Reference no: EM132367306

A researcher has collected data on alcohol consumption for 50 students each from 100 different colleges (50,000 observations). The outcome of interest (yi) is number of drinks consumed in the past 30 days. The researchers have developed an index (xi) that represents the strictness of a college's alcohol use policy with higher values meaning a more strict policy. The authors are interested in estimating an equation of the form y=a+bX+e. The researchers are concerned about measurement error in y. In particular, they believe that students at schools with stricter alcohol policies may be less likely to report actual drinking because they are not supposed to be drinking.

In this case, let y be actual drinking and y* be reported drinking where y* = y + u

In this case, we will continue to assume E[ui]=0, cov(xi, εi)=0, but we will assume measurement error systematic such that cov(ui, xi)<0 (students are more likely to undertstate drinking in areas with the strictest anti-drinking rules.

In this case, with this form of measurement error, will the OLS estimate generated from a regression of Y* on X still be unbiased? If not, is the estimate biased up or down?