Education enables many people to earn more money and obtain employment that is reserved for college graduates. University graduates normally obtain higher salaries upon graduation and typically enjoy higher life time wages with lower rates of unemployment compared to people who didn’t attend college. If one runs looks at the correlation between education and wages a pretty strong statistical relationship can be established. An estimate can be made of the returns to education based on this simple regression, but there is a problem with this simplistic approach to the problem. The model below which represents a simple log-linear regression of education on the logarithm of wages suffers from omitted variable biased.
The omitted variable biased is in the form of unobserved ability in people. Unobserved ability is correlated with the level of education that an individual attains; higher intellectual ability makes the cost of education lower and thus increases the probability of graduating from college. Also individuals with more ability also tend to be higher wages. A more formal treatment of this omitted variable biased is show in the equations below.
Description of the variables and summary statistics are provided in Figure 1 and Figure 2
Figure 2: Summary Statistics (Click to Enlarge)
Ordinary Least Squares Regression of biased equation (1)
Figure 3: Biased OLS Regression on percentage increase in wages per year of education (Click to Enlarge)
Choosing an Instrumental Variable
Instrumental variables need to be correlated with with one of the exogenous variables, in this case education, but must not be correlated with the independent variable in this case wages. A decent instrumental variable for unobserved ability would be a persons father’s education. Father’s education could be related to his off springs education since unobserved ability can be a based on genetically AND one can argue that a father’s education has no impact on his off springs wages, these conditions are shown in equations the covariance conditions below.
Figure 4: Regression of Explanatory Variable (X) on Instrumental Variable (Z) and test for their zero correlation (click to enlarge)
Figure 5: Instrumental Regression to correct for Omitted Variable Biased.
Major Revalation from IV Regression to Correct for Omitted Variable Biased
Return to education in the form of wages was positive and statistically significant in the biased OLS estimate, but after using a wage earners’ father’s information as an instrumental variable to correct for omitted variable biased in the form of unobserved ability, the return to education in the form of wages became statistically insignificant.