In the following examples, explain what we mean by a causal effect: a) the impact of education on...

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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 XXXXXXXXXX), and an IV estimate of XXXXXXXXXXNumbers 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?
	
Document Preview: Econ 1002: Applied Economics
Class Exercise 4
Spring 2013
You have to hand in the exercise by February 28.
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
 XXXXXXXXXX), and an IV estimate of XXXXXXXXXXNumbers 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?

Robert · Accepted Answer

Ans 3. Definition of Instrumental Variable (IV): In the presence of endogenous regressors (Cov(xi,ui) ≠ 0, where xi is a regressor and ui is the error term), Ordinary Least Squares (OLS) estimators are inconsistent. It is therefore required to find a variable zi, which is correlated with xi (i.e., changes in zi directly affects xi, thus Cov(xi, zi) ≠ 0), but uncorrelated with the dependent variable yi (i.e., zi does not directly affect yi, but affects yi through xi, thus Cov(ui, zi) = 0) in order to generate consistent estimates. A variable (here zi) that satisfies these conditions is known as an instrumental variable.  
(a) Reasons why quarter of birth may affect education: Angrist and Krueger (1991) first use quarter of birth as an instrument for educational attainment. They find significant association between quarter of birth and educational attainment for a cohort of men born during the 1920s, 1930s, and 1940s. In their study they show that lower educational attainment is associated with men born during the first quarter of a year than those born during the remainder of the year. Angrist and Krueger (1991) suggest that this association between quarter of birth and educational attainment is due to US compulsory school attendance laws. The law requires students to start their first grade at the age of 6 years and between September and November of a calendar year until their 16th birthday (10th grade). Thus individuals born in the early months of a year will enter first grade when they are nearly seven years of age and will turn 16 in the middle of their 10th grade. However, individuals born in the later quarter (third or fourth quarter) will start their first grade just before or just after they have turned 6 years of age and will finish their 10th grade before they turn 16 years of age. 
(b) Quarter of birth as an instrument for education: Angrist and Krueger (1991) used quarter of birth as an instrument for length of schooling in human capital earnings equations. They use earning as the dependent variable, educational attainment or schooling as an independent variable, and quarter of birth as an instrumental variable for education. The validity of the instrumental variable estimates lies in the fact that quarter of birth is a good instrument for education, that is, validity of their estimates of the causal effect of education on earnings depend on the assumption that there is no direct association between quarter of birth (the instrumental variable) and earnings (the dependent variable), but quarter of birth affects earnings only through its effects on education.

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...

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