^{note (1) page 52} L. A. Dicks-Mireaux, The Interrelationship Between Cost and Price Changes, 1946-1959; A Study of Inflation in Post-war Britain’, Oxford Economic Papers, October 1961.

^{note (2) page 52} L. A. Dicks-Mireaux and J. C. R. Dow, ‘The deter minants of wage inflation : United Kingdom 1946 to 1956’, Journal of the Royal Statistical Society, 1959.

^{note (3) page 52} L. R. Klein and R. J. Ball, Some econometrics of the determination of absolute prices and wages’, The Economic Journal, September 1959.

^{note (4) page 52} R. G. Lipsey, The relation between unemployment and the rate of change in money wages in the UK : 1862 to 1957; a further analysis’, Economica, February 1960.

^{note (5) page 52} A. W. Phillips, The relation between unemployment and the rate of change in money wages in the UK : 1861 to 1957,’ Economica, November 1958.

^{note (6) page 52} J. D. Sargan, Wages and prices in the United Kingdom : a study in econometric methodology’, Colston Papers, 1964.

^{note (7) page 52} W. A. H. Godley and J. R. Shepherd, ‘Long-term growth and short-term policy’, National Institute Economic Review no. 29, August 1964.

where E_t = Desired, or equilibrium, level of employment; E_t = Actual level of employment; Q_t = Level of output; t is a productivity trend; U_t = Level of registered unemploy ment; Lt = Supply of labour.

^{note (2) page 53} See W. A. H. Godley and J. R. Shepherd, op. cit. More recent experience of continuously high unemployment levels suggests, however, that over a wider range of variation the unemployment/employment relationship is non-linear (see J. R. Shepherd, ‘Productive potential and the demand for labour’, Economic Trends, August 1968).

^{note (3) page 53} With k in the system of equations set out in footnote (1) above being given a value of about 0.5 a quarter.

^{note (4) page 53} The index (O/C_t) is the ratio of actual output to ‘pro ductive potential’ where the latter is defined as the level of output corresponding to an unemployment rate of 1 1/2 per cent (see Appendix I).

^{note (5) page 53} Since from the above equations, U_t is simply a lagged, smoothed version of E_t-L_t.

^{note (1) page 54} This suggestion is contained in Phillips's original paper.

^{note (1) page 56} Representing this function in general terms as f(Ut, Pt) and assuming that it is the same for all negotiating groups, we have for the i^th group :

where the error terms e_it are assumed independent and not serially correlated.

If we write n _t/N for the proportion of workers receiving increases in quarter t, changes in the aggregate index become :

where ut is the (weighted) sum of error terms such as e_it and the summation is taken over the k groups for whom a new agreement is reached in quarter t.

^{note (2) page 56} If these conditions were fulfilled, then we could estimate equation (1) in table 1 directly, either by incorporating the fixed value for n_t/N into the regression coefficient or by using seasonal constants to remove the variation in n_t/N.

^{note (3) page 56} There is other evidence which supports this last point : (i) Certain agreements are known to cover a large number of workers, and to cause sudden steps in the wage-rate index when they occur. The classic case is the 1963 engineering settlement which covered about 3 million workers and caused a 1.4 per cent rise in the aggregate index between November and December. (ii) The distribution of union membership is skewed heavily in favour of the larger unions : 36 unions (out of about 600) account for 80 per cent of union membership.

^{note (1) page 57} n_t=4,220-2.55.U_t R²=0.02 SE of coefficient 8.5.

^{note (2) page 57} The R² and the overall standard error of the equations are slightly better when capacity utilisation (O/C)_t is used. The coefficients of O/C are better determined than those for unemployment (U), and their significance is not so sensitive to the introduction of lags (the coefficients of U in equations (6) and (12), for example, are not significant).

^{note (1) page 59} In no case did the F-ratio for either ΔUt or (O/C)_t exceed 3, and in most cases it was lower than 2.

