Self Control in the Market - National Bureau of Economic Research

Transcription

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77
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7;
Figure 1. Contractual Menu
–c
b
–L
attend
contract F
– L0 – L
not
attend
– k’
0
P
0
– c– p
contract P
F
b
F
–L
attend
not
attend
0
t=0
t=1
0
P
t=2
…
49
t = T’
Figure 2. Survival probability (as a function of attendance)
Figure 2.a.
Time-consistent or
sophisticated agents
Figure 2.b.
Naïve agents
Figure 2.c.
Heterogeneity (time-cons./soph.
and naïve agents)
Survival
probability
Survival
probability
Survival
probability
FM
1
FA
1
FA
1
FA
FFMM
FM
Attendance
Attendance
50
Attendance
Monthly attendance
5
4
3
2
1
20
30
40 50 60
Monthly price
70
80
Figure 3a. Kernel regression of attendance on
price (club 1, bandwidth 4).
Average attendance in club 2
Monthly attendance
6
5
4
3
2
1
20
30
40 50 60
Monthly price
70
80
Figure 3c. Kernel regression of attendance on
monthly price (club 2, bandwidth 16).
Monthly attendance
5
4
3
2
1
50
Figure 3e. Kernel regression of attendance on
price (club 3, bandwidth 16)
30
40 50 60
Monthly price
70
80
Price per average attendance in club 2
20
17.5
15
12.5
10
7.5
5
2.5
Price per av. attendance
30
40
Monthly price
20
20
30
40 50 60
Monthly price
70
80
Figure 3d. Price per average attendance as a function
of the monthly price (club 2, bandwidth 16).
6
20
20
17.5
15
12.5
10
7.5
5
2.5
Figure 3b. Price per average attendance as a function
6
Figure 3. Average attendance and price per average attendance (Kernel regressions)
12
10
8
6
4
2
20
30
40
Monthly price
50
Figure 3f. Price per average attendance as a function
Notes: Point estimates and 95 percent confidence intervals plotted. The sample is ‘First spell’ for individuals initially enrolled with a monthly contract. The
individual price variable is the average price over the first six months. The individual attendance variable is the average attendance over the first six months.
Figures 3a, 3c, and 3e show a kernel regression of attendance on price using an Epanechnikov kernel. The bandwidth is determined by cross-validation with a
grid search separately for each club. Figures 3b, 3d, and 3f show the ratio of the price and the expected attendance predicted for that price using the kernel
regression. Confidence intervals are derived using the Delta method.
51
Figure 4. Price per average attendance over time
Figure 4a. Price per average attendance
Annual contracts with annual fee >=$700
Price per average attendance
25
20
15
10
5
0
1
2
3
4
5
6
7
8
9
10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
Month
Figure 4b. Price per average attendance
Monthly contracts with monthly fee>=$70
Price per average attendance
30
25
20
15
10
5
0
1
2
3
4
5
6
7
8
9
10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
Month
Notes: Point estimates and 95 percent confidence intervals plotted. Figure 4a plots the ratio of average price and average attendance at month n of
tenure. The sample is ‘First spell and no subsidy’ for individuals initially enrolled in the annual contract and still enrolled at month n of tenure. Figure
4b plots the ratio of average price and average attendance at month n of tenure. The sample is ‘First spell and no subsidy’ for individuals initially
enrolled in the monthly contract and still enrolled at month n of tenure. Standard errors for the ratio of average price and average attendance computed
using the bivariate Delta method.
52
Figure 5. Predicted survival probability.
Probit specification with quartic polynomial in past attendance
Figure 5a.
0.8
Predicted survival probability
0.7
0.6
0.5
Monthly contract
0.4
0.3
Annual contract
0.2
0.1
0
0
2
4
6
8
10
12
Monthly average attendance in past 12 months
Figure 5b.
0.8
Annual contract
Predicted survival probability
0.7
0.6
Monthly contract
0.5
0.4
0.3
0.2
0.1
0
0
2
4
6
8
10
12
Monthly average attendance in past 4 months
Notes: Figure 5a and Figure 5b plot the predicted probability of membership at the 14th active month after enrollment as a function of a quartic
polynomial in past attendance. Figure 5a follows the probit specification of Column 6 in Table 8. Figure 5b follows the probit specification of Column
1 in Table 9 with an additional quartic polynomial in attendance.
53
Table 1: US Health Club Industry †
Top 10 Clubs for Revenue, year 2000
Corporate
Revenue in
2000 (in m$)
Number
of Clubs
1
in 2000
Number of
Employees in
2000
Number of States
Operates in
Year
Founded
(1)
(2)
(3)
(4)
(5)
1,007
380(O),
5(F)
20,000
28
(and Canada)
1962
2. 24 Hour Fitness Worldwide
San Francisco, CA
943
430(O)
26,300
15
(and 10 countries)
1983
3. Town Sports International
New York, NY
225
1(O),
4(M),
104(L)
6,400
9
1973
4. Wellbridge
Denver, CO
175
23(O),
14(M),
10(L)
5,000
12
1983
5. Life Time Fitness Inc. Eden
Prairie, MN
101
20(O)
3,000
6
(MN,MI,OH,IN,VA,IL)
1992
6. TCA Club Management
Chicago, IL
85
24(O),
22(M)
2,200
16
(and Canada)
1969
7. The Sports Club Co. Inc.
Los Angeles, CA
77
7(O)
2,400
4
(CA,NY,NV,D.C.)
