ECON61001 Econometric Methods Ekaterina Kazak Computer Tutorial 7, page 1 of 1 University of Manchester
The purpose of this session is to introduce you to the instrumental variable approach.
Instrumental Variables
Use the Wooldridge dataset wage 2 to estimate the returns to education. log(wage) = β0 + β1 educ + u.
It is often argue that educ in such model is an endogenous regressor. In order to mitigate the problem we address the instrumental variables approach and use sibsi, the number of siblings of individual i
as an a)
b)
c)
d)
instrument for schooling.
To convince yourself that using sibs as 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.
The variable brthord is birth order (brthord is 1 for the first-born, 2 for a second born child, and so on). Explain why educ and brthord might be negatively correlated. Regress educ on brthord to determine whether there is a statistically significant negative correlation.
Use brthord as an IV for education in the following equation: log(wage) = β0 + β1 educ + u.
Report and interpret the results.
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)=β0 +β1educ+β2sibs+u.
Suppose that we want to use brthord as an IV for educ, assuming that sibs is exogenous. The
reduced form (first-stage) for educ is: educ=π0 +π1sibs+π2brthord+v.
State and test the identification assumption.
Estimate the equation in part (d) using brthord as an IV for educ (and sibs as its own IV).
e) f)
Comment on the standard errors for βˆeduc and βˆsibs.
Using the fitted values from part (d), educ, compute the correlation between educ and sibs. Use this result to explain your findings from part (e).