Econometrics 301 – HW3

Research Question: What are the factors that determine the abortion rate across the 50 states in the USA?

To study this, use the dataset (uploaded on LMS). The variables used in the analysis are as follows:

State: Name of the State (50 US States)

ABR: Abortion rate, number of abortions per thousand women aged 15-44 in 1992.

Religion: The percent of a state’s population that is Catholic, Southern Baptist, Evangelical, or Mormon.

Price: The average price charged in 1993 in non-hospital facilities for an abortion at 10 weeks with local anesthesia (weighted by the number of abortions performed in 1992)

Funds: A variable that takes value of 1 if state funds are available for use to pay for an abortion under most circumstances, 0 otherwise.

Laws: A variable that takes value of 1 if a state enforces a law that restricts a minor’s access to abortion, 0 otherwise

Educ: The percent of a state’s population that is 25-years or older with a high school degree (or equivalent), 1990.

Income: disposable income per capita, 1992.

Picket: The percentage of respondents that reported experiencing picketing with physical contact or blocking of patients

Question:

a) Estimate the following models using lm( ) command. Considering the potential thread posed by heteroscedasticity problem, use the heteroscedasticity-consistent robust errors.

?ABR?_i = ?_1 + ?_2 Religion + e_i

?ABR?_i = ?_1 + ?_2 Religion + ?_3 Price + e_i

?ABR?_i = ?_1 + ?_2 Religion + ?_3 Price + ?_4 Laws + ?_5 Funds + e_i

?ABR?_i = ?_1 + ?_2 Religion + ?_3 Price + ?_4 Laws + ?_5 Funds + ?_6 Educ + ?_7 Income + ?_8 Picket + e_i

b) Calculate the fitted values and residuals for each model.

c) Plot the residuals of each model. Do you think the heteroscedasticity is a problem for our regression model. We have only 50 observations in this dataset. What is the limitation(s) of using the heteroscedasticity-consistent robust errors?

d) Calculate the SER and R^2 using the information you obtained in b) and verify that the summary(lm( )) provides the same SER and R^2.

e) What is the F-test results for each model? What does F-test tell us about the overall significance of our models?

f) What is adjusted R-squared means? Do you think the R^2 and adjusted-R^2 values is similar to each other?

g) How the R^2 value changes with the new variables from Model 1-to-4.

h) Do we have the right to be suspicious about omitted varible bias?

Research Question: What are the factors that determine the hourly wages?

To study this, use the dataset (uploaded on LMS). The variables used in the analysis are as follows:

Wage: Hourly wage in dollars (CPS, 1995)

Female: Gender, coded 1 for female, 0 for male

Nonwhite: Race, coded 1 for nonwhite workers, 0 for white workers

Union: Union status, coded 1 if a union job, 0 otherwise

Education: Education (in years)

Exper: Potential work experience (in years)

Question:

a) Estimate the following regression model:

?Wage?_i = ?_1 + ?_2 Female+ ?_3 Nonwhite+ ?_4 Union + ?_5 Exper + e_i

Interpret the coefficients. Are there any insignificant coefficients?

b) Instead of using wage, use log(wage) to estimate the regression model:

?Log(Wage?_i) = ?_1 + ?_2 Female+ ?_3 Nonwhite+ ?_4 Union + ?_5 Exper + e_i

How the regression outcome has changed? How the interpretation of the coefficients changed? Do you think it is a good idea to use the logarithm of wage instead of wages.

c) Now, think that both years of schooling and years of experience increases the log(wage) with a decreasing rate. How would you modify the Model 2. Once you write down the regression model, estimate the model parameters. Do you think the coefficients satisfies your expectations?

d) Consider Model 2. Now estimate the regression with monthly wages assuming that individuals work for 8 hours in a day, and 22 days in a month. Then, take the logarithm of the monthly wages and estimate the regression model again. Interpret the coefficients.

e) What happens if you mistakenly add “White” to the regression model which is coded 1 if the worker is white, 0 otherwise. Explain the dummy variable trap in detail.