1978
8. Crunch Fitness International
New York, NY
73
19(L),
1(LS)
2,200
5
(NY,CA,FL,IL,GA)
1989
9. Western Athletic Clubs
San Francisco, CA
70
4(O),
5(L)
1,600
2
(CA,WA)
1977
61.5
24(O),
1(M)
1,850
3
(VA,MD,D.C.)
1973
1. Bally Total Fitness
Chicago, IL
10. Sport &Health Clubs
McLean, VA
Concentration Indexes for year 2000
Herfindahl Index (*10,000)
152.65
Concentration Ratio 4 (%)
20.25
23.15
27.84
32.55
†
Notes: Source: “Understanding the Top 100”, Jerry Janda, Club Industry. The Corporate Revenue includes also revenue from international clubs,
whenever applicable. Information comes from a survey of the companies. Since all of the companies but one are private, accuracy of the information is
not guaranteed. The Concentration Indexes are from calculations of the authors using data from the publication by the Club Industry. The Herfindahl
Index is the sum of the squared shares of company revenues over total industry revenue, summed across the biggest 100 companies (the contribution to
the Herfindahl index of the companies past the 100th is bounded above by .00162). The Concentration Ratio n is the ratio of the revenues by the n
biggest companies over industry revenues.
1
(O)=Owned, (M)=Managed, (L)=Leased, (LS)=Licensed, (F)=Franchised.
54
Table 2: Price per Attendance and Attendance Gap †
Sample: First spell and no subsidy
First Contract Monthly
First Contract Annual
(monthly fee ≥ $70)
(annual fee ≥ $700)
(1)
(2)
9.94
7.98
percentile
11.84
9.99
25 percentile
13.02
10.92
Median
Price per attendance
1
th
15 percentile
22
nd
th
25.01
20.01
th
68.39
55.49
th
181.3
277.57
N =912
N = 208
75 percentile
90 percentile
Sequence of consecutive full
months with payment and no
attendance
Sample: Completed first spell ending with monthly contract, enrollment date
before April 1998, no initiation fee, no subsidy
Longest gap – Total Number of Months
Months before contract termination
3.07
2.29
25 percentile
1
0
Median
Average
th
2
1
th
4
3
th
8
7
th
13
11
.2619
.1964
$244.30
$185.43
N = 168
N = 168
75 percentile
90 percentile
95 percentile
P(gap>=4)
Average payment during gap
Notes: The number of observations is denoted by N. An enrollment spell starts whenever an individual enrolls (or re-enrolls) in the club and ends
whenever the individual quits or is censored. The sample “First spell” consists of the first enrollment spell. The sample “First spell and no subsidy”
restricts the sample “First spell” to those spells in which the average adjusted monthly fee is at least $70 if the spell starts with a monthly contract and
at least $58 if the spell starts with an annual contract. The sample “Completed first spell ending with monthly contract, enrollment date before April
1998, no initiation fee, no subsidy” includes only uncensored enrollment spells in the sample “First spell, no subsidy”. The spells must have started
before April 1998 and finished with a monthly contract, and must require no initiation fee. The spells in column “First Contract Monthly” start with a
monthly contract. The spells in column “First Contract Annual” start with an annual contract.
1
The price per attendance is the ratio of the total payments to the club in a spell divided by the total attendance in the spell.
†
55
Table 3: Enrollment Spells, Descriptive Statistics+
Sample: First spell
Club 1
Club 2
Sample: First spell
Club 3 All clubs
Sample: First spell
and no subsidy
All clubs
All clubs
First
First
Contract Contract
Monthly Annual
First
Contract
Monthly
First
Contract
Annual
All
Contr.
All
Contr.
All
Contr.
All
Contr.
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
3548
2984
1446
7978
7079
899
912
208
No. of completed spells
2440
1850
994
5284
4775
509
588
111
Fraction of total spells
0.688
0.620
0.687
0.662
0.675
0.566
0.645
0.534
0.227
0.201
0.162
0.205
0.207
0.196
0.240
0.260
Number of spells
Number of completed spells
Measures of switching
Number of contract switches
0.015
Ever switch to annual contr.
0.008
0.102
Ever switch to monthly contr.
