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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. - PowerPoint PPT Presentation
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Duration Dependence of Donation Behavior: Explaining Heterogeneity in Donation Incidence and
Amount through Community CharacteristicsShameek 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?
4
Houston - 77024
Mission - 78572
El Paso - 79912
78572 : 79912 : 77024 – A Visual Comparison
5Houston - 77024
Mission - 78572 El Paso - 79912
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; home-ownership.
– 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
Low(≤ $15)
Mean = $9.80
Medium($16-$30)
Mean = $24.02
High(≥ $31)
Mean = $77.43
Low(≤ 20 weeks)
Mean = 10.97
Segment 1(N = 5465)
Segment 2(N = 4945)
Segment 3(N = 3283)
Medium(21-50 weeks)Mean = 34.35
Segment 4(N = 3640)
Segment 5(N = 4133)
Segment 6(N = 3154)
High(≥ 51 weeks)Mean = 89.80
Segment 7(N = 3435)
Segment 8(N = 4637)
Segment 9(N = 4075)
Amount of contributions
Inter-contribution duration
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
Solicitation1
Contribution2Contribution1
Duration between two contributions(Budgetary Implications)
Duration between solicitation and contribution(Wait/ Gather Information)
Solicitation2 Solicitation3 Solicitation4 Solicitation5
12
Donation Response Framework
Decision toContributefor Cause
Periods 1,2,…, (t-1) Period t
Solicitation/ No Solicitation
for Cause
Contribution/ No Contribution
for Cause ZIPCODE and County-Level CommunityCharacteristics
Amount of Contribution
for Cause
Modeling Incidence and Amount
Donation Response:Interval-Censored Proportional Hazard With Complimentary Log-log Link
Donation amount: Censored log-Normal Distribution
Donor heterogeneity- Hierarchical Specification
13
Seasonality
Durations
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:
where if donor i makes a contribution in period t
= 0 otherwise.
and : contribution amount of a donor i at time t.
• Likelihood of contribution incidence for donor i –
• Proportional hazard function for donor i :
it it it it itP(Y ,Z ) P(Y )P( Z |Y )
itY 1
itZ
( , ) 1 ( , )it itY Y
i it i ith t X h t X
15
/0
0
( | )( , ) lim ( )exp( )i i i i i
i it i i itt
P t T t t T th t X h t X
t
Donation Incidence Model
• Survival Function:
• Discrete analog of hazard specification:
• Re-arranging:
• Baseline Hazard:
• Hazard function: /( , ) 1 exp[ exp( )]h t X X 16
/
/
( , ) ( ) ( 1, ) ( , )( , ) ( | 1)
( , ) ( 1, )
( , )1 1 exp exp( ) ( 1) ( )
( 1, )
i it i i it i iti it i i i i
i it i it
i iti it i i
i it
S t X d t S t X S t Xh t X P T t T t
S t X S t X
S t XX H t H t
S t X
/0
0
/
( , ) exp ( )exp( )
exp[ exp( ) ( )]
it
i it i i it i
i it i
S t X h u X du
X H t
/log log(1 ( , )) log( ( ) ( 1))i it i it i ih t X X H t H t
0 0
1
log log(1 ( )) log( ( ) ( 1)) log ( )i
i
t
i i i i i it
t
h t H t H t h u du
Donation Incidence Model
with : Duration from last contribution at time t
: Duration from last solicitation at time t
: Seasonality dummy (months November – January)
Heterogeneity specification –
where : demographic and financial variables
: vector of parameters for the donor level covariates
: variance-covariance matrix
0 1 2 log( )y y c y ci i i it i itd d /
1 2 log( )y s y s yi it i it i it i itX d d s
citdsitd
0 0
1 1
2 2
1 1
2 2
~ ,
y yi
y yi
y yi y y
iy yi
y yi
y yi
N w
iwy
y 17
its
Donation Amount Model
• Censored Log-Normal distribution of contribution amount –
• Specification for mean –
• Heterogeneity specification –
: vector of parameters for the donor level covariates
: variance-covariance matrix
22 it z it
it it it z
it
log N( , ) if Y 1[ Z |Y , , ]
I( Z 0 ) otherwise
:
0 1 2 1 2log( ) log( )z z c z c z s z s zit i i it i it i it i it i itd d d d s
zz
18
0 0
1 1
2 2
1 1
2 2
~ ,
z zi
z zi
z zi z z
iz zi
z zi
z zi
N w
Bayesian MCMC Estimation
• Priors on donor-specific parameters –
• Priors on population-level parameters –
• : Non-conjugate Incidence Model
Random-walk Metropolis Hastings
• : Conjugate Amount Model Gibbs Sampler
• 45000 draws; 22500 burn-in samples; thinning parameter:15 19
/ /0 1 2 1 2 0 1 2 1 2[ , , , , , ] ~ ([( , , , , , , )] , )y y y y y y y y y y y y y y
i i i i i i N / /
0 1 2 1 2 0 1 2 1 2[ , , , , , ] ~ ([( , , , , , , )] , )z z z z z z z z z z z z z zi i i i i i N
/ /0 1 2 1 2 00 01 02 01 02 0 0 0
0 0
( , , , , , , ) ~ (( , , , , , , ) , );
~ ( , )
y y y y y y y y y y y y y y
y y y
N
Wishart
/ /
0 1 2 1 2 00 01 02 01 02 0 0 0
0 0
( , , , , , , ) ~ (( , , , , , , ) , );
~ ( , )
z z z z z z z z z z z z z z
z z z
N
Wishart
0 1 2 1 2, , , , ,y y y y y yi i i i i i
0 1 2 1 2, , , , ,z z z z z zi i i i i i
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
23
Community Effects on Donation IncidenceCommunity Characteristics
(ZIPCODE-level)Intercept (Duration
- Gift to Gift)
Log(Dur. Gift to Gift)
(Duration-Appeal to
Gift)
Log(Dur. Appeal to
Gift)
Seasonal Effect
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 -0.0221876 0.4268442 0.2657168 -1.3134540 -0.8715912
24
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
25
Community Effects on Donation AmountCommunity Characteristics
(ZIPCODE-level)Intercept (Duration-
Gift to Gift)
Log(Dur. Gift to Gift)
(Duration-Appeal 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
26
Community Effects on Donation Amount
Community Characteristics(County-level)
Intercept (Duration– Gift to Gift)
Log(Dur. Gift to Gift)
(Duration- Appeal to
Gift)
Log(Dur. Appeal to
Gift)
No. of Violent Crimes -0.0006731 0.0000096 -0.0003637 -0.0000781 0.0004469
% of Republican Votes 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
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
28
El Paso (79912)
Mission (78572)
Houston (77024)
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-of-sample predictions provides a compelling methodology for targeting existing and potential donors with donor portfolios. 29
THANK YOUQuestions and Comments
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