caveats, addressed below, results suggest that, given GDP shocks of historical magnitudes even those caused by the velocity shocks in the 1990s, the performance of an M2 rule
is robust to varying degrees of money control error. Findings regarding the likely success of an M2 rule are in contrast with those obtained
by Dotsey and Otrok 1994— even though both studies used money control errors of similar size. The most probable explanation is the use of different M2 rules. The
adjustment parameters in McCallum’s rule appear to do a better job of mitigating the impacts of money control error on the GDP growth path.
To assess the relative performance of the policy instruments, it is useful to compare the RMSEs in Tables 2–3 with the RMSEs generated by corresponding economic models and
monetary base rules. In the four-variable VAR, the M2 rule performed much better than either of the base rules.
25
When comparing monetary base and M2 rules it appears that even the addition of a plausible degree of money control error doesn’t much mitigate M2’s
advantage of a relatively stronger and more stable relationship with nominal GDP during this time period. The strength and stability of the relationship between the policy
instrument and nominal GDP improves the ability of the feedback adjustment term to offset the undesirable impacts of money control errors. When comparing the performance
of specific policy instruments, precise monetary control seems less advantageous than a stronger and more stable link to GDP.
In the Keynesian and two-variable VAR models, the St. Louis monetary base rule delivered slightly lower RMSEs than the M2 rule with money control error. But, this
difference in performance is small and unlikely to be economically significant. Results suggest that given current monetary control procedures, the Fed could suc-
cessfully utilize an M2 rule to maintain much greater levels of price stability and much lower levels of GDP variability than we have achieved under discretionary monetary
policy. The M2 rule is operationally sound and imposes the discipline necessary to achieve price stability. Findings also indicate that an M2 rule is likely to outperform a base rule.
IV. Caveats in the Analysis of an Adaptive M2 Rule
Conclusions regarding the likely ability of an M2 rule to increase price stability and lower the variability of nominal GDP around a constant trend are subject to many caveats.
All claims regarding the likely performance of any monetary policy rule are subject to the Lucas Critique. An elegant feature of McCallum’s Rule is that its ability to generate
high levels of price stability and low levels of GDP variability is not contingent on the existence of unchanging coefficients linking the policy instrument to nominal GDP. To
better understand this concept, suppose that implementation of an M2 rule by the Fed causes a one-time change in the historical relationship between M2 and nominal GDP.
This would be reflected by changes in M2 velocity, which would be accommodated by the second and third terms in McCallum’s Rule. As long as the adoption of an M2 rule doesn’t
25
The performance of a monetary base rule in VARs that incorporate an interest rate term seems to be dependent on the sample period considered. This is because the apparent strength and stability of the link
between the base and nominal GDP is also time dependent. Use of earlier sample periods [e.g., in McCallum 1988] yields a more stable linkage.
Suitable Policy Instruments for Monetary Rules 393
eliminate or excessively weaken the relationship between M2 and nominal income, the rule will automatically make the necessary adjustments.
26
The apparent ability of the M2 rule to substantially increase price stability and reduce the variability of nominal GDP around a constant trend might be criticized on the grounds
that the simple models used here overstate the strength of the relationship between M2 and nominal income. This criticism is contradicted by two arguments. First, recent studies
cited in Section II on the relationship between M2 and nominal GDP have confirmed the existence of such a strong and stable relationship. Second, examinations of the empirical
significance of the Lucas Critique show that some weakening of the strength of the relationship between M2 and nominal income doesn’t qualitatively change the result that
the adaptive M2 rule could still produce sizable reductions in price instability and in the variability of nominal GDP.
A third criticism is that the rules used here will produce greater variability in the policy instrument and, thus, real output than has been experienced historically. Using the mean
absolute percent change MAPC in the policy instrument as a measure of variability, during the sample period the actual quarterly MAPC in M2 was 7.25 at an annualized
rate. Table 4 illustrates that in the two- and four-variable VAR models, M2 would have been less variable under a rule. This result is robust for all sizes and types of money
control error. In the Keynesian model, only in the case of positively-correlated GDP shocks and money control errors, was M2 slightly more variable then it has been
historically. But, in the worst case, the MAPC rose to 7.42 at an annualized rate—a small increase. It appears that M2 is unlikely to vary more than it has historically.
By comparison, the historical MAPC of the St. Louis monetary base was 7.31 over the sample period. In the Keynesian model, the rule-determined MAPC was 5.04; in the
two-variable VAR model, it was 4.12; but, in the four-variable VAR model it rose to 26.45. The greater variability of the base in the latter model further illustrates that,
unlike M2, the performance of the St. Louis base is not robust to the choice of economic model.
The likely variability of real GDP, resulting from the adoption of an M2 rule, can only be evaluated in the Keynesian and four-variable VAR. The historical MAPC of real GDP
during 1964:Q1–1995:Q4 was 3.98. The MAPC obtained with an M2 rule incorporating money control errors consistent with historical norms i.e., with a mean of zero, a standard
deviation of 5, and uncorrelated with the GDP shocks was 3.55. Thus, in the four-variable VAR model, the variability of real GDP is slightly below the historical
norm. The MAPC of real GDP obtained in the Keynesian model, with an M2 rule incorporating money control errors consistent with historical norms, was 4.76. Although
the MAPC increased in the Keynesian model, the increase was small. These results indicate that the benefits of price stability are not likely to be obtained at the costs of
substantially increased instability in the policy instrument andor in real output. This suggests that the costs of targeting a stable price level are likely to be small, further
strengthening arguments for the adoption of an M2 rule.
26
Examinations of the empirical significance of the Lucas Critique were conducted by McCallum 1988 and Judd and Motley 1991, 1992. The authors found that rule performance is robust to substantial changes in the
parameters of the economic models.
394 S. R. Thornton
V. Conclusion
