Econ7360: Homework I
Econ计量经济学代写 Read questions thoroughly before writing your answer. Please limit your answer to each question to less than four sentences.
Read questions thoroughly before writing your answer. Please limit your answer to each question to less than four sentences. Marking points are provided in the parentheses. The deadline for submission is posted on the ECP. Submit your answers via Blackboard by the due date and time.
1 Endogeneity Issues in OLS Estimation (18) Econ计量经济学代写
In an article, Evans and Schwab (1995) studied the effffects of attending a Catholic high school on the probability of attending college. For concreteness, let college be a binary variable equal to unity if a student attends college, and zero otherwise. Let CathHS be a binary variable equal to one if the student attends a Catholic high school. A regression model is:
college = β0 + β1CathHS + otherf actors + ut
where the other factors include gender, race, family income, and parental education.
(i) Why might CathHS be correlated with ut? (3 marks)
(ii) Evans and Schwab have data on a standardized test score taken when each student was a sophomore. What can be done with these variables to improve the ceteris paribus estimate of attending a Catholic high school? (3 marks)
(iii) Let CathRel be a binary variable equal to one if the student is Catholic. Discuss the two requirements needed for this to be a valid IV for CathHS in the preceding equation. Which of these can be tested? (3 marks)
(iv) Not surprisingly, being Catholic has a signifificant effffect on attending a Catholic high school. Do you think CathRel is a convincing instrument for CathHS? (3 marks)
(v) Give an example of two variables that you would include in the variable otherf actors. (3 marks)
(vi) Which test would you implement in Stata to test if these two variables (that you specifified in part (v)) affffect college ? (3 marks)
2 OLS Estimator (15) Econ计量经济学代写
We consider a randomized experiment, the Tennessee STAR experiment, where students and teachers are randomly assigned to either a small class (15 students) and a regular class (24 students). We want to estimate the effffect of smaller class in primary school and use the following linear model:
Score = β0 + β1ClassSize + Controls + u
where Score is student’s academic score, ClassSize is dummy for small class, and controls includes free lunch status, race, gender, teacher characteristics and so on.
However, you estimate the following model instead:
Score = α0 + α1ClassSize + v
A. Provide the conditions for the OLS estimator for α1 to be unbiased. (3 marks)
B.Provide the Gauss-Markov assumptions for the OLS estimator for α1. (3 marks)
C.Evaluate the sign and the magnitude of bias α1 if teacher’s experience has positive effffect on score and more experienced teachers are more likely to be assigned to regular class. (3 marks)
D.Suppose that teachers and students are randomly assigned to either a small class (15 students) or a
regular class. Compare α1 to β1. (3 marks)
E.How does the OLS estimator for β1 change as we additionally include parental characteristics as
Controls? (3 marks)
3 OLS and Omitted Variable Bias (12) Econ计量经济学代写
Assume A1-A5 in the lecture and true model is given by (1):
ln(wage) = β0 + β1educ + β2exper + β3IQ + u (1)
OLS estimation results (standard errors in parentheses) are provided as follows:
ln(wage) = 5.20 + .06 educ + .03 exper+ .01 IQ
(.12) (.007) (.003) (.001)
where ln(wage) is dependent variable(y) and educ, exper, IQ are the independent variables respectively.
The following covariance table among educ, exper, and IQ can be obtained from Stata: corr educ exper IQ, covariance
A.Provide the formula for the OLS estimator for b1. (3 marks)
B.Given your answer in (A), provide the formula for the bias of the OLS estimator for b1. (3 marks)
C.What does the bias of OLS for b1 depend upon? (3 marks)
D.Can you determine the direction of the bias for b1? (3 marks)
4 IV Method as a Solution to Omitted Variable Bias (19)
We consider the following regression model:
ln(wage) = β0 + β1educ + β2exper + β3IQ + u (2)
Suppose IQ is unobserved. For endogenous educ, z, a dummy variable constructed using information on quarter of birth, is used as an instrument, where z is 0 if born in the 1st quarter and 1 otherwise. You are trying to use an instrument to get β1.
A.What is the rationale for using z as an instrument? State the conditions of z for β1 to be consistent and valid. (5 marks)
B.What is the Wald estimator for β1 where we use z as an IV for educ? (5 marks) Econ计量经济学代写
C.Card (1995) instead uses near4 (distance from student’s home to nearest 4-year college) and near2 (distance from student’s home to nearest 2-year college) as IVs for educ. What is the rationale for using near4 (or near2) as instruments? State the conditions of near4 (or near2) for β1 to be consistent and valid. (4 marks)
D.Previous numerous studies reported that the IV estimate of β1 is greater than the OLS estimate of β1. Provide some of potential reasons why the IV estimates are bigger than the OLS estimates. (5 marks)
