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ECN 702 Econometrics II HW2 Due: Jan 29 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 (X,, U,)s 0, E [Xn]-O and E [x?J-1. Is hisher estimate consistent for Anf not, show which OLS assumption fails and discuss potential solutions. 2. Assume the structural equation is where E [u1x,]-0. It was discovered that we observe x, with a measurement error ui instead of the real value X It is known that E [wi]s 0, V (wi)-σζ, cov (Xi, ui)s cou (14, w.)-0. The OLS estimator is based on regressing Y, on a constant and X (i) Find the value to which the OLS estimator of β1 is consistent for. (ii) Is the value equal to the true value β? If not, how is the bias related to the true value? (iii) Assume we have a consistent estimator for How would you make a correction to consistently estimate β? (iv) Discuss other potential solutions when such estimator in (ii) is not available. 3. Exercise #9.7 (Stock and Watson) Are the following statements true or false? Explain your answer. a. "An ordinary least squares regression of Y onto X will be internally inconsistent if X is correlated with the error term." b. Each of the five primary threats to internal validity implies that X is correlated with the error term."

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