ECONOMETRICS. BRUCE E. HANSEN

Chapter 7. Asymptotic Theory for Least Squares

Exercise 7.7 Of the variables (Y*, Y, X) only the pair (Y, X) are observed. In this case we say that Y* is a latent variable. Suppose Y* = X'B+e E[Xe] = 0 Y = Y* + u where u is a measurement error satisfying E[Xu] = 0 E[Y* u] = 0. Let B denote the OLS coefficient from the regression of Y on X. (a) Is f the coefficient from the linear projection of Y on X? (b) Is B consistent for Bas n - co? (c) Find the asymptotic distribution of vn (B- B) as n - co