Participation and investment decisions in a retirement plan: the influence of colleagues choices

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1 Journl of Public Economics 85 (2002) locte/ econbse Prticiption nd investment decisions in retirement pln: the influence of collegues choices Esther Duflo,b, *, Emmnuel Sez MIT, Deprtment of Economics E52-252g, 50Memoril Drive, Cmbridge, MA 02142, USA b NBER, 1050 Msschusetts Avenue, Cmbridge, MA 02138, USA c Hrvrd University, Deprtment of Economics, Littuer Center, Cmbridge, MA 02138, USA Received 29 My 2000; received in revised form 18 December 2000; ccepted 22 Jnury 2001 b,c Abstrct This pper investigtes whether peer effects ply n importnt role in retirement svings decisions. We use individul dt from employees of lrge university to study whether individul decisions to enroll in Tx Deferred Account pln sponsored by the university, nd the choice of the mutul fund vendor for people who choose to enroll, re ffected by the decisions of other employees in the sme deprtment. To overcome the identifiction problems, we divide the deprtments into sub-groups (long gender, sttus, ge, nd tenure lines) nd we instrument the verge prticiption of ech peer group by the slry or tenure structure in this group. Our results suggest tht peer effects my be n importnt determinnt of svings decisions Elsevier Science B.V. All rights reserved. Keywords: Peer effects; Retirement sving plns JEL clssifiction: D83; I22 1. Introduction Low levels of svings in the United Sttes hve generted substntil interest in the question of wht determines svings decisions. A vst literture hs studied the *Corresponding uthor. MIT, Deprtment of Economics E52-252g, 50 Memoril Drive, Cmbridge, MA 02142, USA. Tel.: ; fx: E-mil ddress: (E. Duflo) / 02/ $ see front mtter 2002 Elsevier Science B.V. All rights reserved. PII: S (01)

2 122 E. Duflo, E. Sez / Journl of Public Economics 85 (2002) impct of Tx Deferred Accounts (herefter, TDA), such s Individul Retirement 1 Accounts (IRAs) nd 401(k)s, on retirement svings decisions, nd, concurrently, the impct of these plns fetures on enrollment nd contribution rtes. A number of studies ttempted to ssess the effect of economic incentives on individul behvior nd found mixed evidence. The presence of mtching contribution from the employer hs generlly been found to be correlted with higher prticiption 2 rtes, but the level of the mtch rte does not seem to mtter. As Bernheim (1999) points out, mtching lso serves s device to focus the employees ttention. This suggests tht pure economic incentives re not sufficient to explin svings behvior. Recent studies emphsize the role of non-economic fctors, such s finncil eduction nd inerti. Mdrin nd She (2000) show tht defult rules hve n enormous impct on employees prticiption, contribution, nd sset lloction. When they re enrolled by defult in TDA, very few employees opt out. Further, most employees do not chnge the defult contribution rte or the defult lloction of ssets. Bernheim nd Grrett (1996) nd Byer et l. (1996) study the role of finncil eduction. They present evidence tht finncil 3 eduction tends to be remedil but tht it increses prticiption in the pln, suggesting tht employees my not be ble to gther the necessry informtion on their own. This pper contributes to this literture by studying the role of peer effects in TDA prticiption nd decisions relted to the pln. There hs never been study of peer effects on sving decisions. This is surprising, becuse the theoreticl literture suggests t lest two resons why peers ply role in this context. First, the plns re sufficiently subtle tht their dvntges re not obvious to someone who hs not thought crefully bout it. Even when people choose to prticipte, they my lck the informtion necessry to mke investment decisions. The evidence presented by Mdrin nd She (2000) suggests tht lrge proportion of people do not think bout these decisions t ll. The literture on informtionl cscdes (Bikhchndni et l., 1992; Bnerjee, 1992; Elison nd Fudenberg, 1993) provide resons why informtion (correct or not) obtined from co-workers my be n importnt fctor in deciding whether to prticipte nd how to invest giving rise to peer effects. Second, svings decisions my be influenced by socil norms or beliefs bout socil norms. By observing co-workers, people cn lern bout the proper behvior of their socil group, s emphsized by models of conformity (e.g., Bernheim, 1994): individuls my wnt to mintin the sme consumption level s wht is common in their socil group. There is growing empiricl literture on peer effects which essentilly focuses 1 See Poterb et l. (1996) nd Engen et l. (1996) in Specil Issue of the Journl of Economic Perspectives. 2 See, e.g., Ppke (1995), Ppke et l. (1993), nd Kusko et l. (1994). 3 Employers resort to it when they fil discrimintion testing becuse the contribution rtes of the not highly compensted employees re too low.

