NBER WORKING PAPER SERIES CROWDING OUT AND CROWDING IN OF PRIVATE DONATIONS AND GOVERNMENT GRANTS. Garth Heutel

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1 BER WORKIG PAPER SERIES CROWDIG OUT AD CROWDIG I OF PRIVATE DOATIOS AD GOVERMET GRATS Garth Heutel Workng Paper ATIOAL BUREAU OF ECOOMIC RESEARCH 1050 Massachusetts Avenue Cambrdge, MA May 2009 I would lke to thank the atonal Scence Foundaton Graduate Research Fellowshp program for fnancal assstance, the atonal Center on Chartable Statstcs for data, and Dean Corbae, Jason DeBacker, Don Fullerton, Shama Gamkhar, Dan Hamermesh, Matt Kotchen, Andreas Lange, John Lst, Rob Wllams, Rchard Zeckhauser, and semnar partcpants at the Unversty of Texas, the BER 2007 Summer Insttute, the Unversty of Colorado Envronmental and Resource Economcs Workshop, and Stanford Unversty for helpful comments. The vews expressed heren are those of the author(s) and do not necessarly reflect the vews of the atonal Bureau of Economc Research by Garth Heutel. All rghts reserved. Short sectons of text, not to exceed two paragraphs, may be quoted wthout explct permsson provded that full credt, ncludng notce, s gven to the source.

2 Crowdng Out and Crowdng In of Prvate Donatons and Government Grants Garth Heutel BER Workng Paper o May 2009 JEL o. H4,L31 ABSTRACT A large lterature examnes the nteracton of prvate and publc fundng of publc goods and chartes, much of t testng f publc fundng crowds out prvate fundng. Ths paper makes two contrbutons to ths lterature. Frst, the crowdng out effect could also occur n the opposte drecton: n response to the level of prvate contrbutons, the government may alter ts fundng. I model how crowdng out can manfest n both drectons. Second, wth asymmetrc nformaton about the qualty of a publc good, one source of fundng may act as a sgnal about that qualty and crowd n the other source of fundng. I test for crowdng out or crowdng n ether drecton usng a large panel data set gathered from nonproft organzatons' tax returns. I fnd strong evdence that government grants crowd n prvate donatons, consstent wth the sgnalng model. Regresson pont estmates ndcate that prvate donatons crowd out government grants, but they are not statstcally sgnfcant. Garth Heutel Harvard Kennedy School 79 JFK Street, Malbox 84 Cambrdge, MA heutel@fas.harvard.edu

3 2 Publc goods are often provded by both governments and ndvduals. Benevolent governments may provde publc goods to overcome the market's falure; altrustc ndvduals may lkewse do so. The nteracton of these two sources of the provson of publc goods ultmately affects the overall level of fundng. In response to an ncrease n government spendng on a publc good or charty, altrustc ndvduals who care about the total level of the publc good may reduce ther contrbutons. Because of ths "crowdng out" effect, a government choosng to ncrease fundng to a charty by a gven amount may actually ncrease the charty's revenues by only a fracton of that amount. The same effect can occur n the opposte drecton. If a government sees that prvate donatons to a charty have rsen, then t may reduce ts support of that charty. Addtonally, government fundng may "crowd n" prvate donatons f governments use grants as a sgnal of the qualty of a publc good. For both ndvduals and governments who are concerned about publc goods, the mpact of the potental crowdng out and crowdng n effects must be consdered. The lterature on crowdng out extends back at least to Warr (1982) and Roberts (1984), who show theoretcally that an exogenous ncrease n government fundng to chartes can decrease prvate donatons. In those models, crowdng out s exactly one-for-one, snce the altrustc ndvduals care only about the total fundng to the charty and not the source of fundng. 1 Emprcal evdence, ncludng Kngma (1989), fnds that the crowdng out effect s less than one-for-one. One explanaton, provded by Andreon (1989), s that ndvduals are "mpure altrusts" n that they receve a "warm glow" from ther own gvng, ndependent of the level of the publc good. 2 Some studes fnd crowdng n of government grants; Khanna and Sandler (2000) fnd ths for chartes n the UK, and Payne (2001) fnds ths for academc research nsttutons. Rose-Ackerman (1986) descrbes condtons under whch government grants can crowd n prvate donatons. For nstance, matchng grants are lkely to spur an ncrease n donatons. Grants may also come wth mandated regulatory changes that make the charty more appealng to donors. If a charty exhbts economes of scale, then ncreased 1 Early extensons of those theoretcal models nclude Bergstrom et. al. (1986) and Bernhem (1986). 2 More recently, Parker and Thurman (2008) fnd that government provson of open space can crowd out purchases from prvate land trusts, Brown and Fnkelsten (2008) fnd that government provson of health nsurance through Medcad crowds out prvate provson of nsurance, Dokko (2008) fnds that changes n government donatons to the atonal Endowment for the Arts after the 1994 Republcan electoral vctores crowded out prvate donatons to arts groups, Gruber and Hungerman (2007) fnd that ew Deal programs durng the Great Depresson crowded out church spendng on socal servces, and Smmons and Emanuele (2004) fnd that government fundng can crowd out ndvduals' donatons of both money and tme.

