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# ps6_sol - Department of Economics Columbia University...

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Department of Economics W3412 Columbia University Spring 2010 SOLUTIONS TO Problem Set 6 Introduction to Econometrics Prof. Marcelo J. Moreira and Seyhan E Arkonac, PhD for all sections Spring 2010 1) Create a new binary variable higdppc, which equals one if gdppc is greater than or equal to the median in the data set, and which equals zero otherwise; also create the interaction variables hi_lackf = higdppc lackpf and hi_lackf = higdppc lackpf 2 . Estimate the regressions in Table 1 and fill in the empty entries. You may write in the entries by hand or type them using the .doc electronic version of the table on the course Web site. Note: for all calculations, only use the countries that have nonzero values of ftmpop and non-missing values of gdppc. See the attached table and the .do file that produced the results. 2) Regression (6) produces two regression lines, one for logdppc = 0 and one for logdppc = 1. Produce a scatterplot of lnftmpop vs. lackpf, showing the two regression lines. This can be done either by producing two scatterplots, one for logdppc = 0 and one for logdppc = 1, or by combining the two scatterplots into a single graph. Use regression (6) to write out the estimated regression lines for the two groups (in slope-intercept form). Log terrorist fatalities Terrorsim and Political Freedoms Lack of political freedom lnftmpop_lo lnftmpop_hi plnft_lo plnft_hi 0 2 4 6 8 -6 -4 -2 0 2

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Regression line for low GDPPC group: ln ftmpop = -.72 – .248 lackpf Regression line for high GDPPC group: ln ftmpop = -3.56 + .397 lackpf 3) Use the results in Table 1 to answer the following questions. a) Is the difference between the two slopes plotted in the scatterplot of Question 2 statistically significantly different from zero at the 5% significance level? Explain. Yes. The hypothesis that the slopes are the same translates into the coefficient on the interaction term in regression (6) being zero, and the t -statistic on that term is t = 6.45/2.38 = 2.71, which exceeds 1.96. b) In a sentence or two, interpret the signs of the two slope coefficients in regression (6) and the scatterplot in Question 2; that is, explain in everyday terms the findings shown in that scatterplot. For countries with GDP per capita below the median, fewer political freedoms (i.e. greater values of lackpf ) are associated with fewer terrorist fatalities. In contrast, in countries with GDP per capita above the median, fewer political freedoms are associated with more fatalities. As pointed out in the response to (a), this difference in slopes is statistically significant. c) Using regression (7), test the hypothesis that the coefficients on higdppc lackpf and higdppc lackpf 2 are zero, against the hypothesis that one or the other (or both) is nonzero. State in words what the hypothesis is that you are testing.
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ps6_sol - Department of Economics Columbia University...

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