140_ps4_solutions

140_ps4_solutions - ECON 140, Fall 2008 Alex Rothenberg...

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Unformatted text preview: ECON 140, Fall 2008 Alex Rothenberg Solutions to Problem Set #4 Problem 1 Return to http://www.fivethirtyeight.com , and gather data for the six swing states (IN, OH, MO, NV, NC, FL) fit models in which you regress the margin on a second order polynomial of time. Fit a second model where you regress the margin on the log of time. Which has a larger R2? For each state settle on your favorite model (dont feel limited by my suggestions). Display the standardized residuals for each model, are there any potential outliers? ANSWER: Regression results for the two models fitted on data from each of the 6 states appear at the end of this document. I’ve defined date as the positive number of days between the time of polling and election day. The dependent variable is coded as the positive margin for Obama and negative for McCain (the sign was chosen arbitrarily and in no way reflects the political preferences of the solution writer). You can see from the residual plots, also attached, that many of the regressions have outliers. 1. Sum the electoral votes for the states that are a lock for Obama as well for the states for McCain. • ANSWER: According to fivethirtyeight.com as of November 3, 2008, the “lock” states for each of the parties are as follows: GOP = 163 1 DEM = 286 2 2. Assuming normal errors, forecast the probability that each candidate wins each of the six swing states. • ANSWER: For a given state, I used the simple quadratic polynomial model to forecast the probability of winning. The model is as follows: M t = β + β 1 t + β 2 t 2 + ε t 1 The GOP states are: { AK, AL, AR, AZ, ID, GA, KS, KY, LA, MS, MT, ND, NE, OK, SD, SC, TN, TX, UT, WV, WY } 2 The DEM states are: { CA, CO, CT, DC, DE, HI, IA, IL, MA, MD, ME, MI, MN, NH, NJ, NM, NY, OR, PA, RI, VA, VT, WA, WI } 1 ECON 140, Fall 2008 Alex Rothenberg Because I’ve defined t as the positive number of days until the election, on election day, t = 0 . Therefore, the margin on election day is just the following: M t = β + ε t So, ignoring sampling error in ˆ β , the probability that each candidate wins is given by the following: P { Obama Wins } = P { M t > } = P { β + ε t > } = P { ε t >- β } = P ε t SE ( ε ) >- β SE ( ε ) = P Z >- β SE ( ε ) where Z ∼ N (0 , 1) . Similar calculations for the other states give the following table: 3 State | beta0 se_reg Obama McCain EV-------------+----------------------------------------------------- Florida |-0.0971 2.766 0.4860 0.5140 27 Indiana | 0.2575 4.782 0.5215 0.4785 11 Missouri |-3.0432 2.676 0.1277 0.8723 11 N. Carolina |-0.6386 2.416 0.3958 0.6042 15 Nevada | 8.5941 4.470 0.9727 0.0273 5 Ohio | 2.8333 4.481 0.7364 0.2636 20 3. Assuming independence among the forecast errors across the six models, calculate the cdf of electoral votes for Obama....
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140_ps4_solutions - ECON 140, Fall 2008 Alex Rothenberg...

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