Palgrave Handbook of Econometrics: Applied Econometrics

48 Methodology of Empirical Econometric Modeling

1920 1940 1960 1980

–12.5

–12.0 a ef^

e

1920 1940 1960 1980

–0.25

0.00

b pf−p

1920 1940 1960 1980

–11.5

–11.0

–10.5

–10.0 c

1920 1940 1960 1980

0.0

0.1

0.2

0.3

d s

1920 1940 1960 1980

–0.1

0.0

0.1 e Δef

1920 1940 1960 1980

1.0

1.2

1.4

1.6 f

log family size

Figure 1.6 Food expenditure and related time series

ona, and was selected by Autometrics at 1% for all candidate variables, including
impulse saturation. All diagnostic tests were insignificant, and the PcGive unit root
test strongly rejected the null of no cointegration (tur=−11.37∗∗: (see Banerjee
and Hendry, 1992; Ericsson and MacKinnon, 2002) with the long-run solution:

c 0 =ef+7.99−0.4e+0.36(pf−p). (1.39)

Transforming to differences and the equilibrium-correction term from (1.39),
Autometrics selected over 1931–89 (at 2.5%, again including impulse saturation):

ef,t= 0.34

(0.02)

st− 1 − 0.32

(0.02)

c0,t− 1 + 0.67

(0.04)

et+ 0.13

(0.03)

et− 1

− 0.64

(0.03)

(pf−p)t− 0.09

(0.01)

I 31 − 0.10

(0.01)

I 32 + 0.04

(0.01)

I 34

+ 0.03

(0.01)

I 41 + 0.05

(0.01)

I 42 + 0.03

(0.01)

I 51 + 0.02

(0.01)

I 52 + 0.03

(0.01)

I 70

(

R∗

) 2

=0.96FM(13, 45)=94.9∗∗̂σ=0.0078Far(2, 44)=1.34

χ^2 (^2 )=1.04Farch(1, 44)=2.25Freset(1, 45)=0.35

Fhet(18, 27)=0.48FChow(9, 37)=0.99. (1.40)