Do households jointly manipulate their debt and filing decisions? Personal bankruptcy with heterogeneous filing behavior

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1 Do households jontly manpulate ther debt and flng decsons? Personal bankruptcy wth heterogeneous flng behavor L Gan, Manuel A. Hernandez and Shuoxun Zhang Abstract Personal bankruptcy can serve as nsurance for large fnancal shocks, but may also provde an opportunty for abusve use. We dentfy two dfferent flng behavor patterns usng data from the Survey of Consumer Fnances (SCF). For a frst type of consumers the fnancal beneft s exogenous to the flng decson, whch s consstent wth a non-strategc behavor or ratonal nattenton to a rare event. For a second type the fnancal beneft s endogenous, whch s consstent, although not exclusve, wth a strategc behavor. he second group also exhbts a hgher probablty of flng and a larger fnancal beneft. he hgher prevalence of the frst group supports the nsurance functon of bankruptcy. Keywords: Personal bankruptcy, heterogeneous behavor, debt manpulaton, non-strategc behavor JEL codes: D4, D, C3 Gan: Department of Economcs, exas A&M Unversty, and NBER, gan@econmal.tamu.edu. Hernandez: Markets, rade and Insttutons Dvson, IFPRI, m.a.hernandez@cgar.org. Zhang (correspondng author): Department of Fnance, School of Economcs & Wang Yanan Insttute for Studes n Economcs, Xamen Unversty, Xamen, Fujan 36005, Chna, hellenzsx@gmal.com. Zhang acknowledges fnancal supports from NSFC

2 . Introducton he number of non-busness or personal bankruptcy flngs n the US are stll hgh and there s a constant debate about the factors drvng ths phenomenon and the polcy responses to address t. As shown n Fgure, after the sgnfcant declne n the number of personal flngs n 006, followng the Bankruptcy Abuse Preventon and Consumer Act (BAPCA) passed by the Congress n October 005, flngs surpassed the mllon n 008 and reached.5 mllon n 00, smlar to the levels exhbted n the early 000s. Whle personal flngs have started to decrease snce 0, the number of flers s stll much hgher than the busness flngs. In 04, there were almost 90 thousand personal bankruptcy pettons compared to the 7 thousand of busness pettons, whch have also been much more stable over the last two decades regardless of the ups and downs of the US economy and the fnancal crss of 008. Despte the contnuous efforts to lmt fraudulent and abusve uses of the bankruptcy system, t s clear the need to further understand the elements and motvatons assocated wth consumers bankruptcy decsons and the prevalence of dfferent types of flng behavor. [Insert Fgure ] hs paper formally accounts for heterogeneous flng types n the bankruptcy decson. he types n the model comprse dfferent bankruptcy behavor patterns resultng from dfferent factors that are not necessarly observable. In partcular, the bankruptcy and debt (fnancal beneft) decsons are condtonal on each consumer type and may or may not be jontly determned, whle the personal characterstcs and adverse events drvng these decsons are See L, Whte and Zhu (0) for a dscusson of the 005 bankruptcy reform.

3 allowed to vary by type. he dentfed types can be further assocated to a specfc set of observable characterstcs. We extensvely dscuss the model dentfcaton and provde evdence on the robustness of the model. We also show that the model helps to better dentfy, although margnally, potental bankruptcy flers and non-flers than tradtonal probablstc models. he exstence of dfferent flng types can be lnked to dfferent ncentves and factors drvng the flng decson. In ther nfluental study, Fay, Hurst and Whte (00) dstngush between strategc and non-strategc models of bankruptcy. 3 Strategc households are defned as forward-lookng households who are more lkely to fle for bankruptcy when ther fnancal beneft for flng s hgher. Non-strategc households are not drven by a fnancal ncentve n ther flng decson and wll only fle n response to unantcpated adverse events lke a dvorce, health or employment shock, whch reduce ther ablty to repay. In ths sense, a postve correlaton between the lkelhood of flng and the fnancal beneft, all else equal, can be assocated wth a strategc behavor, whle a postve correlaton between the lkelhood of flng and the occurrence of an adverse event can be assocated wth a non-strategc behavor. Gross and Notowdgdo (0) also dvde the lterature on consumer bankruptcy nto two strands. A frst strand that emphaszes the strategc nature and potental moral hazard behavor n the household bankruptcy decson and a second strand that focuses on the role of adverse, lkely unforeseen events that may lead to bankruptcy. he authors document the relatve mportance of medcal costs on the bankruptcy decson. he fnancal beneft from flng s the amount of unsecured debt that can be dscharged n bankruptcy. We provde further detals below on the calculaton of ths varable for the analyss. 3 hs behavor dstncton s motvated by the prevous work of Sullvan, Warren and Westbrook (989), Braucher (993), Domowtz and Sartan (999), Gross and Souleless (00), among others.

