^{note (1) page 36} W. A. B. Hopkin and W. A. H. Godley, ‘An analysis of tax changes’, National Institute Economic Review no. 32, May 1965.

^{note (2) page 36} The essential conceptual difference between direct effects (first round) and indirect effects (second and subsequent rounds) is that the indirect effects occur only as a consequence of the direct effects. In particular, the multiplier and acceler ator effects occur as a consequence of the change in output which is itself a more immediate consequence of the original tax change. There is no uniquely valid way of drawing the distinction between direct and indirect effects and the definition adopted here is partly a matter of convenience. A further feature of the multiplier and accelerator mechanisms is that they depend primarily on changes in output and, in most circumstances, can be assumed to operate independently of the type of tax change or other measure involved. A generalised model is therefore applicable and it is these effects which are here referred to as indirect. The direct effects, on the other hand, are taken to be the more immediate effects of the tax change, operating frequently through real personal disposable incomes, on final expenditure, output, and imports (assuming no change in stocks), before multiplier and accelerator effects are taken into account. The present model does not include other types of effect which could logically be classified as indirect, such as any consequences for productivity. Where these are believed to be significant, appropriate allowances must be made in conjunction with the direct effects.

^{note (1) page 37} Such research has been used in a fairly freehand way to obtain what is considered to be an acceptable set of coefficients. Thus, where regression coefficients have been estimated, they may subsequently have been modified in response to other kinds of evidence or to a subjective assessment of plausibility.

^{note (2) page 37} W. A. H. Godley and J. R. Shepherd, Long-term growth and short-term policy’, National Institute Economic Review no. 29, August 1964.

^{note (1) page 38} The analysis is not exhaustive : explicit allowances have been made only for the most substantial influences on income. Apart from the possible qualifications in measuring the income effects (above), there are also some other relatively small effects. For example, the induced change in employment will affect not only income from employment but income from unemployment and supplementary benefits. The importance of this factor has risen somewhat in recent years with the introduction of earnings-related unemployment benefits. It is probably greater also when unemployment is relatively high, since changes in unemployment tend in these circum stances to be greater in relation to changes in employment (see J. R. Shepherd, ‘Productive potential and the demand for labour’, Economic Trends no. 178, August 1968). This factor would tend to reduce the multiplier. On the other hand the multiplier would tend to be increased by any effect on wage-rates of changes in pressure of demand. Price rises would tend to offset effects on consumption, but with a lag. Prices are assumed not to be directly affected by changes in pressure of demand. However costs are defined as trend costs rather than short-run average costs (see W. A. H. Godley and D. A. Rowe, Retail and consumer prices, 1955-1963’, National Institute Economic Review no. 30, November 1964, pages 47-49).

^{note (1) page 40} This relationship does not, of course, imply that the adjustment is completed after the fourth quarter following any change in output. For example, an accelerator model (investment depending on the rate of change of output) implies that a complete version of equation (3) would have negative coefficients for some lagged values of GDP, so that investment would ultimately revert to the same level as if there had been no tax change (though there would be a different capital stock). However, it is perfectly plausible, and con sistent with our empirical work, that these negative coefficients do not appear within a two-year period. The simple form of equation adopted has obvious practical advantages.

^{note (2) page 40} R. J. Ball, J. R. Eaton, and M. D. Steuer, The relation ship between United Kingdom export performance in manu factures and the internal pressure of demand ‘The Economic Journal, September 1966. See also G. A. Renton, Fore casting British exports of manufactures to industrial countries’, National Institute Economic Review no. 42, November 1967.

^{note (3) page 40} The derivation of import forecasting equations has been discussed in W. A. H. Godley and J. R. Shepherd, ‘Forecasting imports, National Institute Economic Review no. 33, August 1965 and in 1. G. Black, J. E. Kidgell, and G. F. Ray, Fore casting imports : a re-examination’, National Institute Economic Review no. 42, November 1967. The coefficients for the components of final sales used here were based on average propensities obtained from input-output data. It was not assumed that marginal propensities were greater than average propensities because the authors' regression equations (which included a time trend) did not produce any evidence to support such an assumption. It is undoubtedly true that the average propensity to import (in volume terms) has risen over time, and this fact is reflected either in a positive time trend or, if this variable is omitted, in coefficients for the expenditure variables greater than the average propensities. Since the expenditure coefficients fall back to approximately the average propensities when a time trend is included, the results tend to suggest that there is no association over time between the growth in expenditure and the growth in the average import propensity, and that cyclical fluctuations in demand do not result in more than proportionate fluctuations in imports. Attempts to introduce indicators of capacity utilisation into the equations actually tended to produce coefficients with perverse signs. Therefore the empirical evidence (whatever the a priori likelihood) provides no ground for employing propensities greater than the current average for estimating the effects on imports of a higher level of final sales at a given point of time. For stockbuilding the relatively high regression coefficient has been used.

^{note (4) page 40} In terms of constant prices the relevant concept is the adjustment to factor cost—that is, indirect taxes calculated at the tax rates and prices of the base year. In allocating a share of the direct effect to the factor cost adjustment it is necessary, as with imports, to take account of the commodity composition. For instance, an increase in tobacco duty would probably reduce consumption of tobacco proportionately more than consumption in total. Since a large proportion of expenditure on tobacco consisted (at base year tax rates) of tax, a relatively high proportion of the direct effect must be allocated to the factor cost adjustment.

^{note (1) page 41} Lagged values of S prior to the introduction of the measure are, by definition, zero. Therefore S can never contain more than 8 non-zero terms, since this is the maximum period to which the model is applicable.