regression OLS estimators
Not sure if you can see the picture, but the question I'm wondering about is: for regression model respond = β0+ β1resplast + β2avggift + β3propresp + β4mailsyear +u
a) Suppose that MLR.1-4 hold for the model when all variables are correctly measured. Further suppose that respond is measured with error: respond = respond* + e (i.e.,observed = truth + error). Would the OLS estimators of βís still be unbiased and consistent and why?
b) Suppose that MLR.1‐4 hold for the model when all variables are correctly measured. Further suppose that one regressor, mailsyear, is measured with an additive error and the error is uncorrelated with the truth mailsyear*. How would the OLS estimator of, say,β1be affected by the measurement error and why?
What concepts am I looking for in answering these two questions?
Re: regression OLS estimators
Hint: If something is unbiased then the expectation of the estimator is equal to that parameter. So if your estimator is for the mean then the estimator is X_bar and E[X_bar] = mu for unbiased-ness. Consistency means that the variance of the estimator goes to 0 as the sample size increases (the variance decreases with higher sample sizes).
For your problem, replace X_bar with Beta_hat.