Empirical evidence on the recent behavior and usefulness of simple-sum and weighted measures of the money stock (commentary)

Money supply

A Reappraisal of Recent Tests of the Permanent Income Hypothesis

Hall (1978) showed that the permanent income hypothesis implies that consumption (1) follows a random walk, and (2) cannot be predicted by past income. Reexamination of Hall's data results in rejection of the random walk hypothesis in favor of the alternative hypothesis of positively autocorrelated changes. Evidently this is due to Hall's choice of a quadratic utility function. A logrithmic utility function implies a random walk in the log of consumption which is supported by the data. Hall reported that past income had a negative but insignificant relation to consumption. Changes in the log of income, however, do have a positive predictive relation to changes in the log of consumption. The adjustment of consumption to income seems to be spread over two quarters. Flavin's (1981) test of the theory is formally equivalent to Hall's except for assuming stationarity around a time trend. Mankiw and Shapiro (1984) have pointed out that the effect of detrending may be to tend to rejection of the theory when it is in fact correct. For Hall's data the effect of detrending is to reverse the sign of the coefficient on past income. Its magnitude is what the Mankiw-Shapiro analysis predicts under the permanent income hypothesis.

Novel properties of the q-analogue quantized radiation field

The 'classical limit' of the q-analog quantized radiation field is studied paralleling conventional quantum optics analyses. The q-generalizations of the phase operator of Susskind and Glogower and that of Pegg and Barnett are constructed. Both generalizations and their associated number-phase uncertainty relations are manifestly q-independent in the n greater than g number basis. However, in the q-coherent state z greater than q basis, the variance of the generic electric field, (delta(E))(sup 2) is found to be increased by a factor lambda(z) where lambda(z) greater than 1 if q not equal to 1. At large amplitudes, the amplitude itself would be quantized if the available resolution of unity for the q-analog coherent states is accepted in the formulation. These consequences are remarkable versus the conventional q = 1 limit