Duration Dependence of Donation Behavior:
Explaining Heterogeneity in Donation Incidence and
Amount through Community Characteristics
Shameek Sinha – IE Business School, IE University
Vijay Mahajan and Frenkel ter Hofstede –
McCombs School of Business, University of Texas at Austin
1
Non-Profit Charities (NPC):
Why do we Marketers even Care?
• Total charitable giving of $290.89 billion which is around 2%
of GDP **
• 73% of total fundraising are individual donors **
• 3.8% growth in charitable giving and 2.7% growth in individual
contributions **
• 1,280,739 NPCs out of which 65% raise more than $10 million
or more *
• Significant majority of NPCs (89%) use direct response
methods for solicitation and 45% of those increased their direct
mail fundraising *
• However, 41% of NPC’s fail to meet their fundraising goals *
* Source: Guidestar Survey for Direct mail Nonprofit Fundraising (2012)
** Source: Giving USA (2011)
2
Background on Empirical Context and Data
• Non-profit organization uses direct mail to solicit contributions
from past donors (Source: DMEF).
• Contributions and solicitations in Texas: Weekly data for
13767 donors.
• Time span covering a period of approximately 15 years
(unbalanced – average ~ 521 weeks).
• Contributions and solicitations by date, amount on each
incidence and costs of each solicitation.
• History of solicitations and contributions – censored data.
• Community characteristics: (Sources: uselectionatlas.org, FBI Crime
Statistics, ARDA, TEA)
– ZIPCODE-level
– Counties-level
3
Donor Heterogeneity: How Communities Differ?
El Paso - 79912
Houston - 77024
Mission - 78572
4
78572 : 79912 : 77024 – A Visual Comparison
Mission - 78572
Houston - 77024
El Paso - 79912
5
78572 : 79912 : 77024 – A Numerical Comparison
Variables
Texas
Mission
(78572)
El Paso
(79912)
Houston
(77024)
No. of Appeals
19.89
17.5
19.72
22.34
No. of Gifts
3.64
3.86
3.46
3.24
Duration from Appeal to Gift
(in weeks)
4.01
3.87
3.76
4.16
Duration from Gift to Gift
(in weeks)
43.96
34.99
45.42
61.16
Gift Amount per incidence
(in dollars)
33.42
21.17
27.82
57.02
6
Community Characteristics: What Matters?
• ZIPCODE-level:
– Socio-Demographics: race; household-size; household-type; age;
education level; income level; wealth-rating; home-value; homeownership.
– Credit-Financials: age of tradelines; balance of tradelines;
tradelines with satisfactory ratings; tradelines with derogatory
ratings; no. of tradelines delinquent.
• County-level:
- Political Beliefs: % of republican votes.
- Religious Beliefs: % of Mainline Christians; % of Evangelical
Christians; % of Catholic Christians; % of Other Christians.
- Community Security: % of violent crimes.
- Educational Quality: no. of public schools; school rating.
7
Targeting Potential Donors Using Donor Profiles
within Communities
Amount of contributions
Inter-contribution
duration
Low
(≤ 20 weeks)
Mean = 10.97
Medium
(21-50 weeks)
Mean = 34.35
High
(≥ 51 weeks)
Mean = 89.80
Low
Medium
High
(≤ $15)
Mean = $9.80
($16-$30)
Mean = $24.02
(≥ $31)
Mean = $77.43
Segment 1
(N = 5465)
Segment 2
(N = 4945)
Segment 3
(N = 3283)
Segment 4
(N = 3640)
Segment 5
(N = 4133)
Segment 6
(N = 3154)
Segment 7
(N = 3435)
Segment 8
(N = 4637)
Segment 9
(N = 4075)
8
Communities – Why they matter? (ZIPCODE-level)
Variables
Texas
Mission
(78572)
El Paso
(79912)
Houston
(77024)
Race (% of whites)
78.59
39
63
90
Household Size
2.75
3.4
2.7
2.3
Household Type (% of families)
72.53
84
71
65
Age
43.68
52
42
50