4 3 government revenue reduces the margnal cost of provdng the servce, makng prvate donatons more effectve. Fnally, grants may provde nformaton, ether explctly through mandated reportng, or mplctly through the sgnal provded by the grant's acceptance. In a model of revenues of research unverstes, Payne (2001) shows that f government fundng acts as a sgnal of nsttutonal qualty, then crowdng n effects may domnate crowdng out effects. A sgnalng model of contrbutons to chartes s presented n Vesterlund (2003) and Andreon (2006). There, "seed money" from large donors or announcements of prevous donatons ncrease others' donatons by actng as a sgnal of the charty's qualty. Evdence of ths effect s found n a feld experment n Lst and Luckng-Reley (2002). 3 That lterature focuses solely on how government spendng affects ndvdual gvng. Ths paper also examnes the opposte drecton of causalty: do prvate contrbutons to chartes crowd out publc funds? I use a model of the nteracton of government and prvate contrbutons to a publc good to show that government grants can crowd out prvate donatons, or prvate donatons, f set exogenously, can crowd out government grants. Addng asymmetrc nformaton about qualty to the model yelds the concluson that one source of fundng can act as a sgnal of qualty and crowd n the other source of fundng. I then emprcally look for evdence of ether crowdng out or crowdng n n both drectons usng data on prvate and publc contrbutons to chartes. Ths paper makes two contrbutons to the lterature on crowdng out and crowdng n of chartable gvng. Frst, though numerous papers test whether government grants crowd out prvate donatons to chartes, none can be found that ether model or emprcally test, usng a large panel dataset on dverse chartes, for crowdng out n the opposte drecton. 4 In fact, a negatve correlaton between government and prvate fundng of chartes could be evdence for ether type of crowdng out. Here, I test for causalty n both drectons by usng nstrumental varables to control for the endogenety of the other sde's contrbuton. Second, I combne the crowdng out lterature wth the lterature on the sgnalng effects of large contrbutons. 3 Landry et. al. (2006) also fnd some evdence that seed money ncreases others' contrbutons, but they fnd a stronger effect from beng entered n a lottery for a cash prze when donatng and from the physcal attractveness of the person askng for a contrbuton. Lange (2006) develops a model where the lottery prze money s provded by donors and thus acts smlarly to seed money. 4 Garrett and Rhne (2008) use tme seres data on total government and prvate contrbutons to chartes to test for Granger causalty n both drectons. They fnd evdence that grants crowd out donatons and that donatons crowd out grants for some types of chartes and some types of government fundng, though ther results are from aggregate tme seres data, not charty-level data.

5 4 Government grants can act lke seed grants n that they convey nformaton to other donors about charty qualty. I use an extensve panel data set wth fnancal data from almost 30,000 chartes over sx years to test the predctons of the models. In a smple extenson to the standard theoretcal model wth perfect nformaton, I fnd that an exogenous ncrease n government fundng to a publc good causes a decrease n ndvduals' contrbutons, whle an exogenous ncrease n ndvduals' contrbutons causes a decrease n government fundng. Ths decrease n fundng can be one-for-one under certan condtons. When both publc and prvate fundng are endogenous, the level of publc good provson depends on the order n whch the players move. When ndvduals are uncertan about the qualty of the publc good but governments are not, government grants can act as a sgnal to ndvduals of the qualty. In ths case, I show that the crowdng out effect of ncreased fundng can be countered by a crowdng n effect from the sgnal. On net, ether crowdng out or crowdng n of prvate donatons s possble. Emprcally, I look for evdence of crowdng out or crowdng n n both drectons. I fnd strong evdence that government grants crowd n prvate donatons and weak evdence that prvate donatons crowd out government grants. The evdence that government grants crowd n prvate donatons s robust to varous specfcatons of the data sample. The presence of crowdng n of contrbutons to chartes s of concern to both governments and ndvduals who make these contrbutons. A government mght choose an optmal level of provson of a charty or publc good and adjust ts fundng to reach that level. Wthout accountng for the crowdng n response by prvate donors, fundng may exceed the optmal level. Lkewse, f the level of prvate donatons affects government support, then an ndvdual's optmal level of gvng ought to account for the reacton of government grants. Many worry that recent large ncreases n prvate fundng for global publc health ntatves, ncludng large grants from the Gates Foundaton, are causng local governments to reduce health spendng, evdence of crowdng out of government grants. 5 The next two sectons present the theoretcal models that provde the foundaton for the emprcal analyss. Secton 1 shows how crowdng out of government grants or of prvate donatons s possble. In secton 2, I add uncertanty about the qualty of the publc good to the 5 See Cohen (2006) and Smth and MacKellar (2007).

6 5 model, and present a sgnalng model that can lead to crowdng n. Secton 3 descrbes the data, secton 4 the estmaton strategy, and secton 5 presents the results. Secton 6 concludes. I. Crowdng out of Prvate and Government Contrbutons The model presented here s a smple statc equlbrum model of the amount of prvate and publc gvng to a charty or publc good. Consder an economy wth ndvduals ndexed by. Each ndvdual has an exogenous ncome allocaton y, s subject to a lump sum tax τ, 6 and chooses a voluntary contrbuton g to the publc good. The ndvdual gets utlty from consumpton, c, and from the level of the publc good, G. 7 The utlty functon s thus U = U(c, G). Suppose that U x > 0, U xx < 0 for x = c, G, and U cg > 0, where U x represents the dervatve of the utlty functon wth respect to the varable x. Also suppose that U x as x 0, assurng an nteror soluton. The level of the publc good s G = g 1, so that prvate and publc contrbutons to the publc good are perfect substtutes n producton. 8 The ndvdual's budget constrant s y c + g + τ, and ths constrant must bnd. The ndvdual thus makes a sngle choce of g to maxmze U(y g τ, ( g ) ). W 1 The government s benevolent, maxmzng a weghted utltaran socal welfare functon: U( c, G). The coeffcents γ represent the weght on each ndvdual's utlty n the socal welfare functon. 9 The government chooses the tax structure {τ } to maxmze socal welfare. As prevous lterature on crowdng out has consdered government acton (the tax schedule τ ) exogenous, I start by consderng that case n the followng secton. Later, I 1 6 The exogenous ncome and lump sum tax mean that ssues of the dstortonary effects of taxaton are not addressed by ths model. Saez (2004) consders optmal tax polcy n the presence of crowd out and tax dstortons. The model here could be amended to nclude proportonal taxes rather than lump sum, or t could nclude a parameter to represent a margnal cost of publc funds that captures tax dstortons. 7 The publc good G may also ncorporate prvate goods provded by a charty to ndvduals (e.g. food, clothng) as long as donors are altrustc. In other words, the fact that donors feel altrustc towards recpents of chartable servces means that the prvate consumpton of those servces becomes a publc good. 8 In Ferrs and West (2003), the cost of provdng the publc good dffers for publc and prvate contrbutons. They use ths cost-sde explanaton rather than Andreon's (1989) utlty-based explanaton for the partal crowdng out of publc contrbutons that s found emprcally. 9 For recent uses of utltaran, or Benthamte, socal welfare functons, see e.g. Armenter (2007) or Echner and Pethg (2006).

