⁽¹⁾ Three valuable recent surveys of the history of theorising in these two traditions are J. A. Frenkel, ‘A monetary approach to the exchange rate; theoretical aspects and empirical evidence’, J. Myhrman,‘ Experiences of flexible exchange rate in earlier periods: theories, evidence and a new view’ and M. Mussa, ‘The exchange rate; the balance of payments and monetary and fiscal policy under a regime of controlled floating’, all from The Scandinavian Journal of Economics, vol. 78, No. 2, 1976 and reprinted in J. Herin, A. Lindbeck and J. Myhrman (Eds), Flexible exchange rates and stabilisation policy (Macmillan, London 1977).

⁽¹⁾ The term ‘purchasing power parity’ was introduced in G. Cassel, ‘Abnormal deviations in international exchanges’, Economic Journal, vol. 28, no. 112 December 1918, but his thinking is set out at greater length in G. Cassel, Money and foreign exchange after 1914 (Constable, London 1922). The background to his work is described in H. S. Ellis, German monetary theory 1905-33 (Harvard 1937) and in J. M. Holmes, ‘The purchasing power parity theory: in defence of Gustav Cassel as a modern theorist’, Journal of Political Economy, vol. 75, no. 3, 1967; its subsequent uses are reviewed in L. M. Officer, ‘The purchasing-power-parity theory of exchange rates: a review article’, IMF Staff Papers, vol. 23, no. 1, March 1976.

⁽²⁾ Cassel believed that expectations were usually convergent, and speculation stabilising—‘An impartial judgment … would most certainly find that the speculation in exchange implies, on the whole, a levelling down of the fluctuations of the exchanges, and not an intensification.’ (Money and foreign exchange, p. 150.)

⁽¹⁾ This is rather negatively stated, and the reference to employment policy is only implicit, as Cassel was primarily interested in the behaviour of floating exchange rates in a pre-Keynesian era: ‘It is clear … that a rise in the price of the currency of country B can never be a reason for a rise in prices in country A, so long as the exchange rate is a true expression for the relative purchasing power of both currencies. Only if the B currency were quoted above the purchasing power parity, and in that sense were overvalued, could the high price of this currency have any influence to raise the prices in country A. But even this influence would not be able to raise the general price level unless it had the support of a more plentiful supply of means of payment …’, Money and foreign exchange, pp. 167-8.

⁽¹⁾ The Canadian dollar floated in 1950 when the authorities despaired of reconciling its sensitivity to both US dollar and sterling movements with the par value system. Buoyant wheat exports helped the rate to remain steady at around $1.03 for the next decade. In 1961, growing unemployment precipitated a crisis over the central bank's tight money policy, and when this was reversed the Canadian dollar fell to $0.925 where it was repegged in May 1962.

⁽¹⁾ Note that the chart plots exchange rates as units, or hundreds of units, per pound sterling. A rise in any series indicates a relative appreciation of sterling (depreciation of the foreign currency) and vice versa. This method of quotation is used throughout the article.

⁽¹⁾ A useful chronology of early postwar sterling crises and the policy responses they evoked is given in F. Hirsch, The Pound Sterling: A Polemic (Gollancz, London 1965), and a discussion of the political and economic circumstances of the 1967 devaluation in J. H. B. Tew, ‘Policies aimed at improving the United Kingdom balance of payments’, forthcoming as chapter 7 of F. T. Blackaby (Ed.), British Economic Policy 1950-74, (Cambridge University Press), 1978.

⁽²⁾ The French franc dropped out of the Snake in January 1974, not because of any internal economic weakness, but because other members—the Belgian franc, the Dutch guilder—were much stronger and the political will of the new Gaullist coalition was in doubt. The chart shows that its performance in terms of sterling improved throughout the second half of 1974. By July 1975 the trade balance was on the upswing of the J-curve, monetary policy was very tight, and negotiations for the deposit of some Iranian oil revenues in Paris had been successful. The French franc was readmitted to the Snake at its old parities, but in March 1976 it was once again dropped, after six months of poor trade figures.

⁽¹⁾ Money supply (M1) was increasing at about 10 per cent per annum early in 1972, but at over 15 per cent per annum by the year's end; visible trade was in surplus through 1971 but in growing deficit in 1972, record monthly levels of over £100 million being reported for August and September.

⁽²⁾ Again, the yen rate does not fit into this general scheme. Japan resisted pressure to revalue in 1972 by instigating a huge public expenditure programme, and floated in 1973 only after threats of tariff discrimination from the United States. The ‘Tanaka Plan’ did little to divert resources from exports, but did severely overheat the economy late in 1973 just when the oil crisis imposed a further inflationary burden. Instead of deflating the government concentrated on further export expansion and campaigned to attract oil funds to Japanese banks. By mid-1975 the inflationary threat had been lifted and, as shown on chart 1, the yen strengthened markedly against sterling.

