The data are so opposite of what standard models assume that even the most die-hard defenders of them should take note: if these data are accurate, then almost everything we say about monetary policy is wrong.
The main debate among standard modelers has been about how much interest rate changes affect each of the two variables. They do not debate a common assumption of their models, that interest rate changes have no effect on the conditional variances of marginal utilities and inflation. That common assumption, however, is grossly inconsistent with a well-established feature of the data: nominal rates of exchange between major currencies are well approximated by random walks. This finding dates back at least to the work of Meese and Rogoff (1983)
Determining how changes in an asset price, the short-term interest rate, affect the economy is clearly at the heart of monetary policy analysis. As we have argued, the data on exchange rates imply that movements in interest rate differentials are reflected almost entirely in fluctuations in excess returns. Thus, for monetary policy, accounting for fluctuations in these excess returns is essential, and monetary models that cannot account for them cannot help us understand the effects of interest rate changes on the economy.
A […] promising direction is […] to develop models in which changes in monetary policy affect the economy primarily by changing risk. In ongoing research (see Alvarez, Atkeson, and Kehoe 2006), we have built such a model based on the idea that asset markets are segmented and that monetary policy affects risk by endogenously changing the degree of market segmentation. We have shown that this model can generate, qualitatively, the type of systematic variation in risk premia called for by the data on interest rates and exchange rates.