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