Palgrave Handbook of Econometrics: Applied Econometrics

932 Monetary Policy, Beliefs, Unemployment and Inflation

Table 18.2 Tests of orders of integration,

sample 1964Q4–1992Q4

Variable DF ADF(4) DF ADF(4)

ln u −0.7 −1.3 −5.4 −4.0

IT −3.0 −3.4 −8.7 −6.1

T −2.3 −2.3 −13.5 −4.2

TT −1.0 −0.3 −13.8 −4.9

Skill −1.5 −3.3 −4.8 −5.7

RR −0.2 −2.0 −3.3 −2.7

UP −1.3 −1.5 −4.0 −3.6

r −2.1 −2.4 −3.3 −2.7

Notes: The first two columns are for levels, the

second two for first differences (ADF followed by

ADF(4) in each case). 95% critical value is 2.9.

Table 18.3 Tests for weak

exogeneity, sample

1964Q4–1992Q4

Variable Wald statistic

lnu 21.9

IT –

T 2.9

TT 6.4

Skills 22.2

RR 19.7

UP 17.1

r 22.4

Note: The relevant test statistic

with three cointegrating vec-

tors isχ^2 ( 3 )with 95% critical

value of 7.8.

The stationary variableITis assumed to enter in thezt− 1 vector in a level form.^23
 1 jare( 5 × 8 )and 2 jare( 2 × 8 )matrices of parameters on the dynamic terms of
all the variables.
To just identify the cointegrating vectors in the model,r^2 restrictions need to
be accepted, with each of thercointegrating equations having exactlyrrestric-
tions successfully applied, as demonstrated in Pesaran and Shin (2002).^24 Further,
Wickens and Motto (2001) show that when the cointegrating vectorα′in (18.20) is
exactly identified, additional overidentication lies in successfully applying restric-
tions on the loading matrix γ.^25 By applying these procedures, it could, in
principle, be possible to derive an equation like (18.18) from the conditional model
(18.20), if all the required restrictions on the long-run vectors and the loading
matrix needed to get from (18.20) to a single equation of the form of (18.18) were