Long Swings in the Exchange Rate and the Excess Returns Puzzle: The Role of
Imperfect Knowledge

William Strauss

The paper is a clear breath of "dirty" air in the sterile world of perfect
foresight. The authors offer a well worked out model of how agents persistently
bid the exchange rate away from the expected long-run equilibrium rate. It
seems intuitively comfortable to see the mathematical justification for the
unexplained excess returns to be a function of the distance from the bench-mark
(PPP). The uncertainty of a switch occurring in a regime (the Peso Problem) is
an interest-ing form within which to embed the imperfect information. It is a
format that seems ready to ex-pand into many other areas of economic modeling in
which expectations are at the core of the model's dynamics.

Of course, the choice of the benchmark is key to the mechanics of the process.
In this case, PPP is an obvious choice… but, since the idea of PPP drives this
model so strongly, it is interesting to look at its place and its
characteristics. In the paper, the authors note that if PPP holds, "relative
excess demand for domestic and foreign goods is zero." The obvious suggestion,
based on the model, is that the flow of goods and services is the foundation for
the equilibrating dynamic. Behind the flow of goods and services is the gap
between the gap between, domestic and foreign short-term rates, and the steady
state long-run interest rate gap that sets goods flows to zero. The assumption
is that the prices of the domestic and foreign goods in their respective for-
eign currencies are "incorrect" based on the fundamentals of the respective
countries and that agents know this (and know that the exchange rate path is
unstable) but cannot be sure of the de-gree of "incorrectness" or the
persistence of the di vergence. Embedded into this model are as-sumptions about
PPP that provide comfort about this benchmark's ability to give the "correct"
relative prices. It is possible that these assumptions, to some degree, mask
the complexity of the situation with respect to PPP's ability to proxy relative
prices. At the theoretical level, PPP should simply offer equal purchasing
power for equal commodity bundles through the exchange rate. Unfortunately, the
problem of explaining stylized facts requires some matching with reality. Set-
tling for getting the signs right mitigates much of the angst, but, as has been
demonstrated by the predictive abilities of many of the models to date, the
problem is not really solved. Perhaps the model of PPP as a function of
interest rates only misses something…

But here we have a BIG step (from the real exchange rate side, not from the side
of better modeling PPP) toward not only getting the signs right, but also
understanding the dynamics of the switch. If PPP were built from a micro-
foundation choice-based model (where demand-side ef-fects influence
saving/investment and interest rates), I suspect that we might see a real
conver-gence toward understanding the excess returns puzzle.

Category: Business