4 More recently, Zhang, Sabarwal and Gan (05) formalze the potental relatonshp between fnancal beneft, adverse events and dfferent flng behavors usng a smple twoperod model of decson-makng followng Gan and Sabarwal (005). In the frst perod, ndvduals receve a nosy sgnal for experencng a fnancal shock (adverse event) n the future and choose ther debt level based on the sgnal; n the second perod, the shock s realzed and consumers decde whether or not to fle. he authors defne a strategc consumer as one who chooses her debt level based on her chances of flng for bankruptcy gven the sgnal. In contrast, a non-strategc consumer s one who chooses her debt level wthout condtonng on the sgnal she plans to repay her debt n the absence of an adverse event and may exhbt a ratonal nattenton to a rare event. 4 As a result, testng for the jont manpulaton of the fnancal beneft and flng decson can provde better nsght about potental dfferent flng behavors, although we cannot fully dsentangle between strategc and non-strategc behavors. he exogenety of the fnancal beneft n the flng decson s consstent wth a non-strategc behavor. Yet, the endogenety of the fnancal beneft s consstent, but not exclusve, wth a strategc behavor; whle an ndvdual who ntends to abuse the law wll conscously ncrease her unsecured debts before flng, an ndvdual who does not ntend to abuse the law may also rollover her debt when faced, for example, wth an adverse event as long as there s a chance of future repayment. In fact, 4 See Sms (003) for a general dscusson of ratonal nattenton behavor and ts mplcatons. he basc dea s that ndvduals exhbt a lmted amount of attenton and must decde how to allocate t. Lmted attenton s assumed to mpose a bound on the nformaton flow or, equvalently, on the sgnal receved by an ndvdual concernng, for example, a fnancal shock. 3

5 personal bankruptcy models generally account for the possblty of a debt ncrease pror to flng, despte no ntent to abuse the law. 5 Besdes varatons n the fnancal beneft from debt dscharge and the reacton to possble adverse events, dfferent flng behavors, whether strategc or not, can also be assocated wth other factors. hese nclude varatons n the socal costs of flng (stgma), tme preferences, rsk averson and other factors correlated wth the debt atttude of an ndvdual. Gross and Souleles (00) defne the socal stgma of flng for bankruptcy as both pecunary costs (e.g., the consequences of a bad reputaton) and non-pecunary costs (e.g., dsgrace). hese costs may dffer across consumers; for example, rcher households, whch generally have a hgher socal status, are more lkely to face hgher pecunary costs than poorer households. Consumers wth dfferent tme preferences,.e. patent versus mpatent ndvduals, may also show dfferent behavor patterns. Labson, Repetto and obacman (003) further argue that ndvduals mght exhbt a quas-hyperbolc dscount functon of the type proposed by Phelps and Pollack (968), behavng patently n ther retrement accumulaton and mpatently n the credt card market. On varatons n the level of rsk averson, Athreya (006) shows that a lower degree of rsk averson mght ncrease or decrease the bankruptcy rate dependng on the bankruptcy exempton level. Gan and Mosquera (008) ndcate that a more rsk averse person 5 Athreya (005) provdes a comprehensve survey of equlbrum models of personal bankruptcy. Recent work on consumer bankruptcy nclude Dubey, Geanakopolos and Shubk (005), Athreya (006), L and Sarte (006), Lvshts, MacGee and ertlt (007, 00), Chatterjee et al. (007), Keys (00), Han and L (0), Gross and Notowdgdo (0), raczynsk (0), Gross, Notowdgdo and Wang (04), Dobbe and Song (05), and Mahoney (05). Keys (00), for example, develops a dynamc, forward-lookng model of bankruptcy behavor wth ncome shocks and shows that adverse events and strategc flng perspectves are both essental and not necessarly mutually exclusve to understand the personal bankruptcy decson. 4

