1) Use the Birthweight_Smoking dataset and associated description file to answer the following questions. Run three regressions: (1) Birthweight on Smoker (2) Birthweight on Smoker, Alcohol, and Nprevisit (3) Birthweight on Smoker, Alcohol, Nprevisit, and Unmarried.
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Regressor |
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Smoker |
Beta Se(beta) [Confidence int.] |
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Alcohol |
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Beta Se(beta) |
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Nprevist |
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Unmarried |
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Intercept |
Alpha Se(Alpha) |
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SER |
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a) Using the blank table above, fill in the estimated coefficient estimates and standard errors for each variable and model.
b) Create 95% confidence intervals for the variable Smoker and add it to the table.
c) Does the coefficient of Smoker suffer from omitted variable bias in regression (1)? How can you come to this conclusion? Make sure your conclusion uses a qualitative argument and quantitative evidence.
d) Does the coefficient of Smoker suffer from omitted variable bias in regression (2)? How can you come to this conclusion? Make sure your conclusion uses a qualitative argument and quantitative evidence.
e) Consider the coefficient on Unmarried in regression (3).
i. Construct a 95% confidence interval, add this to the appropriate place in the table.
ii. Is the coefficient statistically significant? Explain.
iii. Is the magnitude of the coefficient large? Explain.
iv. A family advocacy group note that the large coefficient suggests that public policies that encourage marrigage will lead, on average, to healthier babies. Do you agree (Review the discussion of control variables in Section 6.8. Sicuss some of the various factors that Unmarried may be controlling for and how this affects the interpretation of its coefficient.)
f) A Consider the various other control variables in the data set. Which do you think should be included in the regression? Using a table like Table 7.1 (and related discussion), examine the robustness of the confidence interval you constructed in (b). What is a reasonable 95% confidence interval for the effect of smoking on birthweight?
2) Empirical Exercise 7.2 35 points)
Empirical exercises in Chapters 4 and 5 involved estimating the effect of a person’s height on their earnings. It was found to be large and statistically significant. One explanation for this result is omitted variable bias: Height is correlated with an omitted factor that affects earnings. For example, Case and Paxson (2008) suggest that cognitive ability (or intelligence) is the omitted factor. The mechanism they describe is straightforward: Poor nutrition and other harmful environmental factors in utero and in early childhood have, on average, deleterious effects on both cognitive and physical development. Cognitive ability affects earnings later in life and thus is an omitted variable in the regression form Chapters 4 & 5.
a. Suppose that the mechanism described above is correct. Explain how this leads to omitted variables bias in the OLS regression of Earnings on Height. Does the bias lead the estimated slope to be biased positive or biased negative? Use a DAG and the formula we discussed in class to determine the sign of bias.
If the mechanism described above is correct, the estimated effect of height on earnings should disappear if a variable measuring cognitive ability is included in the regression. Unfortunately, there isn’t a direct measure of cognitive ability in the data, but the data set does include years of education for each individual. Because students with higher cognitive ability are more likely to attend school longer, years of education might serve as a control variable for cognitive ability; in this case, including education in the regression will eliminate, or at least attenuate, the omitted variable bias problem.
Use the years of education variable (educ) to construct four indicator/dummy variables for whether a worker has less than a high school diploma (LT_HS = 1 if educ < 12, 0 otherwise), a high school diploma (HS = 1 if educ =12, 0 otherwise) , some college (Some_Col = 1 if 12< educ<16, 0 otherwise) , or bachelor’s or higher (CollegePlus = 1 if educ >=16, 0 otherwise)
b. Focusing first on women only, run a regression (1) Earnings on Height and (2) Earnings on Height, and the indicators for education you created as controls.
i. Compare the estimated coefficient on Height in regressions (1) and (2). Is there a large change in the coefficient? Has it changed in a way consistent with the cognitive ability explanation? Explain.
ii. The regression omits one of the education control variables, why?
iii. Test the the joint null hypothesis that the coefficients on the education variable equal zero. Why is this test important/relevant?
iv. Discuss the values of the estimated coefficients on LT_HS, HS, and Some_Col. (Each of the estimated coefficients in negative, and the coefficient on LT_HS is more negative than the coefficient on HS, which in turn is more negative than the coefficient on Some_Col. Why? What do the coefficients measure?)
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