882 Macroeconometric Modeling for Policy
The above steady-state properties are derived for an exogenous policy interest rate
R. The nature of the solution is not changed if we instead specify either an estimated
interest rate reaction function on the basis of the data, or a response function
based on theories of optimal policy rules. But the behavior of the dynamics will be
affected, and the policy analysis and the level of predicted long-run inflation will
depend on how the interest rate is modeled.
We agree with Hendry and Mizon (2000) that there are reasons for being prag-
matic about how the policy instrument is “treated” in a macroeconometric model.
For some purposes it is relevant to treat the instrument as exogenous, like in the
analysis of the steady state (this sub-section) and its stability (next sub-section).
That analysis will answer whether there is a fundamental tendency of dynamic
instability in the model that instrument use will have to counteract in order to
avoid the economy taking an unstable course or, conversely, whether there is suffi-
cient stability represented by the modeled relationships. In that case the challenges
to instrument setting are more linked to timing and to meeting a specific inflation
target than to “securing” overall nominal or real dynamic stability.
In the following sections we will use both the open and closed versions of the
NAM model with respect to the policy instrument. In the next section, and the first
section on policy use (section 17.4.2.1), we will use the open model with exogenous
Rt. Later (e.g., when evaluating tracking performance in section 17.4.2.2), we will
use a version with an econometrically modeled interest rate reaction function,
which is documented in Table 17.1. In section 17.4.3, to discuss optimal policy we
will use a version with a theoretically derived interest rate response function.
17.3.3 Stability of the steady state
In an important paper, Frisch (1936) anticipated the day when it would become
common among economists to define (and measure) “normal” or natural values of
economic variables by the values of the variables in a stationary state. The steady-
state defined by the long-run model above corresponds to such natural values of
the model’s endogenous variables. But it is impractical to derive all the “natural
values” using algebra, even in such a simple system as ours. Moreover, the question
about the stability of the steady state, e.g., whether the steady state is globally
asymptotically stable – or perhaps stability is only a saddle-path property – can
only be addressed by numerical simulation of the dynamic system of equations.
We therefore follow Frisch’s suggestion and simulate the dynamic NAM model.
Figure 17.3 shows the “natural values” for inflation(ptabove), the rate of unem-
ployment, wage inflation, GDP growth, growth in import prices and the rate of
currency depreciation. The first solution period is 2007(4) and the last solution
period is 2035(4). The simulation period is chosen to be so long because we want to
get a clear impression about whether these variables approach constant (“natural”)
values or not, and whether the effect of initial conditions die out, as they should
if the solution is globally asymptotically stable. The simulation is stochastic. The
solid lines represent the mean of the 1,000 replications, and the 95% prediction
intervals represented by the distance between the two dashed lines accommodate
only residual uncertainty, not coefficient uncertainty.