Palgrave Handbook of Econometrics: Applied Econometrics

Katarina Juselius 355

1975

0.50

0.75

1.00

0.0

1.25

1975 1980 1985 1990

Log of US CPI

Log of German CPI

The Dmk–$ rate

Relative prices for Germany versus USA

1995 2000

0.5

1.0

1980 1985 1990 1995 2000

Figure 8.1 Time graphs of German and US prices (upper panel) and their relative prices and
nominal exchange rate (lower panel)

The pulling forces are described by the vector equilibrium correction model:

[

ppt

s12,t

]

=

[

α 1

α 2

]

(ppt− 1 −s12,t− 1 −β 0 )+

[

ε1,t

ε2,t

]

,

where (ppt−s12,t−β 0 )=β′xtis the cointegration relation withE(pppt)=β 0. Thus
an equilibrium position, defined asppt−s12,t=β 0 , can be given an interpretation
as a resting point towards which the process is drawn after it has been pushed
away. In this sense, an equilibrium position exists at all time points,t, contrary to
the long-run value of the process, which is the value of the process in the limit as
t→∞and all shocks have been switched off.
The pushing forces are described by the corresponding common trends model:
[
ppt
s12,t

]

=

[

c

c

]

α′⊥

∑t

i= 1

εi+C∗(L)

[

ε1,t

ε2,t

]

,

withα′⊥=α 1 −^1 α 2 [−α 2 ,α 1 ]and withα′⊥

∑t
i= 1 εidescribing the common stochas-
tic trend. Assume now thatα′=[0,α 2 ], i.e., only the nominal exchange rate is
equilibrium correcting whenpppt−β 0 =0. In this caseα′⊥=[1, 0]implies that
the common stochastic trend originates from relative price shocks. This would
conform to the theoretical prior for a period of floating exchange rates.
The question is now whether the empirical reality given by the observed variables
in Figure 8.1 (lower panel) can be adequately represented by the above assumed
pulling and pushing forces. Stationarity ofppptshould imply that the nominal
exchange rate would follow relative prices one-for-one apart from stationary noise.
Figure 8.2 shows a cross-plot of thepptands12,tvariables. If the assumption that