0.111
Measures of duration (months)
Mean duration
12.22
11.71
10.95
11.80
11.38
15.07
13.19
16.77
Standard deviation of duration
(8.75)
(9.70)
(9.14)
(9.20)
(9.28)
(7.80)
(9.72)
(8.30)
10th percentile
3
2
2
3
3
6
3
9
25th percentile
6
4
4
5
5
13
6
13
Median
10
9
8
9
8
13
10
13
75th percentile
16
16
14
15
15
16
18
23
90th percentile
25
26
24
25
25
26
28
29
Notes: An enrollment spell starts whenever an individual enrolls (or re-enrolls) in the club and ends whenever the individual quits or is censored. The sample “First
spell” consists of the first enrollment spell. The sample “First spell and no subsidy” restricts the sample “First spell” to those spells in which the average adjusted
monthly fee is at least $70 if the spell starts with a monthly contract and at least $58 if the spell starts with an annual contract. The spells in column “First Contract
Monthly” start with a monthly contract. The spells in column “First Contract Annual” start with an annual contract. The measures of duration include censored spells.
56
Table 4: Demographic controls, Descriptive Statistics+
Sample: First spell
Total Amount in $
Sample: First spell
Sample: First spell
and no subsidy
All clubs
First
First
Contract Contract
Monthly
Annual
Club 1
Club 2
Club 3
All clubs
All
Contr.
All
Contr.
All
Contr.
All
Contr.
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
548.97 312.24
515.00
501.28
622.97
920.51
1041.80
(509.94) (559.85) (307.50)
N = 3548 N = 2984 N = 1446
(509.07)
N = 7978
(513.41)
N = 7079
(459.66)
N = 899
(713.68)
N = 912
(543.94)
N = 208
569.05
Initiation fee
6.32
1.99
2.85
(26.64)
(12.16)
(12.88)
N = 3548 N = 2984 N = 1446
All clubs
First
First
Contract Contract
Monthly
Annual
4.07
3.87
5.62
14.46
17.07
(20.13)
N = 7978
(19.45)
N = 7079
(24.82)
N = 899
(41.66)
N = 912
(45.15)
N = 208
Average fee per month
52.40
monthly contract
49.37
31.36
(18.34)
(18.93)
(10.91)
N = 3185 N = 2663 N = 1314
47.42
47.31
56.50
78.52
74.82
(19.10)
N = 7162
(19.05)
N = 7079
(20.51)
N = 83
(5.07)
N = 912
(15.33)
N = 22
48.33
43.76
24.15
42.83
45.94
42.48
69.89
66.26
(18.35)
N = 445
(17.34)
N = 405
(8.62)
N = 151
(17.50)
N = 1001
(15.77)
N = 102
(17.66)
N = 899
(4.19)
N =7
(4.21)
N = 208
4.02
3.75
annual contract
Average attendance per month
monthly contract
4.06
(3.85)
(3.82)
(3.67)
N = 3185 N = 2663 N = 1314
annual contract
3.99
3.98
4.62
3.96
5.45
(3.81)
N = 7162
(3.81)
N = 7079
(3.79)
N = 83
(3.77)
N = 912
(4.15)
N = 22
4.45
4.22
4.16
4.31
5.76
4.15
6.07
4.26
(3.90)
N = 445
(4.06)
N = 405
(3.98)
N = 151
(3.97)
N = 1001
(4.20)
N = 102
(3.92)
N = 899
(4.04)
N =7
(3.87)
N = 208
9.18
8.91
8.86
9.02
10.11
0.44
11.70
0.55
(8.78)
N = 7978
(8.70)
N = 7079
(2.12)
N = 899
(9.06)
N = 912
(2.35)
N = 208
1.69
0.15
13.76
0.08
15.16
(5.18)
N = 7978
(1.52)
N = 7079
(7.47)
N = 899
(1.08)
N = 912
(7.97)
N = 208
Number of months
monthly contract
(8.42)
(9.14)
(8.91)
N = 3548 N = 2984 N = 1446
annual contract
1.58
1.95
1.41
(4.75)
(5.79)
(4.84)
N = 3548 N = 2984 N = 1446
freezing
0.28
0.30
0.18
(0.97)
(1.12)
(0.73)
N = 3548 N = 2984 N = 1446
Female
0.44
0.49
0.47
(0.50)
(0.50)
(0.50)
N = 3539 N = 2984 N = 1446
Age at sign-up
30.71
31.54
35.05
(8.43)
(8.94)
(9.27)
N = 3343 N = 2855 N = 1363
Corporate member
0.43
0.61
0.43
(0.50)
(0.49)
(0.50)
N = 3548 N = 2984 N = 1446
Student
0.05
0.00
0.00
(0.22)
(0.04)
(0.06)
N = 3548 N = 2984 N = 1446
0.27
0.30
0.05
0.37
0.04
(1.00)
N = 7978
(1.05)
N = 7079
(0.37)
N = 899
(1.22)
N = 912
(0.32)
N = 208
0.46
0.48
0.34
0.38
0.35
(0.50)
N = 7969
(0.50)
N = 7071
(0.47)
N = 898
(0.49)
N = 912
(0.48)
N = 208
31.81
31.52
34.04
33.14
34.40
(8.92)
N = 7561
(8.78)
N = 6710
(9.65)
N = 851
(9.70)
N = 855
(10.78)
N = 197
0.50
0.50
0.53
0.16
0.16
(0.50)
N = 7978
(0.50)
N = 7079
(0.50)
N = 899
(0.37)
N = 912
(0.37)
N = 208
0.02
0.02
0.01
0.00
0.00
(0.15)
N = 7978
(0.15)
N = 7079
(0.12)
N = 899
(0.06)
N = 912
(0.07)
N = 208
Notes: Standard deviation in parentheses. An enrollment spell starts whenever an individual enrolls (or re-enrolls) in the club and ends whenever the individual
quits or is censored. The sample “First spell” consists of the first enrollment spell. The sample “First spell and no subsidy” restricts the sample “First spell” to
those spells in which the average adjusted monthly fee is at least $70 if the spell starts with a monthly contract and at least $58 if the spell starts with an annual
contract. The spells in column “First Contract Monthly” start with a monthly contract. The spells in column “First Contract Annual” start with an annual contract.
