^{page 61 note (1)} The authors are grateful to Mr G. D. N. Worswick for stimulating their original interest in this topic and for eluci dating the peculiar nature of the redistribution outlined in Part I and Appendix II of the paper. They would also like to thank Mr P. T. Eastham and Mr L. M. Berry of the Canadian High Commission who provided valuable information about the operation of the Canadian indexing scheme, and Professor A. T. Peacock and colleagues at the National Institute for their comments on an earlier draft. Some of the statements in the text are based upon calculations which for reasons of space it has been impossible to reproduce in full.

In the 1950's and 1960's Professor Paish contributed a series of articles on the effects of inflation on tax yields. See, for example, ‘The real incidence of personal taxation’, Lloyds Bank Review, No. 43, 1957.

^{page 61 note (2)} See C. J. Goetz and W. E. Weber, ‘Intertemporal changes in real federal income tax rates, 1954-70’, National Tax Journal, Vol. XXIV, No. 1, 1971 and G. Vukelich, ‘The effect of inflation on real tax rates’, Canadian Tax Journal, Vol. XX, No. 4, 1972. Also J. Bossons and T. A. Wilson, ‘Adjusting tax rates for inflation’, Canadian Tax Journal, Vol. XXI, No. 3, 1973.

^{page 61 note (3)} For a brief analysis of these effects see A. L. King, ‘The impact of inflation on income tax liability’, British Tax Review, No. 6, 1973.

^{page 61 note (4)} The calculations are therefore presented in the form of specific examples based on the notion of a hypothetical taxpayer who claims the basic personal allowances and reliefs to which he is entitled (changes in the basic allowances and reliefs over the period 1961/62 to 1974/75 are set out in detail in Appendix I), but no other reliefs or abatements which might reduce his liability. For example, no account has been taken of income-splitting between husband and wife, of age relief provisions or of deductions in respect of mortgage or other interest payments or of superannuation or pension fund contributions. Furthermore, the concept of ‘gross income’ which is implicit in the analysis excludes certain components which are not subject to assessment for tax purposes but which would normally be incorporated in a comprehensive definition of personal income (e.g. unemploy ment and sickness benefit and interest on small savings). National Insurance contributions are ignored, too. We have also disregarded capital gains, both because they are not unambiguously treated as income for tax purposes and are subject to preferential rates, and because any adjustment of capital gains for inflation would involve severe practical difficulties.

^{page 62 note (1)} For all employed persons income tax is deducted at source by the employer under the PAYE scheme, which from 1973/74 has extended to higher rates of tax. Under the new imputation system, dividend payments by companies are made under deduction of an amount of advance corporation tax which is equivalent to the basic rate charge of income tax.

^{page 62 note (2)} The nominal value of the single allowance increased by 230 per cent, that of the married allowance by 150 per cent and the consumer price index by approximately 67 per cent between 1961/62 and 1972/73.

^{page 63 note (1)} For a single person with earned income alone, for example, the effect of the 1961 Budget was to raise the nominal gross income threshold for surtax from slightly over £2,000 to slightly over £5,000. The budget measures did not, however, affect the level of the surtax threshold for investment income.

^{page 63 note (2)} An algebraic treatment of the effect of inflation on average tax rates is given in Appendix II.

^{page 65 note (1)} The pattern of redistribution is, however, rather dif ferent in the case of investment income. Because taxpayers with investment income could not claim earned income relief and became subject to surtax at a much lower level of taxable income, the turning points occur at very much lower levels of gross income than is the case for taxpayers with earned income.

^{page 66 note (1)} House of Commons, Official Report, Parliamentary Debates, 26 March 1974, col. 322 et seq.

^{page 67 note (1)} Fiscal drag has been defined in a variety of different ways. The relevant definition for measuring the automatic increase in the public sector share of personal income is the automatic increase in the revenue accruing to the Exchequer, which is more than proportional to the total nominal increase in income.

^{page 67 note (2)} This function is not strictly correct. Cross-product terms have been ignored for the sake of convenience.

^{page 68 note (1)} A study by members of the Canadian Department of Finance has attempted to estimate the effect of indexing on the yield elasticity of the income tax system. The technique used was a ‘micro-simulation’ calculating the effect of indexation on individuals in a representative sample of taxpayers and ‘blowing up’ the results to estimate the aggregate effect, cf. J. R. Allan, D. A. Dodge, S. N. Poddar, ‘Indexing the personal income tax’, Canadian Tax Journal (forthcoming).

^{page 68 note (2)} Very rough estimates of the yield elasticities of total central government taxation with respect to the general price level (Ep) and real income (Ey) can be calculated by assigning values of Ep=0 and Ey=1 to ‘specific’ indirect taxes, Ey= Ep=2.0 to the personal income tax, and E_y=E_p=1.0 to all other taxes, and weighting these elasticities by the share of these taxes in total tax revenue in 1974/75. These calculations suggest that for total central government taxation Ep=1.2 and Ey=1.6. With complete index-linking of the personal income tax (assuming Ep = 1 ), the value of Ep for total taxation is reduced to about 0.8. It can then be shown that the rate of inflation would have to be about three times the rate of real growth for total fiscal drag to be negative under a fully indexed personal income tax.

