S.G.B. Henry 93718.5.2 Some model implications
18.5.2.1 Model solutions
Sargent’s (1999) model is recursive and is solved given initial values of the natural
rate (u∗) (assumed constant), the government’s discount rate, the parameter on
inflation surprises in the actual Phillips curve (θ)and the variances of the two error
processes in the model. These parameters are assigned the values 5% for the natural
rate, 0.98 for the discount rate,−1 forθand the variances of the errors are each
taken to be 0.3. The dynamic solutions are calculated over 400 and 1,000 periods,
and it is in the latter that the escapes are a prominent feature (see, for example,
ibid., Ch. 8, p. 108).
The exercise we report next differs from Sargent’s in important ways. It takes
the model described in section 18.5.1 and, given the focus on the period since
1980, is solved over 100 quarters using actual data for the two exogenous vari-
ables in the unemployment equation starting from 1980Q1.^30 In these solutions,
initial values for the parameters of the “perceived” Phillips curve, equation
(18.28),γ 0 t,γ 1 t,δ 1 tandδ 2 t, are required and are set at−0.6,−0.9, 2.0 and 10.0,
respectively.^31 In each solution, the discount rate is set at unity,θis minus unity
and the gain parameter in the updating equations is fixed at 0.0275 to ensure
comparability across the solutions. Stochastic solutions are generated by additive
drawings from standard normal distributions.^32
18.5.2.2 Inflation with a time-varying natural rate
The present exercise is a Beliefs model, but one in which mistakes by the
authorities about the evolution of the natural rate as well as a belief in an
inflation–unemployment trade-off each can account for inflation dynamics.^33
In Figure 18.3 the authorities are depicted as remaining uncertain about the
effects of external shocks on the natural rate and this, together with their mistaken
view about the existence of a trade-off, gives the initial higher rates of inflation.
The interactions of their revisions to all the parameters of the perceived Phillips
curve are then fairly complex, as we describe below. The effects of these are that
they adopt a looser monetary policy to start with in order to reduce unemployment
more than is actually required. Subsequently, the parameter estimates are updated
and the effects of these changes are that monetary policy is tightened, so bringing
down inflation over the first four to five years before it rises modestly and then
falls again.
The falls in inflation can be traced to the evolution of the governments’ estimates
of the parameters on all the variables in the authorities’ unemployment equation.
As in the other examples of the Beliefs literature cited so far, the authorities’ misper-
ception about inflation “surprises” also matter. But, as shown in Figures 18.4(a)–(e),
among the parameters in the authorities’ misperceived Phillips curve,δ 1 tandδ 2 t,
each fall,γ 0 tincreases andγ 1 tfalls in absolute value (though it remains negative).
These revisions largely account for the changes in inflation shown in Figure 18.3,
and they appear to show that the authorities do not learn the full extent of the