Education Level (in years)
13.84
11.7
14.4
16.5
Income Level (in ‘000 dollars)
64.75
31.5
62.3
143.4
Wealth Rating
6.56
2
7
9
Home Value (in ‘000 dollars)
98.04
45.3
97.4
311.5
Home Ownership (in %)
64.65
76
59
66
Age of Tradelines (in months)
74.10
56
68
102
Balance of Tradelines (in dollars)
5122.96
1676
5360
8903
Tradelines – Satisfactory Ratings
11.24
7.4
12.1
13
Tradelines – Derogatory Ratings
0.89
0.97
0.98
0.69
No. of Delinquent Tradelines
1.24
1.24
1.32
0.92
9
Communities – Why they matter? (County-level)
Variables
Texas
Mission
(78572)
El Paso
(79912)
Houston
(77024)
No. of Violent Crimes
4.23
2.17
0.38
2.36
% of Republican Votes
60.32
44.93
43.50
55.14
Mainstream Christians (per ‘000)
84.10
28.18
25.63
81.86
Evangelical Christians (per ‘000)
234.06
73.40
75.28
204.81
Catholic Christians (per ‘000)
198.54
390.10
514.80
181.92
Other Christians (per ‘000)
142.62
69.35
104.96
179.42
No. of Public Schools
475.63
318
264
1083
School Rating (SAT Scores +
Dropout Rates)
2.71
2.47
2
2.75
10
Literature: Donor Characteristics Influencing
Donation Behavior?
• Demographics (Lee and Chang, 2007)
e.g. age, gender, education, race, income, marital status, religion, family
size etc.
• Psychographics (Bussell and Forbes, 2002)
e.g. self-esteem, empathy, guilt, social-justice, familiarity with causes,
awareness, responsibility, generosity etc.
• Past experience with charities ( Schlegelmilch, Love and
Diamantopoulos, 1996)
e.g. previous experience, no. of times approached etc.
• Community Effects (Corcoran et al., 1990; Schultz, 1984; Datcher,
1982, DeMarzo et al., 2005)
e.g. demographic composition, financial composition etc.
11
Duration Dependence of Contribution and
Solicitation Behavior
Duration between two contributions
(Budgetary Implications)
Contribution1
Solicitation1
Solicitation2
Contribution2
Solicitation3
Solicitation4
Solicitation5
Duration between solicitation and contribution
(Wait/ Gather Information)
12
Donation Response Framework
Periods 1,2,…, (t-1)
Period t
Seasonality
Solicitation/
No Solicitation
for Cause
Decision to
Contribute
for Cause
 Donation Response:
Interval-Censored
Proportional Hazard
With Complimentary
Log-log Link
Amount of
Contribution
for Cause
 Donation amount:
Censored log-Normal
Distribution
Durations
Contribution/
No Contribution
for Cause
Modeling Incidence
and Amount
ZIPCODE and County
-Level Community
Characteristics
 Donor heterogeneity
- Hierarchical
Specification
13
Relevant Literature
Customer Response Models, Direct Marketing and
Customer Management
Schmmitlein and Peterson (1994, Mkt. Sc.)
Basu, Basu and Batra (1995, JMR)
Rossi, McCulloch and Allenby (1996, Mkt. Sc.)
Allenby, Leone and Jen (1999, JASA)
Manchanda, Ansari and Gupta (1999, Mkt. Sc.)
Fader, Hardie and Lee (2005, Mkt. Sc.)
Reinartz, Thomas and Kumar (2005, JM)
Rust and Verhoef (2005, Mkt. Sc.)
Gonul and Ter-Hofstede (2006, Mkt. Sc.)
Neslin, Novak, Baker and Hoffman (2009, Mgmt. Sc.)
Diepen, Donkers and Francses (2009, JMR)
14
Donation Incidence Model
• Donors: i = 1, 2… n
• Time Periods: t = 1, 2… T
• Model: P(Yit ,Zit )  P(Yit )P( Zit |Yit )
where Yit  1 if donor i makes a contribution in period t
= 0 otherwise.
and Zit : contribution amount of a donor i at time t.
• Likelihood of contribution incidence for donor i –
 h(ti , X it )  it 1  h(ti , X it )  it
Y
Y
• Proportional hazard function for donor i :
P(ti  Ti  ti  t | Ti  ti )
h(ti , X it )  lim
 h0 (ti ) exp( i / X it )
t 0
t
15
Donation Incidence Model
 ti

