The Complementartes of Competton n Chartable Fundrasng Andreas Lange Unversty of Hamburg Department of Economcs Von-Melle-Park 5 D-20146 Hamburg Germany andreas.lange@wso.un-hamburg.de Andrew Stockng Congressonal Budget Offce Ford House Offce Buldng #480C Washngton, DC 20515 astockng@cbo.gov (202) 226-2815 (phone) (202) 226-0207 (fax) Abstract Ths paper examnes the effect of competton between chartes on solctatons of tme and money donatons. Theory and our feld experment demonstrate that solctatons from a competng charty may prove benefcal n fundrasng, even at the ndvdual level, f complementartes exst. Our feld experment was run wth over 288,000 ndvduals and two chartes. The Treatment Group were exposed to a second charty through a volunteer opportunty, after whch those who volunteered were ncluded n the regular stream of donaton solctatons from that second charty (n addton to the frst). We tracked over 890,000 subsequent tme donatons and $895,000 n contrbutons from the Treatment and Control groups over the next two years to measure the treatment effect. Controllng for a rch set of past behavoral observables, the Treatment Group gave more to the orgnal charty and more overall than the Control Group, provdng evdence that complementartes exst between chartes. Keywords: chartable fundrasng, competton, feld experment, complementartes, matchng, propensty score Correspondng author. The analyss and conclusons expressed n ths paper are those of the author and should not be nterpreted as those of the Congressonal Budget Offce.
The Complementartes of Competton n Chartable Fundrasng 1. Introducton The number of chartes n the Unted States grew by more than 5% per year between 2006 and 2008, such that there are now over 1.5 mllon regstered chartes and foundatons n the Unted States. By large part, those chartes grow ther pool of onlne donors by solctng donatons from the donors of other chartes, typcally by rentng access to ther donor lst. For example, Amnesty Internatonal makes 300,000 donors avalable for rental and the Natonal Parks Conservaton Assocaton makes 183,000 donors avalable for rental through ther respectve lst brokerage companes. 1 Economc ntuton suggests that a charty that exposes ther donors to other chartes runs the rsk of losng future donatons because ther donors may fnd that other chartes better algn to ther nterests. Alternatvely, f there exst complementartes n fundrasng actvtes, such lst rental could be mutual benefcal. In ths paper we address the queston of how chartable competton, partcularly when multple chartes can solct donatons from the same ndvduals, affects donatons of tme and money. The effect of chartable competton on gvng has not been wdely studed n the emprcal economc lterature and we are not aware of feld experments on the topc. 3 Much of the theoretcal work on competton and gvng assumes that multple chartes enter an ndvdual s utlty functon as substtutes (Rose-Ackerman, 1992; Blodeau and Slvnsk, 1997; Aldashev and Verder, 2010). As such, the research concludes that competton ncreases specalzaton between chartes and causes donors to mgrate toward ther preferred specalzed charty. One recent emprcal paper (Rensten 2011) evaluates competton between chartable sectors usng survey data and concludes that donors may substtute between chartable sectors followng a temporary shock (.e., a natural dsaster or other event that ncreases the fundng 1 See Carol Enters Lst Co (www.carolenters.com) and Names n the News (www.nncal.com) and ther selecton of managed lsts. Dscussons wth fundrasng professonals suggest that n a year, chartes are lkely to reach out to as many or more donors from other chartes as they make avalable for rental. There are many other donor or member lsts avalable from lst brokerage companes, ncludng the Amercan Economc Assocaton whch rents ts malng lst to chartes for $90 per 1000 addresses for a one-tme malng to the general lst (see: http://www.aeaweb.org/malng_lst_np.php); hgher fees are avalable for a more targeted subsample of the lst. 3 Whle nter-charty competton has not been studed extensvely, chartable fundrasng has been an ncreasng topc of economc exploraton n the lterature. See, eg., Lange and Stockng, 2009; Lst 2011; Andreon and Lst, 2011. Page 2
need n partcular sector). Two strans of emprcal lterature related to competton are the crowdng out lterature whch fnds that government grants tend to crowd out prvate contrbutons (see, for example, Andreon and Payne 2003) and the lterature on the effect of federal tax ncentves on prvate contrbutons (for recent work, see CBO, 2011). In ths paper, we study the effect of competton among chartes on tme and money donatons. We frst develop a theoretcal model n the tradton of Andreon s (1990) warm-glow model that captures the man effects of multple solctatons at the ndvdual level. It demonstrates that complementartes n warm-glow are necessary for donatons from a small ndvdual donor to ncrease when they are solcted by an addtonal charty. We then test the theory n the feld usng a large-scale feld experment wth over 288,000 subjects across two chartes, both of whch advocate on behalf of envronmental ssues on the natonal level. The treatment conssts of offerng a subset of each charty s audence the opportunty to volunteer for a second charty, whch, f the opportunty s accepted, wll result n the ndvdual s addton to the second charty s regular solctatons. Over 15,000 ndvduals accepted the offer to be contacted by both chartes. Those who dd not accept and those who were not offered the treatment contnued to receve solctaton only from one of the two chartes. We followed all ndvduals for two years and tracked ther donatons of tme (890,000 volunteer nstances), and money ($895,000 donated) over that perod. Usng a propensty score matchng econometrc strategy that reles on our rch set of behavoral characterstcs for each donor, we fnd that there s evdence of complementartes between the two chartes that partcpated n the feld experment. Both chartes receved more tme donatons from those members who were solcted by two chartes nstead of just the orgnal charty and a weakly larger number and value of money donatons. We also fnd that ndvduals n the Treatment Group donated more money to the combnaton of two chartes than they gave when they were solcted by only one charty. Whle that result may not be of nterest to ether of the chartes, t would be useful to any organzaton that s nvested n the fnancal success of both chartes: they can collectvely earn more donatons by sharng ther lsts. Our research suggests that chartes can fnancally beneft from partnerng wth other chartes to jontly solct the audence from whch they request donatons of tme and money. Our paper makes two mportant contrbutons to the lterature: frst, we fnd evdence of the Page 3
exstence of complementartes n the competton between chartes, and second, we fnd dfferences between the effects of competton on solctaton attempts to generate money donatons compared to tme donatons (or volunteerng). The frst result provdes some confrmaton that the donor lst exchanges currently performed by most chartes may not be detrmental to ther fundrasng efforts. The latter result contrbutes to a very small economc lterature on volunteerng. We therefore hope that ths study provdes a sprngboard for related research on the effect of competton wthn the chartable sector. The paper proceeds as follows. Secton II bulds a theoretcal model that llustrates the condtons under whch complementartes exst. Secton III descrbes the expermental desgn and Secton IV descrbes our econometrc strategy for dentfyng the effect of the treatment on the Treatment Group. Secton V dscusses the results and secton VI concludes. 2 Theory We provde a smple model to llustrate the ndvdual s decson when beng solcted by one or two chartes. For ths, we augment Andreon s (1989, 1990) mpure altrusm model. We model an agent who receves utlty from consumng a numerare good, y, two publc goods provded at levels G ( t 1, 2 ), and (possbly) from her own contrbutons to the publc good t b 0. The agent faces a budget constrant y b1 b2 w. We assume that the agent takes the t contrbutons from all other agents as gven and that the two chartes convert contrbutons nto provson of a publc good at unt costs c t ( t 1, 2 ). Thus, an ndvdual s contrbuton leads to an ncrease n the provson of the publc good by g b / c. When takng the contrbutons t t t from other players as gven, we can wrte the utlty of the agent as: U ( b, b ) u ( w b b ) hg h G f ( b, b ) (1) 1 2 1 2 1 1 2 2 1 2 where u () reflects the utlty from consumng the numerare, h t the margnal utlty from the publc good, and f ( b1, b 2) captures feelngs of warm glow of havng contrbuted to the provson of the publc goods. We assume u () and f () are non-decreasng and concave. We also assume that for small dollar donors, as are consdered here, the provson of the publc good Page 4
