Quantile Regression
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Transcript of Quantile Regression
Quantile Regression By: Ashley Nissenbaum
About the Author• Leo H. Kahane• Associate Professor at Providence College• Research• Sport economics, international trade, political science
• Editor of Journal of Sports Economics
Previous Research• Golf earnings are highly positively skewed
• Schmanske (1992) • Value of the marginal product from putting may be in the range of
$500 per hour of practice.• Alexander and Kern (2005)
• “Drive for show, putt for dough”
• Callan and Thomas (2007)• Skills determine score, which determines rank and thus earnings
Earnings and Skewness• Linear Regression• Focuses on the behavior of the conditional mean of the
dependent variable
• Most people make under $300K per event
Reasons for Skewness
Payout Structure• Non-linear
• Top 50% after the first two rounds: 1st place receives 18%, 2nd place receives 10.8%, 3rd place receives 6.8%, 4th place – 4.8%, etc
• Extraordinary Talented Golfers• Tournament wins are spread across a large number of golfers
Tiger Woods• Won 185 tournaments • 14 professional major tournaments, 71 PGA Tour events
• $500 Million net worth• Highest paid athlete from 2001 to 2012
• $132 million from tournaments
Concept of Quantile Regression• Equation for Quantile Regression:
• Where: • y(i)= real earnings per PGA event• Q= Specific quantile associated with the equation• Β = Vector of coefficients to be estimated• Ε = Error term• X(i)= Covariates
Covariates• x(i) = covariates expected to explain golf earnings
• Greens in regulation• The percent of time a player was able to hit the green in regulation (greens
hit in regulation / holes played x 100). Positive correlation expected.• Putting average• Average number of putts needed to finish a hole per green hit in regulation.
Negative correlation expected.• Save percentage• Percentage of time a golfer was able to get the ball in the hole in two shots
or less following landing in a greenside sand bunker (regardless of score). Positive correlation expected.
• Yards per drive• Average number of yards per measured drive. Positive correlation
expected.• Driving accuracy• Percentage of time a tee shot comes to rest in the fairway. Positive
correlation expected.
Empirical Results• Simple level OLS (Ordinary Least Squares) regression estimate:
OLS and Quantile Regression Results
Coefficients Graph