3 E. Duflo, E. Sez / Journl of Public Economics 85 (2002) on socil behvior, nd the doption of new technologies. Mnski (1993) provides forml exposition of the econometric issues involved in identifying peer effects. Correltion of behvior within peer groups is not necessrily due to the fct tht members of the group directly influence ech other. First, members of the sme group shre common environment, which my influence their behvior. Second, except when individuls re rndomly ssigned to peer group, people with similr preferences tend to belong to the sme group. Both of these generte correltion between group behvior nd individul behvior which does not indicte ny cusl reltionship between the two. Finlly, there my be cusl reltionship between the chrcteristics of the peer group members nd individul behvior which does not reflect either lerning or conformity. For exmple, employees working in firms where other people re well pid my directly benefit from some of these dvntges. This is wht Mnski (1993) clls n exogenous (or contextul) socil effect. In this pper, we sk whether the decisions of employees of lrge university to enroll in the TDA pln, nd the vendor they choose once enrolled, re ffected by the decisions of their collegues in the sme deprtment. We begin by presenting n intriguing exmple, nmely the differences in prticiption rtes mong the university s librries. Although verge stff slry nd experience re very similr cross librries, prticiption rtes re very different. This correltion my be due to peer effects, lthough there could be other resons for it. In the reminder of this pper, we focus on the decisions of the dministrtive nd support stff of the university s whole. There re severl resons why the identifiction of peer effects is esier in this context thn in other situtions previously studied. First, the employees shre common progrm, centrlly orgnized by the university. Informtion sessions on benefits re identicl for ll deprtments in the university. The specific deprtment in which one works therefore does not ffect the level of inputs provided by the firm to help the employees mke their TDA decisions. Second, employees do not choose to work for prticulr deprtment becuse it mde enrollment in the TDA pln esier. It is still possible for the propensity to sve to be correlted within deprtments. For exmple, economists probbly know more bout TDA plns thn physicists, nd thus re more likely to prticipte even if we control for ernings levels. Even when we restrict our smple to the stff, we my not remove ll of this correltion. Third, once we control for individul wges or tenure, the verge wge or tenure in the deprtment my not directly ffect individul enrollment decisions. We follow Cse nd Ktz (1991), nd use this ssumption to construct instruments for the verge prticiption in the pln. The instruments cn still be invlid if there is 4 See, for exmple, Cse nd Ktz (1991) nd Evns et l. (1992) on teengers behvior, Scerdote (2000) on college students behvior nd choices, Bertrnd et l. (1998) on welfre prticiption, Munshi (2000) on contrception, nd Besley nd Cse (1994), Foster nd Rosenzweig (1995), nd Munshi (2000b) on technology doption in developing countries.

4 124 E. Duflo, E. Sez / Journl of Public Economics 85 (2002) correltion between verge wge (or tenure) in deprtment nd the individul s unobserved propensity to sve even fter controlling for individul wge nd tenure. Fourth, presumbly, individuls interct mostly with co-workers who shre observble chrcteristics such s gender, ge, or tenure. Put nother wy, women re more likely to tlk to women, men to men, nd newly hired employees to newly hired employees. Therefore, it is plusible tht the relevnt peer group of n individul is sub-group of his deprtment. We use this presumption to construct test of whether our previous results re due to correlted or exogenous effects. We regress individul prticiption on verge prticiption in his or her own subgroup nd the verge prticiption in the other sub-groups. If there is correltion between the instruments nd the error term t the deprtment level, we would see (spurious) positive coefficient for the verge decision of the other sub-group in the deprtment. Lstly, we study the choice of the mutul fund vendor in ddition to the prticiption decision. Becuse vendors offer similr services, we might think tht employees do not feel very strongly bout ny one vendor, nd tht if some hve preference for one vendor over nother, these preferences re probbly not correlted within deprtments. If, using the forementioned techniques, we find positive ssocition between the choice of vendors within sub-groups nd deprtments, it should reinforce our confidence in the previous findings. The reminder of the pper is orgnized s follows. In Section 2, we provide evidence from the university s librries s n introductory exmple. Section 3 summrizes the resons why behvior my be correlted within deprtments. Section 4 describes the fetures of the university s TDA pln nd the dt. In Section 5, we present the results on the prticiption decisions. In Section 6, we turn to the choice of vendor. We find evidence of peer effects for both prticiption nd vendor choice. Section 7 concludes. 2. Cse study: librries In Tble 1 we present some preliminry, but suggestive, evidence. The tble displys the contribution rtes, slry, nd tenure of the stff in the university s 11 independent librries tht re jointly dministered by centrl librry 5 dministrtion. Librries differ in the number of stff members, but the composition of the stff is similr cross librries. Slry nd yers of services re very similr in ll librries. However, prticiption rtes differ substntilly from one librry to nother. The rtes vry from 0.14 to Is there too much vrince in the distribution of 5 There re other librries in the university tht re dministrtively ttched to specific deprtments, nd re not prt of the centrl librry dministrtion.

5 E. Duflo, E. Sez / Journl of Public Economics 85 (2002) Tble 1 Prticiption rtes in the university librries Rnk by prticiption Prticiption Averge Averge Number level (1) rte (2) slry (3) tenure (4) of stff (5) $35, $35, $36, $33, $34, $39, $29, $37, $29, $34, $31, Notes: column (2) displys the prticiption rte in the 403(b) pln in the 11 librries of the university librry system. Columns (3) nd (4) report verge wges nd tenure, respectively, in ech librry. Column (5) reports the number of employees in ech librry. prticiption rtes cross librries reltive to wht we would expect in the bsence of correltion of behvior within librries? Under the null hypothesis tht the individul probbilities of prticiption re independent nd given by the empiricl verge prticiption rte p over ll librries, the vrince of prticiption rtes cross librries would be equl to However, the ctul empiricl vrince is Using simple bootstrp method, we find tht the null hypothesis is 7 rejected with P-vlue of Alterntively, n OLS regression of individul prticiption on the verge prticiption of other employees in the librry leds to coefficient of verge prticiption (0.31) tht is significnt t the 10% level. This evidence suggests tht behviors re correlted within librries. Gleser et l. (1996) interpret the excessive vrince in crime rtes cross cities s evidence of peer effects. Cn this evidence be interpreted s evidence of peer effects in this context s well? Let us consider other possible resons why the prticiption decisions my be correlted within librries. First, employees in different librries my receive different informtion bout the pln. However, ll librries shre common pln, nd re dministered by common humn resources deprtment, which mkes this unlikely. Second, prticiption rtes could be correlted becuse employees in the sme librries shre common unobserved tste for svings. In this exmple, such correltion my be minimized by the fct tht the centrl librry 6 Under the null hypothesis, the vrince of the verge prticiption, P x, in deprtment with Nx ] employees is p(1 2 p)/n x. Therefore, the vrince of œnxpx is p(1 2 p) for ll x. Empiriclly, ] p(1 2 p) nd the vrince of œnp x x cross x is The null hypothesis cnnot be rejected, however, if we exclude the librry with the lrgest prticiption rte.