/
• Survival Function: S (ti , X it )  exp    h0 (ui ) exp( i X it )dui 
 0

 exp[ exp( i / X it ) H (ti )]
• Discrete analog of hazard specification:
S / (ti , X it )d (ti ) S (ti  1, X it )  S (ti , X it )
h(ti , X it )  P(Ti  ti | Ti  ti  1) 

S (ti , X it )
S (ti  1, X it )
S (ti , X it )
 1
 1  exp   exp( i / X it )  H (ti  1)  H (ti )  
S (ti  1, X it )
/
log

log(1

h
(
t
,
X
))




• Re-arranging:
i
it
i X it  log( H (ti )  H (ti  1))
• Baseline Hazard:
 ti

log   log(1  h0 (ti ))  log( H (ti )  H (ti  1))  log   h0 (ui )dui    it
ti 1

/
h
(
t
,
X
)

1

exp[

exp(

X   )]
• Hazard function:
16
Donation Incidence Model
 i   iy0   iy1ditc   iy2 log(ditc )
i/ X it   i1y dits   iy2 log(dits )   iy sit
with d c : Duration from last contribution at time t
it
d : Duration from last solicitation at time t
sit : Seasonality dummy (months November – January)
s
it
   0y 

 y 

 y
  1 

  i1 
 y 

 y


i
2
2
y
y

 ~ N 
   w , 
i
y
y
  

 
i1
1





y
y
 2 

 i2 
  y 

 y 
i 
 

Heterogeneity specification –   iy0 
where wi : demographic and financial variables
 y : vector of parameters for the donor level covariates
 y : variance-covariance matrix
17
Donation Amount Model
• Censored Log-Normal distribution of contribution amount –
log N( it , z2 ) if Yit  1 
[ Z it |Yit , it , ] : 

I(
Z

0
)
otherwise


it
2
z
• Specification for mean –
it   iz0   iz1ditc   iz2 log(ditc )   iz1dits   iz2 log(dits )   iz sit
• Heterogeneity specification
   0z 

  iz0 
 z 

 z 


 1 

 i1 
 z 

–  z 

i
2

 ~ N   2   z w , z 
i
  z 

 z 
i1
1





z
z
 2 

 i2 
  z 

 z 



 i 


 z : vector of parameters for the donor level covariates
 z : variance-covariance matrix
18
Bayesian MCMC Estimation
• Priors on donor-specific parameters –
[ iy0 ,  iy1 ,  iy2 ,  i1y ,  iy2 ,  iy ]/ ~ N ([( 0y , 1y ,  2y , 1 y ,  2y ,  y ,  y )]/ ,  y )
[ iz0 ,  iz1 ,  iz2 ,  iz1 ,  iz2 ,  iz ]/ ~ N ([( 0z , 1z ,  2z , 1z ,  2z ,  z ,  z )]/ ,  z )
• Priors on population-level parameters –
( 0y , 1y ,  2y , 1y ,  2y ,  y ,  y ) / ~ N (( 00y ,  01y ,  02y ,  01y ,  02y ,  0y , 0 y ) / , 0 );
 y ~ Wishart (0y , 0y )
( 0z , 1z ,  2z , 1z ,  2z ,  z ,  z ) / ~ N (( 00z ,  01z ,  02z ,  01z ,  02z ,  0z , 0 z ) / , 0 );
•