⁽¹⁾ This definition comes from R. R. Rhomberg, ‘Indices of effective exchange rates’, IMF Staff Papers, vol. 23, no. 1, March 1976, p. 91.

⁽²⁾ For details of the IMF series and a listing of alternative definitions see R. R. Rhomberg, op. cit. The official UK series was introduced in HM Treasury, ‘The effective exchange rate for sterling’, Economic Trends, no. 248, June 1974. Problems over the coverage and computation of this index were pointed out in National Institute Economic Review, No. 78, November 1976, p. 16, and the series has been recently redefined to resemble more closely the IMF definition (see HM Treasury, Economic Progress Report, March 1977).

⁽¹⁾ The normalised weights are: US dollar=0.3740, French franc=0.1611, deutschemark=0.2699, Italian lira=0.0602, Japanese yen=0.1348.

⁽¹⁾ Several computations of absolute purchasing power pari ties for pairs of countries have been carried out by calculating cost of living indices with common currency weights. The most recent example is I. B. Kravis, Z. Kenessey, A. Heston, R. Summers, A System of international comparisons of gross product and purchasing power (Johns Hopkins for World Bank 1975). The resulting parities deviate systematically from actual exchange rates, being generally more favourable for poorer and less industrialised economies, where much cheap food is not marketed and the relative price of non- traded goods and services is lower vis-à-vis traded goods than in advanced industrial economies.

⁽²⁾ W. F. Stolper, ‘Purchasing power parity and the pound sterling from 1919-1925’, Kyklos, vol. 2, fasc. 3, 1948; F. D. Graham, Exchange, Prices and Production in Hyper- inflation: Germany 1920-1923 (Princeton University Press, Princeton 1930).

⁽³⁾ S. C. Tsiang, ‘Fluctuating exchange rates in countries with relatively stable economies: some european experi ences after World War I’, IMF Staff Papers, vol. 7, no. 3, October 1959; R. Z. Aliber, ‘Speculation in the foreign exchanges: the european experience 1919-1926’, Yale Economic Essays, vol. 2, Spring 1962.

⁽⁴⁾ See L. B. Thomas, ‘Behaviour of flexible exchange rates: additional tests from the post-World-War I episode’, Southern Economic Journal, vol. 40, no. 1, October 1973, Table IV, p. 179.

⁽⁵⁾ See J. S. Hodgson, ‘An analysis of floating exchange rates: the dollar-sterling rate 1919-1925’, Southern Economic Journal, vol. 39, no. 2, October 1972, our elasticities being calculated from Table II p. 252; and J. S. Hodgson and P. Phelps, ‘The distributed impact of price level variation on floating exchange rates’, Review of Economics and Statistics, vol. 62, no. 1, February 1975, our elasticities calcu lated from the results on Table 2, p. 61.

⁽⁶⁾ L. B. Yeager, op. cit., pp. 179-80.

⁽⁷⁾ H. J. Gaillot, ‘Purchasing power parity as an explanation of long-term changes in exchange rates’, Journal of Money, Credit and Banking, vol. 2, no. 3, August 1970.

⁽¹⁾ See H. M. Markowitz, Portfolio Selection (Wiley, New York 1959), J. Tobin, ‘The theory of portfolio selection’, in F. Hahn and F. P. R. Brechling (Eds,). The thoery of interest rates (Macmillan, New York 1965); and S. C. Tsiang, ‘The theory of forward exchange and effects of government intervention on the forward exchange market, IMF Staff Papers, vol. 7, no. 1, April 1959.

⁽²⁾ L. Officer, An econometric model of Canada under the fluctuating exchange rate (Harvard University Press, Cam bridge Mass, 1968), pp. 15-19; R. E. Caves and G. L. Reuber, Capital transfers and economic policy, 1951-1962 (Harvard University Press, Cambridge, Mass., 1971), Chapter 2.

⁽³⁾ An early example is R. R. Rhomberg, ‘Canada's foreign exchange market: a quarterly model’, IMF Staff Papers, vol. 7. no. 4, April 1960.

⁽⁴⁾ J. F. Helliwell, ‘A structural model of the foreign exchange market’, Canadian Journal of Economics, vol. 2, no. 1, February 1969.

⁽⁵⁾ A. P. L. Minford, ‘A model of the UK floating exchange rate’, unpublished typescript 1975; P. A. Armington and C. Armington, ‘A model of exchange rate movements in the short run under conditions of managed floating’, London Business School Econometric Forecasting Unit, Discussion Paper 38, July 1976; J. R. Artus, ‘Exchange rate stability and managed floating: the experience of the Federal Republic of Germany’, IMF Staff Papers, vol. 23, no. 2, July 1976.