6 126 E. Duflo, E. Sez / Journl of Public Economics 85 (2002) dministrtion hires new librry employees. Therefore, they re not hired by different people with different preferences for high or low svings employees. In ddition, initil ssignment to librry seems to be mostly determined by the opening of position suitble to the pplicnt t the time he or she pplied, nd 8 yer to yer trnsitions from one librry to nother re extremely rre. Therefore, it seems plusible tht the ssignment to prticulr librry is not systemticlly relted to one s propensity to sve. However, it is still possible tht the tstes for svings re correlted within librries. First, some librries re more prestigious thn others, nd therefore the humn resources deprtment of the librry dministrtion my direct the most competent pplicnts towrds those librries (the fct tht slries nd tenure do not vry much from one librry to nother is comforting but the stff composition my still differ long unobserved skill dimensions correlted to svings). Second, some librry stff do hve specil skills or chrcteristics (for exmple, employees t the Orientl Studies Librry re more likely to be Asin-Americns), which my be correlted with their propensity to sve. This evidence is therefore suggestive, but by no mens definitive. In the following sections, we present evidence on the importnce of peer effects on the decision to enroll in the TDA nd on the choice of vendor using dt from the university s whole. 3. Interpreting the correltion of behvior within deprtments Does the fct tht behvior is correlted within peer groups imply tht the behvior of n individul is directly influenced by its peer group? Specificlly, cn we use our dt to nswer the following two policy questions: First, if the peer group of n individul chnges, will his prticiption decision chnge? Second, cn svings incentives, such s mtching rtes, or informtion sessions hve multiplier effects, tht is, indirectly influence the decisions of those who were not directly ffected by them? To help nswering these questions, we briefly recll the resons why behvior my be correlted within groups. This section relies hevily on Mnski (1993, 1995). The forml frmework is the following. Ech individul in the university is chrcterized by vector ( y,x,z,u). y is the outcome of interest. In the pper we consider two outcomes. First, we study prticiption decisions. In tht cse, y is dummy for prticiption in the Tx Deferred Account (TDA). Second, we study the choice of the mutul fund vendor conditionl on prticiption. x is the deprtment to which the individul belongs. (Z,u) re individul chrcteristics tht ffect the outcome y. The chrcteristics Z re observbles 8 From totl of 1800 observtions (round 450 employees in librries observed four times over 2 yers), there is only one occurrence of n employee switching from one librry to nother.

7 E. Duflo, E. Sez / Journl of Public Economics 85 (2002) (slry, gender, ge nd yers of service). u is n unobservble sclr which represents unobservble chrcteristics tht might ffect the outcome y, such s tstes for svings or for prticulr vendor tht re not cptured by the observbles. We ssume liner specifiction: y 5 1 be( yux) 1 Zh 1 u. (1) Eq. (1) expresses tht the individul choice y is influenced by the men of y in one s deprtment x (E( yux)), nd by individul chrcteristics (Z,u). The prmeter h cptures the direct effect of observble chrcteristics Z on y. For exmple, individuls with higher slry or with more yers of service re more likely to contribute to the TDA pln. The prmeter b cptures the peer effects or endogenous socil effects in the terminology of Mnski (1993): ech individul is influenced by the verge prticiption in its deprtment. However, there is nother chnnel through which behvior my be correlted within deprtments: some of the unobservble chrcteristics which influence n individul s prticiption (or vendor s choice) my be correlted within deprtment. We cpture this feture with the following expression: E(uuZ,x) 5 U(x). (2) The function U(x) is unknown nd not restricted. Whenever U(x) is not constnt, n OLS regression of y on the men of y in the deprtment genertes non-zero coefficient. In the terminology of Mnski (1993), U(x) is not constnt when there re either correlted effects or exogenous socil effects. Let us describe in more detil the sources of correltion of behvior within groups. Columns (1) nd (2) in Tble 2 summrize this discussion nd nswer, for ech source of correltion, the two questions tht opened this section. First, cn svings incentives (like mtching rtes) or informtion sessions hve multiplier effects? Second, if the peer group of n individul chnges, will his prticiption decision chnge? 3.1. Correlted effects Correlted effects rise when individuls in peer group behve similrly becuse they hve similr unobserved chrcteristics or they shre common environment. First, members of peer group my hve similr preferences. For exmple, fculty members in the deprtment of economics re likely to be more informed bout the dvntges of TDA plns nd hence more likely to prticipte thn fculty members in the deprtment of physics. Likewise, the ssignment of stff to deprtments is not rndom. Most deprtments re responsible for hiring their stff members. Employees my ll be similr becuse they hve been chosen by the sme person, nd ech person in chrge of hiring my emphsize different forms of competence, some of which re quite possibly correlted with propensity to

8 Tble 2 Sources of correltions of behviour: consequences nd identifiction Consequences Identifiction: positive coefficient on verge outcome in deprtment Multiplier Effect of OLS IV Sub-group decomposition Sub-group decomposition effect of chnging OLS IV intervention peer group Own-group Cross-group Own-group Cross-group (1) (2) (3) (4) (5) (6) (7) (8) Correlted effects No No Yes b No/ yes Yes Yes b No/ yes b No/ yes Exogenous socil effects Instrument hs n exogenous socil effect Yes Yes Yes No Yes Yes Yes Yes Instrument hs no exogenous socil effect No No No Endogenous socil effects ( peer effects) Conformity to norm No Yes Yes Yes Yes No Yes No Lerning Yes Yes Notes: column (1) sttes whether we would observe multiplier effect of n intervention such s improving incentives or informtion in the presence of correlted effects, exogenous socil effects, nd peer effects due to conformity or lerning. Column (2) sttes whether we would observe n effect on behvior if the peer group of n individul chnges in the presence of correlted effects, exogenous socil effects, nd peer effects due to conformity or lerning. Columns (3) to (8) indicte, for ech specifiction, whether we obtin positive coefficient on the peer effect prmeter b of Eq. (1) in the text s consequence of correlted effects, exogenous socil effects, nd endogenous socil effects. For Instrumentl Vribles (IV) specifictions, columns (4), (7), nd (8), we ssume either tht the instrumentl vribles generte exogenous socil effects (top) or tht they do not (bottom). For the sub-group decomposition in columns (5) to (8), it is ssumed tht correlted effects re in prt common to the two groups, nd tht there re no cross-group peer effects. b Correlted effects hve no effect on IV estimtes only if instruments re orthogonl to correlted effects (see text for cvets). 128 E. Duflo, E. Sez / Journl of Public Economics 85 (2002)