7 6 consder how government responds to an exogenous change n the level of prvate donatons, and n the Appendx how the two types of agents nteract when both move endogenously. Exogenous government acton Frst, suppose that the government sets ts taxes exogenously and consder the response of g0 j1 ndvduals. Indvdual 's problem s: max U( y g, ( g )). Indvdual takes as gven all other prvate contrbutons g j. The frst order condton for ths maxmzaton problem, assumng an nteror soluton, s U c = U G. The left hand sde of the frst order condton s the margnal cost of an addtonal unt of prvate contrbuton, whch s the foregone consumpton from that unt of wealth, U c. Ths s equated wth the margnal beneft of an addtonal unt of prvate contrbuton, equal to the addtonal amount from the publc good that s created from the ndvdual's contrbuton, U G. At a corner soluton, where the ndvdual optmzes by gvng nothng to the publc good, U c > U G, snce the cost of gvng the frst dollar outweghs the beneft. Crowdng out s analyzed by evaluatng dg /dτ, or the change n prvate contrbuton resultng from a change n the forced level of government contrbuton from ndvdual. (Ths s a comparatve statc result for an agent's best-response functon, not for a ash equlbrum contrbuton.) Ths dervatve s evaluated usng the mplct functon theorem on the frst order condton for the nteror soluton: dg U d U cc cc 2U 2U cg cg U U GG GG 1. Prvate contrbutons are perfectly crowded out by the government's contrbuton. 10 Ths result s ntutve; ndvduals only care about the level of the publc good and not about the source of ts fundng, so they are ndfferent whether t s funded through ther voluntary contrbutons or through ther taxes. 11 Snce g and τ appear together always summed n the ndvdual's utlty j j 10 Ths result s comparable Proposton 3 n Andreon (1990). It can also be seen by ncorporatng taxes nto the model of Cornes and Hartley (2007), whch explctly models ndvduals' decsons as a functon of the total amount of the publc good G. 11 The Appendx shows that allowng a warm glow effect makes ths dervatve more complcated and not necessarly equal to 1. Bergstrom et. al. (1986) show how consderng corner solutons can make the crowdng out less than one-for-one: those ndvduals who contrbute nothng cannot respond to a tax ncrease by contrbutng even less.

8 7 functon, each ndvdual can be seen as just maxmzng ths sum, so that any exogenous change n τ s offset perfectly by changng the choce of g. Exogenous Indvdual Acton The prevous secton assumes that the taxes are set exogenously and consders the response of ndvduals to a change n those taxes. Ths structure of the problem s most commonly seen n the emprcal lterature on crowdng out. However, one may just as easly consder the government's response to a change n prvate donatons to publc goods. A large ncrease n prvate donatons to a charty, due to perhaps a fundrasng drve or a hgh-profle event hghlghtng the charty's need, may cause the government to reduce ts gvng to that charty compared to what t otherwse would have gven under the same condtons but wthout the ncreased prvate contrbutons. To capture ths other drecton of crowdng out, suppose that the actons of each ndvdual are treated as exogenous by the government, who then sets the taxes {τ } to maxmze socal welfare. The government s problem s max { 0} 1 1 U[ y g, j1 ( g j )], where prvate gvng g s exogenous. Assume an nteror soluton for all τ. Ths yelds frst j order condtons U U 0 for = 1,,. The socal margnal cost of ncreasng c j1 j G the tax on ndvdual s the foregone value of consumpton for that person. Ths equals the margnal beneft of ncreasng the tax, whch s the value of the ncrease n the publc good. Ths beneft accrues to each person's utlty functon, and hence t s summed over each ndvdual. To evaluate dτ /dg usng the mplct functon theorem, one must calculate the nverse of an matrx (from the frst order condtons). Instead, one can look at the government's socal welfare functon and note that g and τ are perfect substtutes, appearng only as a sum, as they are n ndvdual 's utlty functon n the secton above. Thus the government can act as f maxmzng ther sum, and so any change n a g wll be offset perfectly by a change n τ. Formally, suppose at equlbrum the government chooses τ 1 *, τ 2 *,, τ * n response to donatons of g 1 *, g 2 *,, g * (all nteror solutons). The value of socal welfare s thus

9 8 U( y g * *, 1 j1 ( g j * *)) W *. Consder an exogenous change n just one j ndvdual's donaton level from g k * to g k **. By replacng τ k ** = τ k * - (g k ** - g k *), and keepng all other tax levels the same, the government can acheve the same level of welfare W*. Can the government do any better n ths case? Suppose t can, so that some such that U ( y k k g U ( y k k ** ˆ, g * ˆ, k jk ( g j j ( g * ˆ ) g j j * ˆ ) g j k ** ˆ ) k k. ** ˆ ) W * k ˆ ˆ,..., ˆ 1, 2 exst If ths nequalty holds, then, gven each g = g * (the ntal equlbrum), the government can set all τ = ˆ except for τ k = ˆ k ( gk ** gk *) and get the same level of welfare as n the left-hand sde of the above nequalty. But then W* s not the maxmum level of welfare achevable gven the ntal equlbrum. Ths contradcts the ntal assumpton. Thus, the government cannot do any better n response to a change from g k * to g k ** than replacng τ k ** = τ k * - (g k ** - g k *), and keepng all other tax levels the same. By replacng these changes wth nfntesmal changes, t follows that dτ /dg = -1 and dτ /dg j = 0 for j. The government thus perfectly crowds out any change n prvate donatons through ndvdually based taxes. The prevous two sectons have each consdered a case where one sde of the market acts exogenously; n the frst secton I followed the lterature by assumng the government sets the tax rates exogenously, and n the followng secton I assumed that prvate donatons were set exogenously. The next logcal extenson s assumng both prvate donatons and government grants are endogenous. 12 In the Appendx, I ntroduce ths extenson and brefly descrbe the multple equlbra that can arse from the fact that the players can move n dfferent orders. 13 I acknowledge that, wthout mposng functonal forms or assumng homogenety, not many results beyond frst order condtons are attanable. 12 Ths s smlar to the contrbuton made by Knght (2002) to the federalsm lterature. He departs from the assumpton of exogenous federal grants to states by supposng that they are determned n a poltcal process, so that federal spendng may help determne state spendng, and vce versa. However, he does not study chartable gvng. 13 In fact, the frst order condtons n each of the prevous two subsectons, assumng ether government or prvate behavor exogenous, are best response functons from the ash equlbrum.

