Desperation or Desire? The Role of Risk Aversion in Marriage. Christy Spivey, Ph.D. * forthcoming, Economic Inquiry. Abstract

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1 Desperaton or Desre? The Role of Rsk Averson n Marrage Chrsty Spvey, Ph.D. * forthcomng, Economc Inury Abstract Because of the uncertanty nherent n searchng for a spouse and the uncertanty of the future ualty and state of the marrage tself, rsk atttudes lkely drectly mpact the tmng of marrage. The effect of an ndvdual s rsk averson, measured va a seres of hypothetcal gambles over ncome, on tme to marrage s examned usng survval analyss. I fnd that rsk averson sgnfcantly affects tme to marrage, wth more rsk averse respondents marryng sooner than ther more rsk lovng counterparts. Wthn-famly analyses usng sblng data reveal a smlar pattern. In addton, the effect of rsk averson on tme to marrage s larger n magntude and more statstcally sgnfcant for men. One possble explanaton for the dfferent results between the sexes s that women value rsk averson as a desrable trat n potental mates. JEL Classfcaton Codes: J10, J12, J16 * Assstant Professor, Department of Economcs and Fnance, Southern Illnos Unversty Edwardsvlle, Edwardsvlle, IL 62026, USA. Phone: Fax: Emal: cspvey@sue.edu. I wsh to thank Danel Hamermesh, Stephen Trejo, Gerald Oettnger, Paul Wlson, Jonathan Fsher, and semnar partcpants at the Unversty of Texas at Austn and Texas A&M Unversty for many helpful comments and suggestons. 1

2 Desperaton or Desre? The Role of Rsk Averson n Marrage I. Introducton Atttudes toward rsk are an mportant determnant of a vast array of decsons. Such decsons nclude ones wth a bg mpact on lfe: the choce of educaton, the choce of career, nvestment decsons, and even when and f to get marred or dvorced. Most emprcal studes of behavor mplctly assume rsk preferences are dentcal across households. Such a research strategy undoubtedly results n apprecably dfferent predctons of behavor than would occur f rsk preferences are permtted to vary. Whle an ncreasng number of surveys are askng respondents uestons that allow for constructon of a measure of nterpersonal varaton n rsk that s based on economc theory, there s stll a paucty of emprcal studes that explctly nvestgate the mpact of rsk preferences on behavor. 1 I use nformaton on rsk preferences from the Natonal Longtudnal Survey of Youth 1979 (NLSY79) to predct how nterpersonal varaton n these preferences affects the tme-tomarrage decson. Because of the uncertanty nherent n searchng for a partner and the uncertanty of the future ualty and state of the marrage tself, rsk atttudes lkely drectly mpact the tmng of marrage. Rsk preference varables are constructed from a seres of hypothetcal gambles over lfetme ncome that were offered to respondents n the NLSY79. I examne how the rsk preference varables affect the hazard rate nto marrage and fnd that the 1 The two man methods that have been used to calculate measures based on economc theory (an Arrow-Pratt measure) are () evaluatng the actual behavor of ndvduals; and () askng them hypothetcal uestons wth specfc scenaros. For both methods, the argument of the utlty functon has vared (consumpton and asset allocaton, for example). Not all datasets contan consumpton nformaton, and asset nformaton s often ncomplete and naccurate. Snce ths s the case wth the NLSY79, the data used n ths study, the focus here wll be on studes that construct an emprcal measure of rsk averson through hypothetcal uestons asked of respondents. Unlke many studes that evaluate actual behavor, these studes allow constructon of a rsk averson measure for a representatve sample of the populaton and do not focus on just one segment of the populaton, such as stock market nvestors or agrcultural producers. 2

3 more rsk averse marry sooner. I also explot sblng data from the NLSY79 to examne the robustness of the emprcal results by controllng for unobserved famly effects that mght be correlated wth rsk atttudes and fnd ualtatvely smlar results. In addton, I fnd that rsk preferences affect the tmng of marrage dfferentally for the sexes, wth a larger and more statstcally sgnfcant effect of rsk preferences on the hazard rate nto marrage for men. One possble explanaton for ths fndng s that women value rsk averson as a desrable characterstc n a spouse. To explore ths possblty, I analyze spouse characterstcs by the rsk averson of the respondent. I fnd that spouse ualty, n terms of educaton and other measurable trats, s generally lower for more rsk averse men than for more rsk lovng men. Ths fndng s n accordance wth a predcton of a search model: the reservaton prce s decreasng n rsk averson. Spouse ualty of more rsk averse women s usually but not always lower than for more rsk lovng women, suggestng that the effect of a woman s own rsk averson on tme to marrage may be more complex than suggested by a search model. Overall, the results suggest that rsk preferences have some causal nfluence on the tmng of marrage, whether t be from a supply-sde standpont, such as n the case of a basc search model, or from a demand-sde standpont, where rsk averson s a desrable trat. Ths paper contrbutes to a sparse lterature that employs emprcal measures of rsk averson. Many of these studes ask how demographc characterstcs affect rsk atttudes. 2 A few ask how these measures of rsk averson affect behavors lke the propensty to smoke or 2 See, for example, Myata (2003), Hartog et al., (2002), and Donkers et al. (1999). A common fndng s that observable characterstcs tend to explan a small amount of the varaton n rsk averson among people. Other fndngs nclude that females are more rsk averse than men, older ndvduals exhbt more rsk averson, the selfemployed are less rsk averse, and ncome s negatvely correlated wth rsk averson, In one dataset used by Hartog et al., sngle and cohabtng ndvduals are less rsk averse than marred couples. Myata, usng the results of nvestment games played by 400 households n rural Indonesa to dentfy atttudes toward rsk, fnds that one s lvng stuaton s sgnfcant; an ndvdual lvng wth parents s less rsk averse than one lvng n a nuclear household. 3

