Geographic Earnings Differentials and Foreign Trade

Abstract

On the basis of this information we may make the flat statement: If the retirement distribution can be assumed to resemble the curve shown in Chart I, and the trend of installations over a past period of double the average service life of the assets can be roughly represented by a constant rate of growth, then, whatever that growth rate and whatever the life average, the gross survivor value computed by the crude method does not deviate by more than 6 per cent from what would be obtained by the correct method.5 In the case of a structurally similar retirement distribution with less relative dispersion the divergence for any given r n, hence also the maximum divergence, would be smaller.6 As far as they go, these findings indicate that the simple cumulation method does yield an acceptably close approximation to the correct result. To secure a fully generalized answer, covering most cases likely to occur in practice, it would be necessary (and probably sufficient) to add a similar analysis for the other f (x) and g (t) types listed above. If survival rates based on a skew retirement distribution curve were applied to the g (t)function underlying the preceding analysis, the divergence between the two S would have different values and different maxima, depending on the degree of skewness and dispersion of f (x). But a maximum divergence for some specifiable rnproduct may again be expected to exist for any assumed f (x). If the assumed g (t)-pattern is anything other than the simple exponential growth function we have used, the percentage deviation between the two gross stock values must be expected to depend also on the specific contour of the installation flow during the past period indicated by the range s, hence on the length of that range and thus, in general, on the life average n as well. 'The margin between 6 per cent and the 5.26 per cent we have derived is certainly sufficient to allow for any possible difference of our result from what would be obtained if annual rather than continuous functions were used. 8In our analysis we have purposely experimented with a retirement distribution curve having a fairly high coefficient of variation, which of course tends to increase the relative disparity between Si and S2. If retirements are completely concentrated at the average service life, the gross survivor values obtained by the two methods are always equal. In this as in any similar analysis, minor erratic oscillations of actual installations around a generally realistic g (t)-trend, or of actual retirements around a generally realistic f (x) -curve, will hardly affect the reliability of the results, except perhaps in the case of very short average service lHves.