9 E. Duflo, E. Sez / Journl of Public Economics 85 (2002) sve. For exmple good deprtments my hire competent people, nd competent people my mke good finncil decisions. Second, members of peer group shre common environment. To tke n extreme exmple, if we compred different firms, some of them my not even offer pln to their employees. In our cse, the pln is common to ll employees. However, they my still receive different informtion bout the pln. For exmple, the dministrtive officer of ech deprtment my be more or less effective t relying the relevnt informtion bout TDA plns to the employees. If the correltion of prticiption rtes within deprtments is entirely due to similrity in preferences, the fct tht OLS estimtion of Eq. (1) leds to positive estimte of b hs no impliction for policy. In prticulr, the behvior of given individul will not be ffected if he moves to nother deprtment or if the prticiption rte chnges in his deprtment for some exogenous reson. If the correltion is due to shred feture of the environment, prticiption would be ffected only by modifiction of this feture Exogenous (or contextul) socil effects Exogenous socil effects rise when there is direct cusl reltionship between the verge chrcteristics in the peer group nd the individul outcome of interest, even fter controlling for the individul s own chrcteristics. For exmple, exogenous socil effects would rise if the fct tht everybody else in the deprtment hs high wges directly induces n individul to contribute to the TDA pln. Often, exogenous socil effects cnnot be ruled out, becuse the chrcteristics of other people in the peer group determine the level of inputs received by ech individul. For exmple, it is likely tht there is cusl link between verge wges in firm nd the prticiption of the employees in the TDA. Employees with high wges re more likely to require nd obtin TDA pln from their firm. They re lso more likely to contribute. In order to stisfy the non-discrimintion test, the firm then needs to tke steps to ensure tht the low-pid employees contribute s well. There is therefore cusl effect of the distribution of wges in the firm on the prticiption of low-pid employees. In contrst, in the cse of deprtments within university, the pln chrcteristics nd the discrimintion testing re common cross ll deprtments. However, exogenous socil effects could operte through other chnnels. For exmple, in deprtment where verge slries re high, the deprtment dministrtor my be more likely to inform employees of the existence of the pln. Moreover, individuls could be directly influenced by the chrcteristics of their collegues: for exmple, they my be more likely to sve for retirement if their collegues re older nd closer to retirement. Exogenous socil effects imply tht individuls re influenced by the bckground chrcteristics of their co-workers, but not directly by their ctions. An

10 130 E. Duflo, E. Sez / Journl of Public Economics 85 (2002) OLS estimtion of Eq. (1) would led to positive coefficient b. Two individuls rndomly ssigned to two different deprtments would hve different contribution rtes. However, if the prticiption rte of some individuls chnged, for exmple following n informtion session, or becuse they were given specific incentives, this would not ffect the prticiption of their collegues Endogenous socil effects Endogenous socil effects, in the terminology of Mnski, rise when the outcomes ( y) of the members of the peer group hve cusl effect on the outcome y for ech individul. This cn hppen for two resons. First, members of group my be sensitive to the prevlent group norm. If everyone round them sve, they my wnt to sve s well by desire of conformity (s in Bernheim, 1994). They lern bout the prevlent norm through the observtion of their collegues ctions. They re then directly influenced by the ction of others in the group, but only to the extent tht these ctions inform them bout the norm. Peer effects cn then be present even if individuls re perfectly informed bout the chrcteristics of the pln. Chnging incentives for some members of the group my not hve ny multiplier effect, since nothing hs chnged for the individul who is not directly ffected by these incentive. Second, they could lern bout the pln from those who prticipte. In this cse, individuls lern from ech other, not bout norm, but bout the best choice given their own preferences. The very fct tht someone prticiptes my convince them tht prticipting is beneficil (s in Bikhchndni et l., 1992; Bnerjee, 1992; Elison nd Fudenberg, 1993), or they could be getting from prticipnts (who hve experimented) the tips tht mke prticiption beneficil (s in Foster nd Rosenzweig, 1995). Finncil eduction would hve multiplier effect in this context: few well informed employees in deprtment would be ble to rely the informtion to others. Furthermore, if individuls re mking inferences from observing the ctions of their peers, inducing some individuls to mke the decision tht would be mde by fully informed individul (by providing them 9 specific incentives, for exmple) would lso led to welfre gins. In this pper, we present evidence showing tht behvior is correlted within groups, nd tht the correltion does not seem to be fully ccounted for by correlted or exogenous socil effects. Our dt, however, will not llow us to tell whether the effects rise out of desire for conformity or out of lerning effects. The next section presents the dt. Our results on prticiption nd vendor choice re presented in Sections 5 nd 6. 9 Note tht, in these models, few misinformed individuls cn led everybody to tke the wrong decision (see notbly Bnerjee, 1992). The welfre effect of n informtionl session cn then be very importnt.