4 nvest n rsky assets. 3 These studes are, however, cross-sectonal and do not employ survval analyss as does ths paper. To my knowledge, only two exstng studes (Schmdt, forthcomng; and Lght and Ahn, workng paper) employ an emprcal measure of rsk averson to nvestgate the relatonshp between rsk preferences and the marrage market. Schmdt focuses on fertlty but also consders martal tmng of employed women, and Lght and Ahn focus on dvorce tmng. The fndngs of both studes are consstent wth mne. 4 My study adds to Schmdt s by consderng all women and men and explorng the dfferences between the genders, ncludng a dscusson of how spousal characterstcs mght dffer by the rsk averson of respondents. I also am able to better address possble reverse causaton by makng use of the fact that the rsk atttudes uestons are asked earler and more than once n the NLSY79. Beyond ths paper s contrbutons of enhancng our understandng of how rsk atttudes affect behavor and what motvates (at least from an economc perspectve) ndvduals to get marred, the fndngs here have broader mplcatons. If earler marrages are more lkely to end n dvorce, or the more rsk averse are more lkely to stay n a bad marrage, then rsk atttudes mpact welfare through the marrage market, not just through the fnancal market. The remander of the paper s organzed as follows. Secton II presents the theoretcal consderatons, whle Secton III dscusses the data and descrptve statstcs. Secton IV presents and dscusses the emprcal fndngs. Fnally, the last secton contans concludng remarks. 3 See, for example, Barsky et al. (1997) and Guso and Paella (2001). Rsk atttudes are found to be correlated n an expected way wth behavor almost wthout excepton. For example, the more rsk tolerant are more lkely to smoke, drnk heavly, have no health or lfe nsurance, hold stocks or rsky assets, work n the prvate sector, be selfemployed, and mmgrate. 4 Whle much of Schmdt s (forthcomng) paper focuses on rsk atttudes and fertlty, she also consders how rsk averson affects martal tmng for women only and fnds that the more rsk averse do marry sooner. She uses the PSID, where the rsk atttudes uestons asked are the same as n the NLSY79. However, n the PSID the uestons are only asked once n 1996 and asked only of employed respondents. Thus, whle almost all unmarred women answered the rsk uestons, only about half of marred women dd so. Lght and Ahn (Oho State Unversty workng paper) use the NLSY79 and fnd that the more rsk averse are least lkely to dvorce from a frst marrage. 4

5 II. Theoretcal Motvaton The ueston remans: Does marrage attract the rsk averse sooner than rsk lovers, all else eual? Ths ueston s an emprcal one, as dfferent theores predct dfferent answers to ths ueston. I propose that there are two man reasons why rsk averson and age at marrage are nversely related. The frst entals a martal search model, n whch ndvduals search for a mate n the presence of uncertanty about the ualty of potental future mates. The second s that marrage provdes a way to pool rsk n the face of potental unexpected shocks such as an llness or a job loss. In the context of the search model, marryng sooner than the average person should be attractve to the rsk averse because t mtgates the uncertanty of the future. Fndng an acceptable mate s easer than fndng the perfect mate, and the rsk averse searcher may be wllng to accept one of the frst optons that come along because watng for a potentally better opton s not worth the uncertanty. As Pssardes (1974) and Lppman and McCall (1976) argue n the job search lterature, more rsk averse ndvduals attach less value to further search because any searcher must compare an offer that s known wth the uncertanty of another draw from the wage dstrbuton. Consder a smple one-sded partal eulbrum model of martal search, n the sprt of the famlar one-sded job search model. Here, however, t s necessary to relax the standard assumpton of rsk neutralty and allow for concavty of the utlty functon. Searchers are nfntely-lved and dentcal n all respects except for ther degree of rsk averson, wth dscount factor β and concave monotoncally ncreasng utlty functons U ( ), where denotes the ualty of the offer receved by searcher n the marrage market. Qualty s an ndex of trats of the ndvdual makng the offer, whch captures ther worth as a marrage partner. It may nclude 5

6 measurable trats such as ncome as well as ntangble characterstcs. Also assume that all sngles are part of the marrage market, women are searchers, wth men makng the offers. Women receve a sngle offer per perod from the dstrbuton F() wth support [0, ), taken as gven for now, so that the probablty of recevng an offer does not depend upon the man s level of rsk averson. The offer at hand can be accepted and the marrage lasts forever 5, or the offer can be rejected and the woman can contnue searchng wthout the possblty of recallng prevous offers of marrage. Denote the present dscounted value of an offer of ualty level as Q and the present dscounted utlty from searchng as S. Then the payoff to acceptng a current offer of can be expressed as follows: 0 β = 1 ) ( 0 0 U Q (1) Assumng no costs to search and that the flow of utlty euals 0 whle searchng, the value of searchng for one more perod s { } ), max( S Q S βe = (2) The offer s accepted f, mplyng a reservaton ualty S Q 0 such that S U = 1 β ) (, or = ) 1 ) (, 1 ) ( max( 1 ) ( β β β β U U E U. (3) Then, + = F U F U U ) ( 1 ) ( ) ( 1 ) ( 1 ) ( 0 β β β β β. (4) Ths s euvalent to + = F U U U U ) ( )] ( ) ( [ 1 ) ( 1 1 ) ( β β β β β, (5) whch smplfes to = F U U U ) ( )] ( ) ( [ 1 ) ( β β. (6) 5 When ths assumpton s relaxed and an exogenous probablty of dvorce s allowed, the relevant predctons of the search model stll follow. 6

