Dynamic relationships among winning in various sports and donations to collegiate athletic departments

Figures & data

Table 1. Panel regressions – Power 5 Conferences, Pacific-12 Conference is the base conference¹

Variable	Donations		Football		Basketball		Other sports
	Coeff.	p-value	Coeff.	p-value	Coeff.	p-value	Coeff.	p-value
FBS Bowl	2.910	0.104	0.095	0.000	−0.0262	0.175	−0.001	0.921
FBS Bowl Win	−1.442	0.389	0.025	0.304	0.0060	0.745	−0.004	0.602
NCAA BB	−1.107	0.473	0.010	0.659	−0.0802	0.000	0.005	0.424
Student	0.005	0.974	−0.002	0.263	0.0014	0.202	0.001	0.151
Right licensing	−0.065	0.718	−0.009	0.001	0.0003	0.863	−0.001	0.379
Salary	0.535	0.013	0.014	0.000	0.0019	0.358	0.002	0.077
GDPdiff	−0.210	0.912	0.035	0.222	0.0248	0.242	0.004	0.582
Distance	2.351	0.269	0.010	0.628	0.0032	0.841	−0.036	0.007
ACC	−1.328	0.783	0.005	0.914	0.0342	0.342	0.045	0.129
Big 10	0.353	0.943	0.090	0.088	−0.0073	0.850	0.000	0.987
Big 12	4.945	0.279	0.074	0.123	0.0176	0.618	0.040	0.131
SEC	4.610	0.311	0.092	0.054	0.0032	0.927	0.039	0.158
Tier 2	3.096	0.483	0.043	0.336	−0.0184	0.572	0.026	0.346
Tier 3	4.616	0.248	0.023	0.575	−0.0036	0.903	0.056	0.024
Constant	−0.697	0.928	0.316	0.000	0.4694	0.000	0.486	0.000
Sigma u	7.652		0.055		0.038		0.050
Sigma e	11.526		0.164		0.120		0.047
Rho^2	0.306		0.101		0.092		0.535
R-Squared
Within		0.04	0.02		0.01		0.01
Between		0.37	0.60		0.57		0.40
Overall		0.19	0.24		0.19		0.30
Wald		30.12	62.35		41.73		32.37
Prob. > χ^2		0.007	0.00		0.00		0.00
Number of observations		322
Number of groups		46
Largest variance inflation factor^3			3.72

¹ Other conferences are Atlantic Coast Conference (ACC), Big 10, Big 12, Southeastern Conference (SEC), and Pacific-12 Conference.

² Fraction of variance attributed to u_ij.

³ Based on ordinary least squares estimation.

Table 2. p-values of differences in contributions between Power 5 Conferences using Pairwise F-tests, Pacific-12 Conference is the base conference

	ACC	Big 10	Big 12	SEC
ACC	–
Big 10	0.75	–
Big 12	0.14	0.30	–
SEC	0.18	0.35	0.93	–

Table 3. Panel regressions – Non-Power 5 Conferences, Western Athletic Conference is the base conference¹

Variable	Donations		Football		Basketball		Other sports
	Coeff.	p-value	Coeff.	p-value	Coeff.	p-value	Coeff.	p-value
FBS Bowl	0.045	0.845	0.107	0.000	0.017	0.405	−0.003	0.716
FBS Bowl Win	−0.048	0.854	0.001	0.975	−0.008	0.741	0.009	0.378
NCAA BB	0.453	0.068	−0.039	0.177	0.051	0.018	−0.001	0.911
Student	−0.082	0.002	0.001	0.609	−0.002	0.222	0.000	0.574
Right licensing	−0.152	0.038	0.001	0.893	0.013	0.021	0.001	0.828
Salary	0.472	0.000	0.001	0.875	−0.003	0.529	0.001	0.517
GDPdiff	0.369	0.102	0.005	0.869	−0.019	0.357	0.002	0.789
Distance	−0.440	0.457	0.032	0.308	−0.074	0.010	0.009	0.634
Big East	5.234	0.000	0.074	0.317	−0.006	0.918	0.026	0.460
CUSA	0.853	0.348	−0.035	0.482	0.082	0.066	0.005	0.852
MAC	−1.374	0.073	−0.039	0.352	0.000	0.995	−0.012	0.611
MWC	0.858	0.294	−0.061	0.244	0.035	0.445	0.022	0.417
Sun Belt	−0.394	0.630	−0.075	0.101	−0.012	0.773	0.017	0.513
Tier 2	0.587	0.397	0.030	0.407	−0.022	0.511	0.021	0.321
Tier 3	−1.519	0.094	0.079	0.110	−0.090	0.042	0.032	0.256
Constant	1.601	0.074	0.384	0.000	0.563	0.000	0.457	0.000
Sigma u	1.570		0.053		0.061		0.047
Sigma e	1.378		0.168		0.121		0.055
Rho^2	0.565		0.091		0.201		0.426
R-Squared
Within		0.23	0.01		0.01		0.00
Between		0.76	0.55		0.42		0.23
Overall		0.69	0.23		0.24		0.14
Wald		252.95	63.67		51.51		14.83
Prob. > χ^2		0.00	0.00		0.00		0.46
Number of observations		346
Number of groups		50
Largest variance inflation factor^3			3.95

