Question

Q2. In their paper "The Rewards to running: Prize structure and performance in professional road racing", Lynch and Zax look at whether races with large prizes record faster times because they attract faster runners, or because they encourage all runners to run faster (the paper can be found on D2L, but you shouldn't need to read it in order to answer this question) They regress the time taken to finish the race on prize difference (defined as the dollar amount of prize money a runner would lose if he relative to other race entrants) and some other controls to see if there is a relationship between prize money at risk, and finishing time. rshe finished one place lower than her pre-race ranking They present the following table, which contains results from two specifications: first where they do not include 1993 points, a variable which is a measure of the runner's ability (the top panel), and second, where they do (the bottom panel). Consider the 8 kilometer race (the second column). Note that the figures in parentheses below the coefficients are t-statistics (and not standard errors). Truncated Regressions Linear Specification One-Time Runners With and Without 1993 Points (dependent variable time in seconds) TABLE 4 10 10 Half Marathon Kilometer Kilometer Kilometer Marathon . Kilometer Mile Without 1993 Points Prize differencel 1000 3 277 (0.3681 (1.650) (2.097) (1.433) (1.740) (1.535) p value LR test of race dummies 0007285 .07203 00005 02185 00000 .00000 00000 28 00 45 122 101 199 402 With 1993 points 1993 points -0.008837-0.05023**-0.06393 -0.004769 -0.02226* -0.01449** -0,003016 (1.082) (2.152) (2.507) (0.327) (0.687) (2.765) (3.351) Prize difference c00 1,004 -294.6 0,03186 41.46 4678 135.9 -15.60 (0,028) (1.837) (0,002) (1.077) (0.598) (1.418) (1.480) NOTE: Figures in parentheses are t statistics. the coefficient on the variable (prize difference/1000) in the regression a. What without 1993 points? b. Did you expect the sign of this coefficient to be negative? Why or why not? d. Based on this coefficient, would you say that there is good evidence that higher prize difference encourages runners to run faster? Explain. e. What is the coefficient on the variable (prize difference/1000) in the regression with 1993 points? f. Is this coefficient significant at the 5% level? Why or why not? g. Based on this coefficient (in the regression with 1993 points), would you say that there is good evidence that higher prize difference encourages runners to run faster? Explain

Answer 1

a. The coefficient on the variable prize difference/1000 for 8km without 1993 points is -502.66

b. Yes I expected the sign of the coefficient to be negative since the regression is about time taken to finish with the money lost by finishing a place lower. (A higher amount of money lost by finishing a place lower is expected to reduce the time taken for the runner to finish i.e. if a higher money is at stake, he is expected to finish earlier)

c. The coefficient is significant at the 5% level. The t value 2.097 is higher than the value at 95% confidence at 100-1= 99 degrees of freedom in t-table which is 1.9842

d. Based on this i would say there is good evidence that higher prize money encourages runners to run faster,since the coefficient is negative(higher prize money and so higher prize at a stake encourages lower times) and is also significant at the 5% level

e. the coefficient of the variable is -294.6

f. the t-test statistic for this is 1.480 which is less the t-test value for 99 degrees of freedom at 5% level as shown in c. so it is not significant at the 0.05 level

g. Based on this I will not say that there is good evidence as the value is not significant at the 5% level of significance according to t-test