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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+
1 ;
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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
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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
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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-
Variables Texas Mission(78572)
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 $eel (in ' dollars) !4.75 1.5 !2. 14.4
ealth Ratin" !.5! 2 7 9
Home *alue (in ' dollars) 98.04 45. 97.4 11.5
Home +wnership (in %) !4.!5 7! 59 !!
A"e of radelines (in months) 74.10 5! !8 102
,alance of radelines (in dollars) 5122.9! 1!7! 5!0 890
radelines - Satisfactor! Ratin"s 11.24 7.4 12.1 1
radelines - Dero"ator! Ratin"s 0.89 0.97 0.98 0.!9
No. of Delinuent radelines 1.24 1.24 1.2 0.92
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Communities .hy they matter0 ,County*level-
Variables Texas Mission(78572)
El Paso(79912)
Houston(77024)
No. of *iolent /rimes 4.2 2.17 0.8 2.!
% of Repu0lican *otes !0.2 44.9 4.50 55.14
1ainstream /hristians (per ') 84.10 28.18 25.! 81.8!
#an"elical /hristians (per ') 24.0! 7.40 75.28 204.81
/atholic /hristians (per ') 198.54 90.10 514.80 181.92
+ther /hristians (per ') 142.!2 !9.5 104.9! 179.42
No. of 2u0lic Schools 475.! 18 2!4 108
School Ratin" (SA Scores 3 Dropout Rates) 2.71 2.47 2 2.75
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Miterature: Donor Characteristics Influencing
Donation Behavior01 Demographics ,Mee and Chang! 355;-
e6g6 age! gender! education! race! income! marital status! religion! family
sie etc6
1 +sychographics ,Bussell and &or'es! 3553-
e6g6 self*esteem! empathy! guilt! social*$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
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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
30