“Average price per month” refers to the out-of-pocket fee in the case of corporate users.
57
Table 5: Price per Average Attendance at Enrollment+
Sample: First spell and no subsidy, all clubs.
Average price
per month
Average attendance
per month
Average price
per average attendance
(1)
(2)
(3)
Users initially enrolled with a monthly contract
Month 1
Month 2
Month 3
Month 4
Month 5
Month 6
Months 1 to 6
55.09
3.45
15.98
(0.78)
N = 873
(0.13)
N = 873
(0.57)
N = 873
80.53
5.45
14.78
(0.44)
N = 797
(0.18)
N = 797
(0.51)
N = 797
70.02
4.97
14.09
(1.04)
N = 780
(0.18)
N = 780
(0.57)
N = 780
81.72
4.61
17.71
(0.26)
N = 766
(0.19)
N = 766
(0.72)
N = 766
81.87
4.43
18.50
(0.25)
N = 701
(0.18)
N = 701
(0.78)
N = 701
81.88
4.32
18.94
(0.28)
N = 639
(0.19)
N = 639
(0.82)
N = 639
83.00
4.85
17.13
(0.40)
N = 912
(0.14)
N = 912
(0.52)
N = 912
Users initially enrolled with an annual contract, join 14 month before the end of sample period.
Year 1
71.02
4.69
15.15
0.50
N = 145
0.38
N = 145
1.24
N = 145
Notes: Standard errors in parentheses. Standard errors for “Average price per average attendance” measure computed using the bivariate Delta method.
The number of observations is denoted by N. An enrollment spell starts whenever an individual enrolls (or re-enrolls) in the club and ends whenever the
individual quits or is censored. The sample “First spell” consists of the first enrollment spell. The sample “First spell and no subsidy” restricts the sample
“First spell” to those spells in which the average adjusted monthly fee is at least $70 if the spell starts with a monthly contract and at least $58 if the spell
starts with an annual contract. The sample for the t -th month includes spells that are ongoing, not frozen, and not miscoded at month t . For the 6-month
period, the sample includes spells that are ongoing, not frozen, and not miscoded in at least one month in the period. For the 1-year period in the annual
contract, the sample includes only spells that started at least 14 months before the end of the sample period, and that were not prematurely terminated
because of medical reasons or relocation.
The “Average price” in period t is the average fee across people enrolled in period t. The “Average attendance” in period t is the average number of visits
across people enrolled in period t. The measure in Column (3) is the ratio of the measure in Column (1) and the measure in Column (2).
58
Table 6: Price per Average Attendance Over Time+
Sample: All clubs, First spell and no subsidy
Sample: All clubs, First spell
Average price
per month
Average
attendance
per month
Average price
per average
attendance
Average price
per month
Average
attendance
per month
Average price
per average
attendance
(1)
(2)
(3)
(4)
(5)
(6)
Users initially enrolled with a monthly contract
Months 1-6
Months 7-12
Months 13-18
Months 19-24
83.00
4.85
17.13
50.44
4.87
10.36
(0.40)
N = 912
(0.14)
N = 912
(0.52)
N = 912
(0.25)
N = 7079
(0.05)
N = 7079
(0.12)
N = 7079
82.04
3.59
22.87
53.03
3.91
13.56
(0.24)
N = 606
(0.16)
N = 606
(1.05)
N = 606
(0.31)
N = 3961
(0.07)
N = 3961
(0.25)
N = 3961
81.47
3.93
20.74
53.03
4.39
12.07
(0.35)
N = 339
(0.23)
N = 339
(1.24)
N = 339
(0.41)
N = 2192
(0.10)
N = 2192
(0.29)
N = 2192
81.67
3.87
21.10
54.18
4.39
12.35
(0.37)
N = 200
(0.29)
N = 200
(1.61)
N = 200
(0.58)
N = 1181
(0.13)
N = 1181
(0.39)
N = 1181
Users initially enrolled with an annual contract
Year 1
Year 2
71.02
4.69
15.15
47.57
4.48
10.62
(0.50)
N = 145
(0.38)
N = 145
(1.24)
N = 145
(0.75)
N = 598
(0.17)
N = 598
(0.44)
N = 598
73.78
6.85
10.77
50.09
6.59
7.60
(1.06)
N = 36
(1.00)
N = 36
(1.57)
N = 36
(1.81)
N = 112
(0.49)
N = 112
(0.60)
N = 112
Notes: Standard errors in parentheses. Standard errors for “Average price per average attendance” measure computed using the bivariate Delta method. The
number of observations is denoted by N. An enrollment spell starts whenever an individual enrolls (or re-enrolls) in the club and ends whenever the individual
quits or is censored. The sample “First spell” consists of the first enrollment spell. The sample “First spell and no subsidy” restricts the sample “First spell” to
those spells in which the average adjusted monthly fee is at least $70 if the spell starts with a monthly contract and at least $58 if the spell starts with an annual
contract.
