Consider a simple time series model where the explanatory variable has classical measurement error:

yt 5 b0 1 b1xp t 1 ut [15.58]

xt 5 xp t 1 et

, where ut has zero mean and is uncorrelated with xp t and et

. We observe yt and xt only. Assume that et has zero mean and is uncorrelated with xp t and that xp t also has a zero mean (this last assumption is only to simplify the algebra).

(i) Write xp t 5 xt 2 et and plug this into (15.58). Show that the error term in the new equation, say, vt

, is negatively correlated with xt if b1 . 0. What does this imply about the OLS estimator of b1 from the regression of yt on xt

?