C1 Use the data in WAGE2.RAW for this exercise.

1. In Example 15.2, if sibs is used as an instrument for educ , the IV estimate of the return to education is .122. To convince yourself that using sibsas an IV for educ is not the same as just plugging sibs in for educ and running an OLS regression, run the regression of log( wage ) on sibs and explain your findings.

2. The variable brthord is birth order ( brthord is one for a first-born child, two for a second-born child, and so on). Explain why educ and brthordmight be negatively correlated. Regress educ on brthord to determine whether there is a statistically significant negative correlation.

3. Use brthord as an IV for educ in equation (15.1). Report and interpret the results.

4. Now, suppose that we include number of siblings as an explanatory variable in the wage equation; this controls for family background, to some extent:

log( wage ) 5 b _0 1 b _1 educ 1 b _2 sibs 1 u.

 

Suppose that we want to use brthord as an IV for educ , assuming that sibs is exog- enous. The reduced form for educ is

educ 5 p _0 1 p _1 sibs 1 p _2 brthord 1 v .

State and test the identification assumption.

5. Estimate the equation from part (iv) using brthord as an IV for educ (and sibs as its own IV). Comment on the standard errors for b ^ˆ _educ and b ^ˆ_sibs .

6. Using the fitted values from part (iv), ^ educ , compute the correlation between ^ educ and sibs . Use this result to explain your findings from part (v).