Consider a family saving function for the population of all families in the United States:
sav = β0 + β1inc + β2hhsize + β3educ + β4age + u,
where hhsize is household size, educ is years of education of the household head, and age is age of the household head. Assume that E(u\inc,hhsize,educ,age) = 0.
(i) Suppose that the sample includes only families whose head is over 25 years old. If we use OLS on such a sample, do we get unbiased estimators of the βj? Explain.
(ii) Now, suppose our sample includes only married couples without children. Can we estimate all of the parameters in the saving equation? Which ones can we estimate?
(iii) Suppose we exclude from our sample families that save more than $25,000 per year. Does OLS produce consistent estimators of the βj?