What Uip Tests on Extreme Samples Reveal About the Missing Variable

Abstract

In their regression tests of uncovered interest parity (UIP), Huisman et al. (1998) focus on days with unusually large cross-sectional variances in forward premia, their regressor, conjecturing that such an "extreme" sample tends to pick episodes with more pronounced expectations about the exchange-rate change. Consistent with the idea that extreme sampling provides a more favorable signal/noise ratio, they do find better regression coefficients. The present paper investigates under what distributional assumptions one can expect such results, and how the moments that generate the regression coefficient are affected by such extreme sampling. We show that, for extreme forward premia to be primarily due to a clear signal (the expectation) rather than loud noise (the missing variable that causes the bias), the signal needs to be thickertailed than the noise. The particular hypothesis that noise is induced by transaction costs seems to have promising properties: the resulting bias in the forward premium is (i) bounded (that is, it has no tails and, therefore, cannot dominate the extreme forward premia), (ii) wide (that is, it may generate betas below 1/2) and (iii) U-shaped in distribution, a feature that turns out to make an "extreme" sample quite effective. We derive theoretical and numerical results in the direction of what Huisman et al. observe.