s addtve n ndvdual donatons only to the charty n queston, and thus, we assume that agents may only donate f solcted by the charty. G t I g t. 4 Fnally, We now consder the stuaton where the agent s solcted by () only one or () both chartes. If the agent s only contacted by charty t, donatons are gven by the frst-order condton wth respect to the solctng charty: (2) u ( w b ) h / c f ( b,0) 0 y 1 1 1 1 1 u ( w b ) h / c f (0, b ) 0 y 2 2 2 2 2 wth equalty f b 0. Here, u () and f () denote the partal dervatves. We denote the soluton by t y t b ˆ,1 t (reflectng that solctaton occurs from one charty only). If the agent s solcted by both chartes, the frst-order condtons are gven by: (3) u ( w b b ) h / c f ( b, b ) 0 y 1 2 1 1 1 1 2 u ( w b b ) h / c f ( b, b ) 0 y 1 2 2 2 2 1 2 wth equalty f b1 0 and b2 0 We denote the soluton by ( bˆ, b ˆ ).,2,2 1 2 Condtons (2) and (3) allow us to categorze the ndvdual s decsons accordng to f she contrbutes to a sngle or to both chartes. For ths, we consder defne threshold values h2( h 1) and h1 ( h 2) as follows: (4) h ( h ) / c f ( b ( h ),0) h / c f ( b ( h ),0),1,1 2 1 2 2 1 1 1 1 1 1 1 h / c f (0, b ( h )) h ( h )/ c f (0, b ( h )),1,1 2 2 2 2 2 1 2 1 1 2 2 b ˆ,1 t as a functon of Here h2( h 1) denotes the threshold of the margnal valuaton of publc good 2 above whch a h t and consumer wll not exclusvely donate to publc good 1 f solcted by both chartes. Thus, the,2 agents wll defntely donate to good 2 ( ˆ b 0 ) when solcted by both chartes f ther 2 margnal value of publc good 2 s greater than h2( h 1). Smlarly, h1( h 2) s the threshold margnal valuaton of publc good 1 above whch the agent wll not exclusvely donate to publc good 2. Note that the threshold values as defned n (4) must exst, though they could be 4 One could magne a case where a large donatons to charty 2 was complementary to charty 1, such as mght occur f charty 2 advocated for land conservaton and charty 1 advocated for wldlfe protecton on that land. Ths paper s focused on small donors (.e., contrbutons less than $1000 and prmarly less than $100) and thus we do not consder such publc good complementartes across smlar chartes. Page 5
negatve. Further note that h ( h ) s ncreasng n c s and decreasng n f (). These threshold s t values allow us to descrbe the donaton decsons of agents as a functon of h 1 and h 2. When solcted by both chartes nstead of only by charty t, the agent would not change ther contrbutons,.e. bˆ bˆ and b ( s t), f and only f:,2,1 t t ˆ,2 s 0 (5) h h ( h ) s s t Note that ths model allows three reasons a donor may not gve to charty s : 1) the publc good provson s small ( h s small); 2) the donaton trggers low warm glow ( fs () small); or 3) the charty s neffcent n provdng the publc good ( c s large). Alternatvely, the agent may completely swtch ther donatons to the new charty s such s that ˆ,2 t 0 b and ˆ,2 s 0 b ( s t). Ths s the case, f and only f: (6) h h ( h ) and h h ( h ) s s t t t s,2 Fnally, agents may decde to gve to both chartes ( ˆ b 0 and only f: 1 bˆ 0 ) whch happens f and,2 2 (7) h h ( h ) and h h ( h ) s s t t t s Fgure 1 llustrates these three possbltes: n regon A2 to the left of h1( h 2), donors wll only gve to charty 2, n regon A1 below h2( h 1) they wll only gve to charty 1; and n the shaded regon B, they gve to both chartes. Ths llustraton s useful for understandng the crcumstances under whch a charty may gan from exchangng ts donor lst wth another charty. Consder a donor who was prevously only contacted by charty 1. If the donor s n regon A1, beng addtonally contacted by charty 2 wll not change hs contrbuton decsons. 5 If the donor s n regon A2, she wll stop gvng to charty 1 and nstead gve to charty 2. That loss of a donor by charty 1 could be offset by gans from newly contacted donors who prevously gave to charty 2 but are n regon A1. We call ths effect sortng. In the emprcal analyss, we wll nvestgate to what extent donors sort to ther preferred charty. 5 Whle we model the ndvdual as havng perfect knowledge about the chartes and how donatons translate nto publc good provson, one can easly perceve an addtonal channel through whch solctaton by an addtonal charty may change donatons to the ntal charty: () t may elevate the ndvdual s awareness of the publc good or the mportance of phlanthropy. () t may also gve the donor new nformaton on the relatve mportance of the cause served by the ntal charty and/or ts qualty. In fact, consstent wth such an nformaton channel, we observes agents that dd not orgnally gve to Charty 1, but started to after recevng nfo from the second charty. Page 6
We are, however, partcularly nterested n the changes of gvng among those who mantan ther connecton wth the ntal charty. We therefore now consder gvng n regon B of Fgure 1, where agents gve to both chartes. Here, a charty may potentally gan even from ncreased donatons from ts orgnal donors when they are solcted from another charty. Dfferentaton of (3) shows that contrbutons to the ntal charty t change accordng to: (8) b u f b u f t yy ts s yy tt As the denomnator s negatve and u 0, contrbutons to the ntal charty can only ncrease f f ts s postve and larger than yy u yy. That s, the ntal charty may beneft from a donor beng contacted by another charty f and only f the warm-glow component shows suffcent complementartes between the two chartes. If that s not the case, the ndvdual s contrbutons to the ntal charty wll lkely decrease as the donor splts her donatons across two chartes. Proposton 1 We obtan the followng proposton: An agent s donatons to a charty can only ncrease when beng contacted by a second charty f gvng s complementary n creatng warm glow ( f 0 ) and suffcently large ( f ts ts u ). A second varable of nterest s the sum of contrbutons across both chartes from the ndvdual, whch represents the beneft to the chartable sector from allowng chartes to solct each other s potental donor base. As long as agents gve to both chartes (regon B, condton yy (3)), the comparatve statc mples b b 1 2 ts tt bs uyy ftt f f, whch s postve as long as f ts f tt and always postve f f 0. Ths leads to the followng proposton: ts Proposton 2 Total contrbutons to both chartes ncrease f the warm glow complementartes are weakly postve ( f 0 ). ts Proposton 1 ndcates that donatons from a charty s ntal donor base may ncrease when the charty allows ts donor base to be contacted by another charty f donatons are Page 7