¹ Other conferences are Big East, Conference USA (C-USA), Mid-American Conference (MAC), Mountain West Conference (MWC), Sun Belt Conference, and Western Athletic Conference (WAC).

² Fraction of variance attributed to u_ij.

³ Based on ordinary least squares estimation.

Table 4. p-values of differences in contributions between Non-power 5 Conferences using Pairwise F-tests, Western Athletic Conference is the base conference

	Big East	CUSA	MAC	MWC	Sun Belt
Big East	–
CUSA	0.00	–
MAC	0.00	0.01	–
MWC	0.00	0.97	0.01	–
Sun Belt	0.00	0.18	0.21	0.17	–

Table 5. Panel regressions – FCS Conferences, Southland Conference is the base conference¹

Variable	Donations		Football		Basketball		Other sports
	Coeff.	p-value	Coeff.	p-value	Coeff.	p-value	Coeff.	p-value
FCS Playoffs	0.059	0.447	0.079	0.003	0.039	0.067	−0.012	0.281
NCAA BB	0.051	0.591	−0.001	0.979	0.036	0.193	0.033	0.015
Student	0.004	0.828	0.006	0.067	−0.001	0.609	0.003	0.057
Right licensing	−0.001	0.866	0.001	0.635	0.000	0.934	−0.001	0.534
Salary	0.083	0.018	0.002	0.828	0.007	0.455	0.006	0.231
GDPdiff	0.039	0.565	−0.033	0.169	−0.008	0.682	−0.015	0.108
Distance	0.280	0.083	0.055	0.013	0.026	0.147	0.018	0.116
MVFC	0.504	0.173	−0.069	0.229	0.057	0.222	−0.009	0.755
Great West	0.431	0.260	−0.013	0.831	−0.036	0.468	−0.036	0.245
Big South/NEC	0.660	0.061	−0.006	0.926	0.048	0.359	−0.013	0.679
Big Sky	−0.001	0.998	−0.111	0.053	0.018	0.695	−0.054	0.069
MEAC/SWAC	−0.418	0.175	−0.092	0.124	−0.012	0.801	−0.094	0.001
OVC/PFL	−0.350	0.350	−0.069	0.199	0.018	0.673	−0.022	0.431
CAA/ATL 10	0.202	0.635	−0.013	0.853	−0.038	0.488	−0.012	0.731
SOCON	−0.157	0.741	−0.063	0.339	−0.013	0.804	−0.013	0.697
Tier 2	0.670	0.174	−0.045	0.502	−0.097	0.069	0.011	0.760
Tier 3	0.084	0.804	0.049	0.284	0.003	0.932	0.001	0.981
Constant	0.251	0.476	0.382	0.000	0.429	0.000	0.414	0.000
Sigma u	0.834		0.087		0.072		0.053
Sigma e	0.471		0.167		0.139		0.068
Rho^2	0.758		0.212		0.211		0.376
R-Squared
Within		0.03	0.01		0.01		0.04
Between		0.35	0.37		0.24		0.38
Overall		0.30	0.18		0.10		0.22
Wald		39.74	40.22		23.24		47.32
Prob. > χ^2		0.00	0.00		0.14		0.00
Number of observations		443
Number of groups		64
Largest variance inflation factor^3			8.29

¹ Other conferences are Missouri Valley Football Conference (MVFC), Great West, Big South and Northeast Conference Football (Big South/NEC), Big Sky, Mid-Eastern Athletic Conference and Southwestern Athletic Conference (MEAC/SWAC), Ohio Valley Conference and Pioneer Football League (OVC/PFL), Colonial Athletic Association and Atlantic 10 (CAA/ATL 10), Southern Conference (SOCON), and Southland Conference is the Base Conference (SOCON).

² Fraction of variance attributed to u_ij.

³ Based on ordinary least squares estimation.

