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1. Suppose the true conditional mean function is but by mistake, a researcher ran least square regression without the X term as in Assume cov (Xi. Ui)s 0, E [Xn] = 0 and E [x?] = 1 . Is his/her estimate consistent for β? If not, show which OLS assumption fails and discuss potential solutions 2. Assume the structural equation is where E uX0. It was discovered that we observe X, with a measurement error w, instead of the real value X It is known that E [m] = 0,V (tr.) = ơz. cou (Xu u) = cov (14, ur) = 0. The OLS estimator is based on regressing Y on a constant and X (i) Find the value to which the OLS estimator of β, is consistent for. (ii) Is the value equal to the true value β? If not, how is the bias related to the true value? (ii) Assume we have a consistent estimator forHow would you make a correction to consistently estimate β? (iv) Discuss other potential solutions when such estimator in (ii is not available I am looking for a solution for question number 2 ONLY with steps please, so I can find my mistake.
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