complementary. The charty, however, also runs the rsk that ndvduals may stop donatng to t ( ( h h h )) or may contrbute less ( b b 0 ). Proposton 2 shows, however, that an t t s t s exchange of donor lsts generates benefts for the chartable sector even f complementartes do not exst and those benefts ncrease as the complementartes become stronger. That occurs because exposure to a second charty can only result n weakly greater margnal utlty from gvng. In the extreme case, donors fully sort and only gve to one charty. In our emprcal nvestgaton, we wll study the changes n gvng at the ndvdual level. If we observe that ndvduals ncrease gvng to the ntal charty, we have evdence for complementartes. In partcular, ths s supported f we observe an ncrease n the ndvdual s jont contrbuton to both chartes. 3 Expermental Desgn We brng data to our theory usng a donor exchange that occurred between two chartable organzatons n 2007. Both organzatons advocate on behalf of envronmental ssues, prmarly n the Unted States, but wth dfferent objectves: organzaton A, hereafter referred to as Electon Charty or EC, prmarly works to elect pro-envronment canddates and organzaton B, hereafter referred to as Wldlfe Charty or WC, prmarly works to support pro-envronment regulatons and polcy. In Aprl 2007, the Electon Charty contacted 178,353 subscrbers on ts emal lst encouragng them to volunteer for the Wldlfe Charty by gong to WC s webste and sendng a letter to Congress on an ssue mportant to WC. Of the 178,353 who were contacted, 10,605 members of EC s lst accepted the nvtaton to volunteer for WC and n dong so agreed to jon WC s onlne emal lst. Two weeks later n May 2007, the same happened n reverse. WC promoted a volunteer letter-wrtng opportunty on EC s webste to 90,569 subscrbers of ts onlne emal lst and 4,470 WC members volunteered and n dong so agreed to jon EC s onlne emal lst (see Fgure 2). Henceforth, the groups are denoted as follows: Treatment Group. The emal lst subscrbers who were solcted by two chartes followng the cross promoton treatment and ther agreement to jon the second charty s emal lst; Control Group 1. The emal lst members who receved the promoton to jon the second charty but dd not accept; and Page 8
Control Group 2. Those who were elgble to receve the promoton but dd not receve t. Wth ths namng conventon, the treatment s the experence of beng solcted by two chartes nstead of just one. Both Control Group 1 and Control Group 2 were subscrbed to the emal lst of just one charty at the tme of the cross promoton and for the subsequent two years of the study. Both EC and WC determned elgblty for recept of the cross promoton based on the set of emal subscrbers who were not requested to be suppressed by the charty and were not large donors. 6 Once the elgble recpents were determned, both chartes selected a subset from that group to promote the other charty, based on a goal of encouragng 5,000 people to volunteer for the other charty s letter-wrtng campagn. EC underestmated the volunteer rate of ther members and more than doubled ths target number by sendng 10,605 volunteers to WC. WC estmated the volunteer rate much closer to ther target and delvered 4,470 volunteers. Typcal communcatons between both chartes and ther emal lst consst of three prmary types of actvtes: 1) fundrasng appeals whch request fnancal contrbutons and are generated by the fundrasng department; 2) letter-wrtng campagns, surveys, and event nvtatons whch request non-fnancal contrbutons of tme and are generated by the polcy department; and 3) educaton or other general notfcatons whch are nformatonal and come from the polcy or communcatons department. Requests for volunteer tme to support each charty s lobbyng efforts through letter-wrtng campagns represent a large majorty of the communcatons. Those emals notfy the lst subscrbers of some stuaton that the charty beleves s mportant to ther consttuency and ask the subscrbers to take acton. Typcally acton nvolves a 5-10 mnute process whereby the lst subscrber vsts a page on the charty s webste and personalzes a letter for emalng or faxng to one or more elected offcals. That was the objectve of both EC s and WC s cross promotonal emals. Followng acceptance of the nvtaton to jon the second charty, the new members receved the three types of communcatons at a frequency dentcal to the rest of the emal lst. That s, they were not solcted or treated dfferently than the other emal lst members. In 6 EC descrbed a large money donor as anyone who donated over $5,000 to the organzaton over ther lfetme. WC defned a large money donor as anyone who had gven over $250 n a sngle gft. Each charty had fewer than 100 large donors. Page 9
addton, both EC and WC worked wth the same consultant for fundrasng and volunteerng solctaton strateges, such that both chartes followed smlarly strateges for generatng money and tme donatons. The treatment effect s measured across the treatment group and two control groups usng three prmary dmensons mportant to both chartes: 1) number of volunteer actons, or tmedonatons; 2) number of money-donatons; and 3) total value of money-donatons. All are measured both one year and two years after the cross promoton n addton to the year before the cross promoton. For the treatment group we record outcomes performed for both the new charty and orgnal charty. We also record the number of unsubscrbe requests, or requests not to receve further nformaton and solctatons from a partcular group, both one and two years after the cross promoton. 4 Econometrc Approach Our econometrc objectve s to determne the effect on tme and money donatons of a margnal ncrease n the number of chartes solctng an ndvdual. Were t possble to randomly assgn ndvduals to multple chartes, the treatment effect could be dentfed smply by a dfference-n-dfference strategy. However, the prvacy rules of most chartes prohbt them from transferrng the contact nformaton for ther subscrbers to a second organzaton wthout the expressed desre of the ndvdual. Consequently, most treatment strateges ths one ncluded requre ndvduals to actvely select nto the treatment group. An evaluaton of hstorcal money- and tme-donatons for the Treatment Group and Control Group 1 for WC and EC llustrate that selecton nto the treatment s not randomly assgned (see Table 1 and Table 2). Those n the Treatment Group became subscrbers of the orgnal charty more recently and were more lkely to make tme- and money-donatons. That result may not be surprsng gven that the treatment recevng solctatons from a second charty s trggered when lst members agree to make a tme-donaton to a second charty. Combnng the Treatment Group and Control Group 1 (Total Offered) and comparng aggregate behavor wth Control Group 2 also ndcates that Control Group 2 s probably not a randomly omtted subset of each charty s subscrber base. Dfferences between Control Group 2 and the Total Offered group stem from dffcultes n replcatng the suppresson lst. Pror to the Page 10
treatment, each charty provded a lst of subscrbers that they wanted suppressed from the treatment mostly those already on ther emal lst but some subscrbers from other sources. Whle we could replcate the small overlap between each charty s emal lst at the tme of the treatment, we could not dentfy those addtonal subscrbers that the chartes requested be suppressed from the treatment they reman n Control Group 2 even though they were suppressed from the treatment. However, hstorcal behavor of Control Group 2 s more smlar to the Treatment Group than Control Group 1, suggestng that t may contan a set of subscrbers who would have selected nto the treatment f gven the opportunty. Our econometrc strategy to dentfy the effect of the treatment on donatons proceeds followng the example of others who have non-randomzed selecton nto a treatment group wthout a perfectly randomzed control: we dfference the dependent varable for the treatment and control groups after condtonng the selecton nto the treatment on observables (Angrst 1998; Deheja and Wahba 1999). 7 Accurate dentfcaton of the treatment effect usng a selecton on observables strategy requres that all varables that contrbuted to selecton nto the treatment are ncluded n the econometrcs and any omtted varables are orthogonal to the treatment. To ease the dffculty of satsfyng that objectve, we construct a dfferenced dependent varable whch precludes the need for tme-nvarant ndependent varables such as gender, educaton, occupaton, and geographc locaton to whch we lack access. Specfcally, we are nterested n estmatng how the number of tme-donatons and number and value of moneydonatons (denoted genercally as D ) change n the perod after the treatment. 8 Because no sngle solctaton event can be used to measure the effect of the treatment, D t, s measured as the count of tme- and money-donatons and the sum of money-donatons over the course of year 7 As a robustness check, we also used an nstrumental varable approach to proxy for selecton nto the treatment. Specfcally, we selected an nstrument that ndcates that the subscrber s aware and readng communcatons from the charty at the tme of the cross promoton. We use each charty s monthly emal newsletter as the ndcator communcaton. For those who receved the emal newsletter, they can choose to clck on any of the story excerpts to read the complete story. We use ths act of clckng on an excerpt to ndcate that the subscrber s aware and readng the charty s outreach and as such, s more lkely to read and consder the nvtaton to jon the second charty than those who do not show nterest n the newsletter. The results from ths IV approach are consstent wth the fndngs below; however, the nstrument was more effectve n dentfyng smaller donors or those who only donated tme and not larger money-donors. IV results are avalable from the authors upon request. 8 For EC and WC, solctatons of money-donatons occur between 12-15 tmes/year and solctatons of tmedonatons occur 40-60 tmes/year, dependng on a varety of factors ncludng poltcal envronment and geographc locaton. Page 11
