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

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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.

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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

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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

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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

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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

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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

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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)

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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*

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Duration Dependence of Donation Incidence

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Duration Dependence of Donation Amount

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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

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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

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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

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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).

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Predictions – Representative Donors

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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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