7 Euaton (6) mplctly defnes the searcher s reservaton ualty, euatng the opportunty cost of searchng one more perod wth the expected lfetme beneft of one more search, gven 0 0 the current offer. In other words, Euaton (6) holds when euals To determne how an ndvdual s rsk averson affects the reservaton wage, Pratt s (1964) Theorem s useful. Pratt defnes the rsk premum as the amount of money that makes an ndvdual ndfferent between a certan amount and a gamble wth an expected value eual to the certan amount;.e., EU r. I) = U ( EI r ). (7) ( If r >0, then the ndvdual s rsk averse. Pratt also shows that the rsk premum vares drectly wth the Arrow-Pratt coeffcent of absolute rsk averson. Gven ths defnton of the rsk premum, t s not dffcult to see how r affects the search problem n the current context. A postve rsk premum ncreases the opportunty cost of searchng one more perod, or, euvalently, decreases the expected lfetme beneft of another search. The hgher the rsk premum, the more ualty that s reured to nduce the ndvdual to gve up the certan offer n the current perod for the uncertan outcome of further search. To show ths more rgorously, assume that there are two levels of rsk averson among searchers. Type A searchers are globally more rsk averse than type B searchers, so U A ( ) = G[ U B ( )] (8) for some strctly concave and monotoncally ncreasng functon G. Pratt s Theorem mples that r A > r B for all. If the two searchers are faced wth the same ualty dstrbuton, then the more rsk averse searcher has the lower reservaton ualty level. In other words, gven F(), f U ( ) G[ U ( )] for all, then A = B A B <. In the context of job search, ths result has been 7

8 establshed by Nachman (1975), Hall et al. (1979), and Vesterlund (1997) 6. It s well known that a lower reservaton level leads to an earler optmal stoppng tme, so the expected duraton of sngledom s shorter for the more rsk averse. Ths results smply because the per perod probablty of acceptng an offer s ( 1 F( )), whch s decreasng n. The one-sded search problem can be extended to a two-sded one, for now mantanng the assumpton that a potental partner s rsk averson does not enter an ndvdual s utlty functon through the ualty ndex. Both sexes are searchng, and for smplcty assume each searcher s matched wth another once per perod. One sex ntates an offer, and does so f the other s ualty exceeds ther reservaton level. The offeree accepts f ther reservaton ualty level s exceeded, so the more rsk averse the offeree, the more lkely the acceptance occurs. Thus, n the basc two-sded model, the predcton that the more rsk averse marry sooner stll holds. The smple two-sded model adds the assortatve matng predcton that the more rsk averse also marry the more rsk averse. Unfortunately, the data at hand wll not allow a test of the assortatve matng predcton. Second, the beneft of poolng and sharng rsk between two people s another reason why a more rsk averse ndvdual mght marry sooner. For example, f both spouses work and one faces an unemployment spell, one ncome remans to support the couple n the nterm. The shorter the tme to marrage the sooner the rsk averse ndvdual can nsure themselves aganst exogenous ncome shocks. However, the hgher the ualty (a functon of ncome) of a potental spouse, the greater the nsurance provded aganst exogenous ncome shocks. Ths could, ceters parbus, ncrease the reservaton ualty level of an ndvdual, and based on the smple search model, actually delay marrage. Thus, a tradeoff exsts, and t s not clear that a more rsk averse person wll marry a spouse of lower ualty f rsk poolng s the only concern. 6 See the Appendx for proof of ths proposton. 8

9 However, there are also plausble arguments that beng rsk averse can uneuvocally delay marrage. It can be argued that marrage tself s a rsky endeavor, gven the possblty of dvorce, whch s more costly than endng a cohabtng unon. Thus, some may prolong the search process to fnd a better match and hence delay marrage. In addton, some ndvduals may fear losng a spouse to an accdent, an llness, or vce versa. Certanly ths argument apples to ndvduals who are emotonally rsk averse, whch, accordng to recent research, s lkely correlated wth fnancal rsk averson. 7 An addtonal reason that rsk averson may delay marrage s that rsk averse ndvduals may prefer to have a larger amount of savngs accumulated before marrage than a more rsk lovng ndvdual. Ths dea relates to the economc provder hypothess, whch argues that a decrease n real wages can lead to a delay n marrage, especally for men who have hstorcally been the breadwnners. 8 III. Data and Emprcal Specfcaton The NLSY79, whch began annual ntervews n 1979 wth over 12,000 ndvduals aged 14 22, contnued ntervewng that sample annually through 1993, and snce 1994 has followed the group wth ntervews every two years. The NLSY79 contans three subsamples: a crosssectonal sample of 6,111 respondents desgned to be representatve of the cvlan U.S. youth populaton; a supplemental sample of 5,295 respondents desgned to oversample cvlan 7 In prevous studes t has been common to assume that a sngle, ntrnsc rsk preference, measured by takng chances over money, dctates rsk takng n all spheres of lfe. However, there are dfferent knds of rsk averson, and t s ute plausble that an ndvdual mght be wllng to take chances wth ther money but not ther health. A recent study by Dohmen et al. (2005) sheds some lght on ths ssue usng the 2004 wave of the German Socoeconomc Panel (SOEP). The survey asks approxmately 22,000 ndvduals several dfferent types of rsk uestons. Respondents are asked the same type of uestons about gambles over lfetme ncome used n the NLSY79, but they are also asked about ther wllngness to take chances n fve dfferent domans: fnancal matters, career, health, car drvng, and sports and lesure. The study fnds that, whle average wllngness to take rsks s dfferent across domans, there s a strong correlaton across domans. Overall, there s evdence that a sngle rsk parameter s relevant for all domans to some extent. The authors argue that ther fndngs may ndcate some malleablty of rsk preferences but more probably are ndcatve of dfferences n how ndvduals perceve rsk across domans. 8 See, for example, Cooney and Hogan (1991). 9

