1. Math
  2. Statistics And Probability
  3. i suppose the true conditional mean function is but by...

Question: i suppose the true conditional mean function is but by...

Question details

I. Suppose the true conditional mean function is but by mistake, a researcher ran least square regression without the X term as in Assume cou (Xi , U) = 0, E [Xa] = 0 and E [x7-1. 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 (uiX]-0. It was discovered that we observe X, with a measurement error w instead of the real value X cou (1. u i )-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? (iii) Assume we have a consistent estimator for σ. 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.
Solution by an expert tutor
Blurred Solution
This question has been solved
Subscribe to see this solution