10 9 Addtonally, the model makes two assumptons to yeld perfect crowdng out n both drectons: lack of "mpure altrusm" or a warm-glow effect, and a benevolent government. Removng ether of these two assumptons may result n crowdng out beng less than one-forone. The assumpton gnorng mpure altrusm s contrary to much emprcal evdence suggestng that ndvduals do n fact experence a "warm glow" when gvng; neurologcal evdence for a warm glow effect s documented n Harbaugh et. al. (2007). A benevolent government s perhaps an equally dubous assumpton. The Appendx thus also extends the model to nclude warm glow and non-benevolent governments. Those extensons are relegated to the Appendx because they do not affect the qualtatve nature of the results shown above (and n the followng secton). The key result, that of prvate donatons crowdng out government grants, can hold also wthout these two assumptons, although wth a dfferent magntude. A fnal extenson that s also presented n the Appendx ncludes the behavor of chartes n response to government grants or prvate donatons. A growng lterature examnes chartes' response, especally n ther choces over fundrasng expendtures (Andreon and Payne 2003, 2009, Breman 2006). Emprcally, I control for a charty's fundrasng expendtures and allow that varable to be endogenously determned. In the Appendx, I provde an outlne for extendng the theory to allow for chartable fundrasng expendtures. II. Qualty Sgnalng In the model n the pror secton, the government and all ndvduals have perfect nformaton. It s lkely, however, that some uncertanty exsts about the qualty of a publc good and how t affects ndvduals' utlty functons. Furthermore, asymmetres between the government and ndvduals may exst concernng ths uncertanty. Governments may have access to more nformaton about a charty or publc good and consequently be more nformed about ts qualty. Alternatvely, some prvate donors, lke large prvate foundatons, may have more nformaton about charty qualty. I capture ths nformaton asymmetry n the model here and show that when the government has full nformaton, t can use ts tax polcy to sgnal charty qualty to ndvduals. Ths sgnalng can lead to a crowdng n effect that works aganst the crowdng out effect found earler, f a hgher tax rate sgnals a hgher qualty charty towards whch ndvduals want to gve more n donatons. Ths model thus combnes the crowdng out

11 10 lterature wth the lterature on qualty sgnalng of seed grants: government grants can provde the same qualty sgnal as prvate seed grants. 14 In the model that follows, I assume that t s the government that has the full nformaton about charty qualty and thus can use ts tax polcy to sgnal that qualty. The predcton that government grants can crowd n prvate donatons s based on ths assumpton about nformaton asymmetry. What f the nformaton asymmetry goes n the opposte drecton; what f ndvduals observe the qualty of the publc good but the government does not? Clearly, the mplcaton must be that crowdng n can occur n the opposte drecton. Although the model s not perfectly symmetrc between ndvduals and the government, ths result s attanable nonetheless, as long as the ndvduals are frst movers (f the party that receves the prvate nformaton does not move frst, t cannot sgnal that nformaton). Thus, a slghtly extended model predcts that prvate donatons may crowd n government grants, and the emprcal work dentfyng the response of government grants to prvate donatons s testng ths predcton as well. I omt ths extenson, but t s straghtforward. A justfcaton for the assumpton that governments have the prvate nformaton s that governments tend to make large grants to organzatons and so are lkely to spend more tme researchng the effectveness of the charty than ndvduals, who make smaller donatons on average. Ths s true both absolutely and as a fracton of total government versus prvate expendture. To ncorporate nformaton asymmetres, suppose that the publc good G can vary n qualty, measured by the varable α. Followng Andreon (2006), let the ndvdual's utlty functon be defned as U(c,G; α) = u(c ) + v(g;α) where, as before, utlty s ncreasng n both consumpton, c, and the level of the publc good, G. Also suppose that dv/dα > 0 and d 2 v/dgdα > 0; that s, both total utlty and the margnal utlty of the publc good ncrease wth α. The separablty of the prvate and publc good n utlty ensures that, under full nformaton (f the ndvdual knows the level of α), an ncrease n α nduces ndvduals to donate more to the publc good. Suppose that ndvduals do not know the value of α, but the government does. The government does not convey ths nformaton drectly to ndvduals, but t sets taxes based on 14 The model s thus qute smlar to the models n Payne (2001), Vesterlund (2003), and Andreon (2006). Of those, only Payne (2001) explctly consders the government actng as the "seed" grant maker or the sgnaler of qualty. However, that model avods dealng wth Bayesan equlbra by supposng a reduced-form functon for the sgnal, where the level of government grants drectly affects ndvduals' belefs about the qualty.