10 Hspanc, black, and economcally dsadvantaged non-black/non-hspanc U.S. youth; and a sample of 1,280 respondents desgned to represent the populaton ages who were enlsted n the mltary. Followng the 1984 ntervew, 1,079 members of the mltary subsample were no longer elgble for ntervew. Followng the 1990 ntervew, none of the 1,643 members of the economcally dsadvantaged, non-black/non-hspanc subsample were elgble for ntervew. In 1993, a key year for ths study, 9,011 ndvduals were avalable for ntervew, and they are followed n ths study from 1979 untl Because the household was the prmary samplng unt n the ntal surveys, several thousand pars of sblngs are ncluded n the data, and ths wll prove useful n the emprcal estmaton. One advantage of usng the NLSY79 for ths analyss s the detal of respondents martal hstores. Informaton on marrages and dvorces s not lmted to martal status at the tme of ntervew. At each ntervew, respondents are also asked for the month and year each of ther marrages began and ended. Ths serves to fll n mssng nformaton f a respondent has not been ntervewed each year of the survey and also serves to clarfy and correct nconsstent martal hstory data. Rsk Measure An underutlzed seres of uestons from the 1993 wave of ntervews allows constructon of a varable ndcatng an ndvdual s atttude toward ncome rsk. Respondents, then aged 28-36, were asked two uestons relevant to constructng ths varable. All respondents were asked the followng ueston (Gamble 1): Suppose that you are the only ncome earner n the famly, and you have a good job guaranteed to gve you your current (famly) ncome every year for lfe. You 10

11 are gven the opportunty to take a new and eually good job, wth a chance that t wll double your (famly) ncome and a chance that t wll cut your (famly) ncome by a thrd. Would you take the new job? If the answer was No, respondents were then asked the followng (Gamble 2): Suppose the chances were that t would double your famly ncome and that t would cut t by 20 percent. Would you take the new job? If the answer to the frst ueston was Yes, respondents were asked the followng (Gamble 3): Suppose the chances were that t would double your famly ncome and that t would cut t n half. Would you stll take the new job? These three uestons allow categorzaton of respondents nto four groups. Respondents who answered No to both uestons wll from now on be referred to as Very Strongly Rsk Averse ; 46% of respondents fall nto ths category. Respondents who answered Yes to both uestons wll be called Weakly Rsk Averse, and 25% fall nto ths category. Respondents who answered No to the frst ueston but Yes to the second wll be called Strongly Rsk Averse, and ths apples to 12% of respondents. Those who answered Yes to the frst ueston and No to the second wll be referred to as Moderately Rsk Averse, whch apples to the remanng 17% of the respondents. Ths dstrbuton of rsk preferences s consstent wth that found n prevous studes, n whch slghtly more than a thrd to slghtly more than one half of ndvduals fall nto the most rsk averse category. The responses of ndvduals are vewed as resultng from an expected utlty calculaton. If U s the ndvdual s utlty functon and I the lfetme ncome, or permanent consumpton n Barsky et al. s termnology, then an expected utlty maxmzer wll accept the gamble of doublng lfetme ncome rather than cuttng t by the fracton 1-α f the followng holds: 11

12 1 1 U (2I) + U ( α I) U ( I) (9) 2 2 In other words, the expected utlty of the gamble s at least as great as the utlty from havng current ncome for certan. Note that the labels assgned to the categores correspond to varyng degrees of rsk averson, snce the NLSY79 gambles are more than actuarally far (the expected values are always greater than I): EI Gamble 1 = EI Gamble 2 = EI Gamble 3 = (2I) + ( I) = I (10) (2I) + ( I) = I (11) (2I) + ( I) = I (12) Therefore, a rsk neutral agent would accept any of the three gambles. As I have labeled the categores, only a Weakly Rsk Averse ndvdual would accept all of the lotteres. An advantage to usng ths rsk measure s that respondents are asked to gamble over famly ncome, and respondents are asked to consder that famly ncome s own ncome. Therefore, f the respondent s not the man breadwnner n the famly, the survey desgn attempts to elmnate the potental problem that the respondent would be more or less lkely to gamble wth the spouse s ncome. Of course, there are vald crtcsms and potental sources of nose n attemptng to measure rsk atttudes through experments and hypothetcal uestons. For example, some respondents may not understand the uestons but nonetheless answer them. In addton, respondents may value ther job for more than pecunary reasons and so be hestant to leave t for a large expected ncrease n ncome. Moreover, perhaps ther responses do not match what ther decsons would be n realty 9. 9 However, Bnswanger (1981), Camerer and Hogarth (1999), and Dohmen at al. (2005) fnd that hypothetcal experments are not at a serous dsadvantage to games wth real fnancal rewards. 12

13 A dsadvantage of ths partcular dataset s that respondents are not asked these uestons n an earler year. When the rsk uestons are frst asked, over 50% of respondents have been or are marred, whch presents possble endogenety problems. Martal decsons could certanly have an mpact on rsk atttudes 10. However, the NLSY79 dd repeat these uestons n 2002, whch proves useful n the emprcal estmaton for makng a case that endogenety cannot explan all of the fndngs. In 2002, 54% of respondents are consdered Very Strongly Rsk Averse, 12% are Strongly Rsk Averse, and 16% are Moderately Rsk Averse, and 18% are Weakly Rsk Averse. Whle a smlar percentage of respondents fall nto the mddle two categores n 2002 as n 1993, there has been an overall shft towards rsk averson. It s not surprsng that fewer respondents are wllng to take bg rsks n 2002, snce respondents are almost ten years older, have more chldren, and face more responsblty n general. The followng descrptve statstcs focus on the 1993 rsk measures snce they avod more endogenety problems than do the 2002 rsk measures. In addton, only 7,224 respondents were avalable to answer the rsk uestons n 2002, compared to over 9,000 n Table 1 presents the dstrbuton of rsk averson by demographc characterstcs. Women are relatvely more rsk averse than men, wth 49% beng Very Strongly Rsk Averse to the men s 43%. As expected, a hgher percentage of men are Weakly Rsk Averse, wth 29% compared to women s 21%. In addton, even wthn the age group of 28-36, the young tend to be more rsk tolerant. It s encouragng that these data reveal the above two patterns wth respect to sex and age, as they corroborate the fndngs of past studes. 10 Dohmen et al. (2006), usng a German panel data set, fnd postve correlaton of rsk atttudes between spouses. Ths postve correlaton s present when couples are frst marred and does not rse much untl retrement age, suggestng that smlartes n rsk preferences are due n large part to postve assortatve matng and not socalzaton. 13

