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6.1. DEVIATIONS FROM UIP 169Table 6.3: Estimates of Regression Equations (6.3) and (6.4)US-BP US-JY US-DM DM-BP DM-JY BP-JYˆβ 2 -3.481 -4.246 -0.796 -1.645 -2.731 -4.295t(β 2 =0) (-2.413) (-3.635) (-0.542) (-1.326) (-1.797) (-2.626)t(β 2 =1) (-3.107) (-4.491) (-1.222) (-2.132) (-2.455) (-3.237)ˆβ 1 4.481 5.246 1.796 2.645 3.731 5.295Notes: Nonoverlapping quarterly observations from 1976.1 to 1999.4. t(β 2 =0)(t(β 2 = 1) isthet-statistictotestβ 2 =0(β 2 = 1).Let’s run the Fama regressions using non-overlapping quarterly observationsfrom 1976.1 to 1999.4 for the British pound (BP), yen (JY),deutschemark (DM) and dollar (US). We get the following results.There is ample evidence that the forward premium contains usefulinformation for predicting the future depreciation in the (generally) signiÞcantestimates of β 2 .Sinceˆβ 2 is signiÞcantly less than 1, uncoveredinterest parity is rejected. The anomalous result is not that β 2 6=1,but that it is negative. The forward premium evidently predicts thefuture depreciation but with the “wrong” sign from the UIP perspective.Recall that the calibrated Lucas model in chapter 4 also predictsanegativeβ 2 for the dollar-deutschemark rate.The anomaly is driven by the dynamics in p t . Wehaveevidencethat it is statistically signiÞcant. The next question that Fama asks iswhether p t is economically signiÞcant. Is it big enough to be economicallyinteresting? To answer this question, we use the estimates andthe slope-coefficient decompositions (6.7) and (6.8) to get informationabout the relative volatility of p t .First note that ˆβ 2 < 0. From (6.8) it follow that p t must be negativelycorrelated with the expected depreciation,Cov[p t , E(∆s t+1 |I t )] < 0. By (6.5), the negative estimate of β 2 impliesthat ˆβ 1 > 0. By (6.7), it must be the case that Var(p t ) is large enoughto offset the negative Cov(p t , E t (∆s t+1 )). Since ˆβ 1 − ˆβ 2 > 0, it followsthat Var(p t ) > Var(E(∆s t+1 |I t )), which at least places a lower boundon the size of p t .