^{page 68 note (3)} Milton Friedman, Monetary Correction, Institute of Economic Affairs, Occasional Paper, No. 41, 1974.

^{page 68 note (4)} Report of the Royal Commission on Taxation, Queen's Printer, Ottawa, 1966, Vol. 2, p. 23.

^{page 69 note (1)} For a simple demonstration see A. T. Peacock and G. K. Shaw, The Economic Theory of Fiscal Policy, University of York Studies in Economics No. 5, George Allen and Unwin, London, 1971, Chapter 7.

^{page 69 note (2)} The full consequences of indexing the tax system on economic stability can only be investigated empirically by an elaborate simulation exercise with a full-scale econometric model. Bossons and Wilson (op. cit.) have compared a simulation of the response of the Toronto Quarterly Fore casting model to an exogenous expansionary shock with a simulation incorporating the new Canadian indexing scheme. They concluded that indexation would slightly enhance the extent to which the tax system helps to stabilise fluctuations in real output and unemployment.

^{page 69 note (3)} For an exploration of the argument see Frank Wilkinson and H. A. Turner, ‘The tax-wage spiral and labour militancy’ in Dudley Jackson, H. A. Turner and Frank Wilkinson, Do Trade Unions Cause Inflation? University of Cambridge, Department of Applied Economics, Occasional Paper 36, 1972.

^{page 69 note (4)} R. J. Gordon, ‘Wage-price control and the shifting Phillips curve’, Brooking Papers on Economic Activity, No. 2, 1972.

^{page 70 note (1)} Thomas A. Wilson, ‘Taxes and Inflation’, Report of the Twenty-Fourth Tax Conference, 1972, Canadian Tax Foundation, 1973.

^{page 70 note (2)} J. Johnston and M. Timbrell, ‘Empirical tests of a bargaining model of wage rate determination’, Manchester School, Vol. XLI, No. 2, 1973.

^{page 70 note (3)} There will not be a full correction unless all parameters of the tax structure are indexed and unless the indexing factor is calculated instantaneously. In Canada, for example, there are certain important exemptions, including the employ ment expense deduction, limits on contributions to pension and retirement savings and contributions to certain federal or state pension plans. Furthermore since the indexing factor is calculated on a lagged basis, real tax liabilities will still tend to rise whenever the rate of inflation is accelerating.

^{page 70 note (4)} For instance, the indexing factor adopted in Canada for adjusting personal income tax exemptions and brackets is derived by dividing the average Consumer Price Index for the 12-month period ending on the 30 September before a given taxation year by the average price level for the 12-month period ending 30 September 1972. The adjustment pro cedure adopted in the Netherlands is similar but the lag involved is considerably longer, the correction factor being computed as the ratio of the average Consumer Price Index in the 7th to 18th months preceding the beginning of the taxation year over an average of values of the same series for the 19th to 30th preceding months.

^{page 70 note (5)} A similar argument may be applied to the treatment of capital gains. However, as already noted, capital gains are subject to preferential rates of tax (vis a vis sources of earned and dividend or interest income) which are partly designed to provide a hedge against inflation. That is not to say that the existing system is ideal; for example, it creates inequities between different classes of asset holding and encourages the ‘locking-in’ of capital gains. A more equitable solution might be to consolidate the capital gains and income taxes, and to design an explicit method of adjusting the cost base of assets for inflation. For some interesting proposals in this direction (which might however run into serious administrative problems) see J. F. Helliwell, ‘Towards an inflation-proof income tax’, Canadian Tax Foundation, 1973, op. cit.

^{page 71 note (1)} A number of studies seem to indicate that there is a general tendency for price trends to be more favourable to the better off than the worse off. See, for example, D. G. Tipping, ‘Price changes and income distribution’, Applied Statistics, Vol. 19, No. 1, 1970 and J. Muellbauer, Prices and inequality: the United Kingdom experience’, Economic Journal, Vol. 84, No. 333, 1974.

^{page 71 note (2)} However, the degree of offset would probably be quite small. As an illustration, consider the 20 per cent cut in the standard rate of VAT effected in the July 1974 Budget. This has an estimated full-year revenue cost of £510 million, equivalent to a reduction of about 1.0 per cent in the con sumer price index (assuming full shifting). Given that Ep = 2.0, the full-year revenue gain resulting from the full indexing of the personal income tax by this price change would be approximately £90 million and the first-round demand effect about £65 million, corresponding to a ‘leakage’ of around 12½ per cent in the indirect tax change. Lags would also cause this leakage to be dissipated through time.

^{page 71 note (3)} The Dutch indexing scheme incorporates an adjustment for indirect taxes by assuming that all changes are fully transmitted into changes in price levels. The Canadians do not adjust for indirect taxes, primarily because of practical difficulties of application within a federal system.

^{page 71 note (4)} ‘The [tax credit] scheme would serve as a major new means of family support … If it is to succeed in that, the benefits it provides could not be allowed to fall far behind those of the social security schemes. This means that the annual review of national insurance and supplementary benefit levels … would have to be matched by regular re-appraisals of tax credit levels’, Proposals for a tax-credit system, Cmnd. 5116, October 1972, para. 119.

^{page 72 note (1)} R. I. G. Allen and D. Savage, ‘The case for inflation- proofing the personal income tax’, British Tax Review, No. 5, 1974.