11 E. Duflo, E. Sez / Journl of Public Economics 85 (2002) Description of the TDA pln nd the dt 4.1. Fetures of the TDA pln The university we study hs pproximtely 12,500 employees. About qurter of the employees re members of the fculty. The university provides retirement benefits to its employees through trditionl pension pln nd supplementl Tx Deferred Account (TDA) pln. Prt of the trditionl pension pln is Defined Contribution (DC) pln where given percentge of n employee s slry is put into n individul mutul fund 10 ccount run by the fund mnger. The university contributes 3.5% of slries into this DC pln for stff employees nd 5 to 10% (depending on tenure nd ge) for fculty. There is 1 yer witing period for the DC pln benefit to begin. 11 Employees cn lso contribute to TDA pln, 403(b) pln which hs no witing period. Every employee cn contribute to the 403(b) pln ny percentge of their slry up to the IRS limit (pproximtely $10,000 per yer for ech individul). The university does not mtch contributions. In both the DC nd the TDA plns, employees cn choose where to invest their contributions from ny number of four different vendors. Ech vendor provides lrge selection of mutul funds (round 40 ech) tht include money-mrket funds, bonds, nd stocks (both U.S. nd foreign). Ech of the four vendors offer very similr services. All vendors llow customers to chnge their portfolios in very flexible wy through the phone or the internet. We will concentrte on the three 12 biggest vendors which ttrct over 90% of totl contributions. We denote these three vendors R, D, nd V Summry sttistics The university provided us with individul dt on TDA prticiption nd contributions. The university collected four wves of dt (October 1997, June 1998, October 1998, nd June 1999) on ll the employees. Individul identifiers re provided so tht the four wves cn be linked. We use the four wves together nd correct the stndrd errors for clustering t the individul level. A number of vribles re included for ech employee nd ech wve. Tble 3 provides summry sttistics of the vribles we use in this study. It displys mens nd stndrd devitions for three groups of employees. Column (1) is the complete smple (both stff nd fculty). We exclude from this smple ll employees 10 Stff employees hve n dditionl Defined Benefits pln in ddition to the DC pln (b) plns re very similr to the better known 401(k) plns but their use is restricted to not-for-profits firms. 12 The fourth vendor represents only 6% of the contributions. The remining 4% re spred mong few vendors which re no longer offered.

12 132 E. Duflo, E. Sez / Journl of Public Economics 85 (2002) Tble 3 Summry sttistics Complete Stff Fculty smple (1) (2) (3) (A) Generl chrcteristics Number of employees, 10/ 97 10, Number of employees, 06/ 98 10, Number of employees, 10/ 98 10, Number of employees, 06/ 99 11, Slry (men) $48,330 $42,040 $67,610 [31,930] [22,398] [46,009] Slry (medin) $38,300 $36,573 $53,000 Gender (mle) [0.50] [0.49] [0.45] Age [11.7] [11.2] [12.7] Tenure (yers of service) [8.8] [7.8] [11.3] (B) TDA prticiption nd vendor choices Prticiption in the TDA pln [0.477] [0.478] [0.472] Prticiption in the TDA pln when tenure,3 months [0.181] [0.22] [0.158] Shre of vendor R [0.455] [0.450] [0.479] Shre of vendor D [0.429] [0.435] [0.408] Shre of vendor V [0.383] [0.374] [0.383] (C) Deprtments (in 06/99) Number of deprtments 358 Averge number of employees over deprtments [58.7] [47.5] [19.9] Medin number of employees Notes: food nd custodil services excluded. Deprtments with one or two employees only excluded. Business school lso excluded. Sttistics reported in (A) nd (B) re verges over the four wves. In (C), numbers reported re for the wve 06/99 only. working in food nd custodil services, becuse their wges nd contribution levels re substntilly below those in the other deprtments. We exclude the business school s well becuse we did not obtin the brekdown by deprtments 13 within the school. We lso exclude ll deprtments with either one or two employees. In totl, these excluded observtions represent slightly less thn 10% 13 As result, the number of employees in the business school is over 700, much more thn the next lrgest deprtment.

13 E. Duflo, E. Sez / Journl of Public Economics 85 (2002) of the initil smple. Becuse there re strong resons to think tht fculty re sorted into deprtments in wy tht is correlted to their propensity to sve, we lmost entirely restrict the nlysis of peer effects to non-fculty employees. Column (2) presents descriptive sttistics for this smple. Since we re restricted to individuls who prticipte in the TDA when exmining the choice of vendor, we will present results for ll stff members who prticipte. Finlly, we present the descriptive sttistics for fculty in column (3). Tble 3A displys demogrphic nd compenstion chrcteristics of the university s employees. The verge slry mong stff is little over $42,000. The percentge of mle employees in the stff smple is 37%. The verge ge is 41 nd the verge tenure is 7.8 yers. Tble 3B presents informtion on TDA pln prticiption nd choice of vendors. The verge prticiption rte is 36% mong stff. The shre of contributions in vendors D, R, nd V re 33, 33, nd 22%, respectively. Tble 3C presents informtion on deprtments. Our smple is divided into bout 358 deprtments. The verge number of employees per deprtment is 34, nd the medin is 14. The medin number of stff members is nine (the verge is 25.3) nd the medin number of fculty members is only one becuse mny deprtments do not hve fculty employees (the verge is 8.4). 5. Peer effects in prticiption decisions In this section, we first show tht prticiption rtes re correlted within deprtments, nd we then present evidence which suggests tht this correltion is, t lest in prt, driven by socil effects OLS results We rewrite Eq. (1) s follows to correct for the mechnicl correltion between own nd verge prticiption: y 5 1 be ˆ i 2i( yux) 1 Zih 1 u i, (3) where i is n individul observtion, nd Ê ( yux) 5 O y /(N 2 1) 2i j x j[x\hij is the verge of y in deprtment x (excluding individul i). Nx denotes the number of individuls in deprtment x. The results of estimting this eqution by OLS re presented in column (1), Tble 4. We control for gender, dummies for ech ge decde, tenure dummies, nd slry dummies indicting in which decile of the university-wide distribution 14 of slries the individul flls. The OLS coefficient shows tht, controlling for 14 Our results re very robust to the functionl form of control vribles.

