Economics of Sports

Assignment Instructions

 

Problem Set 1

 

Ec 370                                                                                                                                                    Summer, 2012

Michigan State University                                                                                                            L. Martin

 

1. In their paper on peer effect in golf, Guryan, Kroft and Nodowidigdo investigate whether a player’s score is lower if his playing partners are better golfers. Ability is measured by the average score per round over the season. Other influences on score are controlled using fixed effects. (Don’t worry about this term – we will study it later.) Standard errors appear in parentheses below the coefficient estimate. The data involve scores from rounds played during several Professional Golf Association seasons. The paper is here:

 

http://www.nber.org/papers/w13422.pdf

 

You should not have to read the paper to answer this question.

 

Consider this regression table from their paper.

 

1. Consider the first regression (left hand column).

 

1. What is the dependent variable?                                                                    _____________
2. What is the hypothesis being tested?
3. Which variable captures the hypothesis?                    ___________
4. What is its coefficient?                                                                                               ____________
5. What does the coefficient mean?
6. Is it significant at the 5% level?                                                                                  ____________
7. What does this mean?
8. Would you say that there is good evidence for peer effects? Explain.

 

i. Is the coefficient on own ability significant at the 5% level?                               ______________

 

j. What type of variable is this?                                                                                           ______________

 

k. What does this estimate mean (in English)?

2. Bobo, who is from Ghana, likes to wrestle. He wrestles on Tuesday and Friday. (By the way, his name means, “born on Tuesday.”)   The following table gives his results this year on the two days.

 

Tuesday                               Thursday

 

Win                        20                                           15

 

Lose                       8                                              13

 

1. He wants to know if he wrestles better on Tuesday. What statistical test should he use?

_____________

 

1. What is the hypothesis to be tested?

 

c. What is the null hypothesis?

 

d.   He performs the test that you recommend and finds a p-value = 0.167. Interpret this number.

 

e. What is learned from this test? Explain.

3. Fred, like all normal people, loves to bowl. He never has an open frame. That is, each frame is either a strike (x) or a spare (/). Strikes are better. Here is his data.

 

xxx/xxx/////xxxx////x

 

1. What is the conditional probability of a strike in the frame following a strike?

_________

 

 

1. How many runs for Fred?                                                                              __________

 

1. The runs test for this data gives the following.

 

Expected Number of Runs: 11.5; sd: 2.2279

z-value= -2.0091

 

Explain the results of this test.   Does it show evidence of the hot hand?

 

1. Draw a nice picture of the distribution of runs and show the actual value, the z-statistic.

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