A cross-sectional population regression is given by y, dle + Where y, and are expressed as deviations from their respective means and sis independently and identically distributed id) with mean 0 and variance o, you have access to a random number of observations on The variable x is a "noisy measure of x. that is x = x, + Where u is lid with mean and variance et a. If if the estimator is of the form IM Show that plim + b. Say that you have access to another variable, which is also expressed as deviation from its mean, that has the following properties in the population. Elx)+0 Bl=0 Will this variable define a consistent estimator of ? Provide a short proof of consistency A cross-sectional population regression is given by y, dle + Where y, and are expressed as deviations from their respective means and sis independently and identically distributed id) with mean 0 and variance o, you have access to a random number of observations on The variable x is a "noisy measure of x. that is x = x, + Where u is lid with mean and variance et a. If if the estimator is of the form IM Show that plim + b. Say that you have access to another variable, which is also expressed as deviation from its mean, that has the following properties in the population. Elx)+0 Bl=0 Will this variable define a consistent estimator of ? Provide a short proof of consistency