Labor economists often study the returns on investment in education (see, e. g., Card 1999). Suppose we have data on salaries of a set of people, some of whom went to college and some who did not. A simple model linking education to salary is:
Salaryᵢ = β₀ + β₁ College graduateᵢ + ϵᵢ
, where the value of Salaryᵢ, is the salary of person i and the value of College graduateᵢ; is 1 if a person i graduated from college and 0 if a person i did not.
(a) What does β₀ mean? What does β₁ mean?
(b) What is in the error term?
(c) What are the conditions for the independent variable X to be endogenous?
(d) Is the independent variable likely to be endogenous? Why or why not?
(e) Explain how endogeneity could lead to incorrect inferences.

a. The intercept terms beta0 depicts the minimum amount of salary that a person will be earning if the person is not a college graduate. beta1 depicts that if a person is a college graduate, then the salary of the person increases by \beta 1 units.

b. The error term include all other variables impacting salary of the person other than the the person being a college graduate.

c. The independent variable X will be endogenous when salary plays an important role in determination of whether a person is college graduate.

d. yes, independent variable can be endogenous in some cases when dependent variable Y is impacting the independent variable X.

e. Endogeneity can lead to relaxation of one of the important assumption of Ordinary Least Squares (OLS) which considers independent variable to be endogenous. This will lead to the problem of multi collinearity. The Simultaneous Equation model can be used in this case rather than OLS model.

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