Consider a simple linear regression model, wage = + male + u, where male is a binary variable (1 if a person is male, and 0 otherwise). Now suppose that we know being a male means there is a lower probability of attaining higher education, another factor that is also expected to affect wage. Which of the key assumptions made to establish unbiasedness of OLS estimates do not hold?
A)Linear in parameters
B)Random sampling
C)Sample variation in the explanatory variable
D)Zero conditional mean

Question

Consider a simple linear regression model, wage =  +  male + u, where male is a binary variable (1 if a person is male, and 0 otherwise). Now suppose that we know being a male means there is a lower probability of attaining higher education, another factor that is also expected to affect wage. Which of the key assumptions made to establish unbiasedness of OLS estimates do not hold?
A)Linear in parameters 
B)Random sampling 
C)Sample variation in the explanatory variable 
D)Zero conditional mean

Quizplus · Accepted Answer

The assumption of zero conditional mean is violated in this case because being male is correlated with lower probability of attaining higher education, which suggests that the error term is not independent of the explanatory variable male. This means that the OLS estimates will be biased and inconsistent. The other assumptions, such as linearity in parameters, random sampling and sample variation in the explanatory variable still hold.

Consider a Simple Linear Regression Model, Wage =