14 134 E. Duflo, E. Sez / Journl of Public Economics 85 (2002) Tble 4 OLS nd 2SLS estimtes OLS OLS 2SLS 2SLS 2SLS highest slry tenure tenure pid nd slry (1) (2) (3) (4) (5) Averge prticiption in the deprtment (0.032) (0.034) (0.082) (0.076) (0.059) Highest pid employee prticiption dummy (0.011) Gender (mle dummy) (0.009) (0.009) (0.010) (0.010) (0.009) Age 10 to (0.118) (0.120) (0.123) (0.121) (0.122) 20 to (0.117) (0.117) (0.121) (0.119) (0.120) 30 to (0.116) (0.118) (0.121) (0.119) (0.120) 40 to (0.116) (0.118) (0.121) (0.119) (0.120) 50 to (0.116) (0.119) (0.121) (0.119) (0.120) 60 to (0.118) (0.120) (0.122) (0.120) (0.120) 70 to (0.124) (0.127) (0.128) (0.127) (0.127) Tenure Less thn 1 yer (0.014) (0.014) (0.014) (0.014) (0.014) 1 to 2 yers (0.016) (0.016) (0.016) (0.016) (0.016) 3 to 4 yers (0.016) (0.016) (0.016) (0.016) (0.016) 4 to 7 yers (0.016) (0.016) (0.016) (0.016) (0.016) 7 to 12 yers (0.015) (0.015) (0.015) (0.015) (0.015) Slry decile Decile (0.015) (0.015) (0.015) (0.029) (0.015) Decile (0.014) (0.014) (0.015) (0.029) (0.015) Decile (0.014) (0.014) (0.014) (0.028) (0.014) Decile (0.015) (0.015) (0.015) (0.030) (0.014) Decile (0.015) (0.015) (0.015) (0.030) (0.015) Decile (0.015) (0.015) (0.015) (0.029) (0.015) Number of obs. 32,940 32,517 32,940 32,940 32,940 F-Sttistic of the first stge Notes: smple restricted to stff employees. Food service nd business school employees excluded. Stndrd errors corrected for clustering t the individul levels. In column (3), the instruments re the proportion of employees of the deprtment whose wge flls into ech decile of the university-wide distribution of wges. In column (4), the instruments re the number of employees of the deprtment whose tenure flls into ech ctegory. In column (5), both sets re used together.

15 E. Duflo, E. Sez / Journl of Public Economics 85 (2002) ge, tenure, nd slry, there is strong correltion between individul prticiption decisions nd verge prticiption in the deprtment. Ech dditionl percentge point of prticiption in the deprtment is ssocited with 0.31 percentge point increse in the individul s probbility of prticipting in the TDA. The coefficients of the control vribles re resonble: women tend to contribute more thn men. Prticiption increses with ge, tenure (especilly during the first 4 yers), nd with wges. If there re correlted or exogenous effects, the error term u is correlted with the vrible of interest E ˆ 2i( yux), nd the OLS coefficient cnnot be interpreted s evidence of the presence of peer effects. This discussion is summrized in Tble 2, column (3). The reminder of the pper will try to ddress this concern with dditionl evidence. Before turning to this evidence, we present in column (2) of Tble 4 n interesting dditionl fct: we estimte version of Eq. (3) where we include in ddition dummy indicting whether the highest pid stff member of the deprtment contributes to the TDA (he is therefore likely to be the dministrtive officer) nd we exclude this individul from the smple. The verge prticiption in the deprtment is still positive nd significnt, nd the dummy indicting whether the highest pid member contributes is lso positive nd significnt, indicting tht he hs n influence over nd bove the verge prticiption in the deprtment. Controlling for verge prticiption, individul prticiption is percentge point higher if he or she contributes. This could be due to the fct tht he or she selects employees with tstes tht re similr to his or hers, or tht he or she is importnt in relying the informtion to others. If more informtion were vilble, it would be very interesting to pursue this nlysis further nd see whether peer effects follow the hierrchicl structure within deprtments Two-stge lest squres To rule out the possibility tht the correltion of behvior within deprtments is driven entirely by unobserved correlted chrcteristics, the idel experiment would be to llocte employees rndomly to deprtments (n exmple of rndom lloction of roommtes is studied in Scerdote, 2000), or to induce modifiction of the contribution rte of rndom subset of employees in some deprtments. One would then need to compre the prticiption of the non-ffected employees between those deprtments nd the deprtments where no intervention took 16 plce. 15 If he or she hd no more influence thn nyone else, the coefficient would be 0. We checked tht when we regress individul prticiption on verge prticiption nd the prticiption of rndom person in the deprtment, the coefficient is zero for the prticiption of the rndom person. 16 We will describe such n experiment in more detil in the conclusion.

