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ECON4004 - Econometrics 2

Tutorial 2

Question 1. (Wooldridge, exercise 17.6). Consider a family saving function for the population of all families in the United States:

 ൌ ⃞  ⃞⃞   ⃞ ଶ   ⃞ ଷ   ⃞ ସ  ⃞ 

Where SAV is household saving, INC is household income, HHSIZE is household size,     EDUC is years of education of the household head, and AGE is age of the household head. Assume that ሺ |, , , ሻ ൌ 0.

a. 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 ⃞ ? Explain.

b. 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?

c. Suppose we exclude from our sample families that save more than $25,000 per year. Does OLS produce consistent estimators of the ⃞ ?

Question 2. Consider a product market with a supply function  ௦  ൌ ⃞  ⃞⃞   ⃞  , a demand function ௗ  ൌ ⃞  ⃞⃞   ⃞  , and a market equilibrium condition  ௦  ൌ  ௗ , where  and u     are mutually independent i.i.d. random variables, both with a mean of 0.

a. Show that  and  are correlated, and that the same is true for  and  .

b. Show that the OLS estimators of ⃞  and ⃞  are inconsistent.

c. How would you estimate ⃞ , ⃞ , ⃞ , and ⃞ ?

Question 3. (Stock and Watson, exercise 12. 10). Two classmates are comparing their          answers to an assignment. One classmate has specified an instrumental variable regression  model  ൌ ⃞  ⃞⃞  ⃞ ଶ   ⃞  , using  as an instrument. The other student has specified the same model but has omitted  .

a. The first student says that if  and  are correlated, then the second student’s IV estimator will not be consistent. Is the first student right about this?

b. The second student argues that if in the true model ଶ  = 0, then their IV estimator will be consistent. Is the second student correct in saying this?