Palgrave Handbook of Econometrics: Applied Econometrics

David F. Hendry 49

In (1.40),

(

R∗

) 2
is the squared multiple correlation when a constant is added,
FM(13, 45)is the associated test of the null, and̂σis the residual standard devia-
tion, with coefficient standard errors shown in parentheses. The diagnostic tests
are of the formFj(k,T−l), which denotes an approximateF-test against the
alternative hypothesisjfor:kth-order serial correlation (Far: see Godfrey, 1978),
kth-order autoregressive conditional heteroskedasticity (Farch: see Engle, 1982),
heteroskedasticity (Fhet: see White, 1980a); theRESETtest (Freset: see Ramsey, 1969);
parameter constancy (FChow(see Chow, 1960) overkperiods; and a chi-square test

for normality (χnd^2 ( 2 )(see Doornik and Hansen, 2008). No misspecification test
rejects.
The result in (1.40) is to be contrasted with the equation reported earlier, which
had a similar equilibrium correction term based on Johansen (1988):

c 2 =ef+7.88−0.4e+0.4

(

pf−p

)

, (1.41)

leading to (D3133 and D4446 are dummies with the value unity over the periods
1931–33 and 1944–46 respectively):

ef,t= 0.27

(0.04)

st− 1 − 0.34

(0.02)

c2,t− 1 − 0.019

(0.004)

+ 0.24

(0.05)

st

+ 0.53

(0.05)

et− 0.46

(0.04)

(pf−p)t− 0.12

(0.01)

D3133+ 0.038

(0.010)

D4446

R^2 =0.936FM(7, 51)=107.2∗∗̂σ=0.0098Far(2, 49)=0.18

χ^2 ( 2 )=0.21Farch(1, 49)=0.59Freset(1, 50)=0.26Fhet(13, 37)=0.47. (1.42)

Thus, six additional outliers have been detected in (1.40), whereas none of the
components of D4446 was found, nor was I 33 : neither dummy is remotely sig-
nificant if added to (1.40). Consistent with that result, when (1.42) and (1.40)
are denoted models 1 and 2 on encompassing tests,FEnc1,2(10, 41) = 4.83∗∗

andFEnc2,1(5, 41)=2.18, so (1.42) is encompassed by (1.40) but not vice versa.

Nevertheless, both models are rejected against the other on Cox (1961) and Ericsson
(1983) non-nested tests witĥσJ=0.0074.
Another recent development that can be implemented based on impulse satura-
tion is to test for the super exogeneity of the parameters of the conditional model in
response to changes in the LDGPs of the two main conditioning variables,etand
(pf−p)t(see section 1.4.5 and Hendry and Santos, 2009). The latter’s equation
revealed no significant breaks, but commencing from one lag ofe,(pf−p),s
anda, the former produced:

et= 0.016

(0.003)

+ 0.256

(0.081)

et− 1 − 0.302

(0.083)

(pf−p)t− 1 − 0.11

(0.02)

I 31

− 0.19

(0.02)

I 32 + 0.10

(0.02)

I 34