For the 6-month periods, the sample includes spells that are ongoing, not frozen, and not miscoded in at least one month in the period. For year 1 in the annual
contract, the sample includes only spells that started at least 14 months before the end of the sample period, and that were not prematurely terminated because
of medical reasons or relocation. For year 2, the sample includes only spells that started with an annual contract at least 26 months before the end of the
sample period, and that lasted at least 25 months. The spells in row “First contract monthly” start with a monthly contract. The spells in row “First contract
annual” start with an annual contract. The “Average price” in period t is the average fee across people enrolled in period t. The “Average attendance” in period t
is the average number of visits across people enrolled in period t. The measure in Column (3) is the ratio of the measure in Column (1) and the measure in
Column (2).
59
Table 7: Average Attendance in Monthly and Annual Contracts (Sorting)+
Average attendance during the n -th month since enrollment
Sample: First spell
Whole
sample
(1)
Male sample
Female sample
Age<=25 Age >25, Age >30, Age >40
Age<=30 Age<=40
(2)
(3)
(4)
(5)
Age<=25 Age >25, Age >30, Age >40
Age<=30 Age<=40
(6)
(7)
(8)
(9)
Month 2
Monthly contract
Annual contract
5.500
5.809
5.769
5.261
5.651
5.974
5.553
4.453
5.442
0.066
N = 6380
(0.2071)
N = 732
(0.1706)
N = 944
(0.1655)
N = 941
(0.2090)
N = 702
(0.1808)
N = 927
(0.1684)
N = 859
(0.1732)
N = 757
(0.2326)
N = 514
5.797
7.277
5.652
5.764
5.644
6.638
5.316
4.825
5.672
0.187
N = 874
(0.6454)
N = 83
(0.4351)
N = 132
(0.4114)
N = 203
(0.4690)
N =163
(0.6703)
N = 69
(0.5595)
N = 79
(0.5081)
N = 80
(0.6405)
N = 64
Month 3
Monthly contract
Annual contract
4.998
5.427
5.074
4.771
5.248
5.539
4.949
4.214
4.655
0.069
N = 5783
(0.2185)
N = 662
(0.1707)
N = 873
(0.1751)
N = 878
(0.2214)
N = 656
(0.1925)
N = 796
(0.1803)
N = 788
(0.1837)
N =673
(0.2368)
N = 452
5.583
6.366
5.813
5.747
5.644
5.613
5.300
4.593
5.111
0.191
N = 858
(0.6920)
N = 82
(0.4949)
N = 128
(0.3896)
N = 198
(0.5001)
N = 163
(0.6138)
N = 62
(0.5914)
N = 80
(0.5638)
N = 81
(0.5525)
N = 63
Month 4
Monthly contract
Annual contract
4.592
4.990
4.907
4.528
4.781
4.904
4.549
3.724
4.254
0.070
N = 5390
(0.2205)
N = 586
(0.1759)
N = 810
(0.1756)
N = 851
(0.2195)
N = 604
(0.2013)
N = 711
(0.1805)
N = 742
(0.1780)
N = 660
(0.2477)
N = 421
5.151
5.813
5.613
4.922
5.727
5.491
4.372
4.012
4.871
0.188
N = 839
(0.6924)
N = 80
(0.4802)
N = 124
(0.3746)
N = 193
(0.4816)
N = 161
(0.7041)
N = 57
(0.5370)
N = 78
(0.5075)
N = 83
(0.6571)
N = 62
Notes: Standard errors in parentheses. The number of observations is denoted by N. An enrollment spell starts whenever an individual enrolls (or re-enrolls) in the
club and ends whenever the individual quits or is censored. The sample “First spell” consists of the first enrollment spell. The spells in row “Monthly Contract” start
with a monthly contract. The spells in row “Annual Contract” start with an annual contract. The sample in month n includes spells that are ongoing, not frozen, and
not miscoded.