t. For a measure of the mmedate effect of the treatment, the dependent varable s the dfference between D t, n the year after the treatment and the year before the treatment ( D D D ). For a longer run effect of the treatment, we use a dependent varable as the 1, t 1, t 0 dfference n donatons n the second year after treatment relatve to the year before treatment ( D D D ). 2, t 2, t 0 Genercally, selecton on observables dentfes the treatment effect as: (9) 1, 0, 1, 0, ATT =E E D T X E D T X 1 1 1 ATT =E E D T X E D T X 2 2 2 where the dentfyng assumpton s that X contans all of the varables determnng selecton nto the treatment. Our dataset contans a rch collecton of behavoral varables, ncludng all of the behavoral characterstcs descrbed n Table 1 and 2. A selecton on observables strategy allows us to use Control Group 1 or Control Group 2 as the relevant comparson group to the Treatment Group to the extent that both control groups have a populaton that resembles the treatment group, as determned by the ndependent varables, and the other members are an unbased sample of the whole populaton. Our frst approach s to begn wth ordnary least squares (OLS) whch assumes a lnear structure on (9) for the treatment effect and all of the ndependent varables. (10) D T X 1 1 1 1 1 D T X 2 2 2 2 2 Here t s the affect of the treatment on the treated for the t th year after the treatment. A consstent estmate of the treatment effect requres that the treatment ( T ) s exogenously determned condtonal on the observed ndependent varables ( X ). The set of ndependent varables used are the full set of quarter dummes for the regstraton date wth the orgnal charty (JQtr*Year), number of tme-donatons made n the year before the treatment (ActB4T), number of money-donaton made n the year before the treatment (DonB4T), value of moneydonatons made n the year before the treatment (ValDonB4T), and number of tme-donatons made n the year before treatment nteracted wth the length of tme between frst regstraton and the treatment date (ActB4T*TOFatT). Page 12
A second approach to selecton on observables that relaxes the lnearty assumpton by allowng for a more complex relatonshp between the ndependent varables and selecton nto the treatment s propensty score matchng (PSM). PSM has been wdely used snce 1983 (Rosenbaum and Rubn, 1983) to dentfy treatment effects n applcatons to publc polcy (Brggeman, Towe, and Morehart, 2009; Long, Stockley, and Yemane 2009) poltcal economy (Persson and Tabelln, 2004; and Gerber and Green 2000) and labor outcomes (Deheja and Wahba 2002; Heckman, Ichmura, and Todd, 1997). The frst underlyng assumpton of PSM s the condtonal ndependent assumpton (CIA) or unconfoundedness whch states that selecton nto the treatment s made on observables. Ths assumpton s smlar to the requrement for consstency n the OLS case: any omtted varables are orthogonal to the treatment. Under CIA, dfferences n the dependent varable condtonal on the propensty score can be assumed to be caused by the treatment. The second assumpton s that there exsts overlap n the propensty scores of treated and untreated observatons. 9 Thus, the average treatment effect on the treated (ATT) usng the PSM model can be wrtten as: (11) 1, ( ) 0, ( ) 1, ( ) 0, ( ) ATT =E E D T P W E D T P W 1 1 1 ATT =E E D T P W E D T P W 2 2 2 Where PW ( ) s the propensty score defned as the probablty of treatment condtonal on a vector of regressors (W ). 10 Gven the senstvty of PSM to CIA, PSM practtoners advocate the use of a dfferenced dependent varable to reduce bas (Heckman, Ichmura, and Todd, 1997; Heckman, Ichmura, Smth and Todd, 1998). In addton, practtoners suggest the use of multple specfcaton tests as a check for whether CIA has been satsfed. The lterature concludes that well-specfed models wll be robust to multple specfcaton tests and multple propensty score methods (Smth and Todd, 2005a, 2005b, 2001; Calendo and Kopeng, 2008). Our specfcaton for selecton nto the treatment (as shown n Appendx A) passes the four most-cted specfcaton 9 For small samples ths overlap or common support assumpton can be mportant; however, n the current analyss gven the large sample szes (rangng from 11,000 to 178,000) t dd not prove to be a bndng assumpton. 10 The mplementaton of fve s dscussed extensvely n a seres of publshed communcatons between Smth and Todd (2005b, 2005, 2001) and Deheja (Deheja and Wahba, 2002; Deheja, 2005). Page 13
tests at standard confdence levels. 11 And we fnd consstent results when we measure the treatment effect usng three dfferent matchng algorthms: The nearest neghbor method compares each member of the Treatment Group wth the one member of Control Group 1 who has the most smlar propensty score. 12 The radus method compares each member of the Treatment Group wth everyone from Control Group 1 who has a propensty score wthn a specfed range (+/- 0.001). The kernel method, developed by Heckman, Inchmura and Todd (1998) compares each Treatment Group member wth a weghted average of the Control Group 1 members wthn a specfed bandwdth wth the weghts fallng n that bandwdth. 13 As a fnal robustness check to our analyss, we complete the analyss usng both Control Group 1 and Control Group 2. Gven that Control Group 2 was not offered the treatment, t lkely contans some subscrbers wth characterstcs smlar to those n the Treatment group. Followng the lterature, we devse a second propensty score specfc for ths comparson that passes all specfcaton tests (Smth and Todd 2005a). And we use the three PSM methods above to compare the Treatment Group to Control Group 2, wth consstent results. 5 Results and Dscusson Wthout dong any regressons, summary statstcs for the treatment group and both control groups provde an ndcaton that solctaton by a second group are unlkely to be harmful and may be benefcal. Tables 3 and 4 descrbe the performance of each charty s newly shared subscrbers for the other charty (row 5) and how newly recruted members from the other 11 The four specfcatons (WC-Control1, WC-Control2, EC-Control1, EC-Control2) pass all four specfcaton tests: 1) the standardzed bas was below 3% on the matched sample for all regressors except one n WC-Control1; 2) a t- test of dfference n covarate means on the matched sample yelds no statstcally sgnfcant dfference for any regressors, except one n WC-Control1; 3) a test where the pseudo-r2 s calculated on the matched sample has 0.000 explanatory power (0.001 for WC-Control1); and 4) a lkelhood rato test on the jont sgnfcance of all regressors on the matched sample s rejected for all standard confdence levels for all four specfcatons. 12 To avod comparsons between treatment and control subscrbers wth drastcally dfferent propensty scores, no comparson was done f there was not a propensty score from the Control Group wthn 0.001 of the treatment group member s propensty score. Ths excluded 200 (1.7%) observatons. 13 Followng Smth and Todd (2005a), Brggeman, Towe, and Morehart (2009), and Frolch (2004) we use the Epanechnkov kernel wth the bandwdth (0.01) that produce the most consstent estmate of the ATT at the expense of effcency. Page 14
