Assume an empirical researcher wants to assess the effect of a college education on a worker's wage. She considers running a simple regression of wage wi on a constant and a variable Xi that equals 1 if the worker has a bachelor degree and zero otherwise:

wi = B0 + B1*Xi + ui

a) (4 points) Describe some components in ui that might lead to omitted variable bias in the OLS estimator. Provide a verbal discussion to justify your answer.

b) (4 points) Explain how the multiple linear regression model differs from (1) and provide a mathematical and verbal description of the slope coefficient on Xi under the standard assumptions of that model.

c) (4 points) Acknowledging that omitted variable bias might still exist in b), the empirical researcher now considers an instrumental variables approach instead. Critically discuss the variable Zi ="years of education of the mother of worker's as an instrumental variable.

d) (4 points) In general, describe another Econometric technique that can be used to eliminate or at least mitigate omitted variable bias in regression settings. What assumptions are needed for that technique to work?