ec homework

Problem Set 1

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). 

a.      What is the dependent variable?                                                      _____________ 

b.     What is the hypothesis being tested?

c.     Which variable captures the hypothesis?                                                 ___________ 

d.     What is its coefficient?                                                                              ____________ 

e.     What does the coefficient mean?

f.      Is it significant at the 5% level?                                                                       ____________

g.     What does this mean?

h.      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. Joe likes to play tennis. He plays either on a grass surface or a clay surface, but he prefers to play on grass. The table below gives his record this year on these surfaces:

Clay                        Grass

                     Win            11                          21

                     Lose           8                             5

a.     Joe wants to see whether he plays better on grass or clay. How would you state the hypothesis that he is testing?

b.     What is the null hypothesis?

c.     What statistical test should he use?

d.     Joe performs the test that you recommended, and finds a p-value of 0.1114. What does this number mean?

e.     What does Joe learn from this test?

3.  Sara loves to bowl. She never has an open frame; each frame is either a strike (X) or a spare (/). Here is a list of her data in the past three games:

xxxx////x////xxxxxx////xxx//xxxxx///xx

a.     What is the probability that Sara rolls a strike on a given frame in this sample?

b.     What is the probability that Sara rolls a strike in a frame following a strike?

c.     How many runs does Sara have?

d.     Go to the following website: http://www.quantitativeskills.com/sisa/statistics/ordinal.htm and perform the runs test.

i.               In the box marked “N group 1” enter the number of strikes.

ii.              In the box marked “N group 2” enter the number of spares.

iii.            In the box marked “Number of Runs” enter your answer to part c.

How many runs were expected? What is the z-value for this test?  Does the test show evidence of the hot hand?

e.     Draw a picture of the distribution of the number of runs, and show where Sara’s number of runs falls on this distribution (i.e. the location of z-statistics). You can copy the picture from page 15 of the Hot Hand slides if that is easier.