Earnings

1
Earnings Skills of Pro Golfers

• Stephen Shmanske, "Earnings and Skills of Pro
  Golfers," Atlantic Economic Journal, September
  1992.

2
Introduction

• Shmanske estimated an earnings equation for pro
  golfers.
• An earnings equations typically looks like
• Earnings a b1Skills b2Experience b3Other
  Factors
• These equations are widely used to explore the
  economic impact of skills, discrimination,
  education, and other factors on earnings of
  individual workers.
• Shmanske is interested in the relative impact of
  golfing skills on the earnings of a pro golfer.
  A question we will consider is whether his
  estimates of the relative impact of driving
  putting are close to what we obtain from our
  scoring equation.

3
Introduction The Equi-marginal Principle

• We will also examine an important principle
  implied by economic optimization the
  equi-marginal principle.
• Example suppose that there are two inputs, A
  B, with marginal products MPA and MPB. If these
  inputs cost PA and PB per unit, optimal input use
  implies that
• MPA/PA MPB/PB
• In this case, we are concerned with the
  allocation of practice time to different skills.
  Assuming the cost of practicing is the same
  across skills, the equi-marginal principle
  implies that the marginal product of practice is
  the same for each skill, i.e. for skills AB
• MPA MPB
• If this were not the case, one would increase
  output by reallocating practicing time to where
  MP was higher. Do this until they equalize.

4
Skill Variables

• SKILLS VARIABLE MEASUREMENT
• DRIVING
• DISTANCE DRIVDIST YARDS OFF TEE
• ACCURACY DRIVACC FAIRWAYS HIT
• APPROACH SHOTS IRONS GREENS IN REG
• BUNKER SHOTS SANDSAVE PARS FROM SAND
• PUTTING PUTTPER PUTTS/HOLE (IN REG)
• SHORT GAME SHORTGAME PUTTS/HOLE (X REG)
•  
• EXPERIENCE EXPER YEARS ON PGA TOUR
•  

5
Earnings Equations

• 2 MEASURES OF EARNINGS
• WINNINGS EARNED ON TOUR IN 1986
• WINPER EARNED PER TOURNAMENT ENTERED
•  
• EQUATION 1
• WINNINGS a b1DRIVDIST b2DRIVACC b3IRONS
• b4SANDSAVE b5PUTTPER b6SHORTGAME
  b7EXPERIENCE
•  
• EQUATION 2
• WINPER a' b'1DRIVDIST b'2DRIVACC b'3IRONS
  
• b'4SANDSAVE b'5PUTTPER b'6SHORTGAME
  b'7EXPERIENCE
• All data is from the 1986 PGA tour.

6
Estimates of the Returns to Skill

• Dept Variable Annual Earnings /Tournament
• Constant 3,192,571 (2.02) 164,683 (2.54)
• DRIVDIST 6,775 (2.76) 341.1 (3.39)
• DRIVACC 2063 (0.51) 170.0 (1.02)
• IRONS 16,037 (2.15) 495.2 (1.62)
• SANDSAVE 64.99 (0.29) -4.23 (-0.47)
• PUTTPER -2,929,565 (-4.76) -136,040 (-5.31)
• SHORTGAME -453,858 (-1.14) -35,549 (-2.19)
• EXPERNCE 1539 (0.59) 202.5 (1.91)
• adj R2 .439 .516

7
Relative Returns to Skills

• Most important skills as measured by precision
  (t-stats) of estd coefficients
• Driving Distance (2.76, 3.39)
• Irons (2.15, 1.62)
• (hitting greens in regulation)
• Putting (-4.76), -5.31)
• Use WINPER regression to evaluate relative
  returns to driving vs. putting

8
Relative Returns to Skills (2)

• Let D DRIVDIST
• Let P PUTTPER
• From Table
• b'1 ?W/?D 341.1
• b'5 ?W/?P -136,040
• On an Earnings Isoquant
• ?WINPER 0 (?W/?D)?D (?W/?P)?P
• ?D/?P - b'5/b'1

W1
D
W2
?D
?P
P
9
Relative Returns to Skills (3)

• What is Slope of Earnings Isoquant?
• How much must D increase if P increases to keep
  ?W0?
• ?D/?P - b'5/b'1 136,040/341.1 398.82
• You must drive the ball 400 yards further to make
  up for 1 putt/hole!
• Divide b'5 by 72 to make it one putt per
  tournament
• -b'5/b'1 1889/341.1 5.54 yards
• You can buy one missed putt per tournament if you
  drive the ball 5.5 yards further on every hole.
  
• This is less than our estimate (7.9 yards) from
  the scoring isoquant. Part of this difference
  may be because pros are driving the ball 350
  yards now, but putting skill has not changed.

10
Practice Time and the Equi-marginal Principle

• Shmanske surveyed PGA golfers on how much they
  practiced each skill each week
• Estimated equation linking skills to practice
  time
• Variables
• St -- current stock of skill
• St-1 -- stock of skill from prior period
• PRACS -- Hours of practice per week
• Equation St a St-1 b PRACS

11
Marginal Product of Practice

• Marginal Products
• Coefficient Estimates t-stats adj R2
• bD 1.789 2.40 .670
• bP -.006 -4.23 .616
• 1 extra hour of practice increases D by 2 yards,
  reduces P by -.006
• (.4 putts per tournament or 2.5 hours per putt
  per tournament)
• patience patience patience!!!

12
Marginal Revenue Product of Practice

• Use value of skills from annual winnings
  regression adjust to weekly measure (divide by
  52).
• How much does one marginal hour of practice per
  week increase weekly earnings?
• MRPD (?WINNINGS/?D)/52 bD
• (6775/52)1.789 233
• MRPP (?WINNINGS/?P)/52 bP
• (-2,979,565/52)(-.006) 344

13
Practice the Equi-marginal Principle

• Putting practice is 50 more valuable than
  driving
• MRPP 344
• MRPD 233
• Is something wrong with these estimates?
• they violate the equi-marginal principle.
• Earnings would increase by 111 if one spent 1
  hour less driving (-233) but 1 more hour putting
  (344)
• Why aren't golfers doing this?
• a) these estimates are bogus
• b) they're stupid
• c) there may be different costs to driving and
  putting