Question

Consider the following regression model, relating birth weight to the number of cigarettes smoked during pregnancy: bwgt=B₀+B₀cigs+ε (a) Do you think that cigs_i and εi are correlated? Explain why or why not. Would the OLS estimator be BLUE in this case? (b) Suppose the mother’s level of education is also related to birth weight. However, you still estimate the equation above, using only cigsi as an independent variable. Do you think the OLS estimator B₁ accurately estimates the association between cigarette smoking and birth weight? Explain your answer. (c) If you answered no in part (b), do you think the OLS estimator will overestimate or underestimate the true B₁? (d) Suppose that the mothers in your sample live in one of three apartment complexes. Explain how this could violate (1) the assumption that εi is homoscedastic, and (2) the assumption that the regression errors are uncorrelated across observations (mothers). (e) You are considering including the mother’s and father’s levels of education as explanatory variables into the regression model. Suppose that, in your sample, all fathers and mothers happen to have the same levels of education (in years). Is this a violation of the classical assumptions or not?

Answer 1

A) No , cigsi and Error term are uncorrelated in this case because the two variables are independent of each other as mentioned in the question . Moreover , OLS estimator will be BLUE in this case .

B ) In this case , the OLS estimator will not be BLUE as the variable "mother’s level of education" will be correlated to the error term as they both are not independent and the correlated part will be accumulated in error term only since we are taking the model mentioned in first part only . Moreover ,  the OLS estimator B1 will not be able to accurately estimate the association between cigarette smoking and birth weight as there will be some correlation between the "mother’s level of education" and birth weight of the child which will not be summed in B1 .So , to conclude , the OLS estimator will not be BLUE and error and cigsi variable will be correlated .

C) Yes , he OLS estimator might  overestimate or underestimate the true B1 as the OLS estimator depends on B1.

D) εi will now not be homoscedastic because each apartment will have different variances and different living conditions . Moreover ,  the error could be correlated because one apartment may have better facility/ sanitation than other so most of the child may have better health than others.

E ) No ,  having an assumption of all fathers and mothers happen to have the same levels of education (in years) as an assumption will not be a violation of the classical assumptions as characteristics might be same for two variables.