Palgrave Handbook of Econometrics: Applied Econometrics

1062 The Econometrics of Exchange Rates

TheilU-statistics than forecasts based on the revised data, indicating the superiority
of real-time data.^73
Engel and West (2005) provide a thorough analysis of the role of market expec-
tations and the value of the discount factor. According to the rational expectations
present value model (22.61), the importance of expected future fundamentals rel-
ative to current fundamentals increases with the discount factor,b. For largeband
non-stationary fundamentals, the movement in the exchange rate at timetwill be
almost uncorrelated with information known at time(t− 1 ), since the exchange
rate will be largely driven by the expected future path of the fundamentals. By
the Engel and West (2005) theorem, ifa′ 1 xt∼I( 1 )anda 2 =0ora′ 2 xt∼I( 1 )
then, asb→1, the exchange rate exhibits near random walk behavior.^74 The
theorem highlights the fact that movements in the exchange rate reflect changes
in expectations. If expectations contain valuable information about future fun-
damentals then changes in the exchange rate should be useful in forecasting
fundamentals. This provides an alternative approach concerning the evaluation
of the performance of the various models under examination.
A different perspective for the implications of the Engel and West theorem is
provided by Evans and Lyons (2005) in the context of market microstructure.
Lyons show that micro-based models can establish a link between expectational
surprises and specific types of non-public information. The key idea is that the
trades of private agents reveal new information to the market makers about future
fundamentals. In this framework prices are determined by the market makers’
expectations,Emt, about the future values of fundamentals. The market makers
construct their information sets and revise their forecasts on the basis of the order
flow,xo,t, that is signed transaction flow. Suppose that innovations in order flow
are correlated with the innovations in fundamentals growth:

xo,t=λxo,t− 1 +ηt, (22.94)

ft=φft− 1 +ut+δηt, (22.95)

and that market makers observe order flow innovations and, hence, the current
state of the economy, with a time delayft−Emtft=δηt. Evans and Lyons (2005)
show that, under these assumptions, the present value model (22.61) implies that
changes in the exchange rate depend on lagged order flow:

st+ 1 =

1 −b

b

(st−Emtft)+

1

1 −bφ

ut+ 1 +

[ 1 +φ( 1 −b)]δ

1 −bφ

(xo,t−λxo,t− 1 ). (22.96)

It follows from the above equation thatb→1 does not rule out forecastability. In
order to test whether order flow contains predictive power for the movements in
the exchange rate, they employ the following regression equations:

st+ 1 −st=α 0 +αxaggo,t+εt+ 1 , (22.97)

wherexaggo,t denotes aggregate order flow, and:

st+ 1 −st=α 0 +

∑^6

j= 1

αjxjo,t+εt+ 1 , (22.98)