Computer exercises
In this exercise you will compute the least squares estimates of a linear regression model in Stata. You will also have to interpret your results. Please write your code in do-file and submit it along with your answers to the questions. The dataset for estimation is uploaded on Moodle - cps09marV12.dta. We are going to work with the following regression model: log(Wage) = b0+b1Education+b2Experience+b3 ·0.01·Experience2+e, (3) where Wage = Earnings/(Hours·Weeks) is hourly wage rate in current US dollars, Education is the number of accomplished years of schooling, and Experience is approximation of labor market experience computed as Experience = Age Education6. Check sections 3.22 and 3.23 in Hansen if you need more detailed data description.
1. Compute descriptive statistics for the dataset and discuss your results. You may use any analytical or graphing commands that in your opinion would give the best description of the data.
2. Use command regress to estimate equation (3) by least squares for males only. How can you interpret estimated relationship between wages and education? What about wages and experience? Explain the role of the multiplier 0.01 at the third term: how would the estimates differ if you dropped it? 3. Add a gender dummy to the equation
(3) and estimate it by least squares using the entire sample. Compare your results to those you obtained for the previous question, and try to explain any differences that you find. Explain why this model might not be the best way to estimate female wage equation.
4. Estimate wage equation with only one explanatory variable - education. Compute residual variance and R-squared for this model. Explain your results. Now include education and experience. How did residual variance and R-squared change with inclusion of a new regressor? Is it consistent with the theory? What happens if you add the square of experience?
5. Recall the structure of the omitted variable bias (Hansen, section 2.24). Use it to explain why dropping the square of experience in the previous question affected the coefficient on experience more than the coefficient on education. Use Stata to compute any relevant statistics required to support your statements.
6. Compute homoskedastic covariance matrix of the least squares estimator for Equation (3) and report standard errors (make sure to include covariance terms).
7. Try to implement as many heteroskedasticity robust estimators for covariance matrix of the least squares estimator given by equations 4.37-4.40 in the text as possible, and report standard errors (look at robust and vce commands). How do they compare, is the magnitude of the standard errors obtained under different methods consistent with your expectations?
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