^{note (1) page 40} I should like to thank M. J. Artis for his many helpful suggestions for improving this article, and I am also indebted to A. D. Roy and J. R. Shepherd for their comments and criticisms on an earlier version. Any remaining errors are my own.

^{note (2) page 40} An early assessment was R. R. Neild and E. A. Shirley, ‘An assessment of forecasts, 1959-1960’, National Institute Economic Review no. 15, May 1961, pages 12-29; it is the source used for the first two forecasts, which were not previously published as numerical estimates. A more recent assessment making use of Theil's inequality coefficient is D. J. Smyth and J. C. K. Ash ‘United Kingdom short-term macro- economic forecasts : an evaluation’, University of Reading Discussion Paper in Economics, no. 1.

^{note (3) page 40} The outlook appraisal published in February 1968 was an exception to this rule. It assumed that the budget would introduce policy changes sufficient to bring the economy on to the 4 per cent target rate of expansion announced by the Government. Unfortunately it had to be excluded from this assessment because it proved impossible to adjust the figures to the normal ‘no policy change’ assumption.

^{note (4) page 40} W. A. B. Hopkin and W. A. H. Godley ‘An analysis of tax changes’, National Institute Economic Review no. 32, May 1965, pages 33-42.

^{note (5) page 40} The measure of GDP is also liable to alteration each time the national accounts estimates are revised, but the assumption made here is that the latest set of estimates represents an improvement upon any earlier set.

^{note (6) page 40} W. A. H. Godley and C. Gillion ‘Measuring National Product’, National Institute Economic Review no. 27, February 1964, pages 61-67.

^{note (1) page 41} The alternative method of assessment gave results which were substantially similar to the main method. It consisted of a comparison of forecast changes, taken from fourth quarter to fourth quarter, with actual changes which were calculated from the average level of the third, fourth, and first quarters to the same period a year later. The object was to act as a check upon the main method and, in particular, to correct for errors of timing in the GDP estimates themselves. Under the alternative assessment the mean bias and mean forecast error for GDP were exactly the same, taking the compromise estimate, as in table 1, and they were within 0.1 per cent of table 1 taking the range estimates.

^{note (2) page 41} The alternative measures, the root-mean square error, $\sqrt{\frac{1}{n}(F-A{)}^2},$ and Theil's inequality coefficient, one version of which is $\sqrt{\frac{1}{n}(F-A{)}^2}/,\sqrt{\frac{1}{n}{A}^2,}$ share the defect that by squaring the error terms they tend to give undue weight to the larger errors. Theil's coefficient, moreover, does not furnish a directly meaningful measure of accuracy. At 0.49 for the forecasts in question it requires some further decomposition before its relevance can be appreciated. See H. Theil, ‘Applied Economic Forecasting’, North Holland Publishing Company, Amsterdam, 1966.

^{note (1) page 42} L. R. Klein, R. J. Ball, A. Hazelwood, and P. Vandome, ‘An Econometric Model of the U.K.’, Blackwell, Oxford, 1961.

^{note (1) page 43} D. B. Suits, ‘Forecasting and analysis with an econo metric model’, American Economic Review, March 1962.

^{note (2) page 43} The Suits model appears to be the only one for which predictions are available over any length of time. The mean absolute prediction errors over shorter periods for some other models may be stated briefly : (i) 1.4 per cent of annual GNP for the Klein-Goldberger model, 1951-55, as recorded in C. F. Christ, Aggregate econometric models’, American Economic Review, June 1956; (ii) 17 per cent of annual GNP for the Klein-Shinkai model, 1959-61, as described by T. Blumenthal, ‘A Test of the Klein-Shinkai Econometric Model of Japan’, International Economic Review, 1965; (iii) 0.9 per cent of annual GNP for Christ's model of the United States, 1960-62; this model uses the reduced form on correct values of the predetermined variables, which included total private income from employment and government expenditure. C. F. Christ, ‘Econometric models and methods’, ch. X, Wiley, 1966.

^{note (3) page 43} After this article was written Professor Suits very kindly sent me his forecasts for the 1962-68 period. The largest error was 2.9 per cent in this period and the mean error was only 1.2 per cent. Even though the mean deviation was lower, at 1.0 per cent, it is difficult to resist the conclusion that there was an improvement in the forecasts. No doubt this came as a result of the exercise of continuously checking and revising the model.

^{note (4) page 43} The numerical percentage is used only for convenience. The real equivalent is the domestic production content of the expenditure, that is, the market price value of the expenditure less the import and indirect tax contents. The domestic production content is estimated at 67 per cent for consumers' expenditure; about 50 per cent for stockbuilding; and 80-90 per cent for other expenditures. (See Economic Trends, August 1964.)

^{note (1) page 45} Unfortunately it has not been possible to separate fixed investment from stockbuilding in all the Michigan forecasts.

^{note (1) page 46} This follows the results of W. A. H. Godley and J. R. Shepherd,’ Forecasting imports’, National Institute Economic Review no. 33, August 1965.

^{note (2) page 46} Oddly enough the same was found true of the Oxford model of the United Kingdom, where the insertion of true values for the exogenous variables led to even worse fore casts. See J. Johnston, ‘An econometric model of the U.K.’, Review of Economic Studies, 1962, vol. 29, pages 29-39.

^{note (1) page 47} Calculations suggest that the effect of the regulator is to reduce GDP by 0.8 per cent after the lapse of three quarters, whilst the effect of 6d on the income tax and similar increases for the sub-standard rates amounts to about 0.4 per cent.

^{note (2) page 47} The argument in the text involves the simplifying assumption that the absolute value of (D—F) is always greater than the margin, M. In reality there will be cases where this is not so and the difference in policy advice under the two strategies will be zero or some small value less than M. Thus the average amount of policy intervention in the certainty equivalence case will exceed that given by the cautious approach not by M. but by an amount less than M but greater than zero.

^{note (1) page 49} W. A. B. Hopkin and W. A. H. Godley, op. cit.

^{note (2) page 49} Provisional summary input-output tables for 1963, Economic Trends, August 1964.

^{note (3) page 49} J. R. Shepherd and M. J. C. Surrey, ‘The short-term effects of tax changes’, National Institute Economic Review no. 46, November 1968, pages 36-41.

^{note (4) page 49} The multiplier would be about 1.25 if the marginal propensity to consume was one half as suggested by D. F. Lomax and B. Reading, ‘Too little saving’, National West minster Bank Quarterly Review, August 1969. This assumption would not alter the assessment of the forecasts a great deal. For example, the mean error for the GDP forecasts would be 1.5 per cent compared with the estimate of 1.4 per cent given in this paper; the mean bias would not be changed.

^{note (1) page 51} For example R. Stone, ‘Private saving in Britain, past, present and future’, Manchester School, May 1964, pages 79-112.