Introductory Econometrics: A Modern Approach 6th Edition by Jeffrey M Wooldridge

Exercise 1

Use the data in PNTSPRD.RAW for this exercise.

(i) The variable favwin is a binary variable if the team favored by the Las Vegas point spread wins. A linear probability model to estimate the probability that the favored team wins is

P(favwin = 1|spread) = ?0 + ?1 spread.

Explain why, if the spread incorporates all relevant information, we expect ?0 = .5.

(ii) Estimate the model from part (i) by OLS. Test H0: ?0 = .5 against a two-sided alternative. Use both the usual and heteroskedasticity-robust standard errors.

(iii) Is spread statistically significant? What is the estimated probability that the favored team wins when spread = 10?

(iv) Now, estimate a probit model for P(favwin = 1|spread). Interpret and test the null hypothesis that the intercept is zero. [Hint: Remember that ?(0) = .5.]

(v) Use the probit model to estimate the probability that the favored team wins when spread = 10. Compare this with the LPM estimate from part (iii).

(vi) Add the variables favhome, fav25, and und25 to the probit model and test joint significance of these variables using the likelihood ratio test. (How many df are in the chi-square distribution?) Interpret this result, focusing on the question of whether the spread incorporates all observable information prior to a game.

Step 1 of 10

(i)

The variable is a binary variable, if the team favored by the Las Vegas point spread wins.

The Linear Probability Model (LPM) is given by:

If the spread incorporates all the information, then there will not be any spread. Under this situation, a fair and unbiased situation arises. Given, equality of chances of winning under this situation for all the teams –whether favorite or not favorite, the team which has been labeled as favorite would have 50% chance of winning. Hence, would be expected to be 50% or 0.5