60
Table 8: Probit of Renewal Decision I
Dependent variable: Enrollment at 14th active month
Sample: First spell with non-missing controls
Controls:
Dummy for enrollment
with monthly contract
no controls
controls
controls +
time dummies
no controls
controls +
time dummies
no controls
controls +
time dummies
(1)
(2)
(3)
(4)
(5)
(6)
(7)
0.0318
0.0509
0.0514
0.1650
0.1803
0.2858
0.2943
(0.0217)
(0.0217)
(0.0218)
(0.0321)
(0.0317)
(0.0508)
(0.0502)
0.0641
0.0656
0.2643
0.2742
(0.0060)
(0.0061)
(0.0635)
(0.0654)
-0.0322
-0.0339
(0.0163)
(0.0170)
0.0017
0.0018
Average monthly attendance
in the first 13 active months
Attendance
(Attendance)
2
(Attendance)
3
(Attendance)
4
Monthly contract*
(Average monthly attendance
in the first 13 active months)
Monthly*Attendance
Monthly*(Attendance)
3
4
(0.0016)
-0.00003
-0.00003
-0.00004
-0.00005
-0.0292
-0.0291
-0.1429
-0.1363
(0.0063)
(0.0065)
(0.0654)
(0.0673)
0.0176
0.0163
2
(0.0015)
(0.0167)
(0.0174)
-0.0008
-0.0007
(0.0015)
(0.0016)
0.00001
0.00001
-0.00004
-0.0576
(0.0143)
(0.0144)
(0.0148)
(0.0149)
Age
0.0202
0.0204
0.0270
0.0280
(0.0047)
(0.0047)
(0.0050)
(0.0050)
Age square
-0.0002
-0.0002
-0.0003
-0.0003
(0.0001)
(0.0001)
(0.0001)
(0.0001)
Corporate member
0.0911
0.0816
0.1105
0.1089
(0.0143)
(0.0144)
(0.0147)
(0.0149)
Student member
-0.1342
-0.1370
-0.1071
-0.0907
(0.0500)
(0.0498)
(0.0530)
(0.0545)
X
X
X
Month and year of enrollment
Baseline renewal probability
for monthly=0
0.3993
0.4033
-0.0566
N =4905 N =4905
-0.0458
0.4161
Baseline renewal probability
for monthly=0 and attendance=0
Number of observations
-0.0453
-0.00005
Female
N =4905
0.1598
0.1679
0.0497
0.0497
N =4905
N =4905
N =4905
N =4905
Notes: Standard errors in parentheses. The number of observations is denoted by N. Entries in the Table represent the marginal coefficients of the probit in
response to an infinitesimal change in the continuous variables, and a discrete change for the dummy variables. An enrollment spell starts whenever an individual
enrolls (or re-enrolls) in the club and ends whenever the individual quits or is censored. The sample “First spell with non-missing controls” consists of the first
enrollment spell for individuals for whom the demographic controls “age” and “female” are available. The sample is further restricted to individuals who join 14
active months before the end of the sample period. See the text for a definition of Enrollment at the 14th active month. The controls "Month and year of enrollment"
indicate that the probit contains 11 dummies for the month of enrollment and 4 dummies for year of enrollment.
61
Table 9: Probit of Renewal Decision II. Robustness
Sample:
Dependent variable:
Controls:
Enrollment at
14th active month
No
Controls +
Controls
Time
Dummies
(1)
Dummy for enrollment
with monthly contract
Average attendance
in last 4 months
Monthly contract*
(Average attendance
in last 4 months)
Female
(2)
First spell with non-missing controls
Enrollment at the
Enrollment at the
Enrollment at the
15th month
16th month
27th month
No
Controls +
Controls
Time
Dummies
(3)
(4)
No
Controls +
Controls
Time
Dummies
(5)
(6)
No
Controls +
Controls
Time
Dummies
(7)
(8)
Enrollment at the
28th month
No subsidy I
Enrollment at
14th active month
No subsidy II
Enrollment at
14th active month
No
Controls +
Controls
Time
Dummies
No
Controls +
Controls
Time
Dummies
No
Controls +
Controls
Time
Dummies
(9)
(10)
(11)
(12)
(13)
(14)
0.1545 0.1698
0.0543 0.0719
0.0376 0.0582
-0.0009 0.0262
-0.0016 0.0294
0.0527 0.0465
0.0812 0.0925
(0.0287) (0.0286)
(0.0217)
(0.0221)
(0.0261)
(0.0264)
(0.0479)
(0.0370)
(0.0219)
(0.0222)
(0.0252)
(0.0252)
(0.0501)
(0.0378)
0.0728 0.0736
(0.0062) (0.0063)
-0.0384 -0.0379
(0.0065) (0.0066)
-0.0462
-0.0405
-0.0405
-0.0759
-0.0811
-0.0443
(0.0149)
(0.0143)
(0.0144)
(0.0166)
(0.0167)
(0.0398)
(0.0280)
Age
0.0256
0.0145
0.0164
0.0239
0.0265
0.0312
0.0253
(0.0050)
(0.0046)
(0.0047)
(0.0054)
(0.0054)
(0.0115)
(0.0083)
Age square
-0.0003
-0.0001
-0.0002
-0.0002
-0.0003
-0.0004
-0.0003
(0.0001)
(0.0001)
(0.0001)
(0.0001)
(0.0001)
(0.0001)
(0.0001)
Corporate member
0.1004
0.0747
0.0700
0.0713
0.0705
0.2071
0.0043
(0.0149)
(0.0144)
(0.0145)
(0.0168)
(0.0169)
(0.0484)
(0.0319)
Student member
-0.1147
-0.1151
-0.0953
-0.0916
-0.0767
0.1527
-0.1616
(0.0525)
(0.0503)
(0.0516)
(0.0591)
(0.0604)
(0.2722)
(0.0669)
X
X
X
Month and year of enrollment
X
X
X
X
Renewal probability
for monthly=0
