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Homework answers / question archive / Problem set 2   Instructions: Please write/type your answers and hand in a hard copy before class starts

Problem set 2   Instructions: Please write/type your answers and hand in a hard copy before class starts

Statistics

Problem set 2

 

Instructions: Please write/type your answers and hand in a hard copy before class starts. The total points for this problem set is 50

1. You are studying the causal effect of experience on wages (i.e. return to experience). ttl_exp is total work experience. You run the following model: 

Wage=β0+β1ttl_exp+ β2age+ β3race+ β4south+ β5industry+ β6grade+ε

The         Stata   output              shows:            

 

 

a. Interpret the estimate for ttl_exp.

  1. Write out the null and alternative hypotheses to test whether there is any relationship between ttl_exp and wage.
  2. Perform hypothesis test manually using p-value approach to explain whether you reject the null hypothesis specified in c. (use α=0.01, prob(t>7.76)=0.0000)
  3. Use confidence interval approach to explain whether you reject the null hypothesis specified in c. (tα/2 for α=0.01, n=1184 is 2.58)
  4. What is the null hypothesis for the F-test that all independent variables have no explanatory power in wage? Do you reject or fail to reject the null based on the Stata output? Explain.
  5. Explain in words what R-square means in this example. Does big R-square necessary mean better model for this research project?

2. (Consistency and the notion of control) Use the same model: Wage=β0+β1ttl_exp+ β2age+ β3race+ β4south+ β5industry+ β6grade+ε

  1. What is the condition for
     to be unbiased? What is the condition for
     to be consistent?

 

  1. Will
     to be consistent in this case? If not, think of variable that violates the consistency condition. Explain how exactly will it violates the consistency condition.

 

  1. Now give an example of the good, bad and useless control. Explain clearly your reasoning process. 

 

 

3. (Stata application)

Load the data nlsw_ps2.dta. Our research question is to examine whether being in the union affects one’s wage. For the following questions that requires STATA command, you can either paste the STATA output or write/type the key results.

 

  1. Before getting to the data, what is your prior expectation? Do you think being in the union has a positive, negative or no effect on one’s wage?

 

  1. Run a simple regression of hourly wage on one’s union status. Write down your codes. 

 

  1. What is the coefficient and standard error of union status? Interpret the meaning of the coefficient and its standard error.

 

  1. Look at its t-stat or p-value, do you think there is a relationship between union status and wage? Explain.

 

  1. Now based on the confidence interval, do you think there is a relationship between union status and wage? Explain

 

  1. Using the estimated regression, let’s make predictions for wage given each person’s union status. Write down the STATA codes below. What is the predicted wage for someone in the union?

 

  1. Now include two additional variables race and age in your regression. Write down the codes. What is the coefficient and standard error for union?

 

  1. What values are the ESS and TSS from the STATA output? Explain what they mean in this case

 

  1. Compare the R-square with adjusted R-square, which one do you trust more and why?

 

  1. Compare the simple regression with the multiple regression. Which model have more explanatory power in the variation in wage? Why?

  

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