52 sinha shameek

8/9/2019 52 Sinha Shameek

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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 "niversity

#i$ay %aha$an and &renkel ter Hofstede

%cCom's School of Business! "niversity of (exas at Austin

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)on*+rofit Charities ,)+C-:

.hy do /e %arketers even Care0

1 (otal charita'le giving of 2345674 'illion /hich is around 38of 9D+

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Background on Empirical Context and Data

1 )on*profit organiation uses direct mail to solicit contri'utionsfrom past donors ,Source: D%E&-6

1 Contri'utions and solicitations in (exas: .eekly data for =;donors6

1 (ime span covering a period of approximately =? years

,un'alanced average ?3= /eeks-6

1 Contri'utions and solicitations 'y date! amount on eachincidence and costs of each solicitation6

1 History of solicitations and contri'utions censored data6

1 Community characteristics: ,Sources: uselectionatlas6org! &BI CrimeStatistics! ADA! (EA-

I+CFDE*level

Counties*level3


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Donor Heterogeneity: Ho/ Communities Differ0

4

Houston - 77024

Mission - 78572

El Paso - 79912


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;7?;3 : ;44=3 : ;;53@ A #isual Comparison

5Houston - 77024

Mission - 78572 El Paso - 79912


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;7?;3 : ;44=3 : ;;53@ A )umerical Comparison

Variables Texas Mission(78572)

El Paso(79912)

Houston(77024)

No. of Appeals 19.89 17.5 19.72 22.4

No. of Gifts .!4 .8! .4! .24

Duration from Appeal to Gift(in weeks)

4.01 .87 .7! 4.1!

Duration from Gift to Gift

(in weeks)

4.9! 4.99 45.42 !1.1!

Gift Amount per incidence(in dollars)

.42 21.17 27.82 57.02

6


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Community Characteristics: .hat %atters0

1 I+CFDE*level:

Socio*Demographics: raceG household*sieG household*typeG ageGeducation levelG income levelG /ealth*ratingG home*valueG home*o/nership6

Credit*&inancials: age of tradelinesG 'alance of tradelinesGtradelines /ith satisfactory ratingsG tradelines /ith derogatory

ratingsG no6 of tradelines delinuent6

1 County*level:* +olitical Beliefs: 8 of repu'lican votes6

*eligious Beliefs: 8 of %ainline ChristiansG 8 of EvangelicalChristiansG 8 of Catholic ChristiansG 8 of Fther Christians6

* Community Security: 8 of violent crimes6

* Educational uality: no6 of pu'lic schoolsG school rating6

7


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(argeting +otential Donors "sing Donor +rofiles

/ithin Communities

"o#,J 2=?-

Mean $ %9.80

Me&iu',2=>*2


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Communities .hy they matter0 ,I+CFDE*level-


El Paso(79912)

Houston(77024)

Race (% of whites) 78.59 9 ! 90

Household Size 2.75 .4 2.7 2.

Household !pe (% of families) 72.5 84 71 !5

A"e 4.!8 52 42 50

#ducation $eel (in !ears)1.84 11.7 14.4 1!.5

&ncome $eel (in ' dollars) !4.75 1.5 !2. 14.4

ealth Ratin" !.5! 2 7 9

Home *alue (in ' dollars) 98.04 45. 97.4 11.5

Home +wnership (in %) !4.!5 7! 59 !!

A"e of radelines (in months) 74.10 5! !8 102

,alance of radelines (in dollars) 5122.9! 1!7! 5!0 890

radelines - Satisfactor! Ratin"s 11.24 7.4 12.1 1

radelines - Dero"ator! Ratin"s 0.89 0.97 0.98 0.!9

No. of Delinuent radelines 1.24 1.24 1.2 0.92

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Communities .hy they matter0 ,County*level-


El Paso(79912)

Houston(77024)

No. of *iolent /rimes 4.2 2.17 0.8 2.!

% of Repu0lican *otes !0.2 44.9 4.50 55.14

1ainstream /hristians (per ') 84.10 28.18 25.! 81.8!

