Homework3-AK - Homework # 3 ECO 7427 ANSWER KEY Prof. Sarah...

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1 Homework # 3 ECO 7427 ANSWER KEY Prof. Sarah Hamersma 1. a) Make a scatterplot of the change in infant mortality rates (from 1971 to 1972) on the y-axis against the TSP pollution rates in 1970. The TSP threshold was 75 milligrams/m 3 , so firms above this level were -500 -400 -300 -200 -100 0 0 50 100 150 tsp1970 It does appear that there may be a relationship between the regulation and the change in infant mortality rates there is a big drop in the growth rate in infant mortality for groups above a TSP level of 75. This is what we’d expect if the regulation caused a reduction in pollution, and this reduction in pollution improved infant health. b) Generate a dummy variable that indicates whether a firm was regulated (based on their 1970 TSP level). Then run a simple linear regression of the form:
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2 Y i, 1972 Y i, 1971 = α + γ*(TSP i, 1970 ) + θ*( REG i ) + ε . regress changey tsp1970 reg Source | SS df MS Number of obs = 40 -------------+------------------------------ F( 2, 37) = 185.46 Model | 755522.162 2 377761.081 Prob > F = 0.0000 Residual | 75363.8383 37 2036.86049 R-squared = 0.9093 -------------+------------------------------ Adj R-squared = 0.9044 Total | 830886 39 21304.7692 Root MSE = 45.132 ------------------------------------------------------------------------------ changey | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- tsp1970 | -1.648911 .3559904 -4.63 0.000 -2.370216 -.9276057 reg | -186.2507 22.49673 -8.28 0.000 -231.8334 -140.668 _cons | -31.37541 22.9018 -1.37 0.179 -77.77887 15.02806 ------------------------------------------------------------------------------ -500 -400 -300 -200 -100 0 0 50 100 150 tsp1970 changey Fitted values What does your result imply about the effect of regulation? (be specific)
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3 The result suggests that while the general pattern was for counties with higher pollution to have larger reductions in infant mortality over time, the regulation seemed to have a large added effect on infant mortality reduction. The coefficient is 186, which is 186 fewer infant deaths per 100,000 live births (sorry, I forgot to give you the units in which infant mortality is measured in the problem set it is per 100,000 births). c) Now allow the regression to be more flexible by allowing an interaction between the TSP i, 1970 variable and the REG i variable. Also include a squared term for TSP i . Does this change your results? Describe why this model is more flexible than the one in part (b). . gen tspreg = tsp1970*reg . gen tspsq = tsp1970^2 . regress changey tsp1970 reg tspreg tspsq Source | SS df MS Number of obs = 40 -------------+------------------------------ F( 4, 35) = 102.44 Model | 765497.356 4 191374.339 Prob > F = 0.0000 Residual | 65388.6441 35 1868.24697 R-squared = 0.9213 -------------+------------------------------ Adj R-squared = 0.9123 Total | 830886 39 21304.7692 Root MSE = 43.223 ------------------------------------------------------------------------------ changey | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- tsp1970 | -4.542843 2.11105 -2.15 0.038 -8.828501 -.2571842 reg | -169.9316 173.9444 -0.98 0.335 -523.0575 183.1943 tspreg | -.0151372 2.204432 -0.01 0.995 -4.490373 4.460098 tspsq | .0150489 .0182908 0.82 0.416 -.0220834 .0521813 _cons | 82.43457 64.60525 1.28 0.210 -48.72105 213.5902 ------------------------------------------------------------------------------ . predict changeyhat2 (option xb assumed; fitted values) . graph twoway (scatter changey tsp1970) (line changeyhat2 tsp1970) The main result does not change too much the effect of the regulations appears to be slightly smaller, but it is still estimated to be very large (it is also not as precisely estimated as before, but recall at the beginning of the problem I told you not to worry about this, since it is just due to the small size of this fake sample). The interaction term suggests that the slope becomes more negative for points beyond the regulation, although the squared term dampens this effect (because it is contributes positively to the slope, with its contribution increasing as the tsp1970 gets higher). This model is more flexible than the one in part (b) because it does not constrain the relationship
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Homework3-AK - Homework # 3 ECO 7427 ANSWER KEY Prof. Sarah...

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