Question

Question 4 5 pts A researcher studies the causal effect of education on earnings for male adults using data from a random sample of U.S. adult male workers. She plans to regress individual male workers' earnings (Y) on the number of years of education (X1) the workers have, controlling for work experience and other characteristics of the individuals (Z, e.g. experience). Assume that the unemployment rate is low and the unemployment distribution is random. The researcher is worried that the estimate of the coefficient on X may suffer from omitted variable bias if she does not include the individual's ability (X2) in the regression because individuals with a higher level of ability tend to earn more and also tend to attain a higher level of education. If the researcher does not include X2 as a regressor and estimates the following equation: Y = Bo + B1X1 + B,Z+u. Although X, is an omitted variable, it does not cause omitted variable bias in the estimate of the coefficient on X1 in this specific case. O , does not suffer from omitted variable bias because X2 is not the key regressor and therefore omitting X2 would not affect the estimate of the coefficient ê, on Xı. O suffers from omitted variable bias, and it causes a downward (negative) bias < B). o suffers from omitted variable bias, and it causes an (a) upward (positive) bias ( 1 > 81).

Answer 1

Omitted variable bias is when two explanatory variables on the RHS of regression are correlated and we omit one of them in the model. However, if x1 and x2 are not correlated and we omit x2 , it doesn't lead to this bias.

In this case, number of years of education (x1) and the ommitted variable- individual's ability (x2) are positively correlated. More ability means pursual of higher education and higher years of education means more ability.

As positively related, the bias in the estimates from the ommitted variable will be positive.

Therefore, answer is D i.e., upward variable bias and beta (hat) > beta.