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 or she finished one place lower than her pre-race ranking relative to other race entrants) and some other controls to see if there is a relationship between prize money at risk, and finishing time. 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)
5 Kilometer 8 Kilometer 10 Kilometer 15 Kilometer 10 Mile half Marathon Marathon
Without 1993 Points Prize difference/ -31.34 42.00 -26.49** 1,000 -502.6* -18.22 -84.83 - 31.31 (1433) (1650) (2.097) (1.740) (1.535) (0.368) (3.277)
p value LR test of 02185 0007285 .07203 00005 00000 .00000 00000 race dummies 128 345 122 402 N 100 101 199
With 1993 points 1993 points -0,02226**-0.01449** -0,00301 -0.05023**-0.06393* -0,004769 -0.00883 (1.082) (2.152) (2.507) (0.327) (0.687) (2.765) (3.351
Prize difference/ 1,000 -294.6 0.03186 46.78 135.9 -15.60* 1,004 41.46 (0.028) (0.002) (1.077) (0.598) (1.418) (1.837) (1.480)
1. What is the coefficient on the variable (prize difference/1000) in the regression without 1993 points?
2. Did you expect the sign of this coefficient to be negative? Why or why not?
3. Is this coefficient significant at the 5% level? Why or why not?
4. Based on this coefficient, would you say that there is good evidence that higher prize difference encourages runners to run faster? Explain.
5. What is the coefficient on the variable (prize difference/1000) in the regression with 1993 points?
6. Is this coefficient significant at the 5% level? Why or why not?