0.3983 0.4162 0.3925 0.4077 0.2677 0.2853
Renewal probability for
monthly=0 & attend.=0
0.1823 0.1832
Number of observations N =4905 N =4905 N =4990 N =4990 N =4860 N =4860 N =2874 N =2874
-0.0306
0.2589 0.2730
0.4701 0.5426
0.4366 0.4373
N =2777 N =2777
N =704
N =1362 N =1362
N =704
Notes: Standard errors in parentheses. The number of observations is denoted by N. Entries in the Table represent the marginal coefficients of the probit in response to an infinitesimal change in the continuous variables,
and a discrete change for the dummy variables. An enrollment spell starts whenever an individual enrolls (or re-enrolls) in the club and ends whenever the individual quits or is censored. The sample “First spell with nonmissing controls” consists of the first enrollment spell for individuals for whom the demographic controls “age” and “female” are available. The sample is further restricted to individuals who join 13 active months before
August 2000. See the text for a definition of Enrollment after 13 active months. The controls "Month and year of enrollment" indicate that the probit contains 11 dummies for the month of enrollment and 4 dummies for year
of enrollment.
62
Table 10: Loss from choice of contracts with flat fee
Sample: First spell and no subsidy, First
contract monthly
Join before
Join before
Join before
October 1997 April 1998 October 1998
(1)
(2)
(3)
Loss from choice of
contract with flat fee in $
Total money spent per
spell in $
Percentage of loss over
money spent
Number of observations N
Sample: First spell and no subsidy, First
Contract annual
Join before
October 1997
(4)
Join before
April 1998
(5)
Join before
October 1998
(6)
230.01
698.16
607.35
595.00
-61.65
220.17
(106.05)
(53.33)
(41.40)
(424.22)
(193.95)
(146.08)
1516.88
1309.07
1256.48
1832.34
1562.73
1445.00
(114.96)
(59.73)
(46.15)
(169.77)
(101.25)
(76.47)
47.87%
51.28%
51.83%
6.01%
28.45%
27.18%
(4.78)
(2.93)
(2.60)
(17.62)
(9.66)
(8.63)
N = 70
N = 238
N = 345
N = 15
N = 43
N = 68
Notes: Standard errors in parentheses. The number of observations is denoted by N. An enrollment spell starts whenever an individual enrolls (or reenrolls) in the club and ends whenever the individual quits or is censored. The sample “First spell” consists of the first enrollment spell. The sample
“First spell and no subsidy” further restricts the sample “First spell” to those spells in which the average adjusted monthly fee is at least $70 if the spell
starts with a monthly contract and at least $58 if the spell starts with an annual contract. The spells in Column “First contract monthly” start with a
monthly contract. The spells in Column “First contract annual” start with an annual contract. The measure “Loss from choice of contract with flat fee
in $” is the average saving in $ that a user who chose a contract would have attained if she had purchased a 10-visit pass for $100 and attended the
same number of times. A negative value denotes that the user would have lost money by purchasing the pass.
Table 11: Correlations †
Sample: Last contract Monthly, Join before April 1998
Correlation for n = 1
ρ(price per average attendance with 1 month distance, cancellation gap) =
.2131
ρ(price per average attendance with 2 months distance, cancellation gap) =
.2185
.2110
.2041
(.0000, N = 2186)
(.0000, N = 1873)
(.0000, N = 1586)
(.0000, N = 1358)
Correlation between
cancellation gap and freezing
measure
ρ(freezing measure, cancellation gap) =
-.1042
(.0000, N = 4323)
Notes: Entries are the simple correlation between the variables. In parenthesis the p-value for the hypothesis of zero correlation and the number of
observation over which correlation are calculated. The cancellation gap is measured as log(1 + number of consecutive full months between last
attendance and contract expiration). The price per average attendance is measured as log(1 + [payments to health club / attendance from enrollment
until n months before last attendance]). An enrollment spell starts whenever an individual enrolls (or re-enrolls) in the club and ends whenever the
individual quits or is censored. The sample “Last contract Monthly, Join before April 1998” consists of all spells that start before April 1998, and end
with a monthly contract. The spells cannot be ongoing, and have to have at least two months of paid contract preceding the n months before the last
attendance. See the Text for details on the freezing measure.
