error’ is defined as model error plus mechanical rule error and is the difference between the ‘actual’ values in 1979 and those forecast dynamically by the model including the mechanical residual rule.

^{page 27 note (4)} Of course different mechanical rules might produce better forecasts than the judgemental residuals.

^{page 27 note (5)} See for example C. Bean, (1978) ‘The determination of consumer expenditure in the UK’, Treasury Working Paper, no. 4, July, and J. E. H. Davidson, D. F. Hendry, F. Srba, and S. Yeo (1978), ‘Econometric modelling of the aggregate time series relationship between consumers’ expenditure and income in the UK', Economic Journal, vol. 88, no. 4, and K. Cuthbertson, op. cit.

^{page 28 note (1)} As published in October 1980 and defined in table 13 footnote (f).

^{page 28 note (2)} Thus the model is used to give an ex-post dynamic forecast.

^{page 28 note (3)} An analysis of errors for the year as a whole is given in the Appendix to Brooks and Cuthbertson, op. cit.

^{page 28 note (4)} In table 14 we present the average annual error and the average annual absolute error for the whole period 1971-79. If the quarterly errors for a year are all either over-predictions or under-predictions then the absolute error for the year (that is the sum of the quarterly errors ignoring signs) will equal the annual error described above; however if the quarterly predictions are a mixture of over- and under estimates, the annual absolute model error will exceed the annual model error. The higher the annual absolute error for the year for a given annual error the greater the quarterly errors. We also give the average (quarterly) percentage error for each category. In all cases average absolute errors will exceed average errors (i.e. disregarding sign) if the errors do not all have the same sign.

^{page 29 note (1)} Shown in Brooks and Cuthbertson, op. cit.

^{page 29 note (2)} Minford, op. cit.

^{page 29 note (3)} ‘The effect of macroeconomic management in the UK of the transition from fixed to floating rates’, Journal of Economic Studies vol. 7, no. 2, 1980, p. 73; ‘A rational expectations model of the UK under fixed and floating exchange rates’ in K. Brunner and A. Meltzer (eds.), ‘The State of Macro-economics’, Amsterdam: North-Holland. ‘Monetarism, inflation and economic policy’ in Is Monetarism Enough?, Institute of Economic Affairs, Readings, No. 24, 1980.

^{page 30 note (1)} The Liverpool model does not use the ‘actual’ values of the exogenous variables in its ex-post, within sample, calculation of errors, but values obtained from ARIMA time-series models which have also been estimated over the sample period.

^{page 30 note (2)} The estimation period of the NIESR model ends in 1977, so this result indicates that the model continued to forecast after the estimation period with an accuracy similar to that with which it explained behaviour during it.