charty perform (row 6). Each row s dvded nto three sub-rows that descrbe the group actvty n the year before the treatment, the year after the treatment (0-12 months after treatment) and two years after treatment (13-24 months after treatment). 14 Comparng the summary statstcs n Table 3 and 4 shows that the Treatment Group performed better than Control Group 1 or Control Group 2 n terms of donatons n the frst and second year after the treatment (e.g., average money donatons for WC fell by 9.3 percent and 7.7 percent n the frst year after treatment for Control Group 1 and Control Group 2, respectvely; whereas they rose by 28.1 percent n the frst year for the Treatment Group). 5.1 Charty Treatment Effect Each charty appears to fare weakly better wth respect to ther subscrbers who accepted the nvtaton to jon the second charty, suggestng that complementartes exst wth respect to chartable solctaton at least for the two smlarly themed chartes examned here (compare wth Proposton 1). Ths result s shown n Tables 5 and 6 based on the varous econometrc strateges dscussed above. The tables compare the Treatment Group wth the two control groups across three dmensons: 1) number of actons taken 1 and 2 years after the treatment; 2) number of money donatons made 1 and 2 years after the treatment; and 3) value of money donatons made 1 and 2 years after the treatment. Table 5 shows evdence of complementartes: those that were solcted by an addtonal charty make statstcally more tme donatons to ther orgnal group than those who were only solcted by one charty. That result s stronger for WC whch receved 3 to 5 more tme donatons per subscrber n the year subsequent to the treatment compared to EC whch receved between 1.3 and 1.5 more tme donatons. The two chartes also receved a weakly hgher number of money donatons from ther subscrbers who were also solcted by the other charty, though the statstcal sgnfcance vares across econometrc methods. The OLS and at least one of the PSM algorthms show sgnfcant results of 11 to 20 more money donatons per 1000 subscrbers n the year after the treatment for both groups from those n the Treatment Group. Results for the value of the money donatons are more mxed. EC saw lower total money 14 Due to the dfferent treatment dates for the two groups, the descrpton of one year after the promoton for WC does not cover exactly the same date range as one year after the promoton for EC, thus row 5 from Table 3 does not exactly equal row 6 from Table 4 even though they descrbe the same people and ther actvty for the same charty. Page 15
donatons from the Treatment Group, though the results were not sgnfcant; whereas, WC saw hgher total money donatons, though n all but one case the results were not sgnfcant. The complementartes evdent n the frst year carry through to the second year, though appear to be somewhat muted across all three dmensons. The number of tme-donatons, whle remanng statstcally sgnfcant, falls for EC to 0.5 addtonal tme donatons per year per person for the Treatment Group and falls for WC to 2 per year per person. EC observes statstcally more money donatons (13 to 20 per 1000 subscrbers n the second year after the treatment) but the total value of money donatons s nsgnfcantly dfferent from the untreated group. WC sees no statstcal dfference between number and value of money donatons two years after the treatment. Those results for EC and WC suggest that the complementarty effect of the treatment has some endurng effects but becomes muted over tme. The same analyss usng Control Group 2 (Table 6) shows smlar results for both chartes wth respect to the number of tme and money donatons. However, relatve to Control Group 2, the Treatment group makes a statstcally greater value of money-donatons for WC n the year after the treatment and wth respect to EC, two years after the treatment. Those results renforce the possblty that complementartes are present n chartable solctaton. We can summarze these results as follows: Result 1 Tme donatons and, to a lesser extent, the number of money donatons from ntal donors ncrease f they are contacted by the second charty, demonstratng complementartes n gvng when solcted by two chartes. 5.2 Sector Treatment Effect Next we consder how the chartable communty fared followng the treatment,.e., by how much dd donatons ncrease overall for those n the Treatment Group who were solcted by two chartes nstead of one. Followng Proposton 2, an ncrease n total gvng necessarly occurs when complementartes exst. Gven that the ntal charty observed weakly larger donatons of tme and money, one would expect that f those n the Treatment Group donated at all to the second charty, ther total donatons would ncrease. Page 16
Tables 7 and 8 provde strong evdence that ndvduals n the Treatment Group ncreased the number of total tme and money donatons and the value of total money donatons when they were solcted by both chartes. Those n the Treatment Group made between 7 and 9 more tme-donatons per year and were 5 to 7 percent more lkely to make a money donatons n the year after the treatment. Wth respect to value of money donatons, those n the Treatment Group who were orgnally from WC gave n total $2.70 to $5.08 more (statstcally sgnfcant) n the year subsequent to the treatment. Those orgnally n EC gave between $0 and $2.71 more n the year after the treatment, though most of the statstcal sgnfcance comes from Table 8 n comparng the Treatment Group to Control Group 2. Two years after the treatment, ndvduals mantaned ther elevated money-donaton frequency and amount, but decreased ther number of tme donatons. Those n the Treatment Group who were orgnally from WC made statstcally more tme donatons than the control group but fewer than they made n the frst year after the treatment. However, money donatons remaned elevated for those n the Treatment Group for both chartes: the Treatment Group was 5 to 7 percent more lkely to make a money donaton and when they donated, gave more. Those effects are consstent when the Treatment Group s compared to ether Control Group 1 or Control Group 2. We summarze our fndngs n the followng result: Result 2 Donors ncrease ther total tme donatons and money donatons when they are contacted by two chartes nstead of a sngle charty. The extent of ths ncrease dffers dependng on whch charty the agents were ntally solcted from. 5.3 Evdence of Sortng and Heterogeneous Donor Qualty Independent of the presence of complementartes, one potental cost to each charty that partcpated n the exchange s that ther subscrbers who were exposed to a new charty may decde to swtch afflatons as was descrbed n the theory secton for those subscrbers orgnally n regons A1 or A2 of Fgure 1. Such swtchng could occur when an ndvdual just stops readng or respondng to the communcatons from one charty, but that s dffcult to Page 17
observe or know. Alternatvely, swtchng can be observed n the data when ndvduals choose to unsubscrbe from communcatons from one charty. Due to prvacy laws, an unsubscrbe request mandates that the charty not contact the subscrber agan for any purpose unless the ndvdual actvely requests to be contacted agan. Four types of unsubscrbe requests can be used to tell the mgraton story: the two requests from subscrbers n the Treatment Group to ther orgnal charty and the two requests from subscrbers n the Treatment Group to ther new charty. Table 9 shows that EC was less profcent n retanng both ther new subscrbers and ther orgnal subscrbers compared to WC and thus, there s evdence of a mgraton from EC to WC through the treatment. Because the selecton nto the new group s not somethng controllable by each group, t s approprate for each group to consder the new members as exogenously assgned to the group. Consequently, we evaluated the unsubscrbe rate usng a probt regresson on the Treatment varable. In the analyss comparng the unsubscrbe rate of the Treatment Group to the sum of Control Group 1 and 2, EC observed a 7.0 percentage pont hgher unsubscrbe rate for new members receved from WC and a 3.3 percentage pont hgher unsubscrbe rate for members shared wth WC as a result of the treatment. Conversely, WC observed only a 1 percentage pont hgher unsubscrbe rate for new members receved from EC, but a 1.5 percentage pont lower unsubscrbe rate for exstng members shared wth EC. Thus, had each group receved an equal number of subscrbers n the exchange, WC would have retaned a larger number of ther orgnal subscrbers and new subscrbers relatve to EC. Result 3 A subset of donors sorts from one charty to the other by unsubscrbng. Dfferences n the success of retanng donors ndcate qualty dfferences between the chartes. To llustrate these qualty dfferences we agan refer to Fgure 1. If one charty, say charty 1, has a hgher qualty (e.g., more effcent n provdng a publc good, provdng a superor good, etc.), regon A1 would be relatvely large compared to regon A2. Dependng on the ntal dstrbuton of donor types, ths would lead to a stronger movement of donors from charty 2 to 1 than n the opposte drecton. Page 18