Research Question: What are the factors that determine the abortion rate across the 50 states in the USA?

To study this, use the dataset (uploaded on LMS). The variables used in the analysis are as follows:

State: Name of the State (50 US States)

ABR: Abortion rate, number of abortions per thousand women aged 15-44 in 1992.

Religion: The percent of a state’s population that is Catholic, Southern Baptist, Evangelical, or Mormon.

Price: The average price charged in 1993 in non-hospital facilities for an abortion at 10 weeks with local anesthesia (weighted by the number of abortions performed in 1992)

Funds: A variable that takes value of 1 if state funds are available for use to pay for an abortion under most circumstances, 0 otherwise.

Laws: A variable that takes value of 1 if a state enforces a law that restricts a minor’s access to abortion, 0 otherwise

Educ: The percent of a state’s population that is 25-years or older with a high school degree (or equivalent), 1990.

Income: disposable income per capita, 1992.

Picket: The percentage of respondents that reported experiencing picketing with physical contact or blocking of patients

Question:

a) Estimate the following models using lm( ) command. Considering the potential thread posed by heteroscedasticity problem, use the heteroscedasticity-consistent robust errors.

?ABR?_i = ?_1 + ?_2 Religion + e_i

?ABR?_i = ?_1 + ?_2 Religion + ?_3 Price + e_i

?ABR?_i = ?_1 + ?_2 Religion + ?_3 Price + ?_4 Laws + ?_5 Funds + e_i

?ABR?_i = ?_1 + ?_2 Religion + ?_3 Price + ?_4 Laws + ?_5 Funds + ?_6 Educ + ?_7 Income + ?_8 Picket + e_i

b) Calculate the fitted values and residuals for each model.

c) Plot the residuals of each model. Do you think the heteroscedasticity is a problem for our regression model. We have only 50 observations in this dataset. What is the limitation(s) of using the heteroscedasticity-consistent robust errors?

d) Calculate the SER and R^2 using the information you obtained in b) and verify that the summary(lm( )) provides the same SER and R^2.

e) What is the F-test results for each model? What does F-test tell us about the overall significance of our models?

f) What is adjusted R-squared means? Do you think the R^2 and adjusted-R^2 values is similar to each other?

g) How the R^2 value changes with the new variables from Model 1-to-4.

h) Do we have the right to be suspicious about omitted varible bias?

Research Question: What are the factors that determine the hourly wages?

To study this, use the dataset (uploaded on LMS). The variables used in the analysis are as follows:

Wage: Hourly wage in dollars (CPS, 1995)

Female: Gender, coded 1 for female, 0 for male

Nonwhite: Race, coded 1 for nonwhite workers, 0 for white workers

Union: Union status, coded 1 if a union job, 0 otherwise

Education: Education (in years)

Exper: Potential work experience (in years)

Question:

a) Estimate the following regression model:

?Wage?_i = ?_1 + ?_2 Female+ ?_3 Nonwhite+ ?_4 Union + ?_5 Exper + e_i

Interpret the coefficients. Are there any insignificant coefficients?

b) Instead of using wage, use log(wage) to estimate the regression model:

?Log(Wage?_i) = ?_1 + ?_2 Female+ ?_3 Nonwhite+ ?_4 Union + ?_5 Exper + e_i

How the regression outcome has changed? How the interpretation of the coefficients changed? Do you think it is a good idea to use the logarithm of wage instead of wages.

c) Now, think that both years of schooling and years of experience increases the log(wage) with a decreasing rate. How would you modify the Model 2. Once you write down the regression model, estimate the model parameters. Do you think the coefficients satisfies your expectations?

d) Consider Model 2. Now estimate the regression with monthly wages assuming that individuals work for 8 hours in a day, and 22 days in a month. Then, take the logarithm of the monthly wages and estimate the regression model again. Interpret the coefficients.

e) What happens if you mistakenly add “White” to the regression model which is coded 1 if the worker is white, 0 otherwise. Explain the dummy variable trap in detail.

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