#an"elical /hristians (per ') 24.0! 7.40 75.28 204.81

/atholic /hristians (per ') 198.54 90.10 514.80 181.92

+ther /hristians (per ') 142.!2 !9.5 104.9! 179.42

No. of 2u0lic Schools 475.! 18 2!4 108

School Ratin" (SA Scores 3 Dropout Rates) 2.71 2.47 2 2.75

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Miterature: Donor Characteristics Influencing

Donation Behavior01 Demographics ,Mee and Chang! 355;-

e6g6 age! gender! education! race! income! marital status! religion! family

sie etc6

1 +sychographics ,Bussell and &or'es! 3553-

e6g6 self*esteem! empathy! guilt! social*$ustice! familiarity /ith causes!a/areness! responsi'ility! generosity etc6

1 +ast experience /ith charities , Schlegelmilch! Move andDiamantopoulos! =44>-

e6g6 previous experience! no6 of times approached etc6

1 Community Effects ,Corcoran et al6! =445G Schult! =47@G Datcher!=473! De%aro et al6! 355?-

e6g6 demographic composition! financial composition etc6

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Duration Dependence of Contri'ution and

Solicitation Behavior

Solicitation=

Contri'ution3Contri'ution=

Duration 'et/een t/o contri'utions,Budgetary Implications-

Duration 'et/een solicitation and contri'ution

,.aitN 9ather Information-

Solicitation3 Solicitation< Solicitation@ Solicitation?

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Donation esponse &rame/ork

Decision toContri'ute

for Cause

+eriods =!3!O! ,t*=- +eriod t

SolicitationN

)o Solicitation

for Cause

Contri'utionN

)o Contri'ution

for CauseI+CFDE and County

*Mevel Community

Characteristics

Amount of

Contri'utionfor Cause

%odeling Incidence

and Amount

Donation esponse:

Interval*Censored

+roportional Haard

.ith Complimentary

Mog*log Mink

Donation amount:

Censored log*)ormalDistri'ution

Donor heterogeneity* Hierarchical

Specification

13

Seasonality

Durations


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elevant Miterature

*usto'er +es,onse Mo&els ire/t Maretin an&*usto'er Manae'ent

Schmmitlein and +eterson ,=44@! %kt6 Sc6-

Basu! Basu and Batra ,=44?! P%-

ossi! %cCulloch and Allen'y ,=44>! %kt6 Sc6-

Allen'y! Meone and Pen ,=444! PASA-

%anchanda! Ansari and 9upta ,=444! %kt6 Sc6-

&ader! Hardie and Mee ,355?! %kt6 Sc6-

einart! (homas and Qumar ,355?! P%-ust and #erhoef ,355?! %kt6 Sc6-

9onul and (er*Hofstede ,355>! %kt6 Sc6-

)eslin! )ovak! Baker and Hoffman ,3554! %gmt6 Sc6-

Diepen! Donkers and &rancses ,3554! P%- 14


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Donation Incidence %odel

1 Donors: i = 1, 2… n

1 (ime +eriods: t = 1, 2… T

1 %odel:

/here if donor i makes a contri'ution in period t

L 5 other/ise6

and : contri'ution amount of a donor i at time t 6

1 Mikelihood of contri'ution incidence for donor i

1 +roportional haard function for donor i :

it it it it it P(Y ,Z ) P(Y )P( Z |Y )=

it Y 1=

it Z

( ) ( ), ! - = , ! -it it Y Y

i it i it h t X h t X −

15

N

55

, R -, ! - lim , -exp, -i i i i ii it i i it

t

P t T t t T t h t X h t X

t

β ∆ →

≤ < + ∆ >= =

∆


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Donation Incidence %odel

1 Survival &unction:

1 Discrete analog of haard specification:

1 e*arranging:

1 Baseline Haard:

1Haard function:

N

, ! - = expS exp, -Th t X X β γ = − − + 16

( )

N

N

, ! - , - , =! - , ! -, ! - , R =-

, ! - , =! -

, ! -= = exp exp, - , =- , -

, =! -

i it i i it i it

i it i i i i i it i it

i it i it i i

i it

S t X d t S t X S t X h t X P T t T t

S t X S t X

S t X X H t H t

S t X β

− −≈ = > − = =

−

= − = − − − − −

N

5

5

N

, ! - exp , - exp, -

expS exp, - , -T

it

i it i i it i

i it i

S t X h u X du

X H t

β

β

= −

= −

∫

( ) Nlog log,= , ! -- log, , - , =--i it i it i ih t X X H t H t β − − = + − −

[ ]5 5=

log log,= , -- log, , - , =-- log , -i

i

t

i i i i i it

t

h t H t H t h u du γ −

− − = − − = =

∫


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Donation Amount %odel

1 Censored Mog*)ormal distri'ution of contri'ution amount

1 Specification for mean

1 Heterogeneity specification

: vector of parameters for the donor level covariates

: variance*covariance matrix

22 it z it

it it it z

it

log N( , ) i Y 1! Z |Y , , "

