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