16 136 E. Duflo, E. Sez / Journl of Public Economics 85 (2002) In the bsence of such n experiment, verge exogenous chrcteristics of the groups could be used s instruments for the verge prticiption (for previous ppliction of this strtegy, see Cse nd Ktz, 1991). As we sw in the previous subsection, tenure nd wges re strong determinnts of prticiption in the pln. Therefore, verge wges nd or tenure in the deprtment re lso strongly correlted with verge prticiption. Thus E(Z1ux), where Z1is set of wge nd tenure vribles, cn potentilly be used s n instrument. The F-sttistic of the first stge correltion between E ˆ ( yux) nd E(Z ux) is strong. These vribles re 2i 1 vlid instruments only if they do not directly ffect the prticiption rtes (through exogenous socil effects), nd if they re not correlted with the unobserved determinnt of svings, two points to which we will return below. In columns (3), (4), nd (5) of Tble 4, we re-estimte Eq. (1) using, respectively, the proportion of individuls in the deprtment who fll in ny given decile of the university-wide distribution, the proportion of individuls in ech tenure ctegory, nd both together, s instruments for verge prticiption. The three coefficients obtined by instrumentl vribles re similr, nd they drop from 0.31 to between 0.17 nd 0.23, which indictes tht the OLS coefficient is upwrd bised, probbly due to omitted correlted effects. The coefficient remins sizeble nd significnt. The effect on individul prticiption of rising the verge prticiption in the deprtment by one percentge point is lrger thn the effect of moving from the first to the fourth decile in the wge distribution. The similrity of the estimtes obtined with the two lterntive instruments is ressuring: n over-identifiction test does not reject the joint vlidity of the instruments. At the bottom of Tble 4, the F-sttistics of the first stge re reported. These sttistics re lrge (between 11 nd 25), showing tht the instruments re significntly correlted with the prticiption rte in ech 17 deprtment. These 2SLS results lone do not constitute definitive evidence, becuse the two conditions necessry for the vlidity of the wge nd tenure vribles s instruments my fil. First, s discussed in Section 3, there my be direct exogenous effect of verge wges or tenure in the deprtment on n individul s prticiption, even fter conditioning for one s wge. Second, unobserved chrcteristics correlted with propensity to sve (e.g., competence ) could well be correlted with the deprtment s verge wge, even fter conditioning for n individul s wge. For exmple, professors slries in the well renowned deprtments my be higher thn in other deprtments, nd these deprtments my lso be ble to hire more competent stff. This discussion is summrized in Tble 2, column (4). A simple wy to ssess whether 2SLS helps to solve the problem is to replce the prticiption vrible with ge. Obviously, ge cnnot be ffected by the ge of 17 The F-sttistics re obtined by running the first stge t the deprtment level. They re, therefore, conservtive.

17 E. Duflo, E. Sez / Journl of Public Economics 85 (2002) collegues through peer effects. An OLS regression of individul ge on verge ge in the deprtment (controlling for gender nd slry) produces positive nd significnt coefficient. However, when verge ge is instrumented with verge slry in the deprtment, the coefficient is much smller nd insignificnt. This suggests tht the IV strtegy cn be successful in removing correlted effects. In the next subsection, we provide dditionl evidence to reinforce our confidence in these results Looking t sub-groups within deprtments Actul peer groups re in mny cses smller thn deprtments. This fct cn be used to help identify peer effects. If peer groups re only subset of ech deprtment, there is n priori restriction on the pttern of peer effects: there should be no effects of the prticiption of members of the other sub-groups on the members of one sub-group. There re sub-groups within deprtments where peer effects cn be expected to be stronger thn for the deprtment s whole. For exmple, newly hired employees my tlk more to other newly hired employees thn to estblished employees, nd vice-vers. Moreover, if estblished employees hve lredy mde their decisions, they re not likely to be ffected by wht newly hired employees do (since decisions re rrely reversed fter length of tenure). Women probbly tlk more to women thn to men, nd men more to men thn to women. Here, we follow n ide developed by Munshi (2000) which proposes to regress individul prticiption for ech sub-group seprtely on the prticiption 18 in their own nd in the other sub-group. If there is deprtment-level correlted effect, it should cuse the coefficient of verge cross-group prticiption to be positive (even in the bsence of peer effects). In other words we run k k k k k y 5 b E( yux,k) 1 g E( yux,k ) 1 Zh 1 u, (4) where k is the sub-group within deprtment (we ssume tht ech deprtment is k prtitioned into two sub-groups with k 5 0ork 5 1) nd y is the outcome of n individul in group k. We denote by k the complement of k. As before, we llow k for the possibility of correltion between u nd x. If we believe tht cross-group k effects re zero (tht is, the prmeter g is equl to 0) nd tht the error terms in ech sub-group re correlted then we cn estimte Eq. (4) by OLS or 2SLS, nd k 19 k test whether the estimte ˆ g is 0. If ˆ g is different from 0, it will indicte tht 18 Bertrnd et l. (1998) exploits relted ide: they study whether the number of welfre prticipnts who spek n individul s lnguge ffect his prticiption, fter controlling for the frction of prticiption in his re of residence. 19 The instruments re constructed s the expecttion of the subset Z in Z in ech sub-group for ech 1 deprtment (E(Z ux,k)). 1

18 138 E. Duflo, E. Sez / Journl of Public Economics 85 (2002) there re correlted or exogenous effects t the deprtmentl level, which bised k our previous estimte. If ˆ g is equl to 0, it will indicte tht previous estimtes were not bised by ny correlted or exogenous effects tht re t lest in prt common to the entire deprtment. There could still be problem with the OLS version of this test: If women nd men re doing different jobs, different person could be in chrge of hiring them or the sme person could emphsize different skills (men nd women would then in effect form two different deprtments ). The sme could pply to tenure, if the person in chrge of hiring hd chnged (lthough it is difficult to imgine tht it would hppen in ll deprtments t the sme time). However, when we combine the sub-groups nd the 2SLS strtegy, we would need to tell complicted stories to explin why ll cross-group effects re zero. For exmple, when we use the slry instrument, we llow for the fct tht womn with high propensity to sve would be more likely to work in deprtment where slries re high. For exmple, if highly pid deprtment hired high svings employees, it would still led to k positive ˆ g, for exmple, unless only women were involved in the hiring of women employees, n implusible ssumption. For ll the sub-groups we consider, it seems resonble to consider tht n omitted deprtmentl effect should be correlted cross sub-groups within deprtment. Tking the results together should therefore give us good ide of the presence of peer effects in retirement pln decisions. Note tht, if the strength of the (group-specific) peer effects vries cross deprtments, nd if they re stronger in deprtments where prticiption rtes re lso higher (for exmple, becuse the dministrtion both encourges interction mong employees nd informs them well bout the pln), the coefficient of own group in this regression will be n overestimte of the verge influence of collegues choices in the university. However, the fct tht we find positive nd significnt coefficient on own group nd zero coefficient on cross-group prticiption will still indicte tht peer effects re present. This discussion is summrized in Tble 2, columns (5) to (8). In Tble 5 we present the results on peer effects mong sub-groups. The first two columns present the results for the prticiption of individuls in group 1, nd the lst two columns present the results for the prticiption of individuls in group 2. In ech pnel, the first line displys the effect of the verge prticiption of members of group 1 nd the second line displys the effect of the verge prticiption of members of group 2. The third line reports the P-vlue for the test tht the two coefficients re equl. Columns (1) nd (3) report the OLS results, columns (2) nd (4) report the 2SLS results using both slry nd tenure s instruments. In Tble 5A we present the effect of the verge prticiption broken down by gender. In columns (1) nd (2) of Tble 5, we see tht prticiption of the femle employees is significntly ffected by the verge prticiption of other women (the OLS nd IV coefficients on femle prticiption re, respectively, 0.20 nd 0.36 nd ll re significnt) but not by tht of men (the coefficients re smller,