One way to evaluate the qualty of the new subscrbers s to consder each charty s success at generatng tme or money donatons from the new subscrbers relatve to the rest of ther lst. Table 10 compares the Treatment Group wth each charty s orgnal members. In the year after the treatment, those n the Treatment Group were more lkely to make tme or money donatons than others subscrbers. The ncremental qualty of the new members jonng EC appears to be hgher than those jonng WC, as evdenced by a larger number and value of money donatons made to EC than WC. Specfcally, those members who were new to EC were 3 percent more lkely to donate and gave $1.21 per person per year more than the Control Groups n the year after the treatment; those new to WC were 1.6 percent more lkely to donate and gave a statstcal ndstngushable amount relatve to the Control Groups. That provdes support for the suggeston that WC began wth a hgher qualty lst than EC. That effect s ncreased n the second year of the treatment. WC shows some evdence of elctng more tme donatons from ther new members (4 more tme donatons per year) but dd not receve larger money donatons from ther new members. Conversely, EC saw fewer tme donatons n the second year for ther new members, relatve to the rest of ther lst, but observed no decrease n the qualty of the new members wth respect to number and value of money donatons. 6 Conclusons Competton between chartes for donatons from a fnte group of potental donors s a queston that nterests chartes and ther fundrasers, partcularly as they consder how aggressvely to allow ther current donors to be solcted by other chartes. We provde an analytcal model to predct that donatons from any ndvdual donor to a sngle charty can only ncrease when she s addtonally solcted by another charty, f complementartes n gvng exst. Usng a unque dataset and experment, we fnd evdence for such complementartes n chartable competton; namely, that when ndvduals are solcted by two chartes nstead of just one, ther contrbutons to each charty and ther collectve contrbuton to both chartes ncreases. We thereby demonstrate that for the observed chartes, swappng ther donor lsts ndeed proved benefcal. Extendng those results to the chartable sector at large depends on whether the observed complementartes do generally occur. It s obvous that the mutual benefts cannot occur f one Page 19
charty domnates the other, e.g. by provdng the same publc good n a more effcent way. The results from ths study already provde a warnng for those chartes who beleve they would beneft by sharng ther subscrbers wth other organzatons: WC saw more quantty and value of donatons from ther exchanged subscrbers and fewer unsubscrbe requests from ther new members compared to EC. Thus, ths research suggests that some chartes may beneft more than others from exchanges. Anecdotal evdence suggests that WC was the more effectve of the two groups n terms of campagn content and achevng successes for ther consttuents. That could explan the superor performance of ther new recruts from the exchange. Complementartes also may be weaker f the two nteractng chartes are not engaged n related chartable gvng sectors. Ths study examned two chartes that advocated on envronmental ssues, but does not necessarly provde nsght nto the complementartes between chartes that provde completely dstnct servces. Speculatng about the exact psychology of how the complementarty works, one mght post that recevng communcatons from two chartes may elevate an ndvdual s awareness of the publc good or the mportance of phlanthropy. Smlarly, solctatons from an addtonal charty may also gve the donor new nformaton on the relatve mportance of the cause served by the ntal charty and/or the effcency of the charty n generatng the publc good. In ths paper, we provde frst nsghts that competton among chartes for donors may prove benefcal for the chartes nvolved. To nvestgate the generalty and the source of the complementartes that we dentfed n ths paper remans a benefcal area of future research. Page 20
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Table 1. Behavor Comparson of Control and Treatment Groups for EC Control Group 1 Treatment Group Total Offered Control Group 2 1 Total Number 167,748 10,605 178,353 12,380 2 Average Years on Fle (std) 1.50 (0.779) 0.886 (0.782) 1.47 (0.793) 1.49 (0.765) Money Donor Behavor 3 % Prevous Money Donors 1.80% 5.13% 2.00% 2.59% 4 snce Reg, cond on gvng 62.66 (242.56) 45.05 (54.37) 59.97 (224.39) 38.13 (30.50) 5 Average Total $ M- Donaton snce Reg, cond on gvng 1.66 (2.20) 1.87 (2.13) 1.69 (2.19) 2.14 (2.95) 6 1 yr before Offer 0.0218 (0.271) 0.0755 (0.487) 0.0250 (0.289) 0.0353 (0.378) 7 1 yr before Offer, cond on 1 T- Don 1.54 (1.69) 1.68 (1.61) 1.56 (1.68) 1.88 (2.04) 8 Val. of M- 1 yr before Offer 1.28 (40.61) 3.42 (30.55) 1.41 (40.09) 1.16 (11.07) 9 Val. of M- 1 yr before Offer, cond on 1 T- Don 90.59 (329.11) 75.99 (123.56) 88.15 (304.61) 61.58 (52.88) Tme- Donaton (Acton) Behavor 10 % Prevous Tme Donors 43.57% 89.84% 46.32% 58.34% 11 snce Reg 1.44 (3.05) 5.55 (6.40) 1.69 (3.49) 4.31 (7.35) 12 snce Reg, cond on 1 T- Don 3.72 (4.27) 6.27 (6.51) 4.08 (4.73) 8.44 (8.82) 13 1 yr before Offer 0.838 (1.79) 3.92 (3.70) 1.02 (2.09) 2.22 (3.73) 14 1 yr before Offer, cond on 1 T- Don 2.49 (2.32) 4.48 (3.62) 2.78 (2.64) 4.63 (4.23) Table 2. Behavor Comparson of Control and Treatment Groups for WC Control Group 1 Treatment Group Total Offered Control Group 2 1 Total Number 86,099 4,470 90,569 7,014 2 Average Years on Fle 2.23 (1.43) 1.41 (1.41) 2.19 (1.44) 2.61 (1.36) Money Donor Behavor 3 % Prevous Money Donors 4.45% 7.47% 4.60% 6.06% 4 snce Reg, cond on gvng 1.50 (1.00) 1.80 (1.50) 1.53 (1.05) 1.82 (1.46) 5 Average Total $ M- Donaton snce Reg, cond on gvng 70.1 (253.2) 48.5 (56.9) 68.4 (243.4) 41.2 (28.6) 6 1 yr before Offer 0.0262 (0.188) 0.0707 (0.352) 0.0284 (0.199) 0.0391 (0.265) 7 1 yr before Offer, cond on 1 T- Don 1.16 (0.498) 1.39 (0.780) 1.19 (0.539) 1.31 (0.829) 8 Val. of M- 1 yr before Offer 2.19 (56.11) 3.77 (42.28) 2.27 (55.51) 1.71 (15.01) 9 Val. of M- 1 yr before Offer, cond on 1 T- Don 97.54 (361.51) 73.99 (173.15) 95.06 (346.58) 57.54 (66.10) Tme- Donaton (Acton) Behavor 10 % Prevous Tme Donors 70.85% 98.10% 72.20% 85.22% 11 snce Reg 6.30 (15.11) 20.46 (30.29) 6.99 (16.49) 24.82 (34.89) 12 snce Reg, cond on 1 T- Don 12.39 (20.89) 21.39 (30.76) 13.33 (22.30) 36.67 (38.59) 13 1 yr before Offer 2.09 (4.85) 9.67 (9.13) 2.46 (5.40) 7.00 (10.11) 14 1 yr before Offer, cond on 1 T- Don 4.97 (6.45) 10.18 (9.08) 5.51 (6.96) 11.22 (10.79) Page 23