#( Z $ ) oth%&wis%

µ σ µ σ

=

= :

5 = 3 = 3

log, - log, - z z c z c z s z s z

it i i it i it i it i it i it

d d d d s µ α α α δ δ γ = + + + + +

z Φ z

Σ

18

5 5

= =

3 3

= =

3 3

C !

z z i

z z i

z z i z z

i z z i

z z

i

z z

i

N w

α α

α α

α α

δ δ

δ δ

γ γ

÷ ÷ ÷ ÷ ÷ ÷ ÷ ÷ ÷ ÷ ÷ ÷ + Φ Σ ÷ ÷ ÷

÷ ÷ ÷ ÷ ÷ ÷ ÷ ÷ ÷ ÷


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Bayesian %C%C Estimation

1 +riors on donor*specific parameters

1 +riors on population*level parameters

1 : )on*con$ugate Incidence %odel

andom*/alk %etropolis Hastings

1 : Con$ugate Amount %odel

9i''s Sampler

1 @?555 dra/sG 33?55 'urn*in samplesG thinning parameter:=? 19

N N5 = 3 = 3 5 = 3 = 3S ! ! ! ! ! T C ,S, ! ! ! ! ! ! -T ! -

y y y y y y y y y y y y y yi i i i i i N α α α δ δ γ α α α δ δ γ Φ Σ

N N

5 = 3 = 3 5 = 3 = 3S ! ! ! ! ! T C ,S, ! ! ! ! ! ! -T ! - z z z z z z z z z z z z z z

i i i i i i N α α α δ δ γ α α α δ δ γ Φ Σ

N N

5 = 3 = 3 55 5= 53 5= 53 5 5 5

5 5

, ! ! ! ! ! ! - C ,, ! ! ! ! ! ! - ! -G

C , ! -

y y y y y y y y y y y y y y

y y y

N

'ish(&t

α α α δ δ γ α α α δ δ γ

λ

Φ Φ Λ

Σ ΣN N

5 = 3 = 3 55 5= 53 5= 53 5 5 5

5 5

, ! ! ! ! ! ! - C ,, ! ! ! ! ! ! - ! -G

C , ! -

z z z z z z z z z z z z z z

z z z

N

'ish(&t

α α α δ δ γ α α α δ δ γ

λ

Φ Φ Λ

Σ Σ

{ }5 = 3 = 3! ! ! ! ! y y y y y y

i i i i i iα α α δ δ γ

{ }5 = 3 = 3! ! ! ! ! z z z z z z

i i i i i iα α α δ δ γ


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Donation Incidence and Amount %odel esults

n/i&en/e 'ount

&ntercept -5.!553 .01853

Duration - Gift to Gift 0.0553 56555@

$o" (Duration - Gift to Gift) -0.7573 0.00803

Duration - Appeal to Gift -1.5493 0.00553

$o" (Duration - Appeal to Gift) !.8903 *565=@5

Seasonalit! #ffect 5.!783

20


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Duration Dependence of Donation Incidence

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Duration Dependence of Donation Amount

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23

Community Effects on Donation Incidence

*o''unit *ara/teristi/s(P*6E-leel)

&ntercept (Duration4 Gift to

Gift)

$o"(Dur.Gift to

Gift)

(Duration4 Appeal to

Gift)

$o"(Dur. Appeal to

Gift)

Seasonal #ffect

&ntercept -5.65480

23

0.05459

59

-

0.75730

65

-

1.54926

86

6.89028

48

5.67859

42

Race (% of whites)0.00402

77

0.000073

5

-

0.00006

48

-

0.001011

5

0.001785

0

-

0.004017

7

Household Size -

0.0285814

0.0004487

-

0.0151614

-

0.0197261

0.0614435

0.0127006

Household !pe (% of families)0.004042

6

0.000017

3

-

0.00004

58

0.001252

8

-

0.007700

2

-

0.002319

2

A"e0.001214

3

0.000269

9

0.00000

53

-

0.01138

43

0.03171

53

0.001570

3

#ducation $eel (in !ears) -

0.017635

9

0.000327

1

0.01093

37

-

0.024274

4

0.135305

2

0.069630

6

&ncome $eel (in ' dollars) -

0.001893

2

0.00010

48

-

0.00405

09

0.002875

1

-

0.010664

6

-

0.003678

2

ealth Ratin" -

0.05789

16

-

0.000778

6

0.01311

31

-

0.009166

3

0.081617

8

0.10282

09


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24

Community Effects on Donation Incidence

*o''unit *ara/teristi/s(*ount-leel)

&ntercept (Duration-

Gift to

Gift)

$o"(Dur.