19 E. Duflo, E. Sez / Journl of Public Economics 85 (2002) Tble 5 Peer effects on prticiption decisions mong sub-groups Group 1 Group 2 OLS 2SLS OLS 2SLS Instruments slry slry tenure tenure (1) (2) (3) (4) (A) Group 1: femle (19,635 obs.) nd group 2: mle (11,756 obs.) Averge prticiption in group 1 (femle) (0.042) (0.079) (0.048) (0.085) Averge prticiption in group 2 (mle) (0.040) (0.069) (0.046) (0.088) P-vlue of test coeff. differ (B) Group 1: tenure below 3 yers (11,715 obs.) nd group 2: bove 7 yers (13,165 obs.) Averge prticiption in group 1 (young) (0.038) (0.076) (0.046) (0.094) Averge prticiption in group 2 (old) (0.034) (0.082) (0.050) (0.137) P-vlue of test coeff. differ (C) Group 1: young (35 nd below, 12,468 obs.) nd group 2: old (bove 36, 19,049 obs.) Averge prticiption in group 1 (young) (0.040) (0.078) (0.039) (0.069) Averge prticiption in group 2 (old) (0.041) (0.081) (0.042) (0.080) P-vlue of test coeff. differ (D) Group 1: stff (17,849 obs.) nd group 2: fculty (9719 obs.) Averge prticiption in group 1 (stff) (0.059) (0.100) (0.048) (0.066) Averge prticiption in group 2 (fculty) (0.025) (0.033) (0.050) (0.062) P-vlue of test coeff. differ (E) Group 1: deprtment nd group 2: other deprtments in the sme school (27,114 obs.) Averge prticiption in group 1 (own deprtment) (0.033) (0.060) Averge prticiption in group 2 (other deprtments) (0.038) (0.038) P-vlue of test coeff. differ Notes: stndrd errors re corrected for clustering. The regressions include ll the control vribles in Tble 2. Instruments re the proportion of employees in the deprtment whose wge flls into ech decile of the university-wide distribution of wges nd the number of employees in the deprtment whose tenure flls into ech ctegory. In (B), only the slry instruments re used. respectively nd ). The equlity of coefficients of own- nd crossgroups is rejected in both cses. Symmetriclly, in the IV specifiction, the prticiption of the mle employees seems to be ffected by prticiption of other men, but not by the prticiption of women.

20 140 E. Duflo, E. Sez / Journl of Public Economics 85 (2002) In Tble 5B, C, nd D we repet the exercise by breking the smple ccording to tenure (below 3 yers nd bove 7 yers), ge (below or bove 36), nd fculty 20 versus stff. In ll cses, we might expect to find positive cross-group effects, becuse there is no strong priori reson to believe tht peer effects re completely bsent cross these sub-groups. In ll cses, however, cross-group coefficients re very smll (sometimes negtive) nd insignificnt, while owngroup effects re lwys positive. In the 2SLS specifictions, equlity of the coefficients is rejected t the 10% level in ll cses, except one where it is rejected t the 15% level. These results, tken together, suggest both tht there re no peer effects cross these sub-groups within the deprtments nd tht the 2SLS results on own-group verge prticiption re not spurious. It would be interesting to look t other groups (neighbors within deprtment, employees with or without children, etc.). Unfortuntely, we do not hve this informtion. In Tble 5E we present test bsed on the opposite ide. In the university, deprtments re grouped into lrger units (such s librries or the medicl school), which we improperly cll schools. There re 337 deprtments distributed mong 34 schools in our smple. We regress individul prticiption on deprtment prticiption nd verge prticiption of other deprtments in the sme school. A positive coefficient on other deprtments in the sme school would suggest tht there is spurious correltion, t lest t the school level. The coefficients of the own deprtment re essentilly unffected (compred to Tble 4), nd the coefficient of the other units within the school re smll nd insignificnt. The results on prticiption suggest tht the decisions of individuls within one s peer group influence one s decision. They indicte tht people my shre their knowledge bout the pln (nd possibly other svings mechnisms). Mdrin nd She (2000b) hve replicted these specifictions in nother context (for lrge helth insurnce compny) nd find similr results to those we present here. They lso present interesting dditionl evidence. In the firm, ll the employees hired fter 1998 were utomticlly enrolled in the TDA. Mdrin nd She (2000) hd previously shown tht very lrge frction of these employees remined enrolled in the TDA. Interestingly, they show tht the vritions in prticiption cross deprtments cused by the vrition in the number of employees enrolled under utomtic enrollment does not predict lrger prticiption. This is wht we expect if workplce effects operte through discussion nd informtion shring rther thn through pure imittion: presumbly the utomtic enrollees gve very little thought to the problem, nd my even not know tht they re enrolled. We would therefore not expect tht their enrollment would trigger ny enrollment mong their peers. If this interprettion is correct, then we might lso expect to see other decisions 20 For this lst sub-group decomposition only, we use dt on fculty members.

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