14 Table 1 also reveals that respondents wth chldren n the house are more rsk averse n general, although those wth chldren ages 6 to 13 are the most rsk averse among parents. The dstrbuton of rsk averson s smlar for all races, wth whtes slghtly less Weakly Rsk Averse. Respondents wth less than a hgh school educaton are more polarzed than the general populaton, wth a comparatvely large percentage fallng nto the Very Strongly Rsk Averse and Weakly Rsk Averse categores. Hgh school graduates are more rsk averse than the general populaton, whle college graduates and those who have attended graduate school are less rsk averse, wth a hgher percentage fallng nto the mddle two categores of rsk averson. Table 2, whch s crtcal to explorng the relatonshp between marrage and rsk averson, presents the dstrbuton of rsk averson by age at frst marrage. There s a clear trend between age at frst marrage and rsk category. For the total populaton, the percentage of Very Strongly Rsk Averse respondents never ncreases and almost always decreases wth age at frst marrage, and the percentage of Weakly Rsk Averse respondents never decreases and almost always ncreases wth age at frst marrage. When the same analyss s carred out by sex, the trends reman almost as strong for both sexes. For women, the only excepton s the year age group, at whch pont the percentage of Weakly Rsk Averse ndvduals falls before ncreasng for the subseuent age group. For men, the same age group s the excepton, where the percentage of Weakly Rsk Averse ndvduals falls temporarly and the percentage of Very Strongly Rsk Averse ncreases temporarly. Fgure 2 presents smlar nformaton graphcally va a cdf by age at frst marrage. Age at marrage s measured n months snce turned 16, and the cumulatve share of respondents marred s presented for each month by rsk preference group. A smaller proporton of people n the least rsk averse rsk group ever marry, and a smaller proporton s marred at almost all ages. Whle a larger share of people n the most rsk averse group are marred at ages less than 200 months from age 16, after that age the proporton 14

15 marred of those n the Strongly Rsk Averse group overtakes the proporton marred of those n the most rsk averse group. Nevertheless, ths fgure also shows a strong relatonshp between rsk preferences and age at frst marrage. Emprcal Specfcaton I estmate a hazard model to nvestgate the determnants of tme to frst marrage. Survval analyss s approprate for the uestons at hand for at least two reasons. Frst, t s necessary to substtute for the normalty assumpton that Ordnary Least Suares reures, snce assumng normalty of tme to an event s problematc. Second, rght-censored spells (those ndvduals who never get marred durng the tmeframe of the data) should be ncluded n the analyss n order to fully utlze the nformaton contaned n the data. Hazard models handle both rght-censored spells and tme-varyng covarates farly easly. I use the semparametrc Cox proportonal hazards model because no assumpton s made about the underlyng shape of the baselne hazard. Under proportonal hazards, the hazard rate nto marrage for person j at tme t s j h ( t) = h e (13) j 0 ( t) X ( t)β where h 0 (t) s the baselne hazard faced by everyone at tme t. The estmated coeffcents (β s) on the explanatory varables (X s) shft the hazard rate up or down, dependng on ther sgns. In the jargon of survval analyss, falure n ths analyss means a frst marrage occurs. I assume ndvduals become at rsk to fal at age Whle respondents are not legally adults at ths age, they gan a certan measure of ndependence snce, at the tme, 16 was the youngest age at whch ndvduals could marry wthout parental consent n most states. On a more practcal note, several hundred respondents get marred before the age of 18, but only about 11 Results are not substantvely dfferent when I assume ndvduals frst become at rsk at age

16 60 are marred pror to age 16. Analyss tme t s thus measured n months from turnng age 16, and the falure tme s marked by the number of months that elapse untl frst marrage. The emprcal specfcaton ncludes dummy varables for the rsk categores, excludng the Weakly Rsk Averse category. Other explanatory varables nclude educaton, the log of the respondent s weekly real ncome, dummy varables for sex (male; female s the base group), race (whte and black; other s the base group), dummy varables for the age of respondent s chldren n the household (no chldren and chldren less than 6; chldren over 6 s the base group), regon (south, west, and northeast; north central s the base group), dummy varables for whether the current resdence s urban or rural, whether respondents are currently lvng wth ther parents, and whether respondents lved wth both bologcal parents untl age 18. Explanatory varables are collected annually for respondents, and every two years startng n The emprcal estmaton of a hazard model wth tme-varyng covarates reures the assumpton that the explanatory varables reman constant between respondent ntervews. Ths s clearly an oversmplfcaton, but, as Wooldrdge (2001) ponts out, researchers cannot get very far emprcally wthout ths assumpton. The hazard model specfed n Euaton (13) assumes there s no unobserved heterogenety n the probablty of transton to frst marrage. It s lkely, however, that unobserved famly-specfc trats, such as atttudes about marrage and age at marrage, affect tme to frst marrage. Moreover, t s possble that the unobserved heterogenety s correlated wth one or more of the covarates. If ths s the case, parameters estmated va the typcal proportonal hazards model wll be based, as the hazard framework usually assumes that any unobserved heterogenety s uncorrelated wth the covarates. Famly-specfc unobserved heterogenety may be correlated wth our covarates of nterest, the rsk atttude varables. Dependng on when rsk atttudes form, parental atttudes about rsk may be transferred to 16