Table 6. p-values of differences in contributions between FCS Conferences using Pairwise F-tests, Southland Conference is the base conference

	MVFC	Great West	Big South/NEC	Big Sky	MEAC/SWAC	OVC/PFL	CAA/ATL 10	SOCON
MVFC	–
Great West	0.76	–
Big South/NEC	0.71	0.60	–
Big Sky	0.22	0.31	0.15	–
MEAC/SWAC	0.03	0.05	0.01	0.37	–
OVC/PFL	0.04	0.06	0.02	0.44	0.87	–
CAA/ATL 10	0.48	0.61	0.33	0.66	0.18	0.23	–
SOCON	0.16	0.23	0.11	0.76	0.30	0.14	0.48	–

Figure 1. Responses of donations to a one time shock in the endogenous variables (listed beneath the graphs) along with 95% confidence interval.

Figure 2. Responses of winning percentages (listing in each column row) to a one time shock in the endogenous variables (listed beneath the graphs) for Power 5 Conferences along with 95% confidence interval.

Figure 3. Responses of winning percentages (listing in each column row) to a one time shock in the endogenous variables (listed beneath the graphs) for Non-power 5 Conferences along with 95% confidence interval.

Figure 4. Responses of winning percentages (listing in each column row) to a one time shock in the endogenous variables (listed beneath the graphs) for FCS Conferences along with 95% confidence interval.

Table 7. Forecasts error variance decompositions for the Power 5 Conferences from the PVAR assuming a Cholesky decomposition order of basketball, football, other sports programs, and donations

Year ahead	Donations	Football	Basketball	Other sports programs
Donations
0	0.346	0.523	0.126	0.006
1	0.224	0.335	0.081	0.361
2	0.227	0.321	0.078	0.373
3	0.224	0.311	0.075	0.390
Football
0	0.000	0.994	0.006	0.000
1	0.098	0.703	0.006	0.192
2	0.097	0.699	0.008	0.196
3	0.097	0.695	0.008	0.200
Basketball
0	0.000	0.000	1.000	0.000
1	0.008	0.016	0.859	0.117
2	0.023	0.017	0.845	0.115
3	0.024	0.017	0.839	0.120
Other sports
0	0.000	0.116	0.004	0.880
1	0.006	0.154	0.005	0.835
2	0.016	0.163	0.008	0.813
3	0.023	0.166	0.009	0.802

Notes: Forecast Error Variance Decompositions are partitions based on observed innovations from the estimated error correction model (see Doan, 2000 for a generic description of their derivation). The entries sum to one (within rounding error) for any particular row. The interpretation of each row is as follows: looking ahead at the horizon given in the far left-hand column (0, 1, 2, and 3 years ahead), the uncertainty in the variable given in the centered sub-category (e.g. Basketball) is attributable to variation in each series labeled as the column heading in the proportions given in each cell entry.

Table 8. Forecasts error variance decompositions for the Non-power 5 Conferences from the PVAR assuming a Cholesky decomposition order of basketball, football, other sports programs, and donations

Year ahead	Donations	Football	Basketball	Other sports programs
Donations
0	0.354	0.166	0.431	0.049
1	0.224	0.189	0.569	0.018
2	0.154	0.212	0.594	0.039
3	0.130	0.222	0.594	0.054
Football
0	0.000	0.442	0.558	0.000
1	0.108	0.267	0.565	0.060
2	0.117	0.233	0.587	0.063
3	0.120	0.227	0.590	0.063
Basketball
0	0.000	0.000	1.000	0.000
1	0.109	0.145	0.716	0.030
2	0.125	0.209	0.616	0.050
3	0.123	0.222	0.596	0.058
Other sports
0	0.000	0.187	0.569	0.244
1	0.064	0.230	0.567	0.138
2	0.100	0.232	0.582	0.086
3	0.114	0.228	0.588	0.069

Note: See Table 7 for forecast error variance decompositions discussion.

Table 9. Forecasts error variance decompositions for the FCS Conferences from the PVAR assuming a Cholesky decomposition order of basketball, football, other sports programs, and donations

Year ahead	Donations	Football	Basketball	Other sports programs
Donations
0	0.241	0.061	0.671	0.027
1	0.423	0.031	0.459	0.087
2	0.418	0.038	0.338	0.206
3	0.360	0.053	0.276	0.311
Football
0	0.000	0.607	0.393	0.000
1	0.004	0.554	0.297	0.145
2	0.082	0.482	0.265	0.171
3	0.208	0.406	0.242	0.144
Basketball
0	0.000	0.000	1.000	0.000
1	0.051	0.011	0.773	0.166
2	0.046	0.030	0.616	0.308
3	0.050	0.043	0.532	0.375
Other sports
0	0.000	0.042	0.178	0.780
1	0.017	0.034	0.153	0.797
2	0.083	0.039	0.120	0.758
3	0.200	0.036	0.104	0.660

Note: See Table 7 for forecast error variance decompositions discussion.