Table 3. Average Treatment Affects 1 and 2 Years after the Treatment for EC 1 3 4 5 6 Total Offered 2 Treatment Group Control Group 1 Control Group 2 EC Members On WC Ste New Members from WC ste Number n EO Group Avg # Tme % Increase from "1 Year Before" Avg # Money % Increase from "1 Year Before" Avg Value Money Donaton % Increase from "1 Year Before" % Unsub from EC 1 Year Before 1.02 - - 0.0250 - - $1.41 - - - - 1 Year After 178,353 0.62-39.2% 0.0253 1.2% $1.14-19.1% 10.0% 2 Years After 0.25-75.9% 0.0275 10.3% $1.28-8.9% 20.0% 1 Year Before 3.92 - - 0.0755 - - $3.42 - - - - 1 Year After 10,605 3.37-14.1% 0.0896 18.6% $3.02-11.6% 12.7% 2 Years After 1.36-65.4% 0.0971 28.6% $3.77 10.3% 18.4% 1 Year Before 0.84 - - 0.0218 - - $1.28 - - - - 1 Year After 167,748 0.45-46.6% 0.0212-2.6% $1.02-20.4% 9.9% 2 Years After 0.18-78.8% 0.0233 6.9% $1.13-11.8% 20.1% 1 Year Before 2.22 - - 0.0353 - - $1.16 - - - - 1 Year After 12,380 1.02-53.8% 0.0292-17.4% $0.83-28.3% 3.4% 2 Years After 0.42-81.0% 0.0292-17.3% $0.92-20.8% 28.2% 1 Year Before - - - - - - - - - - - - - - ** 1 Year After 10,605 7.38 - - 0.0456 - - $2.06 - - 12.3% 2 Years After 7.39 - - 0.0469 - - $1.93 - - 14.7% 1 Year Before - - - - - - - - - - - - - - 1 Year After 4,470 4.57 - - 0.0568 - - $2.33 - - 16.4% 2 Years After 1.76 - - 0.0714 - - $2.44 - - 18.8% **Note that the unsubscrbe rate here s the unsubscrbe rate from WC. Table 4. Average Treatment Affects 1 and 2 Years after the Treatment for WC 1 3 4 Total Offered 2 Treatment Group Control Group 1 Control Group 2 WC 5 Members On EC Ste New 6 Members from EC ste Number n WG Group Avg # Tme % Increase from "1 Year Before" Avg # Money % Increase from "1 Year Before" Avg Value Money Donaton % Increase from "1 Year Before" % Unsub from WC 1 Year Before 2.46 - - 0.0284 - - $2.27 - - - - 1 Year After 90,569 2.95 19.9% 0.0297 4.9% $2.13-6.2% 9.4% 2 Years After 2.49 0.9% 0.0323 13.9% $2.27-0.2% 14.3% 1 Year Before 9.67 - - 0.0707 - - $3.77 - - - - 1 Year After 4,470 15.78 63.1% 0.0787 11.4% $4.84 28.1% 7.9% 2 Years After 11.95 23.5% 0.0746 5.5% $4.70 24.6% 13.0% 1 Year Before 2.09 - - 0.0262 - - $2.19 - - - - 1 Year After 86,099 2.29 9.5% 0.0272 4.0% $1.99-9.3% 9.5% 2 Years After 1.99-5.0% 0.0301 14.9% $2.14-2.5% 14.4% 1 Year Before 7.00 - - 0.0391 - - $1.71 - - - - 1 Year After 7,014 7.59 8.5% 0.0345-11.7% $1.58-7.7% 8.6% 2 Years After 8.30 18.7% 0.0345-11.8% $2.35 36.8% 11.7% 1 Year Before - - - - - - - - - - - - - - ** 1 Year After 4,470 4.22 - - 0.0573 - - $2.34 - - 16.6% 2 Years After 1.52 - - 0.0729 - - $2.50 - - 18.9% 1 Year Before - - - - - - - - - - - - - - 1 Year After 10,605 6.57 - - 0.0461 - - $2.09 - - 10.4% 2 Years After 7.20 - - 0.0452 - - $1.86 - - 14.2% **Note that the unsubscrbe rate here s the unsubscrbe rate from EC. Page 24
Table 5. to Orgnal Charty Comparng Treatment Group wth Control Group 1 for EC and WC; Results are dfference n annual actvty summed across both chartes for 1 year and 2 years after treatment compared to 1 year before treatment. ndep var = Treat (relatve to Offer) (From EC only to EC & WC) 1 Year After X- Promoton 2 Year After X- Promoton (1) OLS 1.506*** 0.0208*** - 0.493 0.520*** 0.0206*** - 0.159 (n = 178,353) [0.0287] [0.00594] [0.901] [0.0167] [0.00634] [0.796] (2) Matchng - Nearest Neghbor 1.303*** 0.0113-1.867 0.465*** 0.0160* - 0.888 (n = 178,337) [0.0379] [0.00937] [1.338] [0.0263] [0.00950] [1.111] (3) Matchng - Radus 1.337*** 0.0148** - 0.335 0.481*** 0.0182** 0.135 (n = 178,337) [0.0367] [0.00730] [0.865] [0.0276] [0.00819] [0.683] (4) Matchng - Kernel 1.378*** 0.0139* - 0.816 0.514*** 0.0137* - 0.272 (n = 178,350) [0.0420] [0.00714] [0.756] [0.0333] [0.00718] [0.710] ndep var = Treat (relatve to Offer) (From WC only to EC & WC) (1) OLS 5.320*** 0.0176*** 0.780 3.703*** 0.0105** 0.959 (n = 90,569) [0.183] [0.00527] [0.736] [0.176] [0.00498] [0.684] (2) Matchng - Nearest Neghbor 3.167*** 0.00405 0.565 2.012*** - 0.00942 0.454 (n = 90,552) [0.248] [0.00789] [0.861] [0.247] [0.00932] [0.922] (3) Matchng - Radus 3.171*** 0.00899 0.916 1.951*** 0.00530 0.952 (n = 90,552) [0.211] [0.00699] [0.656] [0.229] [0.00658] [0.662] (4) Matchng - Kernel 3.241*** 0.0111* 1.001* 2.002*** 0.00424 0.774 (n = 90,567) [0.200] [0.00593] [0.579] [0.212] [0.00652] [0.639] Notes: Standard errors are robust for OLS and bootstrapped (100 teratons) for all matchng estmators. Dep var s dfference between 1 year after or 2 years after treatment and 1 year before treatment; Reg (1) ncludes a varable measurng the tme snce regstraton wth the orgnal group at the tme of treatment (TOFatT ), # actons n year before treatment (ActB4T ), # donaton n year before treatment (DonB4T ), value of donatons n year before treatment (ValDonB4T ), # actons n year before treatment nteracted wth tme on fle at treatment (ActB4T*TOFatT ); Propensty score probt estmaton underlyng reg (2)- (4) nclude full set of year and quarter dummy varables for regstraton date wth the orgnal group (JQtr*Year ), ActB4T*TOFatT, ActB4T, ActB4T^2, ActB4T^3, ActB4T^4, DonB4T, ValDonB4T ; Nearest Neghbor matchng was done on a common support wth calper=0.001, matchng the sngle nearest neghbor(s) (plus others wth dentcal propensty score to that closest nearest neghbor), radus matchng compares all neghbors wthn calper=0.001, Kernal matchng done usng Epanechnkov kernal wth bandwdth set at 0.01. * p<0.10; ** p<0.05; *** p<0.01. Page 25
Table 6. Robustness Check on to Orgnal Charty Comparng Treatment Group wth Control Group 2 for EC and WC; Results are dfference n annual actvty summed across both chartes for 1 year and 2 years after treatment compared to 1 year before treatment. ndep var = Treat (relatve to Control) (From EC only to EC & WC) 1 Year After X- Promoton 2 Year After X- Promoton (1) Matchng - Nearest Neghbor 1.292*** 0.0143 0.643 0.389*** 0.0188 1.057 (n = 22,643) [0.0765] [0.0132] [0.868] [0.0499] [0.0162] [0.860] (2) Matchng - Radus 1.331*** 0.00883 0.313 0.429*** 0.0196 1.065* (n = 22,643) [0.0672] [0.0145] [0.686] [0.0621] [0.0157] [0.588] (3) Matchng - Kernel 1.302*** 0.0206* 0.727 0.445*** 0.0183 0.998* (n = 22,867) [0.0656] [0.0120] [0.573] [0.0503] [0.0138] [0.528] ndep var = Treat (relatve to Control) (From WC only to EC & WC) (1) Matchng - Nearest Neghbor 2.838*** 0.0174 1.508* 2.065*** 0.00412 0.895 (n = 11,284) [0.474] [0.0122] [0.826] [0.499] [0.0173] [2.948] (2) Matchng - Radus 3.217*** 0.0214 2.212** 2.324*** 0.0225 1.760 (n = 11,284) [0.538] [0.0148] [0.979] [0.541] [0.0194] [4.178] (3) Matchng - Kernel 3.197*** 0.0289** 2.845*** 2.882*** 0.0157 0.942 (n = 11,475) [0.405] [0.0134] [0.959] [0.490] [0.0163] [2.413] Notes: Standard errors are bootstrapped (100 teratons) for all matchng estmators. Dep var s dfference between 1 year after or 2 years after treatment and 1 year before treatment; Propensty score probt estmaton ncludes a varable measurng the tme snce regstraton wth the orgnal group at the tme of treatment (TOFatT ), # actons n year before treatment (ActB4T ), # donaton n year before treatment (DonB4T ), value of donatons n year before treatment (ValDonB4T ), # actons n year before treatment nteracted wth tme on fle at treatment (ActB4T*TOFatT ) and TOFatT^2, TOFatT^3, ActB4T^2, ActB4T^3, ActB4T^4 ; Nearest Neghbor matchng was done on a common support wth calper=0.001, matchng the sngle nearest neghbor(s) (plus others wth dentcal propensty score to that closest nearest neghbor), radus matchng compares all neghbors wthn calper=0.001, Kernal matchng done usng Epanechnkov kernal wth bandwdth set at 0.01. * p<0.10; ** p<0.05; *** p<0.01. Page 26