17 chldren to a certan extent. For ths reason, I also estmate a model wth famly fxed effects by explotng the avalablty of sblng data n the NLSY79. The hazard rate becomes h jk X jk ( t ) β +δ k ( t) = h ( t e (14) 0 ) for sblng j n famly k, where δ k represents the unobserved famly heterogenety. IV. Results Table 3 presents the results of two Cox proportonal hazards estmatons. Frst, I present estmates of the proportonal hazards model n Euaton (13) for the full sample ntervewed n 1993, assumng no unobserved heterogenety (Specfcaton 1). Second, I present estmates of the same proportonal hazards model for the full sample wth standard errors adjusted to allow for possble correlaton wthn famles (Specfcaton 2). Ths specfcaton also stratfes on varables that fal the proportonal hazards test at the 0.01 level of sgnfcance. Ths means that a separate baselne hazard s estmated for the stratfed varables, whch are sex, race, regon of resdence, whether or not the respondent s enrolled n school, and whether or not they lve n an urban locaton. In other words, for example, I do not constran the hazard functon for males to be a proportonal replca of the hazard functon for females. As a result, no coeffcents can be estmated for varables that fal to meet the proportonal hazards assumpton. Fortunately, the rsk atttudes varables do satsfy the proportonal hazards assumpton. The results ndcate rsk preferences do matter. A Wald test shows that all of the coeffcents on the rsk preference varables are sgnfcant at the 1% level. Relatve to the Weakly Rsk Averse, beng n any other rsk category shfts the hazard up and ncreases the condtonal probablty of marrage. The sgns of the coeffcents ndcate whch drecton the hazard shfts (up for postve, and down for negatve). Ther magntudes are dffcult to nterpret untl ther exponental s taken to yeld hazard ratos. The hazard ratos are presented for ease of 17

18 nterpretaton. The hazard ratos for Specfcaton 1 tell us that someone who s Very Strongly Rsk Averse faces a hazard rate that s 1.31 tmes (or 31% greater than) the hazard faced by someone who s Weakly Rsk Averse, whle someone who s Moderately Rsk Averse faces a hazard rate that s 1.19 the hazard faced by the Weakly Rsk Averse. The hazard ratos for Specfcaton 2 are very smlar. Fgure 2 compares the estmated hazards for the Weakly Rsk Averse and Very Strongly Rsk Averse groups. The shape of the hazard s not surprsng; t ncreases sharply at frst and almost monotoncally decreases thereafter. After about 75 months of analyss tme (months snce age 16), the hazard exhbts consstent duraton dependence n the sense that the longer a respondent remans sngle, the lower the condtonal probablty of marrage. Moreover, the hazard for the Very Strongly Rsk Averse les above that for the Weakly Rsk Averse at all analyss tmes 12. Most of the other explanatory varables n Specfcaton 1 shft the hazard n the expected drecton. For example, beng male shfts the hazard down snce, n any gven nterval, the condtonal probablty of marrage s lower for men. In the NLSY79, men marry an average of two years later than women. Lvng n an urban area or n the Northeast decreases the condtonal probablty of marrage. Whle there may be a larger selecton of mates n urban areas, there are also a larger varety of actvtes than n rural areas and perhaps less tradtonal vews about marrage and famly. Conversely, lvng n the South ncreases the probablty of marrage. Beng enrolled n school and currently lvng wth parents also decreases the hazard rate. Havng lved wth both parents untl age 18 ncreases the hazard rate, but ths coeffcent s not statstcally sgnfcant at the 10% level. Income ncreases the hazard rate, and educatonal attanment decreases t at frst. Surprsngly, after about the hgh school level of educatonal attanment, educaton begns to ncrease the hazard. Ths unexpected result could be due n part 12 These results are ute robust to estmatng the hazard models separately by educaton and race. 18

19 to reverse causalty, where marrage decsons cause educatonal outcomes. The hazard ratos for the varables reman very smlar under Specfcaton 2, wth the one excepton that havng no chldren n the household now reduces the hazard rate. Ths seems to capture demand-sde behavor more than n Specfcaton 1, snce sngle women wth no chldren have no need for a father fgure. Reverse causalty s a potental problem, where gettng marred or the length of tme one has been marred can affect one s rsk averson. Although the deal stuaton would nvolve the rsk uestons beng asked before any marrages occur, t could also be helpful to perform the survval analyss only for marrages that occur after the 1993 uestons are asked. Unfortunately, ths s problematc because the respondents are already aged n 1993 and only a few hundred respondents are marred after In fact, the freuency of frst marrages peaks almost a decade before Nevertheless, the hazard analyss performed on the sample lmted to those who marry after 1993 yelds the expected sgn for all rsk categores. Results are presented n Appendx Table A1. Whle the estmated coeffcents are not statstcally sgnfcant, the fact that beng Very Strongly Rsk Averse ncreases the hazard rate the most relatve to the Weakly Rsk Averse category s encouragng. To support the dea that at least some element of rsk atttudes s ntrnsc, I have repeated the Cox hazards estmaton usng the rsk preference varables for The results are presented n Appendx Table A2. The sgns of the rsk varable coeffcents and the pattern of the hazard ratos are the same as n Specfcaton 1 n Table 3, whch uses the 1993 rsk varables. The estmated coeffcents are statstcally sgnfcant at the 5% level, whch s less sgnfcant than n Specfcaton 1. It s encouragng that the results hold up farly well when usng a rsk measure that s collected almost ten years after the frst measure. Also, perhaps most mportantly, the hazard ratos are smaller n magntude when the 2002 rsk measures are used 19

