Econometrics worksheet

Additional years of education are supposed to result in higher earnings. With this view you wish to model a person i’s hourly wage (π’˜π’‚π’ˆπ’†π’Š ) in terms of his/her education (π’†π’…π’–π’„π’Š ) and other characteristics. To estimate this model, you use a cross-sectional dataset that contains 1,000 observations on hourly wages rates, education, and other individual characteristics from the 2008 Current Population Survey (CPS) in the US. The description and sample average of the variables in the dataset are listed in Table 1 below: Table 1. Summary statistics of main variables of interest Variable name wage educ exper hrswk married female metro north midwest south west black asian Definition individual i’s earnings per hour (π’˜π’‚π’ˆπ’†π’Š ),measured in US$ individual i’s years of education individual i’s years of work experience individual i’s hours worked per week dummy variable that takes the value of 1 if individual i is married and 0 otherwise (π’Žπ’‚π’“π’“π’Šπ’†π’…π’Š ) dummy variable that takes the value of 1 if individual i is a female and 0 otherwise (π’‡π’†π’Žπ’‚π’π’†π’Š ) dummy variable that takes the value of 1 if individual i lives in a metropolitan area and 0 otherwise (π’Žπ’†π’•π’“π’π’Š ) dummy variable that takes the value of 1 if individual i lives in the North and 0 otherwise (π’π’π’“π’•π’‰π’Š ) dummy variable that takes the value of 1 if individual i lives in the Midwest and 0 otherwise (π’Žπ’Šπ’…π’˜π’†π’”π’•π’Š ) dummy variable that takes the value of 1 if individual i lives in the South and 0 otherwise (π‘Ίπ’π’–π’•π’‰π’Š ) dummy variable that takes the value of 1 if individual i lives in the West and 0 otherwise (π‘Ύπ’†π’”π’•π’Š ) dummy variable that takes the value of 1 if individual i is black and 0 otherwise (π’ƒπ’π’‚π’„π’Œπ’Š ) dummy variable that takes the value of 1 if individual i is asian and 0 otherwise (π’‚π’”π’Šπ’‚π’π’Š) Sample average 20.62 13.80 26.51 39.95 0.58 0.51 0.78 0.22 0.24 0.30 0.24 0.11 0.04 1. Please provide a brief interpretation of the summary statistics of the variables wage and metro presented in Table 1. 2. Which STATA’s command(s) would you use to perform an OLS estimation of the following linear regression? π’π’π’˜π’‚π’ˆπ’†π’Š = 𝜷𝟏 + 𝜷𝟐 π’†π’…π’–π’„π’Š + π’†π’Š [1] where: π’π’π’˜π’‚π’ˆπ’†π’Š is the natural logarithm of a person i’s hourly earnings (π’˜π’‚π’ˆπ’†π’Š ). 3. How would you modify equation [1] to see whether (for a given level of education) a person who lives in a metropolitan area earns on average more (or less) than a person who lives in a non- metropolitan area. 1 of 3 Please Turn Over 4. How would you modify equation [1] to see if the effect of education on wages is different for individuals that live in metropolitan areas versus individuals that live in nonmetropolitan area? 5. How would you modify equation [1] to see if the effect of education on wages is different for individuals that live in different regions in the country (i.e. Midwest, West, South, North). 6. After doing a thorough revision of the literature, you decided to estimate the following specification: π’π’π’˜π’‚π’ˆπ’†π’Š = 𝜷𝟏 + 𝜷𝟐 π’†π’…π’–π’„π’Š + πœ·πŸ‘ π’†π’…π’–π’„πŸπ’Š + πœ·πŸ’ π’†π’™π’‘π’†π’“π’Š + πœ·πŸ“ π’†π’™π’‘π’†π’“πŸπ’Š + πœ·πŸ” (π’†π’…π’–π’„π’Š × π’†π’™π’‘π’†π’“π’Š ) + πœ·πŸ• π’‰π’“π’”π’˜π’Œπ’Š + πœ·πŸ– π’‡π’†π’Žπ’‚π’π’†π’Š + π’†π’Š [2] Which STATA command(s) would you use to estimate model [2] using OLS with robust standard errors? 7. Using the STATA command(s) in the previous question you obtained the following STATA output: Number of obs F(7, 992) Prob > F R-squared Root MSE lnwage educ educ_sq exper exper_sq educ_exper hrswk female _cons Coefficient 0.073 0.002 0.056 -0.001 -0.001 0.004 -0.213 0.886 Robust std. err. 0.038 0.001 0.011 0.000 0.001 0.002 0.032 0.355 t 1.940 1.680 4.980 -6.950 -1.830 2.480 -6.720 2.500 P>t 0.053 0.094 0.000 0.000 0.067 0.013 0.000 0.013 = 1,000 = 61.18 = 0 = 0.2931 = 0.4899 [95% conf. interval -0.001 0.148 0.000 0.004 0.034 0.078 -0.001 0.000 -0.002 0.000 0.001 0.007 -0.276 -0.151 0.190 1.583 Where: 𝒆𝒙𝒑𝒆𝒓_𝒔𝒒 = π’†π’™π’‘π’†π’“πŸπ’Š ; 𝒆𝒅𝒖𝒄_𝒔𝒒 = π’†π’…π’–π’„πŸπ’Š ; and 𝒆𝒅𝒖𝒄_𝒆𝒙𝒑𝒆𝒓 = π’†π’…π’–π’„π’Š × π’†π’™π’‘π’†π’“π’Š a. Please write down the estimated sample regression function. b. What is the marginal effect of education on π’π’π’˜π’‚π’ˆπ’†π’Š ? Calculate and interpret the marginal effect of education on π’π’π’˜π’‚π’ˆπ’†π’Š for 2 workers Jim and William; Jim has 2 of 3 Please Turn Over 16 years of education and 2 years of experience, while William has 12 years of education and 2 years of experience. What can you say about the marginal effects of education as education increases? c. What is the motivation to estimate equation [2] using robust-standard errors? 3 of 3 Please Turn Over

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