Homework answers / question archive / Econ 300 Fall 2016  Problem set 4 Due Tuesday 11/1   Instructions: Please write/type your answers and hand in a hard copy before class starts

Econ 300 Fall 2016  Problem set 4 Due Tuesday 11/1   Instructions: Please write/type your answers and hand in a hard copy before class starts

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Econ 300 Fall 2016

 Problem set 4

Due Tuesday 11/1  

Instructions: Please write/type your answers and hand in a hard copy before class starts. The total points for this problem set is 50. For STATA questions, paste codes/screenshot if relevant. 

1. What is the difference in the identifying variation between OLS with controls and instrumental variable? You may give an example to explain.

 

 

2. Evaluate the following IVs’ exclusion restriction. Come up with an example for each when the exclusion restriction is violated. 

 

1. Impact of sexually transmitted disease prevalence on risky sex behaviors. Instrument:

distance from your home to the origin of the AIDS virus

 

2. Impact of eating breakfast on infant health. Instrument: having a long work commute

 

3. Impact of adult depression on wages. Instrument: depression measured as a teenager 

 

4. Impact of being a female science professor on whether women major in science. Instrument: The fraction of female instructors who teach in a particular semester.

 

 

3. When studying the impact of immigrants on wages of natives, you use the percentage of immigrants in cities from 10 years earlier as the instrumental variable. 

 

1. What are outcome Y, treatment status D, and instrument T?

 

2. Why is OLS biased? In other words, can you come up with an omitted variable that may bias the OLS result?

 

3. What is the relevance condition? Write out its mathematical expression, and access if it is likely to hold in this case

 

4. How would you go and check the relevance condition in your data?

 

5. Who are always-takers, never-takers, compliers and defiers?

 

6. Specify the first stage regression (don’t have to include controls)

 

7. Specify the reduced form regression (don’t have to include controls)

 

8. Explain what ITT and LATE are in this example (What they mean, which parameters they correspond to)

 

 

4. Explain why weak instrument may cause problems

 

 

5. (STATA application) How does fertility affect labor supply? That is, how much does a woman’s labor supply fall when she has an additional child? In this question you will estimate the effect of having an additional kid on women’s weeks worked. The data, fertility.dta contain married women from the 1980 U.S. Census. (For the following questions, paste your codes or relevant screenshots.)

 

 

 

1. Our outcome variable is weeksm1. Regress weeksm1 on the dummy variable morekids, which is our treatment variable. On average, do women with more than two children work less than women with two children? How much less? Is it statistically different from 0?
2. Explain why the OLS regression estimated in part a is inappropriate for estimating the causal effect of fertility (morekids) on labor supply (weeksm1). 
3. The data set contains the variable samesex, which is 1 if the first two children are of the same sex (boy-boy or girl-girl) and 0 otherwise. This is our instrumental variable. Are couples whose first two children of the same sex more likely to have a third child? Is the effect large? Is it statistically significant? Use the regression to answer.

(hint: this is the first stage, regress treatment D on the instrument T)  

4. Explain why samesex can be a valid instrument (hint: assess two important IV assumptions)
5. Run the reduced form regression and report your ITT with its standard error. Interpret the ITT.
6. What is the LATE? 
7. Now manually do 2SLS. Write down the codes and report LATE (IV estimate) and its standard error.
8. Use STATA package to perform 2SLS. Write down the codes and report its LATE and standard error. What is the first stage F-stat? Do you worry about the weak IV problem in this case?
1. Repeat part h including covariates agem1, black, hispan, and othrace. Does the results change?  
10. Compare OLS with IV estimate (with controls in part i). Which one is bigger? What might have caused the difference?