Question

We know how difficult it is to find a convincing instrumental variable Zi to overcome the “unobserved ability” problem in a wage regression to measure the returns to education. Critically discuss whether Zi =”distance in miles of high school location of workeri to closest four year college”satisfies the two properties of a valid instrument.

Answer 1

The two important properties that is satisfied by an instrumental variable Zi are as follows:

(i) They are related to the explanatory variable(s) - This property ensures that the predicted values are related to explanatory variables xi (endogenous variables)

(ii) They are uncorrelated with the errors ui - This property ensures that the predicted values are uncorrelated with ui

Zi =”distance in miles of high school location of workeri to closest four year college” , the instrumental variable  was suggested in the article "Using geographic variation in college proximity to estimate the return to schooling" written by Card, D. in 1995

It shall be noted that returns to education is considered endogenous variable and is said to exhibit high correlation with the error term ui.

It shall be noted that return to education can be considered to be increase in the ability of the workeri with gain of knowledge and exposure.

The instrumental variable Zi =”distance in miles of high school location of workeri to closest four year college” can be considered a proxy of return to education and at the same time would ensure that this instrumental variable does not exhibit any correlation with the error term ui.