Appendix
Is the price level anchored under a mixed price level/inflation targeting regime?
A legitimate question arises on whether the price level would be anchored under
simple/optimal rules penalising a mixture of price level and inflation deviations from
target, or anything that was not a pure price level target.
We would expect the price level to be anchored in any rule with   0 but 1 (i.e. in
any rule feeding back on the price level or mixtures of this and the inflation rate, but
not in rules feeding back only on the inflation rate). This is because such rules (either
simple or optimal) feed back on price level deviations from target, on top of other
things (inflation and output deviations from target and potential, respectively). This
ensures that, under those rules, the price level will be returned to base after a shock 
even if over a long time period in the mixed targets case relative to the pure price
level target case.
As the charts 1b-7b show, the variance of the price level is bounded over a 200periods time period following a shock, both under optimal and simple rules of that
‘mixed’ kind.1 This provides prima facie evidence that the price level is stationary
under those rules (a non-stationary process would display infinite variance, and so an
estimate of the variance on a 200-period sample would be very large).
Below we provide further corroborative evidence on this issue. For this purpose, we
computed impulse responses of the price level and inflation after a temporary,
positive, 1 % shock to aggregate demand, using variant BH1 of model closed, for the
sake of argument, by a simple rule as (2) with k = 8, and  p   y  0.5 .
Charts 10 and 11 show that, while inflation goes back to base no matter what the
value of  (0, 0.5 or 0), the price level does not for some value of . In fact, pt does
not return to base under inflation targeting (  = 1)  being permanently shifted
1
This is not the case for Chart 2b, but the large variability of output and the price level found in that
case are conceivably not attributable to the fact that the price level is not anchored.
24
below base even if the demand shock was temporary, because the  = 1 case permits
a unit root in the price level. But it does, even if over different time periods, under
both the pure (  =0), and the mixed (  =0.5) price level targeting specifications of
the rule. So, in line with our intuition, a mixed price level/inflation targeting rule does
anchor the price level.
25
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