 z ~ Wishart (0z , 0z )
y
i0
,  iy1 ,  iy2 ,  i1y ,  iy2 ,  iy  : Non-conjugate Incidence Model
Random-walk Metropolis Hastings
•  iz0 ,  iz1 ,  iz2 ,  iz1 ,  iz2 ,  iz : Conjugate Amount Model
Gibbs Sampler
• 45000 draws; 22500 burn-in samples; thinning parameter:15
19
Donation Incidence and Amount Model Results
Incidence
Amount
Intercept
-5.655*
3.0185*
Duration – Gift to Gift
0.055*
0.0004
Log (Duration – Gift to Gift)
-0.757*
0.0080*
Duration – Appeal to Gift
-1.549*
0.0055*
Log (Duration – Appeal to Gift)
6.890*
-0.0140
Seasonality Effect
5.678*
20
Duration Dependence of Donation Incidence
21
Duration Dependence of Donation Amount
22
Community Effects on Donation Incidence
Community Characteristics
(ZIPCODE-level)
Intercept
(Duration
- Gift to
Gift)
Log(Dur.
Gift to
Gift)
(DurationAppeal to
Gift)
Intercept
-5.6548023
0.0545959 -0.7573065
-1.5492686
6.8902848
5.6785942
Race (% of whites)
0.0040277
0.0000735 -0.0000648
-0.0010115
0.0017850
-0.0040177
Household Size
-0.0285814
0.0004487 -0.0151614
-0.0197261
0.0614435
0.0127006
Household Type (% of families)
0.0040426
0.0000173 -0.0000458
0.0012528
-0.0077002
-0.0023192
Age
0.0012143
0.0002699
0.0000053
-0.0113843
0.0317153
0.0015703
Education Level (in years)
-0.0176359
0.0003271
0.0109337
-0.0242744
0.1353052
0.0696306
Income Level (in ‘000 dollars)
-0.0018932
0.0001048 -0.0040509
0.0028751
-0.0106646
-0.0036782
Wealth Rating
-0.0578916
-0.0007786
0.0131131
-0.0091663
0.0816178
0.1028209
Home Value (in ‘000 dollars)
0.0002859
0.0000403 -0.0007553
0.0001005
-0.0007951
-0.0007979
Home Ownership (in %)
0.0003312
-0.0000568
0.0012439
0.0011314
-0.0012518
-0.0008817
Age of Tradelines (in months)
-0.0059405
-0.0001890
0.0009466
0.0013966
-0.0024169
0.0060231
Balance of Tradelines (in dollars)
0.0000088
-0.0000012
0.0000218
-0.0000066
0.0000261
0.0000005
Tradelines – Satisfactory Ratings
-0.0022249
0.0000763 -0.0003999
-0.0195011
0.0461571
-0.0021922
Tradelines – Derogatory Ratings
-0.4444138
0.0276862 -0.4243750
-0.2173995
1.1924347
0.5032717
No. of Delinquent Tradelines
0.7691765
0.2657168
-1.3134540
-0.8715912
-0.0221876
0.4268442
Log(Dur.
Appeal to
Gift)
Seasonal
Effect
23
Community Effects on Donation Incidence
Community Characteristics
(County-level)
Intercept
(Duration–
Gift to
Gift)
Log(Dur.
Gift to
Gift)
(Duration
- Appeal
to Gift)
Log(Dur.
Appeal to
Gift)
Seasonal
Effect
No. of Violent Crimes
0.0009001
0.0001300
-0.0020267
0.0007786
-0.0046003
-0.0040102
% of Republican Votes
0.0004652
-0.0002205
0.0035310
-0.0008852
0.0035071
0.0041955
Mainstream Christians (per ‘000)
-0.0006112
0.0000133
-0.0003035
0.0008095
-0.0017561
0.0002322
Evangelical Christians (per ‘000)
0.0000297
0.0000052
-0.0001057
-0.0001046
-0.0001125
-0.0005236
Catholic Christians (per ‘000)
-0.0001643
-0.0000132
0.0002097
-0.0000126
0.0003505
0.0003472
Other Christians (per ‘000)
0.0008925
-0.0000290
0.0007337
0.0000069
0.0000427
-0.0000008
No. of Public Schools
-0.0001629
-0.0000029
0.0000165
-0.0000609
0.0003154
0.0002604
School Rating (SAT Scores +
Dropout Rates)
-0.0383286
0.0027923
-0.0500683
0.0108848
0.0014005
0.0492250
24
Community Effects on Donation Amount
Community Characteristics
(ZIPCODE-level)
Intercept
(DurationGift to
Gift)
Log(Dur.
Gift to
Gift)
(DurationAppeal to
Gift)
Log(Dur.
Appeal to
Gift)
Intercept
3.0185213
0.0004018
0.0080055
0.0055162
-0.0139680
Race (% of whites)
0.0001357
0.0000227
-0.0002569
-0.0002354
0.0010621
Household Size
0.0675114
-0.0000333
0.0044736
-0.0105192
0.0203713
Household Type (% of families)
-0.0089478
0.0000199
-0.0009420
0.0002197
-0.0005320
Age
-0.0009603
0.0000100
0.0002324
-0.0003136
0.0009489
Education Level (in years)
0.0038578
-0.0002022
0.0034078
0.0028845
-0.0023037
Income Level (in ‘000 dollars)
-0.0014282
0.0000273
-0.0004760
-0.0002861
