RDP 8601: New Classical Models and Unobserved Aggregates 5. Tests of the New Classical Hypotheses

The orthogonality principle and the assumption of covariance stationarity, may be used to show that^[16]

The first hypothesis to arise from the New Classical models is that anticipated movements in the money supply are neutral with respect to output. Using the equation for output in (20) and the covariances (25), it is found that

If an econometrician were to test this hypothesis using the measured money stock, the result would be^[17]

Equations (26) and (27) both use the result, shown in the Appendix, that σ² is the root of the quadratic in curly brackets.

Thus, in this model, the unobservable nature of the true money supply makes no difference to the testing of the neutrality hypothesis; anticipated movements in both the true aggregate and the measured one are neutral for output.^[18]

The second New Classical hypothesis is that unanticipated movements in the money supply are positively correlated with fluctuations in output. For this model,

which is not necessarily positive but depends on the parameter φ, because the lagged value of the true money supply is not in agents' information sets. Testing this hypothesis with the measured money supply would give

where the sign depends on the parameterisation of the measurement error in equation (8). A sufficient condition for unanticipated fluctuations in the measured money supply to be positively correlated with output is that the measurement error depend positively on output (β>0), or on the monetary base (δ>0), but not on prices (γ=0).

From a statistical point of view, if one is testing the null hypothesis of zero correlation against a two-sided alternative, the sign is not of major importance. However, it is likely that in the past some researchers may have “pre-tested” out results of a negative correlation between unanticipated fluctuations in the observed money supply and movements in output. Moreover, to the extent that certain parameterisations of the measurement error can produce measured correlations (29) much closer to zero than the true one (28), the use of the measured aggregate could lead to a failure to reject the (false) null hypothesis of zero correlation. This could explain some of the instances of a lack of a sizeable measured correlation between real output and money supply innovations that are found in the literature.^[19]

Footnotes

I make use of the result that σ² solves a particular quadratic equation given in the Appendix. [16]

More correctly, tests should be based on partial covariances. However, in the cases considered here, the orthogonality principle ensures that the partial and simple covariances are the same. [17]

Abel and Mishkin (1983) analyse tests of neutrality based on incorrectly specified information sets. They show, more generally, that exclusion of relevant variables (such as M_t) and inclusion of irrelevant variables (suchas ) will not of itself lead to the rejection of the null hypothesis of neutrality. These results follow from the orthogonality principle. [18]

See, for example, the results reported in Mishkin (1982) and Mishkin (1983) when the lag length restrictions are relaxed. [19]