FOOTNOTES
1. The "long and variable lag" for nominal income and
money was first documented for the U.S. by Milton Fried-
man, in “The Lag in the Effect of Monetary Policy,” in his
The Optimum Quantity of Money and Other Essays. See
also the article on “Inflation and Monetary Accommodation
in the Pacific Basin” by Michael Bazdarich in the Summer
1978 issue of this Economic Review, as well as the article
by Michael Keran and Stephen Zeldes in this issue.
2. See, for example Gordon (1976), pp. 201-02.
3. The conditions for money neutrality are fairly stringent.
First, transfers of wealth among individuals resulting from
price-level changes must not affect aggregate demand and
supplies. Second, open-market exchanges of money for
government bonds will not be neutral unless individuals
discount future tax liabilities in calculating their wealth, so
that for the “typical” individual, government bonds are not
net wealth. Furthermore, the proposition does not apply to
money-supply changes accompanied by variations in real
government expenditure or taxes. Finally, money neutrality
refers to changes in the level of money with its long-run
growth rate held constant; if anything, there is a consensus
that changes in the long-run money-growth rate are not
neutral.
4. Specifically, most economists would now agree that
money changes have negligible long-run impacts on real
output and unemployment, that is, the “Phillips” curve is
vertical in the long-run. This factor, combined with empirical
estimates of money-demand relations (where real balances
are generally a function of real output and interest rates)
suggests that a rise in money (with no change in its ex-
pected growth rate) will raise the price level proportionally.
5. Trends in real output and velocity enter because they
influence the real demand for money. This real demand can
be permanently affected by factors, such as financial inno-
vations, that are not easily summarized quantitatively—and
indeed are not always observable, and thus cannot be ac-
counted for explicitly. Since these factors then enter the
disturbance term in the empirical relation, the relation (1 ’.)
relating price and money changes is most often used; these
factors would cause the constant term relating the level of
prices and money to shift about during the sample period.
Consequently, this relation is less practical as a form for
estimation. For this reason, the empirical results referred to
later will be of the second form, and we will normally refer
to the money-growth inflation relation in the text.
6. In other words, we can imagine a system where prices,
output, and interest rates are simultaneously determined
as, for example,
I ∆p(t) ∖ / ∆p(t) ∖
I ∆q(t) =Al ∆q(t) I + C∆m(t)
∖ KO / ∖ KO /
where i(t) is the interest rate, A is a matrix of lag polyno-
mials, and C is a vector of such polynomials. The lagged
relation between money and prices referred to in the text is
defined as the “reduced form” solution of this system where
prices depend only upon money: This is obtained by solving
the above system to obtain an equation relating price and
money changes only. This is the text relation (1) and it
includes all indirect effects upon prices of output and inter-
est rate responses to money. This fact makes it often difficult
to interpret the empirical counterparts of (1).
7. See Rutledge (1979) and (1977) for a more detailed
discussion.
8. This is the rationale implicit in Barro (1979).
9. Indeed, nearly all rational-expectations models imply that
economic decisions depend upon expectations of future
policy variables. Some concrete illustrations of this are de-
scribed in the Appendix.
10. Arthur Okun (’’Inflation; its Mechanics and Welfare
Costs," Brookings Papers on Economic Activity:2,1975)
discusses the reasons why price fluctuations may be limited
by tacit agreement in what he describes as “customer mar-
kets." See especially pp. 358-73.
11. That is, decisions about inventory levels, work sched-
ules, etc., are all likely to depend upon firm anticipations of
“typical” patterns of behavior of variables affecting firm
costs and profits.
12. This is, of course, implied by the hypothesis of “rational
expectations”—but it is more general. Individuals may not
make use of all information potentially available, but they
are likely to adapt whatever forecasting techniques they do
use to changed policies, at least given enough time.
13. This observation is relevant to tests of the influence of,
(say) government deficits on prices. Suppose that the deficit
is found to be a significant variable, in addition to current
and past money, in a regression “explaining” inflation. Does
this imply that the deficit affects inflation independently of
money growth? The arguments in the text suggest that this
is not necessarily the case if the monetary authorities react
to deficits so that deficits provide a “signal” of future money
growth. As will become clearer in the next section, tests
about the causes of inflation cannot generally be based upon
relations such as (1 ) alone. This point has been emphasized
by Lucas (1970).
14. In Britain, for example, the authorities define monetary
objectives for M-3, while in Japan targets are set for M-2.
See the OECD’s Monetary Targets and Inflation (p. 27) for
an assessment of the stability of money-demand relations
using alternative aggregates. This finds M-2 inferior to M-1
for Germany, while M-2 is at best marginally “preferable” to
M-1 for Japan. The choice also does not seem clear-cut in
the U.K.; see also Goodhart and Crockett (1970).
15. Another reason for including this dummy variable is the
possible shift in the perceived long-run growth rate of
money—that is its unconditional mean—in several coun-
tries. If so, the models developed in the Appendix also imply
a shift in the constant term in a regression of price changes
on current and past money growth. This change does not
necessarily arise from the resulting change in interest rates
(although it may, at least in part). For example, in the simple
contracting model in the Appendix, there is no interest rate
impact on prices. However, a rise in the long-run money-
growth rate will lead to an increase in the “shift” parameter
used by rational forecasters to predict permanent money,
47