12 11 the value t observes. In the standard sgnalng model, the holder of prvate nformaton s unable to drectly convey that nformaton, usually because such an announcement cannot be credble, and thus a sgnal s requred. Why can the government n ths case not merely announce the α t observes? Frst, ths s not n fact observed; governments do not announce the qualty of varous chartes. Second, the government wll want to mpose a tax and make contrbutons to the publc good to overcome the free rder problem. Snce the tax wll end up actng as a sgnal, the value added of a drect announcement s zero, and none s made. Therefore, the government does not announce α because t does not need to after settng the tax rate. For smplcty, assume that the government sets a sngle tax rate τ for all ndvduals. 15 Indvduals choose ther level of prvate donatons, g, smultaneously n response to the government's tax level. Let the government be the frst mover. The game can thus be characterzed by the followng steps: 1. ature chooses a value of the qualty of the publc good, α. 2. Government observes α and sets a tax τ. 3. Indvduals smultaneously choose ther level of prvate donatons to the charty, g, observng τ but not α. Ths game lends tself to beng analyzed n the framework of a perfect Bayesan equlbrum (PBE), n a manner smlar to that of the sgnalng model of Spence (1973). A PBE s defned by a set of strateges of the ndvduals g (τ) and of the government τ(α), and a belef functon of the ndvduals μ(α; τ) that gves the ndvduals' common probablty densty functon for α gven τ, such that the government's strategy s optmal gven the ndvduals' strateges, the belef functon s derved from the government's strategy usng Bayes's rule when possble, and ndvduals' strateges consttute a ash equlbrum of the smultaneous-move game n whch the probablty of α s gven by μ(α; τ). The model can be solved backwards, startng wth the ndvduals' responses to government polcy. Indvdual chooses a non-negatve contrbuton level g to maxmze hs utlty, gven τ and all other contrbutons g -, such that y c + g + τ and G = g + g - + τ. Defne μ(α; τ) as the ndvdual's densty functon of belefs about the value of α upon observng the sgnal τ. The ndvdual's problem s 15 By makng the tax rate dentcal, ths ensures that the sgnal s a scalar. Otherwse, the government has an dmensonal vector wth whch to sgnal the qualty of the good. Ths assumpton smplfes the analyss of the separatng equlbrum, where each value of α s assocated wth a unque value of τ.

13 12 max u( y g ) v( g g ; ) ( ; ) d, g A where A s the support of α. The frst order condton, assumng an nteror soluton, s u' ( y g ) vg ( g g ; ) ( ; ) d 0. A The key results of the model are found n ths condton. Suppose there s a strctly separatng equlbrum, so that for any value of α observed, the government sets a unque tax τ(α). Then ths functon must be nvertble to α(τ). Snce ndvduals' belefs must be derved from Bayes' rule, t follows that μ(α;τ) = 1(α = α(τ)), where 1( ) s the ndcator functon equal to 1 f the argument s true and 0 otherwse. In a PBE wth a separatng equlbrum, ndvduals are certan about the true value of α after observng the sgnal. The ntegral then falls out of the frst order condton, whch becomes u' ( y g ) v ( g g ; ( )) 0 G. Ths condton can be used to fnd the effect of the tax on prvate donatons va the mplct functon theorem: dg u''( c ) vgg ( G; ( )) vg ( G; ( )) '( ). d u''( c ) v ( G; ( )) The denomnator s strctly postve. The numerator can be dvded nto two parts. The frst two terms are strctly negatve, and they represent the crowdng out effect found n the last secton. 16 Wth no uncertanty about the qualty of the publc good, α'(τ) = 0 and the fnal term n the numerator vanshes. Wth uncertanty, ths last term, the sgnalng effect, can ether ntensfy or oppose the crowdng out effect. The frst part of t, v Gα, s postve by assumpton. Suppose that the second part, α'(τ), s also postve, that s, a hgher tax s used to sgnal a hgher qualty charty. Then the sgnalng effect s postve: a hgher tax rate ncreases the level of prvate donatons. The two effects oppose each other. When the tax ncreases, ndvduals want gve to less because more of the publc good s provded for by the government, and they want to gve more because the tax ncrease sgnals that the publc good s hgh qualty. 17 The two effects oppose each other only when α'(τ) > 0. Otherwse, they go n the same drecton. If a hgher tax sgnals a lower qualty publc good, then ndvduals want to donate GG 16 The frst two terms dvded by the denomnator do not equal -1, as n the pror secton, snce here the model has been smplfed by assumng the government sets an dentcal tax on each ndvdual. 17 Compare ths equaton to Equaton 3 n Payne (2001).

14 13 less to that good because of both the crowdng out effect and the sgnalng effect. To fnd α(τ), the government's problem must be solved. Upon observng α, the government maxmzes socal welfare, takng nto account the ndvduals' responses to the tax t sets. It thus solves max ( u( y g ) v( 1 j1 g j ; ), subject to the condton that g satsfes the ndvdual's frst order condton: u '( y g ) v'( g ; ) 0. The government's frst order condton for ths problem, assumng an nteror soluton, s 1 ( u'( c ) v G j ( G; )) j 1 ( u''( c ) v GG ( G; )) 0, where λ s the Lagrange multpler for the constrant from ndvdual 's optmzaton problem. Ths frst order condton mplctly defnes τ(α), though t s dffcult to nterpret wthout further assumptons. Two assumptons can separately be used to show that dτ/dα > 0. One s assumng that the thrd dervatves of both u and v are zero. Under that assumpton, α'(τ) > 0, and the sgnalng effect opposes the crowdng out effect. 18 A more ntutve assumpton s the followng. Assume that v(g; 0) = 0, so that when α = 0 the publc good provdes no utlty. Then, α'(τ) > However, even under ether assumpton the magntudes of the two effects are unknown, as they depend on the utlty functon and parameters. It s possble that the sgnalng effect opposes and domnates the crowdng out effect. In ths case, government grants crowd n prvate donatons. The condtons for that to hold are complex when the utlty functon s left ths general, so ths secton merely demonstrates that crowdng n s possble when government grants act as sgnals of charty qualty. 20 The above results hold under the assumpton of nteror solutons, for both the government's and the ndvduals' choces. At corner solutons, no nterestng results are 18 Ths can be seen from usng the mplct functon theorem on the frst order condton of the government's problem. Droppng all of the thrd dervatves from the result yelds a strctly negatve dervatve. 19 When v(g;0) = 0, the ndvduals' response wll always be to contrbute nothng, and the government's response wll be to set the tax at zero. Snce, n a separatng equlbrum, the tax must be dfferent for dfferent each value of α, as α ncreases from zero so must τ(α). 20 When the utlty functon s specfed as n Vesterlund (2003) and when there are only two values that the qualty varable α can take, the condtons under whch crowdng n occurs can be found analytcally. Intutvely, t s when the dfference n charty qualty s suffcently greater than the dfference n the tax sgnals. When mposng the same utlty form but allowng a contnuous level of charty qualty α, t s not possble to fnd these condtons, snce the sgnal functon α(τ) cannot be found.

