Palgrave Handbook of Econometrics: Applied Econometrics

S.G.B. Henry 935

Table 18.4 Tests of orders of integration,

sample 1980Q1–2005Q4

Variable DF ADF DF ADF

u −0.24 −2.1 −2.6 −3.2

OIL −2.2 −2.14 −8.8 −6.2

COM −1.7 −2.0 −7.8 −4.1

RPM −0.27 −0.62 −7.4 −4.7

Notes: See Table 18.2.

Table 18.5 Tests for weak

exogeneity, sample

1980Q1–2005Q4

Variable Wald statistic

u 10.9

OIL 0.5

COM 3.2

Note: The relevant test statistic

with one cointegrating vector is

χ^2 ( 1 )with a 95% critical value

of 3.8.

variables except unemployment are weakly exogenous as required (see Table 18.5).
It is this empirical model of long-run unemployment that is used in the application
of the Beliefs model in the next section.

18.5 Applying the Beliefs model to the UK

This section brings together the positive policy model emphasizing the role of
beliefs set out in section 18.3 and the econometric analysis of the UK natural rate
from section 18.4. It outlines optimal control solutions from the Beliefs model
when the crucial equation for long-run unemployment in the Beliefs model of
section 18.3 (equation (18.6)) is replaced with the cointegrating equation (equation
(18.25)) derived in the previous section. This econometric equation has impor-
tant “exogenous” determinants of the natural rate which arguably account for its
longer-term variation. In common with other examples of the Beliefs model, it
takes a static model of the supply side, and dynamic implications are then due
to the assumptions made about the authorities’ uncertainty and their processes of
learning. This change to the determination of long-run unemployment is profound
in its effect on the dynamic properties of the model, which are described later.
Uncertainties about the variation in the natural rate, due to changes in the external
economy, are advanced as a principal explanation for changes in UK inflation
since 1980.