Exchange Rate Economics: Theories and Evidence

216 Real exchange rate determination
8.4.2 The Clarida–Gali SVAR approach
In order to understand the structural restrictions used by Clarida and Gali (1994)
we first present a stochastic version of the Mundell–Fleming–Dornbusch model.
This model is based on Obsfeld (1985) and Clarida and Gali (1994) and since most
of the relationships are familiar from previous chapters,our discussion here will
be relatively brief. The open economy IS equation in the model is given by:
y d ′
t = d ′
t + η(s t − p ′ t ) − σ(i′ t − E t(p ′ t+1 − p′ t )),(8.34)
where a prime denotes a relative (home minus foreign) magnitude. The expression
indicates that the demand for output is increasing in the real exchange rate and
a demand shock (which captures,say,fiscal shocks) and decreasing in the real
interest rate. The LM equation is familiar from our previous discussions
m s′
t − p ′ t = y ′ t − λi′ t ,(8.35)
where the income elasticity has been set equal to one. The price setting equation
is taken from Flood (1981) and Mussa (1982) and is given as:
p ′ t = (1 − θ)E t−1 p e′
t + θp e′
t . (8.36)
Expression (8.36) states that the price level in period t is an average of the marketclearing
price expected in t − 1 to prevail in t,and the price that would actually
clear the output market in period t. With θ = 1 prices are fully flexible and output
is supply determined while with θ = 0,prices are fixed and predetermined one
period in advance. The final equation in this model is the standard UIP condition:
i ′ t = E t (s t+1 − s t ). (8.37)
The stochastic properties of the relative supply of output, yt s′ , d ′
t and m′ t are assumed
to be:
yt s′ = yt−1 s′ + z t,(8.38)
d t ′ = d t−1 ′ + δ t − γδ t−1 ,(8.39)
m t ′ = m t−1 ′ + v t,(8.40)
where z t , δ t and v t are random errors. Therefore both relative money and output
supply are random walks and the relative demand term contains a mix of permanent
and transitory components (i.e. a fraction γ of any shock is expected to be of
offset in the next period).
By substituting (8.38) and (8.39) into (8.34) a flexible price rational expectations
equilibrium,in which output is supply determined,for the expected real exchange
rate (q = s − p) is given by:
q e t = (y s t − d t )/η + (η(η + σ)) −1 σγδ t ,(8.41)