20 than when the 1993 measures are used. If reverse causalty was a problem n that the longer an ndvdual s marred, the more rsk averse he or she becomes, then we would expect to see hazard ratos of a larger magntude when the 2002 varables are used. I also take advantage of the 2002 rsk preference uestons by analyzng how major lfe changes such as havng chldren and gettng marred or dvorced affect how one s rsk atttudes change between 1993 and If reverse causalty exsts, so that gettng marred or tme snce marrage ncreases rsk averson, then we would expect to fnd that gettng marred after the 1993 rsk atttudes uestons were asked but before the 2002 uestons were asked would have some mpact on whether someone becomes more rsk averse. Table A3 presents a probt estmaton, where the dependent varable ndcates whether the ndvdual has become more rsk averse between 1993 and The frst explanatory varable s a dummy varable ndcatng whether the respondent had ther frst chld between 1993 and 2002, after answerng the rsk atttudes uestons n The other varables represent changes n martal status and the tmng of those changes. The second and thrd varables are dummy varables ndcatng whether the respondent was marred or dvorced for the frst tme after answerng the 1993 rsk atttudes uestons but pror to answerng the 2002 rsk atttudes uestons. Fnally, the last two dummy varables ndcate whether the respondent was marred or dvorced for the frst tme pror to The coeffcent on whether the respondent had chldren s sgnfcantly dfferent from 0 at the 1% level, ndcatng that havng chldren ncreases the probablty of becomng more rsk averse by a farly small amount, approxmately.045. Once the probablty of becomng more rsk averse s condtoned upon havng chldren, none of the coeffcents on the marrage or dvorce varables are sgnfcant at anythng less than the 14% level. Whle the effect of gettng marred between 1993 and 2002 s postve, the effect of gettng marred pror to 1993 s 20

21 negatve, supportng my prevous results that beng marred for a longer perod of tme does not euate to becomng more rsk averse 13. The above results support a robust relatonshp between rsk preferences and tmng of frst marrage; nevertheless, causalty cannot be assumed. It may be that unobserved heterogenety n famles explans the results, but the NLSY79 can be used to shed some of ths doubt. A useful feature of the NLSY79 s ts ncluson of multple-respondent households. In 1979, over 46% of the total sample conssted of sblngs n 2,448 households. Table 4 presents the estmaton of the basc hazard rate n Euaton (13) for the sample of sblngs ntervewed n 1993 (Specfcaton 3). The hazard ratos for the rsk preference varables are extremely smlar as n the full sample. Table 4 also presents estmates of the model n Euaton (14) for the sample of sblngs ntervewed n 1993, allowng for fxed unobserved heterogenety at the famly level (Specfcaton 4). The results ndcate that unobserved heterogenety at the famly level cannot explan the results found n the cross-secton regardng the effect of rsk atttudes on tme to marrage. The statstcal sgnfcance of the rsk varables remans comparable to prevous results. In addton, the effect of rsk preference on tme to marrage s actually magnfed once fxed effects are ncluded. For example, once fxed heterogenety s taken nto account, the Very Strongly Rsk Averse face a hazard 75% greater than the Weakly Rsk Averse compared to a hazard 34% greater when fxed effects are excluded. Fndng that the basc results are upheld when famly fxed effects are ncluded makes a causal nterpretaton of the effect of rsk atttudes on marrage more plausble. Supply-Sde or Demand-Sde Behavor? Table 5 presents the basc hazard estmaton separately for the two sexes and reveals an nterestng dfference. Whle the sgns on the coeffcents of the rsk varables reman the same 13 These general conclusons are vald when the probt euaton s estmated separately for the sexes. 21

22 as for estmaton on the whole sample, the hazard ratos suggest that the effect of rsk preference on tme to marrage s magnfed for men for the Very Strongly Rsk Averse and the Weakly Rsk Averse. Moreover, the statstcal sgnfcance of these two rsk categores s much greater for men 14. Overall, the results suggest that rsk preferences matter more for men than women when t comes to the tmng of marrage. On frst consderaton, these results mght seem surprsng for a number of reasons, among them that a tckng bologcal clock mght result n more rsk averse women marryng sooner. A possble explanaton of the dfferental results between the sexes observed here s that demand-sde behavor, n addton to supply-sde behavor, s reflected n the estmates. On the supply sde, the more rsk averse may marry sooner because of the uncertanty of future prospects. On the demand sde, women may vew rsk averson as a desrable trat n a mate because rsk averse men may exhbt more responsble behavor, fnancally and otherwse, than ther more rsk lovng counterparts. Rsk averson sgnals that a potental husband wll not take unnecessary rsks and wll therefore be a good provder or partner. Rsk averson should also have some bearng on who an ndvdual marres, not only when they marry. If the basc job search model holds, then the rsk averse respondents wll not only marry sooner than ther more rsk lovng counterparts but wll also settle for a lower reservaton ualty level. Thus, ther spouses should have less desrable characterstcs than the spouses of more rsk lovng respondents. On the other hand, on the demand sde, f rsk averson s a trat that women fnd desrable n men, then rsk averse men may have other desrable trats as well. Spousal characterstcs are lmted n the NLSY79, but Tables 6.1 and 6.2 present the majorty of spousal characterstcs of marred respondents by rsk category. Table 6.1 presents the spousal characterstcs for the two most extreme categores of respondent rsk averson, whle 14 The same pattern s observed when the Cox proportonal hazards estmaton s performed separately for the sexes usng the 2002 rsk preference varables. Results are avalable upon reuest. 22