⁽¹⁾ An acceleration scheme was proposed in J. R. Hicks, Value and capital (Oxford, Clarendon Press, 2nd Ed, 1948) Chapter 16, pp. 204-209; error-learning, or ‘adaptive expectations’, by P. H. Cagan, ‘The monetary dynamics of hyper- inflation’ in M. Friedman (Ed.) Studies in the Quantity Theory of Money (Chicago University, Economic Research Centre, 1956); and model-based expectations by R. F. Muth, ‘Rational expectations and the theory of price movements’, Econo metrica, vol. 29, no. 3, July 1961.

⁽²⁾ He wrote: ‘If currencies are left free to fluctuate, “speculation” in the widest sense is likely to play havoc with the exchange rates…. Any considerable or continuous move ment of the exchange rate is liable to generate anticipations of a further movement in the same direction, thus giving rise to speculative capital transfers of a disequilibrating kind’. See R. Nurkse, International currency experience (Princeton, for the League of Nations, 1944), pp. 137-8.

⁽³⁾ M. Friedman, ‘The case for flexible exchange rates’, in Essays in positive economics (University of Chicago Press, Chicago 1953).

⁽⁴⁾ For example, in N. C. Millar and M. von N. Whitman, ‘A mean-variance analysis of United States long-term portfolio foreign investment’, Quarterly Journal of Economics, vol. 84, no. 2, May 1970, the variability of GNP is substituted for risk; and in Z. Hodjera, ‘Short-term capital movements of the United Kingdom 1963-1967’, Journal of Political Economy, vol. 79, no. 3, July-August 1971 periods of low confidence in sterling are identified by dummy variables.

⁽¹⁾ Consider the difference between deviations in actual rates in two periods i and j from their absolute purchasing power parities, (S_j—S_oj)/S_oj—(S_i—S_oi)/S_oi. Applying equation (1) to S_oi and S_oj and simplifying, this becomes P_o(S_jP_i— S_iP_j)/S_o(P_iP_j); and since So(P_j/P_o)≃S_j≃S_i(P_j/P_i)=S_ij, this further simplifies to (S_j-S_ij)/S_ij. If we write the value ϕ, ϕ in period j as ϕ(X_j) where x is the vector of arguments of of applying equation (2) yields (S_j- S_ij)/S_j = ϕ(X_j) - ϕX_i); and if ϕ is linearly homogeneous, this becomes ϕ(X_j-X_i).

⁽¹⁾ Note that any backward projection, such as a purchasing power parity for 1951 based on 1952, will simply yield an observation of minus the forward projection so such data are not informative. This means that if we have n observations there are only 1/2(n ²-n) independent pieces of data; and for the m—th observation we obtain m -1 observations in which it is the target year and n—m in which it is the base.

⁽²⁾ In the notation of the previous footnote, the relative extent of sterling overvaluation in year m is

⁽³⁾ Experiments with measures of expected real rates and rates for different maturities did not improve upon the reported equations, which all use short-term nominal interest rates.

⁽¹⁾ These collinearity problems led us to estimate a condensed form of the model in which all objective indicators except interest rates, and all subjective indicators except the trade balance, were suppressed. The level of explanation offered by these equations is naturally lower than that of the complete model, but the reduction in R ² is appreciable only in the dollar export price based equation, both franc equations and the lira consumer price based equation. In return, the interest rate coefficients remain broadly unchanged and highly significant, while a positive trade balance effect on the US dollar is uncovered.

⁽¹⁾ Suppose in period j the deviation of the exchange rate from purchasing power parity changes by only a fraction d ₁ of the distance between its previous value and the value indicated by ϕ_j. Then D{(S_j-S_oj)/S_oj}=d ₁[ϕ_j-L{(S_j-S_oj)/S_oj}], which implies that (S_j-S_oj)/S_oj=d ₁ϕ_j+ (1—d ₁)L{(S_j—S_oj)/S_oj}. This is our new estimating equation. Since ϕ_j is linearly homogenous in its arguments, it is also homogenous with respect to its parameter vectors a, b and c. So d₁Φ_j can be written Φ_j(d ₁a,d ₁b,d ₁c), implying that the short run impact effects of determining variables are only a fraction d ₁ of their true long-run effects.

⁽¹⁾ J. Durbin, ‘Testing for serial correlation in least-squares regressions when some of the regressors are lagged dependent variables’, Econometrica, vol. 38, no. 3, May 1970. If h > 1.65 we reject the hypothesis of zero autocorrelation at the 5 per cent level.