Gift to

Gift)

(Duration

4 Appeal

to Gift)

$o"(Dur.

Appeal to

Gift)

Seasonal

#ffect

No. of *iolent /rimes0.000900

1

0.000130

0

-

0.00202

67

0.000778

6

-

0.0046003

-

0.00401

02

% of Repu0lican *otes0.000465

2

-

0.0002205

0.00353

10

-

0.000885

2 0.0035071

0.004195

5

1ainstream /hristians (per ') -0.000611

2 0.0000133

-

0.000303

5

0.000809

5

-

0.0017561

0.000232

2

#an"elical /hristians (per ')0.000029

7 0.0000052

-

0.000105

7

-

0.000104

6

-

0.0001125

-

0.000523

6

/atholic /hristians (per ') -0.000164

3

-

0.0000132

0.000209

7

-

0.000012

6 0.0003505

0.000347

2

+ther /hristians (per ')0.000892

5

-

0.0000290

0.000733

7

0.000006

9 0.0000427

-

0.000000

8

No. of 2u0lic Schools -0.00016 - 0.00001 6

-

0.000060 0.00026


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25

Community Effects on Donation Amount

*o''unit *ara/teristi/s(P*6E-leel)

&ntercept (Duration4Gift to

Gift)

$o"(Dur.Gift to

Gift)

(Duration4 Appeal to

Gift)

$o"(Dur. Appeal to

Gift)

&ntercept 3.01852

13

0.000401

8

0.00800

55

0.005516

2

-

0.013968

0

Race (% of whites)0.000135

7

0.000022

7

-

0.000256

9

-

0.0002354

0.001062

1

Household Size0.06751

14

-

0.000033

3

0.004473

6

-

0.0105192

0.020371

3

Household !pe (% of families) -

0.00894

78

0.000019

9

-

0.000942

0 0.0002197

-

0.000532

0

A"e -

0.000960

3

0.000010

0

0.000232

4

-

0.0003136

0.000948

9

#ducation $eel (in !ears)0.003857

8

-

0.000202

2

0.003407

8 0.0028845

-

0.002303

7

&ncome $eel (in ' dollars) -

0.001428

2

0.000027

3

-

0.000476

0

-

0.0002861

0.001877

4

ealth Ratin" - -


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26

Community Effects on Donation Amount

*o''unit *ara/teristi/s(*ount-leel)

&ntercept (Duration-

Gift to Gift)

$o"(Dur.

Gift to

Gift)

(Duration4

Appeal to

Gift)

$o"(Dur.

Appeal to

Gift)

No. of *iolent /rimes -

0.000673

1 0.0000096

-

0.000363

7

-

0.000078

1 0.0004469

% of Repu0lican *otes0.00341

20

-

0.0000196

0.000537

9

-

0.000551

6 0.0014927

1ainstream /hristians (per ') -

0.000507

3 0.0000104

-

0.000171

5

-

0.000040

3 0.0000553

#an"elical /hristians (per ') -

0.000238

9

-

0.0000002

-

0.000008

8

0.000090

3

-

0.000389

3

/atholic /hristians (per ') -

0.00029

00 0.0000028

-

0.000037

3

0.000006

8

-

0.0000016

+ther /hristians (per ')0.000348 - 0.000134

-0.00020 0.000802


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Incidence and Amount %odel +redictions

1 (hree sets of predictions: ,for approximately 358 of the total

donor*time o'servations- In*sample for existing donors /ithin the o'servation period ,individual

level parameters- 6

Fut*of*sample for existing donors outside the o'servation period

,individual level parameters-6 6ut-o-sa',le or ne# &onors outsi&e te obseration ,erio&

(,o,ulation leel ,ara'eters).

1 Incidence model predictions: Dynamic method for incidence and

duration ,approximately >;8 accuracy 'ased on hit rate-6

1 Amount model predictions: Conditional on incidence! static

method ,approximately ;4 8 accuracy 'ased on hit rate-6

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+redictions epresentative Donors

28

El Paso

(79912)

Mission

(78572)

Houston

(77024)


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TH: ;6<

uestions and Comments

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52 sinha shameek

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