BASKETBALL PLAYER SALARIESA. IntroductionB. Choice of variablesC. Regressions1. Linear specification2. Multiplicative Specification3. An alternate specificationD. Other ways of detecting discrimination.1. Do whites play longer in general than their skills would suggest?2. Do cities with a higher percentage of whites, play whites a higher percentage of the time?3. Do teams with more white players do worse than teams with more black players?4. Discrimination among fans and sportswritersE. Opportunistic Empiricism1. White Men Can't Jump2. Predicting draft number3. How skilled are basketball scouts?BASKETBALL PLAYER SALARIES(Bbal.dta)A. IntroductionSports statistics create a great opportunity to measure the relationship between productivity and income. The data is much more detailed than that typically available to economists. The basketball data set collected by Kahn and Sherer is very rich and allows us to test a number of hypotheses. Suppose that we want to find out the role of race in determining salaries. A simple-minded way of doing this is to run the following regression:ls SAL c RACEwhere RACE is 1 if white; 0 otherwise. The results suggest that there is no discrimination against black basketball players since the coefficient of RACE is negative, implying that whites make less than blacks (Please note that I sometimes use black and white for a short hand to the preferred African-American and European-American). While simple income comparisons (between ethnic backgrounds or genders) are commonly done, it is wrong methodologically, since one needs to control for productivity. In this case, productivity means how many baskets and rebounds each player makes. The work by Kahn and Sherer provides guidelines on proper econometric methodology. B. Choice of variablesThe Kahn and Sherer article, like most of the articles chosen for study in this course, is anexemplary model of research. Its results are convincing for a variety of reasons: (1) Thereis not one, but several related studies employing different data, all of which confirm in different ways the basic ideas. (2) The authors undertook various formulations of the econometric model and the effect of RACE was robust to the alternative formulations. (3)the authors have chosen a good data set -- the performance variables are relatively close to the ideal. (4) the authors are aware of the possible biases inherent in the data and account for them.The purpose of this course is to get you to think for yourself and develop critical understanding. You will not just replicate someone else's work (including mine). In this spirit, one should always critically assess others' work and try to improve on it. With regard to Kahn and Sherer's study, I believe that there is room for improvement in their choice of variables. In choosing variables one should think carefully. One does not justthrow in variables which seem to make sense. One chooses the formulation that makes the most sense. Furthermore one needs to carefully consider the data. I start with the last point first. In this study income is a function of performance. If we do not include bonuses for playoff games, then income does not depend on this year's performance but rather on previous years' performance. That is, salary contracts are madebefore the start of the season and depend on previous years' performance with the preceding year's performance being most influential (unless there was a multi-year contract). Ideally we would have salary as a function of lagged performance. In this data set, we are given the total points over all seasons. Thus this data set implicitly assumes that performance is the same each year. Such an assumption is incorrect. But that is what we have to work with.In this study Kahn and Sherer use logs so that, in the original formulation, the variables are multiplied. Suppose that one thought that salary (SAL) should be a function of total offensive rebounds (OFFREB) in a year. Then one might want to have either OFFREB per year as a summary or break it down into constituent parts OFFREB PER MINUTE * AVERAGE MINUTES PER GAME PLAYED* GAMES PER YEAR. The authors have these last two variables denoted by MINS and GAMES respectively, but they have OFFREB per game not per minute. Given MINS and GAMES, it makes more sense to have offensive rebounds per minute than per game.Also note that POINTS is career points scored. It should be in the same units as OFFREB(either per game as the author did or per minute as I have suggested). I believe that the interesting variable is average minutes played by year, MINPYEAR, rather than its constituent parts, GAMES * MINS. Therefore MINPYEAR should be substituted since the constituent parts give no clue as to worth, and we should save on degrees of freedom when there is no cost in doing so. Also, I think that the variables should be per minute rather than per game (then minutes instead of games) since per game conflates productivity per minute and number of minutes per game and the variable games may not vary as much as minutes played per game. Also the negatives are more meaningful per minute. Someone who plays only a few minutes per game will have fewer fouls per game than someone who plays a lot of minutes per game; a measurement of fouls per game would make it look like the more fouls, the higher the pay. We want to capture the negatives and one of the negatives is missing shots. The authors use career field goal percentages (fraction made) but this is already embodied in total points. Again one might want to think of this as a formula. Instead of total field goal points, the authors should have used field goal points attempted per minute times field goal percentage. But better yet, instead of having FTPCT and FGPCT the authors should have had FTMISSED and FGMISSED (field goals missed per minute and free throws missed per minute). Once again, the negatives are in the same unit of account as the positives.I am somewhat skeptical about the use of CENTER and FORWARD. If players in these positions are better, they should be captured in the other variables such as OFFREB or ASSISTS. To also include CENTER would then be double counting. I do not see CENTER and FORWARD as proxies for other unmeasured variables, but those who know more about basketball may disagree and want to include them. While the authors do not use height, some students wanted to include height because taller players would bemore productive, other things being