Table 7. Combned Treatment Effect comparng Treatment Group wth Control Group 1 for EC and WC; Results are dfference n annual actvty summed across both chartes for 1 year and 2 years after treatment compared to 1 year before treatment ndep var = Treat (relatve to Control) (From EC only to EC & WC) 1 Year After X- Promoton 2 Year After X- Promoton (1) OLS 8.355*** 0.0650*** 1.534 6.477*** 0.0606*** 1.506* (n = 178,353) [0.108] [0.00687] [0.936] [0.105] [0.00729] [0.818] (2) Matchng - Nearest Neghbor 8.642*** 0.0565*** 0.181 6.920*** 0.0567*** 0.792 (n = 178,337) [0.126] [0.00987] [1.302] [0.124] [0.0108] [1.077] (3) Matchng - Radus 8.676*** 0.0599*** 1.713** 6.935*** 0.0589*** 1.815*** (n = 178,337) [0.114] [0.00879] [0.734] [0.115] [0.00958] [0.571] (4) Matchng - Kernel 8.755*** 0.0595*** 1.243 6.999*** 0.0548*** 1.421* (n = 178,350) [0.131] [0.00821] [0.968] [0.118] [0.00902] [0.763] ndep var = Treat (relatve to Control) (From WC only to EC & WC) (1) OLS 9.380*** 0.0722*** 3.001*** 4.915*** 0.0685*** 2.975** (n = 11,484) [0.215] [0.00985] [0.915] [0.191] [0.00963] [0.741] (2) Matchng - Nearest Neghbor 7.385*** 0.0588*** 2.770** 3.278*** 0.0494*** 2.435*** (n = 11,284) [0.244] [0.0121] [1.116] [0.278] [0.0133] [0.928] (3) Matchng - Radus 7.389*** 0.0638*** 3.121*** 3.216*** 0.0641*** 2.933*** (n = 11,284) [0.215] [0.0114] [0.976] [0.205] [0.0107] [0.780] (4) Matchng - Kernel 7.462*** 0.0675*** 3.312*** 3.269*** 0.0647*** 2.838*** (n = 11,475) [0.217] [0.0107] [0.782] [0.208] [0.0102] [0.666] Notes: Standard errors are robust for OLS and bootstrapped (100 teratons) for all matchng estmators. Dep var s dfference between 1 year after or 2 years after treatment and 1 year before treatment; Reg (1) ncludes a varable measurng the tme snce regstraton wth the orgnal group at the tme of treatment (TOFatT ), # actons n year before treatment (ActB4T ), # donaton n year before treatment (DonB4T ), value of donatons n year before treatment (ValDonB4T ), # actons n year before treatment nteracted wth tme on fle at treatment (ActB4T*TOFatT ); Propensty score probt estmaton underlyng reg (2)- (4) nclude full set of year and quarter dummy varables for regstraton date wth the orgnal group (JQtr*Year ), ActB4T*TOFatT, ActB4T, ActB4T^2, ActB4T^3, ActB4T^4, DonB4T, ValDonB4T ; Nearest Neghbor matchng was done on a common support wth calper=0.001, matchng the sngle nearest neghbor(s) (plus others wth dentcal propensty score to that closest nearest neghbor), radus matchng compares all neghbors wthn calper=0.001, Kernal matchng done usng Epanechnkov kernal wth bandwdth set at 0.01. * p<0.10; ** p<0.05; *** p<0.01. Page 27
Table 8. Robustness Check on Combned Treatment Effect comparng Treatment Group wth Control Group 2 for EC and WC Results are dfference n annual actvty summed across both chartes for 1 year and 2 years after treatment compared to 1 Year before treatment. ndep var = Treat (relatve to Control) (From EC only to EC & WC) 1 Year After X- Promoton 2 Year After X- Promoton (1) Matchng - Nearest Neghbor 8.533*** 0.0586*** 2.622*** 6.785*** 0.0594*** 2.697*** (n = 22,643) [0.146] [0.0136] [0.599] [0.125] [0.167] [0.581] (2) Matchng - Radus 8.572*** 0.0532*** 2.291*** 6.826*** 0.0601*** 2.705*** (n = 22,643) [0.121] [0.0144] [0.657] [0.119] [0.0138] [0.484] (3) Matchng - Kernel 8.627*** 0.0651*** 2.712*** 6.900*** 0.0589*** 2.641*** (n = 22,867) [0.140] [0.0118] [0.627] [0.125] [0.0156] [0.657] ndep var = Treat (relatve to Control) (From WC only to EC & WC) (1) Matchng - Nearest Neghbor 6.982*** 0.0640*** 3.273*** 3.314*** 0.0578*** 2.815 (n = 11,284) [0.547] [0.0153] [0.978] [0.530] [0.0205] [3.458] (2) Matchng - Radus 7.362*** 0.0680*** 3.977*** 3.573*** 0.0762*** 3.680 (n = 11,284) [0.534] [0.0167] [1.205] [0.549] [0.0164] [2.894] (3) Matchng - Kernel 7.416*** 0.0845*** 5.080*** 4.147*** 0.0758*** 2.984 (n = 11,475) [0.471] [0.0158] [0.970] [0.497] [0.0180] [1.870] Notes: Standard errors are bootstrapped (100 teratons) for all matchng estmators. Dep var s dfference between 1 year after or 2 years after treatment and 1 year before treatment; Propensty score probt estmaton ncludes a varable measurng the tme snce regstraton wth the orgnal group at the tme of treatment (TOFatT ), # actons n year before treatment (ActB4T ), # donaton n year before treatment (DonB4T ), value of donatons n year before treatment (ValDonB4T ), # actons n year before treatment nteracted wth tme on fle at treatment (ActB4T*TOFatT ) and TOFatT^2, TOFatT^3, ActB4T^2, ActB4T^3, ActB4T^4 ; Nearest Neghbor matchng was done on a common support wth calper=0.001, matchng the sngle nearest neghbor(s) (plus others wth dentcal propensty score to that closest nearest neghbor), radus matchng compares all neghbors wthn calper=0.001, Kernal matchng done usng Epanechnkov kernal wth bandwdth set at 0.01. * p<0.10; ** p<0.05; *** p<0.01. Page 28
Table 9. Comparson of Unsubscrbe Rate for Treatment Group One Year after Treatment Group EC Probt, New Unsub (mfx) Probt, Old Unsub (mfx) Treat Dscrpton New from WC Exstng To WC # n Treat Group 4,470 10,605 Treat (d) 0.0698*** 0.0328*** [0.00558] [0.00331] Baselne Obs. 0.0956 0.0958 # Observatons 184,598 190,733 Psuedo- R 2 0.00178 0.000950 Group WC 1 Year After X- Promoton Probt, New Unsub (mfx) Probt, Old Unsub (mfx) Treat Dscrpton New from EC Exstng To EC # n Treat Group 10,605 4,470 Treat (d) 0.00976*** - 0.0145*** [0.00311] [0.00416] Baselne Obs. 0.0949 0.0933 # Observatons 103,718 97,583 Psuedo- R 2 0.000158 0.000184 Margnal effects; Standard errors n brackets; * p<0.10; ** p<0.05; *** p<0.01; Dep var s whether member requested no addtonal emal contact (Unsubscrbe); Frst row of regressons: New from other group=1, Control Group 1 + 2 = 0; Second row of regressons: Treatment Group=1; Control Group 1 + 2 = 0. Page 29
Table 10. Donaton Behavor for Treatment Group members new to each charty EC Group Year 1 Year 1 Year 1 Year 2 Year 2 Year 2 Treat (d) 3.923*** 0.0313*** 1.212** 1.239*** 0.0347*** 0.904* [0.0264] [0.00556] [0.612] [0.0133] [0.00571] [0.502] Constant 0.647*** 0.0255*** 1.121*** 0.233*** 0.0250*** 1.139*** [0.00400] [0.000841] [0.0926] [0.00202] [0.000865] [0.0760] # Observatons 195,203 195,203 195,203 195,203 195,203 195,203 Adj R 2 0.101 1.57e- 04 1.50e- 05 0.0423 1.84e- 04 1.15e- 05 F 22007.4 31.69 3.926 8614.0 36.97 3.239 WC Group Year 1 1 Year After X- Promoton 2 Years After X- Promoton Year 1 Year 1 Year 2 Year 2 Year 2 Treat (d) 3.277*** 0.0160*** 0.00171 4.029*** 0.0111*** - 0.395 [0.0885] [0.00225] [0.485] [0.0731] [0.00226] [0.420] Constant 3.288*** 0.0301*** 2.091*** 2.425*** 0.0294*** 2.061*** [0.0277] [0.000704] [0.152] [0.0229] [0.000709] [0.132] # Observatons 108,188 108,188 108,188 108,188 108,188 108,188 Adj R 2 0.0125 4.60e- 04-9.24e- 06 0.0273 2.14e- 04-1.07e- 06 F 1369.9 50.82 1.23e- 05 3036.1 24.16 8.85e- 01 Standard errors n brackets; * p<0.10; ** p<0.05; *** p<0.01; Dep var s actvty for new members from other charty 1 year after treatment and 2 years after treatment compared to Treatment Group, Control Group 1, and Control Group 2 Page 30
Fgure 1. Illustraton of sortng of donor types Fgure 2. Expermental Setup Charty WC 4,470 Promoted & Accept Charty EC 4,470 New from WC Treatment Group 86,099 Promoted & Not Accept 167,748 Promoted & Not Accept Control Group 1 7,014 Elgble, No Promoton 10,605 New from EC 12,380 Elgble, No Promoton 10,605 Promoted & Accept Control Group 2 Treatment Group Page 31
Appendx A Frst stage of matchng estmaton for Tables 5-8 ndep Var # Actons before Treat (ActB4T) ActB4T * TOFatT # before Treat (DonB4T) Value of before Treat (ValDonB4T) ActB4T^2 ActB4T^3 ActB4T^4 Tme On Fle at Treat (TOFatT) TOFatT^2 TOFatT^3 (1) (2) (3) (4) Table 5 & 7 Table 6 & 8 Table 5 & 7 Table 6 & 8 WC only to EC & WC EC only to EC & WC Treat = 1 Treat = 1 Treat = 1 Treat = 1 Control Group 1 = 0 Control Group 2 = 0 Control Group 1 = 0 Control Group 2 = 0 0.302*** 0.239*** 0.378*** 0.347*** [0.00755] [0.0103] [9.241e- 04] [9.486e- 03] 4.059e- 09-1.435e- 07-4.447e- 06*** - 5.078e- 05*** [1.083e- 07] [1.240e- 06] [5.258e- 07] [5.224e- 06] 5.520e- 03*** 5.452e- 02** 1.004e- 03-1.736e- 02 [1.495e- 03] [2.283e- 02] [7.225e- 04] [1.280e- 02] - 1.590e- 05 3.839e- 04-4.848e- 06 1.889e- 03*** [1.255e- 05] [3.938e- 04] [6.783e- 06] [3.976e- 04] - 7.996e- 04*** - 5.435e- 03*** - 4.898e- 03*** - 5.518e- 02*** [3.871e- 05] [3.703e- 04] [2.516e- 04] [2.701e- 03] 1.928e- 05*** 1.230e- 04*** 3.487e- 04*** 3.897e- 03*** [1.341e- 06] [1.162e- 05] [2.694e- 05] [2.787e- 04] - 1.464e- 07*** - 8.895e- 07*** - 8.920e- 06*** - 9.634e- 05*** [1.441e- 08] [1.100e- 07] [8.858e- 07] [8.902e- 06] - - - 1.215e- 03*** - 5.221e- 03*** - - [1.026e- 04] [1.784e- 04] - - 6.169e- 07*** 1.220e- 05*** - - [1.531e- 07] [5.634e- 07] - - - 7.721e- 11-8.755e- 09*** - - [5.971e- 11] [4.763e- 10] Jon Qtr x Year Dummy Included - - Included - - N 90,569 11,484 178,353 22,985 P- bar 0.0182 0.36 0.0232 0.442 Pseudo R2 0.2719 0.2407 0.2721 0.2499 Note: Margnal effects from a probt wth robust standard errors n brackets; * p<0.10; ** p<0.05; *** p<0.01 Page 32