A Reconsideration of Measures of Instability’
نویسنده
چکیده
Using three measures, namely, the standard deviation of the ratio of the deficit to GDP and the slope and standard error of the estimate of regressing this ratio on time, Brewer (1985) concludes that the developing countries’ deficits, as a group, are not notably larger or more unstable than the industrial countries’ deficits. This comment demonstrates that by using a more appropriate measure of instability, the developing countries as a group actually exhibit greater stability. Variation over time is an indicator of instability. The greater the variation., the greater the instability. Because standard deviation is one measure of variation, it is often used as a measure of instability. In some cases, however, standard deviation may not be an appropriate measure to reflect instability. For a set of time-series observations, the underlying pattern demonstrated by them may be composed of two parts: a trend part which is predictable, and an uncertainty part which is unpredictable. Since the trend part can be predicted with much confidence and the uncertainty part cannot, we think that only the uncertainty part reflects the essence of instability. Because the calculation of standard deviation does not explicitly consider the trend part, we doubt the appropriateness of using the standard error to measure instability for time-series observations. Case 1 and case 2 in Table 1 are good examples. The mean is the same in the two cases, but the standard deviation of case 1 is higher than that of case 2. This seems to suggest hat case 1 is more unstable than case 2. But an examination of data in Table 1 shows that case 1 is more stable than case 2 since the former has a constant increase of amount q for each time period. This points to the limitation of using standard deviation as the measure of instability. If the values of observation are steadily decreasing
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