15 14 possble, snce ndvduals are contrbutng nothng, and margnal changes n the level of the tax have no effect on prvate contrbutons. More realstc s the case where the tax s set so that some ndvduals are at a corner soluton contrbutng nothng and others are at the nteror wth postve contrbutons. In that case, the above results hold for the subset of ndvduals at nteror solutons, whle those contrbutng nothng have a zero crowdng out effect and sgnalng effect. Thus n the aggregate, the above results hold, though the magntude of the crowdng out or crowdng n s reduced nsofar as some ndvduals are not donors. Ths follows from the analyss of Bergstrom et. al. (1986). Chartes typcally advertse the grants they receve from both governments and prvate grant makers on ther webstes, n newsletters, and n press releases. If government grants crowded out prvate gvng, t s unlkely that chartes would make publc the recept of such grants. On the other hand, grants sgnalng qualty and crowdng n donatons are more consstent wth ths observed behavor. In the emprcal work below, I fnd robust evdence of government grants crowdng n prvate donatons, suggestng that the sgnalng effect domnates the crowdng out effect. III. Data The data on nonproft organzatons come from IRS tax returns fled by elgble organzatons. These data are collected and dstrbuted by the atonal Center for Chartable Statstcs (CCS) at the Urban Insttute. 21 They are based on the Forms 990 or 990EZ that must be fled by all 501(c)(3) nonproft organzatons except for relgous organzatons and any organzaton wth less than $25,000 n gross recepts. 22 These data from are contaned n the Gudestar-CCS atonal onproft Research Database, whch contans 1,388,480 observatons from all publc chartes that fled wthn those fscal years. The data set does not nclude 501(c)(3) prvate foundatons, whch receve most of ther money from nvestments and endowments and use t prmarly to make grants to organzatons rather than drectly for chartable servces; prvate foundatons fle IRS Form 990-PF Relgous organzatons receve over half of all chartable gvng n the Unted States (Ronsvalle and Ronsvalle, 2001). Relgous organzatons that receve the majorty of ther revenue from servng the general publc are requred to fle Forms 990. These nclude the Ssters of Mercy hosptal chan and Lutheran Socal Servces. About 15,000 such relgous organzatons were requred to fle n Examnng donatons to Presbyteran Church congregatons, Hungerman (2005) fnds that government provson of chartable servces crowd out church donatons by cents on the dollar.

16 15 Organzatons are classfed accordng to the atonal Taxonomy of Exempt Enttes (TEE), a system developed by the CCS. The TEE dvdes chartes nto 645 centle level codes, collapsble nto 26 major groups and 10 major categores. In order to make my results more comparable wth pror research, I lmt my scope to a partcular set of chartes. Most research n crowdng out or crowdng n of chartable donatons has examned socal servce chartes, and so I select organzatons from the followng TEE categores: crme, employment, food and nutrton, housng, human servces and communty mprovement. 23 The large data set, contanng entres from all 501(c)(3) nonproft chartes that fled wth the IRS between 1998 and 2003, s useful for analyss but also presents problems wth messy data. Froelch et. al. (2000) dscuss the adequacy and relablty of the data from IRS Form 990. Whle t s beleved that the IRS reportng requrements are not treated wth much mportance by chartes, Froelch et. al. (2000) fnd that the reported data are farly consstent wth more detaled audt nformaton, especally n the basc categores of contrbutons, programmng, and fundrasng. Stll, I undertake measures to clean the data. The data set contans 339,716 observatons on 76,725 chartes. I drop observatons for whch there s clear evdence of reportng error. Some chartes report revenues by category (e.g. prvate donatons, government grants) that do not add up to the reported level of total revenues. Lkewse, for some chartes the expendtures do not add up correctly. I purge all of these observatons from the data set, leavng 321,094 observatons (95%) and 75,226 chartes (98%). Though the data are a panel, t s a very unbalanced one. To compensate, I nclude n the base case regressons only those chartes that appear for all sx years, leavng 175,242 observatons (55% of the prevous total) and 29,207 chartes (39%). Below, I consder how lmtng the data set to a balanced panel affects both the summary statstcs and the regresson results. Fnally, I elmnate chartes that ever report a negatve value for prvate donatons, government grants, or program servce revenue, elmnatng an addtonal 69 chartes (only 0.2%). Regressons are performed on ths cleaned data sample as well as on a number of subsamples that elmnate certan types of chartes or observatons, as descrbed below. In general, the results that I obtan n the base case are robust to these dfferent sample specfcatons. Ths s especally mportant to note for ths applcaton, snce prevous 23 These are the organzatons lsted under the 1-dgt TEE codes of I, J, K, L, P and S. Ths s the same set of codes used by Andreon and Payne (2003) for ther set of socal servce organzatons. Andreon and Payne (2003) also exclude some organzatons that they descrbe as not drectly provdng servces, whle I nclude all 501(c)(3) organzatons n those categores (see ther fn 15).