23 Table 6.2 compares the spousal characterstcs of the most rsk averse respondents to the spousal characterstcs of all other respondents. The spouses of marred, Very Strongly Rsk Averse men are of lower ualty (educaton, ncome, hours worked, fracton that work, fracton of weeks worked) than the spouses of all other marred men. The dfferences are sgnfcant at the 5% level for educaton, ncome, and hours worked. The spouses of Very Strongly Rsk Averse men are also of lower ualty than the spouses of Weakly Rsk Averse men n all but two cases, where ualty s eual. However, the dfferences are only sgnfcant for the ncome varable. The educaton varable may be the most relevant measure of ualty n ths stuaton, snce the labor supply varables for wves are partly determned by household preferences over the wfe s allocaton of tme 15. However, these results may also be evdence that rsk averson s a sgnal of beng a good provder, snce the more rsk averse men match up wth women who work less. Overall, these basc descrptve statstcs support the predctons of a basc marrage search model n whch the rsk averse ndvdual accepts a lower reservaton ualty and therefore marres earler. When comparng the spousal characterstcs of women by rsk averson, the results are only slghtly more mxed. The spouses of marred, Very Strongly Rsk Averse women are not consstently of lower ualty than the spouses of marred, Weakly Rsk Averse women. The ncomes and years of educaton are sgnfcantly lower for spouses of the most rsk averse women. However, husbands fare better n other categores, although only the dfference n the fracton of husbands that work s statstcally sgnfcant. When comparng the husbands of the most rsk averse women and all other women, lower spouse ualty s observed for the most rsk averse women n all but two cases. Thus, the dfferences observed here across genders 15 Measurng spousal ualty n tself s problematc, and these measures are not completely exogenous. However, t should be noted that these spousal characterstcs are measured n the year of or the year after the marrage took place. Thus, educaton levels would be close to exogenous, and the other ualty varables would be more so than f they were measured well nto the marrage. 23

24 are slght. Perhaps the search model of marrage s also very relevant for women, but the search model alone s not adeuate to explan the relatonshp between ther rsk averson and tme to marrage. The results n ths paper are consstent wth the fndngs of related research n economcs as well as other felds such as evolutonary psychology. In the feld of economcs, Hamermesh and Bddle (1994) fnd that success n the marrage market, as measured by spouse s educaton and potental earnngs ablty, s reduced for below-average-lookng women, but not for men. Gould and Paserman (2003) fnd that women search longer for a spouse n ctes where men s wage neualty s hgher. In ths case, ncreased ncome neualty ncreases the value to women of holdng out for a better offer. These results seem to ndcate that men value physcal attractveness more than women, whereas women value other measures of ualty, such as fnancal resources. Ths s perhaps related to why the spouse ualty of the more rsk averse women s not consstently lower than that of the more rsk-lovng women. Evolutonary psychologsts would, for the most part, agree. They argue that matng behavor observed today s rooted n strateges that were necessary many thousands of years ago. Male desres for chldren and ther ablty to produce many wthout cost to ther health had them searchng for short-term relatonshps wth young and attractve females, where female youth and attractveness represented fertlty and health (Klen, 2006). On the other hand, women sought companons wth the resources to provde for herself and her offsprng. In a 1980s study of dozens of cultures and thousands of ndvduals, Buss (1994) fnds that women value fnancal resources twce as much as men, and ths demand for men wth resources exsts even when women are fnancally ndependent. Wlke et al. (2006) fnd that women s perceved rskness of actvtes n varous domans (ethcs, nvestment, gamblng, and health) s negatvely correlated wth the attractveness of men partcpatng n those actvtes. Norman P. L, assstant professor 24

25 of psychology at the Unversty of Texas, ponts out that, n practce, the characterstcs of one s mate are related to what one has to offer. Extremely ntellgent and successful women may have a harder tme fndng partners because men want somebody ntellgent enough so that they can recognze the man s brllance, but not necessarly enough to challenge them or so smart that they fnd someone else more nterestng (Klen, 2006, p.60). Ths could be related to why very rsk averse men n the current study marry women wth lower ualty compared to more rsklovng men, who may be wllng to take a chance wth the ntellgent women. V. Concluson Understandng the role that rsk preferences play n nfluencng behavor s mportant, snce rsk atttudes lkely play a central role n all knds of decson-makng. Whle ths need to understand the relatonshp between ndvdual varaton n rsk atttudes and behavor s wdely acknowledged, lmted emprcal studes exst that undertake the task. The current study attempts to contrbute to ths relatvely sparse lterature. The ntal theoretcal motvaton s a basc search model nspred by job search. The model predcts that the more rsk averse searcher s penchant for a certan outcome results n a lower reservaton ualty compared to ther more rsk lovng counterparts, and thus they enter nto marrage sooner. In addton, the beneft of poolng rsk may also entce the rsk averse nto marrage sooner. The ntal emprcal results, ncludng wthn-famly analyses, support ths basc predcton. Further nspecton of the data suggests that rsk preferences affect martal decsons dfferentally between the sexes. Rsk atttudes seem to have a larger and more statstcally sgnfcant effect on tme to marrage for men than for women. Ths leads to the hypothess that demand-sde behavor, not only supply-sde behavor, may be reflected n the emprcal results. Women may vew hgh levels of rsk averson as a desrable characterstc, so 25

26 that a potental mate s ualty ncreases wth rsk averson. Snce the basc search model predcts that the rsk averse have a lower reservaton ualty level than other searchers, one mght expect the characterstcs of ther spouses to be less desrable than the spousal characterstcs of the more rsk lovng. Some basc descrptve statstcs support ths predcton for spouses of men and, to a lesser degree, spouses of women. Ths paper expands upon our understandng of what motvates ndvduals to get marred and how these decsons mght affect larger trends observed n socety. Studyng ndvdual marrage decsons has broader mplcatons for assortatve matng and eulbrum n the marrage market. For example, n recent decades the average age at frst marrage has been on the rse for the populaton as a whole, as has the fracton of people cohabtatng. There are lkely many factors that have contrbuted to ths, but can changes n atttudes toward rsk partally explan these phenomena? Also, n eulbrum, search theory predcts that the more rsk averse wll marry the more rsk averse at an earler age, whle the rsk lovers wll be more lkely to marry each other later n lfe. A theory of rsk poolng has dfferent mplcatons for assortatve matng. What do we observe emprcally, and what are the mplcatons for the ualty of the match and hence dvorce rates? These uestons could be answered wth more extensve data than are avalable n the NLSY79. 26