Table

Abbreviation	Conference
ACC	Atlantic Coast Conference
Atlantic 10	Atlantic 10 Conference
Big 10	Big Ten Conference
Big 12	Big Twelve Conference
Big East	Big East Conference
Big Sky	Big Sky Conference
Big South	Big South Conference
CAA	Colonial Athletic Association
CUSA	Conference USA
Great West	Great West Conference
MAC	Mid-American Conference
MEAC	Mid-Eastern Athletic Conference
MVFC	Missouri Valley Football Conference
MWC	Mountain West Conference
NEC	Northeast Conference
OVC	Ohio Valley Conference
Pac 12	Pac 10/12 Athletic Conference
PFL	Pioneer Football League
SEC	Southeastern Conference
SOCON	Southern Conference
Sun Belt	Sun Belt Conference
SWAC	Southwestern Athletic Conference
WAC	Western Athletic Conference
WAC	Western Athletic Conference

Table

Power 5 conferences				Non-power 5 conferences
Conference	University	Conference	University	Conference	University	Conference	University
ACC	Clemson	Pac 12	Colorado	Big East	Connecticut	MWC	Boise State
	Florida State		Arizona		Rutgers		Colorado State
	Georgia Tech		Arizona State		West Virginia		Nevada-Las Vegas
	Maryland		California		Cincinnati		New Mexico
	North Carolina		Oregon		Louisville		San Diego State
	North Carolina State		Oregon State		South Florida		Utah
	Virginia		UCLA	CUSA	Cincinnati		Wyoming
	Virginia Tech		Utah		Louisville	Sun Belt	Arkansas State
Big 10	Illinois		Washington		South Florida		Florida Atlantic
	Indiana		Washington State		UAB		Florida International
	Iowa	SEC	Alabama		East Carolina		Louisiana-Lafayette
	Michigan		Arkansas		Houston		Louisiana-Monroe
	Michigan State		Auburn		Memphis		Middle Tennessee State
	Minnesota		Florida		Southern Mississippi		North Texas
	Ohio State		Georgia		Central Florida		Troy
	Purdue		Kentucky		Marshall		Western Kentucky
	Wisconsin		LSU		Texas-El Paso UTEP		Idaho
	Nebraska		Mississippi	MAC	Akron		Utah State
Big 12	Colorado		South Carolina		Ball State		New Mexico State
	Nebraska		Tennessee		Bowling Green	WAC	Texas-El Paso UTEP
	Iowa State				Buffalo		Idaho
	Kansas				Central Michigan		Utah State
	Kansas State				Eastern Michigan		New Mexico State
	Missouri				Kent State		Fresno State
	Oklahoma				Miami Ohio		Hawaii
	Oklahoma State				Northern Illinois		Louisiana Tech
	Texas				Ohio		Nevada
	Texas A&M				Toledo		San Jose State
	Texas Tech				Central Florida
					Marshall

Table

FCS Conferences
Conference	University	Conference	University	Conference	University
Atlantic 10	Massachusetts	MVFC	Delaware State	SWAC	Arkansas Pine Bluff
	New Hampshire		Norfolk State		Mississippi Valley State
	Rhode Island		North Carolina Tech		Texas Southern
	Towson		North Carolina Central
	William & Mary		Illinois State
Big Sky	Eastern Washington		Indiana State
	Idaho State		Missouri State
	Montana		Northern Iowa
	Northern Arizona		Southern Illinois
	Portland State	NEC	Stony Brook
	Sacramento State		Albany (NY)
	Weber State		Central Conn State
	Northern Colorado	OVC	Eastern Illinois
Big South	Coastal Carolina		Eastern Kentucky
	VMI		Murray State
	Stony Brook		Southeast Missouri St
CAA	Massachusetts		Tennessee Martin
	New Hampshire		Tennessee State
	Rhode Island		Tennessee Tech
	Towson		Austin Peay
	William & Mary		Morehead State
	Delaware	PFL	Austin Peay
	James Madison		Morehead State
	Maine	SOCON	Appalachian State
Great West	California Polytechnic		Citadel
	California-Davis		Georgia Southern
	South Dakota State		Tennessee-Chattanooga
	North Dakota State		Western Carolina
	Southern Utah	Southland	Central Arkansas
	North Dakota		McNeese State
	South Dakota		Nicholls State
MEAC	Delaware State		Sam Houston State
	Norfolk State		Southeastern Louisiana
	North Carolina Tech		Stephen F. Austin State
	North Carolina Central		Texas State

Doan, T. (2000). RATS: User’s guide version 5. Evanston, IL: Estima.

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