S.G.B. Henry 921Equation (18.1) is the AS (or Phillips curve) equation, whereπtis domestic inflation
and(yt−y∗t)is the output gap. As written, this is in the so-called “hybrid” form
for the New Keynesian Phillips curve (NKPC), which depends on both lagged and
future expected inflation rates. Equation (18.2) is the AD equation dependent on
expected output and the real interest rate. The last equation (equation (18.3)) is
a simple form of policy rule for interest rates,r, which is shown as depending
on deviations of expected inflation from target and the output gap.^4 A significant
difference in practice is how this equation is treated. First, it may be explicitly
derived by optimising a dynamic objective function depending on government
macroconomic objectives (inflation and output deviations from their equilibrium
levels) subject to the constraints given by the model above, as in Ball (1997) and
as in the models in sections 18.3 and 18.5 later, for example. But, most often the
policy rule is taken as simply a reasonable description of the authority’s behavior
and is estimated; however, substantial problems can arise when it is estimated, and
some of it is discussed next in a short review of US literature.
18.2.2 Evidence for and against monetary regime change in the US
Under the heading of the “Great Moderation,” considerable effort has been directed
at finding possible explanations of the marked reduction in the volatility of infla-
tion and output in the US (BoE, 2007, draws attention to similar developments in
the UK). It is probably fair to say that the results of this have been inconclusive,
with some papers finding evidence for regime change in monetary policy whilst
others have reported equally strong findings against. In part, this reflects different
modeling approaches, as we illustrate immediately below.
There are now many examples of single equation estimates of both NKPCs and
interest rate policy rules, both of which are directed at detecting changes in the
effectiveness of monetary policy. They mainly assume that expectations are formed
rationally. In the research on the NKPC, a major interest has been whether the
degree to which the equation is forward-looking has increased, but this issue is
largely unresolved. Thus, for example, using marginal costs rather than output
gaps as the driving variable in the equation, Rudd and Whelan (2005) argue for
the unimportance of forward-looking terms. In turn, Gali, Gertler and Lopez-Salido
(2005) rebut this by observing that Rudd and Whelan use incorrect weights in form-
ing the required forward-looking terms. Turning to the estimated policy reaction
function (that is, the estimated version of (18.3) above), this has typically been of
the form:
rt=( 1 −ρ)α+( 1 −ρ)βπt+n+( 1 −ρ)γxt+ρrt− 1 +εt. (18.4)In this equationα= ̄r−βπ∗, wherer ̄is the long-run equilibrium nominal interest
rate,π∗the target inflation rate andβis the weight on inflation deviations from
target in the authority’s objective function. The variablextis defined asyt−y∗, and
in (18.4) allowance is made for interest rate smoothing with a weightρ. Henry and
Pagan (2004) draw attention to a problem of the interpretation of such equations
when they are used to infer what central banks’ behavior has been. An example of
such an interpretation is found in Clarida, Gali and Gertler (2000). Drawing such