Introductory Econometrics: A Modern Approach 6th Edition by Jeffrey M Wooldridge

Exercise 12

Consider a family saving function for the population of all families in the United States:

sav = ?0 + ?1inc + ?2hhsize + ?3educ + ?4age + 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 ?j? 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 ?j?

Step 1 of 3

Consider the family saving function for all families in US which is given by:

Where,

=Household size

=Years of education of household head

=Age of the household head

Assume,

(i)

If the families whose household head is of age 25 years and above is considered, it is one sample of the various possible samples that can be drawn from the given population and the sample of such families are taken to run OLS based on the regression model

Only the coefficient of the sample regression function would get affected.

The estimators of would remain unbiased, because the is a population estimates

Under OLS technique, , given the assumptions of classical linear regression model