This paper develops asymptotic econometric theory to help understand data generated by a present value
model with a discount factor near one. A leading application is to exchange rate models. A key assumption
of the asymptotic theory is that the discount factor approaches one as the sample size grows. The finite
sample approximation implied by the asymptotic theory is quantitatively congruent with the modest
departures from random walk behavior that are typically found and with imprecise estimation of a wellstudied
regression relating spot and forward exchange rates.