In our 1980 paper we tested the joint hypothesis that prices are determined by the mean-variance (MV) capital asset pricing model (CAPM) and that beliefs are stationary. By focusing on the Invariance Law of Prices we avoided the questionable practice of estimating ex ante expectations with ex post returns. Moreover, we circumvented the need to identify the true market portfolio and hence avoided the ambiguity, noted by Richard Roll (1977), in the traditional security market line (SML) tests of the same joint hypothesis. However, Stuart Turnbull and Ralph Winter (T-W) and Richard Sweeney point to a further inconsistency in the joint hypothesis, that they believe can be removed by relaxing the stationarity assumption. This new concern is fundamental in that it applies to all empirical tests which assume stationarity of the return distribution, whether they are simply tests of the CAPM or tests employing the CAPM. The concern would apply a fortiori to tests that assume stationary betas as well. Both comments also suggest that the ad hoc addition of a random error term to our Invariance Law equation and the subsequent statistical tests of it are unnecessary. We first address these two criticisms and then address some further criticisms raised separately by T-W and Sweeney.

Why should a rationally motivated political decision process generate an inverse relationship between tax rates and tax revenues? There would never seem a logical reason for increasing tax rates beyond maximum revenue limits. In this note, we explain how such a position can emerge and show why, once in such a position, political decision makers may find it difficult to escape.