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Quantile Regression

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QuantileRegression

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

- Highest paid athlete from 2001 to 2012

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.

- Greens in regulation

Empirical Results

- Simple level OLS (Ordinary Least Squares) regression estimate:

OLS and Quantile Regression Results