17 16 authors have found that when workng wth data from Form 990s the choce of sample matters greatly for the results. Prevous authors have found dscrepances or errors n smlar data sets, especally n the dentfer varables for the charty's type (TEE code) and state. Among the chartes n the balanced panel, none change ther TEE code over the sx year perod. Some chartes (1,206, or 4.1%) do change states. Ths could be due to data error, whch s problematc snce many of my control varables and nstruments are at the state-year level. Or, t could result n the charty actually relocatng, n whch case I want to take advantage of that varaton. I dentfy the chartes that are erroneously coded as changng states n the followng way. Of the chartes that are reported to change states, 830 of them (68.8%) have the same state lsted for fve out of the sx years, and the year n whch the state s lsted dfferently s not the frst or last year of the sample. As t s unlkely that a charty would relocate one year and then relocate back the followng year, I nterpret these observatons as errors and replace the state varable wth the state from the charty's other fve observatons. The remanng 376 chartes ether moved n the frst or last years of the sample perod or had more than one year n a dfferent locaton, and I do not change the state varables for them. An nspecton of the scans of the orgnal 990 forms for several of these chartes supports ths dstncton between those that actually moved and those that were naccurately reported. 24 The chartes' revenue sources can be seen n Fgure 1, whch dvdes up the average source of fundng nto several categores. 25 The chartes receve 14% of ther revenue from drect publc support, ncludng ndvdual donatons. A larger fracton comes from government 24 Smply droppng all chartes that report movng states from the regresson analyss results n coeffcents of approxmately the same value as n the base case. 25 The frst category s drect publc support, whch s the man category of donatons from ndvduals. Second s ndrect publc support, comprsed manly of donatons gven to the chartes collected by federated fundrasng agences, such as the Unted Way. The next category s government grants, whch ncludes mones from federal, state, and local governments. Program servce revenue s the money collected from the servces that form the organzatons' exempton from tax. For example, a hosptal would count as program servce revenue all of ts charges from medcal servces. Dues collected ncludes only the amount of dues receved that are not contrbutons, for example the dues that go towards a subscrpton to a newsletter or some other beneft. Investment ncome ncludes dvdends and nterest on savngs and cash accounts; rents and sales nclude net revenue from rents and from sales of securtes, nventory, or other assets. Fnally, the last category ncludes all other revenue, ncludng from specal events such as dnners, raffles, or door-to-door sales of merchandse. Revenues are dsaggregated nto these categores only for chartes that fle Form 990, not Form 990-EZ. 87% of chartes do so. onprofts wth ncome less than $100,000 and total assets less than $250,000 may fle Form 990-EZ nstead of Form 990 f they prefer.

18 17 grants (26%). About half of ther revenue comes from program servces. 26 The remanng sources of revenues, ncludng nvestment ncome, are small. Table 1 presents revenues aggregated nto four man categores and compares summary statstcs from the full, uncleaned data set to those from the smaller sample used n the analyss. As a measure of prvate donatons, I combne drect publc support and ndrect publc support. Government grants and program servce revenue have ther own categores, and the remanng revenues are classfed as "other." I also present statstcs on chartes' reported fundrasng expendtures. Table 1 shows that the mean values are all much hgher than the medan values, and even the 75 th percentle values, suggestng a data set that s skewed towards hgh-revenue frms. The dfferences between correspondng statstcs n the full data set and the cleaned sample are small; the mean values of all varables are smaller and the medan and 75 th percentles are larger n the lmted data compared to the full set. The lmted data are slghtly less skewed than the full data, and hence performng econometrc analyses on ths lmted sample may overemphasze the effect from larger chartes. Ths s nvestgated n the regresson results below. Trends n these values from the cleaned data are presented n Fgure 2. The values presented are the average per charty value of government grants and prvate donatons n constant 2002 dollars. The presence of crowdng out n ether drecton mples that spkes n government grants would be accompaned by dps n prvate donatons, and vce versa. o such pattern emerges, snce both values appear to be ncreasng. I turn to regresson analyss to dentfy the presence of crowdng out or crowdng n. IV. Econometrcs Two dfferent emprcal questons are nvestgated. Frst, do government grants crowd out or crowd n prvate donatons to chartes? Second, do prvate donatons crowd out or crowd n government grants? Whle numerous papers have tested for causalty n the frst drecton, no paper has examned causalty n the opposte drecton usng panel data on a large number of chartes. Because of these two questons, I run two separate regressons, one n whch the level of prvate donatons to a charty s the dependent varable and the level of government grants s an ndependent varable, and one wth those two varables reversed. It should be noted that n 26 Segal and Wesbrod (1998) test for crowdng out between all donatons, ncludng prvate and government grants, and program servce revenue.

19 18 these ntal regressons I am merely dentfyng whether crowdng out or crowdng n occurs n ether drecton, and I am not attemptng to dentfy the sgnalng effect modeled n Secton 2. The presence of crowdng n s consstent wth sgnalng but not suffcent to dentfy sgnalng as ts source. Followng these ntal regressons, whch fnd crowdng n of government grants, I wll test whether ths s explaned by sgnalng. I show that crowdng n s stronger among those chartes for whch less nformaton s known by donors,.e. newer chartes. The level of prvate donatons s defned as n Table 1 above: the sum of drect and ndrect publc support. I also add control varables to the regressons. At the charty level, these are the level of program servce revenues and all other revenues. Furthermore, I gather a number of state-year or county-year level varables to control for economc, demographc, and poltcal condtons. These are matched to the charty by the state or county where the charty s located. From the Bureau of Labor Statstcs I obtan the county-year level unemployment rate, and from the Bureau of Economc Analyss the county-year level ncome-per-capta and total populaton. At the state-year level I nclude the fracton of the populaton 65 or older, the fracton of a state's US Congress and Senate delegatons that are Democrats, and a dummy for whether the state governor s a Democrat. Poltcal and economc varables may have mportant effects on the levels of both prvate and publc contrbutons to chartes. A state wth a hgher proporton of Democrats n power s lkely to be composed of more lberal ctzens who may be more wllng to provde fnancal support for chartes. Lkewse, Democratc congresses may be more wllng to approve hgher levels of fundng for these groups. If so, leavng out poltcal proxes causes an upward bas on the coeffcent of nterest. Fnally, because I have sx years of data from thousands of organzatons, I am able to control for organzaton-specfc unobservable effects usng panel data econometrc methods. The Hausman specfcaton test rejects the assumpton that the unobservable effect s uncorrelated wth the other regressors, so a fxed-effects model s employed rather than a random-effects model. Estmates are lkely to suffer from endogenety bas. The amount of prvate donatons and government grants are jontly determned. Unobservable effects may lead to an ncrease n both of these smultaneously, basng the coeffcent estmates upwards. For example, an exogenous event may ncrease the need (or perceved need) for a partcular charty, whch would ncrease that charty's prvate donatons and government grants. Alternatvely, endogenety could bas the estmates downwards. A restructurng of the charty could cause t to reallocate ts