†
63
Appendix Table 1: Predictability of aggregate day-to-day attendance
Dependent variable: Log (1 + Daily health club attendance)
Club 1
(1)
Constant
Tuesday dummy
Wednesday dummy
Thursday dummy
Friday dummy
Saturday dummy
Sunday dummy
Log (1+no. of new monthly memberships)
Log (1+no. of ongoing monthly memberships)
Log (1+no. of new annual memberships)
Log (1+no. of ongoing annual memberships)
Clubs 2 and 3
(2)
-0.4433
0.3942
(0.9203)
(0.3233)
0.0552
0.0261
(0.0354)
(0.0400)
-0.0177
-0.019
(0.0355)
(0.0402)
-0.116
-0.1572
(0.0357)
(0.0403)
-0.3395
-0.319
(0.0357)
(0.0402)
-0.8298
-1.4736
(0.0356)
(0.0401)
-1.0933
-2.0501
(0.0355)
(0.0401)
-0.0203
0.1826
(0.0660)
(0.0468)
0.8902
0.3664
(0.2341)
(0.0389)
0.0850
0.0600
(0.0479)
(0.0396)
0.0117
0.2550
(0.1368)
(0.0297)
11 Month dummies
X
X
3 Year dummies
X
X
Dummy for 2001
X
15 Holiday dummies
X
Observations
R-squared
N = 1181
0.8991
N = 1445
0.9287
Notes: Standard errors in parentheses. The sample includes all the days between June 1, 1997 and August 24, 2001 for club 1 and all the days between
April 1, 1997 and March 15, 2001 for clubs 2 and 3. The dependent variable is the log of 1 + the total number of attendances in a given day. The 4 controls for
the number of people enrolled are the log of 1 + the number of people enrolled in a given contract in that month. The set of 15 Holiday dummies includes a
separate dummy for each of the federal holidays, plus dummies for the Christmas week, the Thanksgiving week, and after NewYear.
64
+
Appendix Table 2: HMO reimbursement of health club expenses
Monthly contract
Annual contract
Pay-per-visit
Applicable clubs
(1)
20% reduction
(2)
20% reduction
(3)
6$ copayment
(4)
Selected clubs
Neighborhood Health
Plan
No Plan
No Plan
No Plan
One Health Plan of
Massachusetts
No Plan
No Plan
No Plan
Aetna U.S. Healthcare
25-60% reduction
No Plan
No Plan
Gyms in Globalfit Network
CIGNA HealthCare of
Massachusetts
No Plan
10% reduction
No Plan
Planet Fitness, Metropolitan,
Gold’s, Mike’s Gym
Harvard University
Health Services
$25
reimbursement
$25
reimbursement
No Plan
All clubs
MIT Health Plans
Up to $150
reimbursement
Up to $150
reimbursement
Up to $150
reimbursement
All clubs
Blue Cross Blue Shield
Up to $150
reimbursement
Up to $150
reimbursement
Up to $150
reimbursement
All clubs
Discount on
initiation fee
Discount on
initiation fee
Tufts Health Plan
Fallon Community
Health Plan
Harvard Pilgrim
Health Care
Typically, 50% off Typically, 50% off
initiation fee
initiation fee
Selected clubs
Health New England
No plan
No plan
No plan
Kaiser Foundation
No plan
No plan
No plan
Notes: Fitness programs for health clubs located in the state home to the three clubs in the sample. Information from HMOs websites and telephone calls by the
authors. The discount on MIT Health Plans only active since September 1999; previously it was only a $20 discount. The health clubs in our sample are not part of
the Globalfit Network.
Appendix Table 3: Price per average attendance in subsamples+
Average price
per month
(1)
Average attendance Average price per
per month
average attendance
(2)
(3)
Subsample 1: First spell and no subsidy, No locker use, Users initially enrolled with a monthly contract
Months 1 to 6
83.03
4.87
17.05
(0.42)
N = 835
(0.15)
N = 835
(0.53)
N = 835
Subsample 2: First spell, Tufts members, Users initially enrolled with a monthly contract
Months 1 to 6
53.08
4.98
10.65
(0.36)
N = 1342
(0.12)
N = 1342
(0.25)
N = 1342
Notes: Standard errors in parentheses. Subsample 1 includes users in the sample "First Spell and no Subsidy" who
enroll with a monthly contract and never rent an overnight locker. Subsample 2 includes users in the sample "First Spell"
who enroll with a monthly contract as a member of the Tufts HMO. The price shown is net of the NMO reduction. The
relevant price per visit for Tufts members if $6.
65

Self Control in the Market - National Bureau of Economic Research

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