0.0018774
Wealth Rating
0.0349815
-0.0001378
0.0042747
0.0009441
-0.0148661
Home Value (in ‘000 dollars)
0.0012085
-0.0000030
0.0000133
0.0000318
-0.0002779
Home Ownership (in %)
0.0028647
-0.0000172
0.0002348
0.0002095
-0.0006810
Age of Tradelines (in months)
0.0019144
0.0000216
-0.0006265
-0.0004666
0.0003478
Balance of Tradelines (in dollars)
0.0000326
0.0000001
-0.0000001
-0.0000027
0.0000023
Tradelines – Satisfactory Ratings
-0.0236607
-0.0000965
0.0038958
0.0046234
-0.0074093
Tradelines – Derogatory Ratings
0.3052949
-0.0006096
0.0216013
-0.1060769
0.1819225
No. of Delinquent Tradelines
-0.4131844
0.0030482
-0.0750442
0.0330594
-0.0332528
25
Community Effects on Donation Amount
Community Characteristics
(County-level)
Intercept
No. of Violent Crimes
-0.0006731
% of Republican Votes
(Duration–
Gift to Gift)
Log(Dur.
Gift to
Gift)
(DurationAppeal to
Gift)
Log(Dur.
Appeal to
Gift)
0.0000096
-0.0003637
-0.0000781
0.0004469
0.0034120
-0.0000196
0.0005379
-0.0005516
0.0014927
Mainstream Christians (per ‘000)
-0.0005073
0.0000104
-0.0001715
-0.0000403
0.0000553
Evangelical Christians (per ‘000)
-0.0002389
-0.0000002
-0.0000088
0.0000903
-0.0003893
Catholic Christians (per ‘000)
-0.0002900
0.0000028
-0.0000373
0.0000068
-0.0000016
Other Christians (per ‘000)
0.0003482
-0.0000073
0.0001345
-0.0002006
0.0008020
No. of Public Schools
0.0000956
0.0000002
0.0000036
0.0000073
-0.0000480
School Rating (SAT Scores + Dropout
Rates)
0.0357002
-0.0007928
0.0112964
0.0086440
-0.0309685
26
Incidence and Amount Model Predictions
• Three sets of predictions: (for approximately 20% of the total
donor-time observations)
– In-sample for existing donors within the observation period (individual
level parameters) .
– Out-of-sample for existing donors outside the observation period
(individual level parameters).
– Out-of-sample for new donors outside the observation period
(population level parameters).
• Incidence model predictions: Dynamic method for incidence and
duration (approximately 67% accuracy based on hit rate).
• Amount model predictions: Conditional on incidence, static
method (approximately 79 % accuracy based on hit rate).
27
Predictions – Representative Donors
3.5
25
3
20
2.5
2
El Paso
(79912)
1.5
1
15
10
5
0.5
0
0
1 6 11 16 21 26 31 36 41 46 51 56 61 66 71
3.5
60
3
50
2.5
2
3
4
1
2
3
4
40
2
Houston
(77024)
1.5
1
30
20
10
0
0
1
6
11
16
21
26
31
36
41
46
51
56
61
66
71
76
81
86
91
96
101
0.5
3.5
1
20
3
2.5
15
Mission
(78572)
2
1.5
1
10
5
0.5
0
0
1 6 11 16 21 26 31 36 41 46 51 56 61 66 71 76 81 86
In-Sample
Out-of-Sample
giftdum
1
In-Sample
2
Out-of-Sample
3
giftdum
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Lessons Learned about Donation Behavior
• Durations from past gifts and past appeals have impact on current gift
incidence and gift amount.
• Evidence of both linear and non-linear effects more pronounced for donation
incidence, not so much for donation amount.
• Significant seasonal patterns evident in donation incidence, absent for
donation amount.
• Community characteristics impact incidence – race, age, income level,
wealth rating, balance of tradelines, number of delinquent tradelines, political
affiliation, crime rate, public education system.
• Community interactions also matter for amount – household size, household
with families, home value, home ownership, balance of tradelines, tradelines
with satisfactory ratings, number of delinquent tradelines, wealth rating,
political affiliations, public education system , religious beliefs (Catholics,
Evangelicals and Other Christians).
• In-sample predictions support targeting existing donors efficiently; out-ofsample predictions provides a compelling methodology for targeting existing
and potential donors with donor portfolios.
29
Questions and Comments
THANK YOU
30