Expectations, money, and the forecasting of inflation

done because of the assumption that individ-
uals would require some time to observe the
behavior of money before arriving at a final
notion of how to predict it; thus the relations
estimated over these earlier periods may better
reflect individuals’ expectations than relations
estimated for later periods. We then have the
following:

∆m(t) = c + a_l∆m(t-l) +
a₂Δm(t-2) + δ(t-l) +
b₂δ(t-2) + b₄δ(t-4)              (4)

where ∆m(t) is the quarter-to-quarter change
in the logarithm of money. This relation can
also be written in a form where current money
growth depends upon past money changes and
the current value only of δ( ).²⁷ In this, δ( )
stands for money changes in excess of those
already anticipated on the basis of past money
changes. Its meaning can be seen from the
computation of the impact of money growth
on the level of money in the long-run (Table
2). Assume that money, after growing steadily
at its long-run average rate, rises by one per-
cent more in the current period; then δ( ) is
equal to one percent. The long-run effect of
this increase on the level of money then equals
the sum of the current and future money
changes generated by this “blip” in money
growth; it equals (1 + b₁ + b₂ + b₄)∕(l - a₁
- a₂). Of course this ultimate impact will take
some time for completion, and indeed this in-

Table 2
Summary of Univariate Time-Series Estimates for Changes
in Log Values of the Money Supply

'Ultimate effect upon future money of a 1-percent unanticipated change in current money.

²Test of the significance of the entire set of parameters. A value above 2.3 is significant at the 5-percent level.

³The model contains moving average parameters at lags 1, 2 and 4 and autoregressive parameters at lags one and two. Thus
the model can be written as,

∆m(t) = a_o∆m(t--l) + a_lΔm(t-2) + δ(t) + b, δ(t--l) + b,δ(t-2) + b₄δ(t - 4)

where ∆m(t) is the quarterly first difference of the log of Ml, and the δ() are white-noise errors.

⁴For Canada for the first period, the estimated model is (barely) unstable in the sense that the changes in money following
the initial increase persistently grow in absolute value (however, the estimates are fairly ‘close’ to being stable). When the
model is reestimated dropping the second autoregressive term (a, assumed to equal zero), the response becomes stable.
The revised model implies a negative long-run impact for the earlier period (- .62), that is, an initial rise in money leads
ultimately to a fall in its level. For the second period, the long-run impact calculated from the revised model is 13.2;
however, the fit compared with the original model is substantially worse in this case.

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