1. In the following examples, explain what we mean by a causal effect:
a) the impact of education on wages
b) the impact of hospitalization on health
c) the impact of parental income on child's academic achievement in school.
2. In each of the examples, explain why an OLS regression of education on wages in example a), of hospital visits in the last year on health indicators in example b), and of parental income on school test scores in example c) is unlikely to identify the causal effect.
3. What is an instrumental variable? Angrist and Krueger use quarter of birth as an instrument for education.
a) Explain why quarter of birth may affect education.
b) Carefully explain the assumptions under which the IV estimator, using quarter of birth as an instrument for education, identifies the causal effect of education.
c) Write down the IV estimator for the return to schooling.
d) Angrist and Krueger report an OLS estimate of the return to schooling of 0.083 (0.005), and an IV estimate of 0.077 (0.030). Numbers in parentheses are standard errors. Interpret these estimates. What do they imply about the selection bias in the OLS regression?
e) Before Angrist and Krueger suggested using quarter of birth as an instrument, researchers often used parental income as an instrument for
education. Carefully discuss the assumptions under which instrumenting education with father's income identifies the causal effect of education on wages. Do you find these assumptions reasonable?