^{note (1) page 60} Ignoring the constant and the term in nt/N the partitioned form of equation (21) is :

where w_t is the ‘equilibrium’ level of wage-rates in quarter t.

^{note (2) page 60} Apart from the two adjustment equations—(32) and (36) -the F-ratio (square root of the ratio of the coefficient to its standard error) is never given as more than 0.5. (Broadly, an F-ratio of 2.8 indicates that the coefficient is significantly different from 0 at the 10 per cent level, an F-ratio of 4 indicates significance at the 5 per cent level and F-ratios higher than 7 indicate significance at the 1 per cent level.)

^{note (3) page 60} Its removal results in a sharp drop in the value of R² from 0.80 to 0.20.

^{note (1) page 61} Equation (43), for example, can be written : (W+S)_t=0.6(0.6w_t+0.4w_t-1) and in equations (40), (41) and (42) the coefficient of w_t-1 is larger and more significant than that of Wt.

^{note (1) page 63} That is something along the lines of :

^{note (1) page 64} R²=0.67.

^{note (2) page 64} R²=0.35 and 0.38.

^{note (3) page 64} See W. A. H. Godley and C. Gillion, Measuring national product’, National Institute Economic Review no. 27, February 1964. For a similar use of the residual error term see W. A. H. Godley and J. R. Shepherd, ‘Forecasting imports’, National Institute Economic Review no. 33, August 1965.

^{note (4) page 64} Terms in N_t and N_t-1 are both significant although attempts to introduce N_t-2 and N_t-3 were unsuccessful.

^{note (1) page 65} In the Survey equations (56) and (57) the coefficients of p_t/p_t-4 and p_t-1/p_t-5 are significant at the 10 per cent level but not at the 5 per cent level. By comparison with equation (55), the value of R² has increased from 0.72 to 0.75, but the size and significance of the unemployment coefficients has been reduced from —0.0071 (0.0019) to −0.0048 (0.0022)—an effect similar to that observed in the earlier wage-rate studies. Since the Survey equations are based on six-monthly changes, the possibility of feed-back makes these results doubtful.

^{note (2) page 65} Since a coefficient of −1/120 = 0.0083 for ΔU cor responds to a coefficient of 1.0 for E and the remaining part of the coefficient of ΔU, -(0.0145-0.0083)= −0.0062, is of the same magnitude as the coefficient in equation (58).

^{note (3) page 65} And that the value of R² should show such a marked increase, from 0.40 in equation (58) to 0.56 in equation (64).

^{note (4) page 65} Also R^a is again increased—from 0.46 in equation (59) to 0.62.

^{note (1) page 67} On their data a X² test rejected the hypothesis that n_t/N=a constant.

^{note (2) page 67} In this study the structural equation is : wt=k+a(pt-Pt-₄)+bdt+ut where p is the retail price index, d_t is the authors' index of the pressure of demand for labour, and the variables are expressed in logarithms. The estimating equation is : W_t=K+aP_t+bD_t+U_t where the variables in capital letters denote four-quarter moving averages of the corresponding terms in the structural equation (for example, the price variable P is a four-quarter moving average of quarter on quarter-on-year earlier changes).

^{note (3) page 67} w_it =k+a(p_t-p_t-4)=bd_t+e_it or 0 if no agreement is reached in quarter t. The difficulty is that if the e_it are assumed to be serially independent, then the moving average U_t must be serially correlated, which immediately throws doubt on the use of ordinary least squares as a method of estimation. Conversely, if U_t is assumed serially independent, then some complicated and implausible relationship is implied among the individual error terms eit.

^{note (4) page 67} J. Johnston, Econometric Methods’, McGraw Hill 1963, page 216 : auto-correlated disturbances alone do not lead us to expect biased estimates; lagged variables would lead us to expect in this case a negative bias; yet the simultaneous presence of the two complications produces substantial positive bias’. Sargan's comment on this problem is : the only criterion is that the optimum form should have errors which are independent in different time periods’. Colston Papers, 1964.