20 19 fundng between donatons and grants, whch would create a negatve correlaton between these two values not due to crowdng out. (Regressons n both drectons wthout usng nstrumental varables are presented n Appendx Tables A1 and A2.) Instrumental varables regresson s used to correct the endogenety bas. Ths requres two separate sets of nstruments: one to nstrument for the level of government grants n the determnaton of prvate donatons and one for the level of prvate donatons n the determnaton of government grants. As nstruments for the level of government grants, I use state-level measures of government transfers to ndvduals from Supplemental Securty Income (SSI) programs. 27 Ths represents the overall level of transfers and government gvng n a state a partcular year. Some states may be more "generous" n ther gvng, and these nstruments should pck that up. 28 The generosty of government s determned n a poltcal process, and thus t may be drectly correlated wth prvate donatons and fal the exogenety requrement: more generous donors elect more generous governments. Ths s controlled for by the ncluson of the poltcal and economc varables descrbed above. Whatever varance there s n a state's level of transfers to SSI that s not accounted for by poltcal or economc varables ought to capture somethng about the government tself rather than about the underlyng electorate, and thus these nstruments ought to satsfy the exogenety assumpton. As an nstrument for prvate donatons I explot the fact that fundng from ndvduals can come from two sources, lsted separately on the Form 990: drect publc support (donatons) and dues. Though membershp dues may seem lke just another name for prvate contrbutons, the nstructons for completon of the Form 990 specfcally state that only payments that are not contrbutons should be lsted under dues. For example, when dues receved exceed the value of avalable membershp benefts (e.g. subscrptons to publcatons or newsletters, reduced-rate admssons to events), the dfference s to be lsted under contrbutons, not dues. Dues are thus what members pay for the prvate goods consstng of membershp benefts, not the publc good that s the charty's prmary purpose. The amount of dues that a charty receves s lkely to be correlated wth the amount of prvate donatons receved, snce chartes wth hgher membershp bases may get more of both types of revenues. However, gven that chartes provde publc 27 Khanna and Sandler (2000), Andreon and Payne (2003), and Payne (1998) use smlar nstruments. Data are avalable from the U.S. Socal Securty Admnstraton webste. 28 Though the basc level of SSI benefts s set at the federal level, many states choose to supplement that value. I also used the level of OASDI benefts as nstruments, but addng those had no effect on the results.

21 20 goods only usng mones from ther contrbutons and not usng mones from dues, the level of government grants ought not to respond to the level of dues. 29 An addtonal consderaton nvolves the response of the charty tself to exogenous changes n recept of grants and/or donatons. A growng lterature examnes, n partcular, how a charty's expendtures on fundrasng for prvate donatons change n response to changes n government grants (Andreon and Payne 2003, 2009). Fundrasng s thus ncluded n the regresson where prvate donatons are the ndependent varable. Furthermore, ths lterature shows that fundrasng expendtures are endogenously determned. Therefore, I add nstrumental varables for fundrasng. I use two dfferent varables at the charty-level as nstruments for fundrasng expendtures. Frst, I use the amount of admnstratve expendtures reported by a charty on the Form Snce the same personnel can be employed to do both admnstratve and fundrasng tasks, the two types of expendtures may be correlated. In years when an organzaton has a hgher level of management expenses, t s lkely to be able to spend more effort and money on fundrasng; the frst stage regresson results support ths clam (see the Appendx tables). Furthermore, the level of prvate donatons that a charty receves n a gven year ought not to be affected by management expenses, snce management expenses are expressly not those expenses used n solctng funds (.e., fundrasng expenses). 31 Second, I use the total labltes of the charty reported n the current year. The dea behnd ths nstrument s that t measures the fnancal securty of the organzaton, whch wll help determne ts fundrasng strategy ndependent of prvate or publc fundng. A charty that n a partcular year faces a less secure fnancal status (as measured by hgher total labltes) may seek to ncrease ts fundrasng expendtures to compensate; ths clam s verfed n frst stage regresson results. A charty's fnancal securty could drectly affect ts level of prvate donatons f donors respond to ths level of fnancal securty (e.g. a donor does not want to gve money to a charty that s on 29 An alternatve nstrument for prvate donatons s a measure of the prce of a dollar of chartable donaton based on the state's ncome tax and rules for allowng deductons of those contrbutons. Ths, however, s a poor nstrument because the donatons to a charty n a partcular state do not necessarly come from donors wthn that state, because tax rates are heterogeneous wthn a state, and because tax rates are lkely to be drectly correlated wth government budgets and hence grants to chartes. 30 Accordng to the nstructons for the Form 990, admnstratve expenses, or "management and general" expenses, are a charty's "expenses for overall organzaton and management, rather than for ts drect conduct of fundrasng actvtes or program servces." 31 Breman (2006) uses the same varable to nstrument for fundrasng expenses n a data set from Swedsh chartes. She notes that n the Swedsh data, some of the management expenses are used towards solctng government grants. In the US data from the Form 990s used here, however, ths s not the case. Thus, for my applcaton, where fundrasng expenses are an endogenous determnant of prvate donatons, the exogenety assumpton s justfed.