Assignment #6

PPol 603

Due: Thursday, 11 October 2012

Type up your answers. Give proper credit to those you work with and/or the text(s).

Solve the following problems. Show all of your work, but keep your answers concise. Highlight your (final) answer to distinguish it from your other numbers and text. Include a copy of your input (e.g. do file) or output (e.g. log file), when it is an appropriate way to show your work. However, do not include unnecessary output (i.e. no data dumps), and format any output so that it is easily readable. An appropriate time to include output is when you put your results in a table--if your results are wrong, then graders have no idea how you came to your conclusions (i.e. give partial credit) unless you provide some output. Explanation includes statistical and substantive explanation (explain so that a statistical layperson can understand it, and so that a statistical analyst will see your erudition).

1. {5 points} Do Problem 6.6 in Stock and Watson. You may use the formula we discussed in class to assess positive/negative bias, rather than Equation (6.1).
2. {20} This problem asks you to import an Excel spreadsheet into Stata. The U.S. government has posted student-teacher ratios for each state here. Save this file and import the data into Stata. Test the hypothesis that total student membership affects total student/teacher ratio. Name a possible omitted variable, and what the direction of bias is for the included coefficient. [Note: Make sure you can import the data by yourself for this problem, or you will have difficulties later.]
3. {35} [from Stock 2007] In this problem, you continue to explore the determinants of economic growth using an expanded cross-country data set found here. school60 is equivalent to yearsschool in the growth.dta data set. revc is equivalent to rev_coups. capstock60 is capital stock, in thousands of US$, per capita, in 1960 (the capital stock is the value of all fixed structures and machines). civil is an index of civil liberties, on a scale of 1 (most civil liberties) to 10 (none).
   a. Table 1, which you can download here, presents the results of three regressions, one in each column. Estimate the indicated regressions and fill in the values. For example, to fill in column (1), estimate the regression with growth as the dependent variable and tradeshr and school60 as the independent variables, using the robust option, and fill in the estimated coefficients and standard errors; also compute and fill in the value of the F-statistic and p-value testing the hypothesis that the coefficients on tradeshr and school60 are both zero. The adjusted R² can be computed by rerunning this regression without the robust option (or by typing display e(r2_a) right after the regression). Note: The data set includes the observation on Malta, but regressions in Table 1 all exclude Malta.
   b. Explain in words what the coefficient on school60 means in regression (1).
   c. Using regression (1), test the hypothesis that the coefficient on tradeshr is zero, against the alternative that it is nonzero, at the 5% significance level. In everyday words (not statistical terms), what precisely is the hypothesis that you are testing? Now test the hypothesis that the coefficient on tradeshr is one. Interpret the results.
   d. Does the coefficient on tradeshr differ in regressions (1), (2), and (3) in a substantively important way, that is, is the difference between the three estimates large in a real-world sense?
   e. Economic theory predicts that tradeshr, school60, and capstock60 all are determinants of economic growth. Use regression (2) to test the hypothesis (at the 5% significance level) that the coefficients on these three economic variables are all zero, against the alternative that at least one coefficient is nonzero.
   f. Using regression (3), consider the coefficient on revc. Do the sign and magnitude make sense? Explain.
   g. Using regression (3), consider the coefficient on civil. Do the sign and magnitude make sense? Explain.
   h. In regression (3), is the coefficient on revc statistically significant at the 5% significance level? Is the coefficient on civil statistically significant at the 5% significance level?
   i. Use the heteroskedasticity-robust F-statistic to test the hypothesis (at the 1% significance level) that the coefficients on the political variables (revc and civil) in regression (3) are both zero, against the alternative that one or the other or both are nonzero. Discuss in light of your answer to part h. What happens if you only include revc or civil in (3)? Evaluate the following statement: "Because revc and civil are correlated, they have no business being in the same regression."
   j. Explain why the coefficient on school60 and its standard error are so different in regressions (1) and (2).
   k. Suppose you recoded civil so that higher numbers indicate more civil liberties (e.g. something like generate civilrev = 11 - civil). What would happen if you included both the original civil and the recoded civil in a regression? Check this in Stata.
   
4. {40} [roughly from Wooldridge 2006] Case Study: Birth Weight and Cigarette Smoking
   "A problem of interest to health officials (and others) is to determine the effects of smoking during pregnancy on infant health. One measure of infant health is birth weight; a birth weight that is too low can put an infant at risk for contracting various illnesses."

   The state of Utah is considering taking steps to address this problem. A legislator's intern got a hold of a data set and found there was a negative correlation between birth weight and cigarettes smoked. The legislator is now proposing a massive tax increase on cigarettes to promote infant health.

   As the statistical analyst for the Department of Health, you have been asked by the chair of the legislature's health committee to assess the effects of the proposed bill. You should address the relationship between birth weight and cigarette smoking, and the relationship between cigarette smoking and prices/taxes. Remember that you are writing the (professional) report for a politician, but need to provide documentation, perhaps in the form of an appendix. The following data set, which includes potential control variables, is provided here and described here. Note that the data set is in text format. [Note: Make sure you can import the data by yourself for this problem, or you will have difficulties later.]

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