Economics 515 Assignment #2 Professor Thornton
Winter 2017
This homework is due Wednesday, March 15. You should do your own work and not consult with others in the class. Any questions related to the assignment should be directed at me. When answering each question, please begin by copying the question. Make sure you answer each part of the question.
QUESTION
You have been hired as a consultant by the U.S. Department of Labor to conduct an empirical study.
Objective of Study
The Labor Department wants you to analyze factors that affect the wage of a typical adult. The population of interest is working-age adults in the U.S. The Labor Department is particularly interested in addressing the following question. Does hours worked have a causal effect on the wage? If so, what is the direction and size of the effect?
Data
The data file cps12 consists of 4838 randomly selected working-age adults from the May 2012 current population survey conducted by the Department of Commerce. The variables are as follows. hrs is the number of hours worked per week. wage is hourly earnings in dollars. edu is years of schooling. exp is years of work experience. age is worker age in years. fem is a dummy variable for gender. fem = 1 if female; fem = 0 if male. mar is a dummy variable for marital status. mar = 1 if married; mar = 0 if not married. mcaid is a dummy variable for Medicaid insurance coverage. mcaid = 1 if Medicaid insurance; mcaid = 0 otherwise. kids is the number of children that live with the adult.
Get to Know Your Data
1. Report the mean, standard deviation, maximum, and minimum values for the variables. Describe a typical adult in the sample. (6 points)
Statistical Model
To analyze factors that affect the wage you specify the following simultaneous equations regression model.
(1) waget = β1 + β2 hrst + β3 edut + β4 expt + β5 mart + β6 femt + μt
(2) hrst = α1 + α2 waget + α3 edut + α4 aget + α5 mcaidt + α6 kidst + α7 femkidst + vt
Equation (1) is a wage equation. Equation (2) is an hours of work equation. The variable femkids is an interaction variable between fem and kids. It is equal to the product of fem and kids.
2. If the objective of your study is to estimate the wage equation (1) and analyze factors that affect the wage, why does your model include the hours of work equation (2)? (6 points)
3. Create the variable femkids. How is it related to the marginal effect of kids on hours worked? To be sure you understand what femkids measures, estimate the hours of work equation (2) using the OLS estimator. Given your estimates of α6 and α7, what is the marginal effect of kids on hours worked for males? For females? Is this what you would expect? Is there evidence that the marginal effect of kids on hours worked differs for males and females? Yes or no? Support your answer. (6 points)
Variables
4. For the simultaneous equations regression model given above, what are the endogenous variables and what are the exogenous variables? Make sure you explain the statistical meaning of an endogenous and exogenous variable, and how you determined which variables are statistically endogenous and exogenous in the model. (6 points)
Identification
5. Is the wage equation (1) identified? If so, is it exactly identified or overidentified? Provide an argument to justify your answer. (6 points)
Estimation
6. Estimate the wage equation (1) using the OLS estimator. Do not report the results. Do a White test for heteroscedasticity. Interpret the result. Now estimate the wage equation (1) using the OLS estimator with White robust standard errors. Report the results. Interpret the estimate of β2. Is there strong, moderate, weak, or little or no evidence that hours worked has an effect on the wage? Justify your answer. Do you think the OLS estimate of β2 is an unbiased and consistent estimate? Yes or no. Explain. (6 points)
7. Use a Breusch-Pagan test of independent errors to test the hypothesis of no contemporaneous correlation among the error terms in the wage equation and hours of work equation. Show your work. Interpret your result.
8. Given the result of the Breusch-Pagan test, do you believe you can obtain more efficient (precise) parameter estimates of the wage equation (1) using Zellner’s SUR estimator than the OLS estimator? Yes or no. Carefully explain. (6 points)
9. Estimate the wage equation (1) and hours of work equation (2) jointly using Zellner’s SUR estimator. Report the results. Compare the OLS and SUR estimates of β2 in the wage equation. Why do you think they differ? Is there evidence that one of these estimates is more precise than the other estimate? If so, what is the evidence? Do you think the SUR estimate of β2 is an unbiased and consistent estimate? Yes or no. Explain. (6 points).
10. Estimate the wage equation (1) using the 2sls estimator with White robust standard errors. Report the results. You do not need to discuss the results. What variable(s) are identifying instruments for the 2SLS estimator in the wage equation (1)? (6 points)
11. Compare the OLS and 2SLS estimates of β2. Does the OLS estimate appear to be biased up or down relative to the 2SLS estimate? Does the bias appear to be relatively large or small? Now test the hypothesis that hrs is exogenous in equation (1) using a Hausman test. Interpret the result. What does this tell you about the bias in the OLS estimate relative to the 2SLS estimate of β2? (6 points)
12. Estimate the first-stage regression for hrs using the OLS estimator and White robust standard errors. Do the estimates of the coefficients of the identifying instruments have expected signs? Yes or no. Explain. Check for instrument relevance (the strength of the instruments). Do you believe the instrument(s) are relatively weak or strong? What does this tell you about the bias in the 2SLS estimate relative to the OLS estimate of β2 ? (6 points)
13. Discuss under what conditions the GMM estimator would produce better estimates of the parameters than the 2SLS. In what sense would the GMM estimates be “better”? Carefully explain. (6 points)
14. Estimate the wage equation (1) using the GMM estimator. Report the results. Do the GMM estimates of the coefficients of the explanatory variables differ noticeably from the 2SLS estimates? (6 points)
15. Choose an appropriate test, and test the overidentifying restrictions for the wage equation (1). Explain why the test you selected is the most appropriate test. Interpret the result. What does this tell you about the validity of your instruments? Does the result of your test provide evidence that the instruments are exogenous? (6 points)
16. Use the GMM results to draw conclusions about factors that affect the wage. For each explanatory variable in the wage equation, address the following questions. 1) Is there strong, moderate, weak, or little or no evidence it has an effect on the wage? 2) What is the direction of the effect? Is this consistent with what you would expect? 3) What is the size of the effect? For the quantitative variables hrs, edu, exp, which one has the biggest effect and which one the smallest effect? Do you believe that your estimate of the effect of hrs on the wage is a good estimate? Yes, no. Carefully explain. (10 points)
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