6 may or may not exhbt a hgher probablty of default dependng on the rato of her current and future ncome. Ultmately, dfferent flng atttudes may result from a combnaton of elements, both observable and unobservable. he types n our model summarze all these potental factors nto dfferent groups and we can correlate the dentfed types to specfc observable characterstcs. Dsentanglng these factors, however, s beyond the scope of the study. he estmaton results support the exstence of two flng behavors (types). We dentfy a frst type of consumers whose fnancal beneft s exogenous to ther bankruptcy decson and a second type of consumers whose fnancal beneft s endogenous. he flng behavor of the frst group s n lne wth a non-strategc behavor or a ratonal nattenton to a rare event whle the behavor of the second group s consstent, but not exclusve, wth a strategc behavor. he probablty of flng for bankruptcy s more than 4.5 tmes hgher among the second type of consumers relatve to the frst type, and the second group exhbts a larger fnancal beneft from flng. In addton, the factors assocated wth the flng decson appear to dffer by type. he frst type of flers seem to be manly composed of households wth a hgher ncome and less rsk averse. he hgher proporton (6%) of the frst type of ndvduals n the data, who do not jontly manpulate ther debt and flng decson, also provdes evdence for the nsurance functon of bankruptcy. Addtonal estmatons support the robustness and predctve power of the model. he contrbuton of the paper to the bankruptcy emprcal lterature s twofold. Frst, we mplement a more general approach than prevous related studes. he model permts to dentfy varyng behavor types regardng the bankruptcy and fnancal beneft decsons, whch may result, n turn, from a combnaton of factors. Fay, Hurst and Whte (00) do not account for the 5

7 potental endogenety of the fnancal beneft n the flng decson. Zhang, Sabarwal and Gan (05) test the endogenety of fnancal beneft n the flng equaton, but do not allow for the exstence of dfferent behavor types n the data. he study provdes strong evdence for the exstence of two unobserved flng types. Second, our model s more nformatve than tradtonal probablstc models n that the factors drvng the flng decson appear to dffer by flng type and the model can help to better dentfy potental flers and non-flers gven ther lkelhood of beng of a certan type. hs s crtcal n the absence of expermental and quas-expermental data to unravel dfferent flng atttudes, and n a context where reducng nformaton asymmetres (moral hazard) can play a key role when evaluatng bankruptcy provsons. he model mplemented n ths study can also help to better uncover heterogeneous behavors n other settngs such as loan repayment, nsurance, educaton and employment decsons. Gan, Hernandez and Lu (03), for example, analyze heterogeneous behavor n group lendng schemes n Inda, but do not allow for the potental endogenety of some of the regressors n the repayment equaton. Dong, Gan and Wang (05) examne varyng neghborhood effects on educatonal attanment, but do not formally test for the endogenety of the movng choce on the schoolng decson and just fx one type of ndvduals as endogenous movers and another type as exogenous movers. 6 he remander of the paper s organzed as follows. Secton presents the emprcal model mplemented to account for heterogeneous flng behavor n the bankruptcy decson. 6 Other studes that use mxture densty specfcatons to model unobserved types nclude Keane and Wolpn (997) to examne heterogeneous ablty endowment n the career decson, Knttel and Stango (003) to assess whether state-mandated prce celngs serve as focal ponts for tact colluson among credt card companes, and Gan and Hernandez (03) to model collusve and non-collusve regmes among clustered versus solated hotels n exas. hese studes, however, do not formally test the dentfcaton of the mxture model proposed. 6

8 Secton 3 descrbes the data used n the analyss. Secton 4 reports and dscusses the estmaton results. Secton 5 concludes.. Model Consder frst the followng decson of flng for bankruptcy of ndvdual fle ln( fb ) X AE e 0 () where fle s the observed bnary outcome equal to one f an ndvdual fles for bankruptcy, s a constant term, fb s the net fnancal beneft from flng defned below n equaton (8), X s a vector of observable controls, AE s a set of dummy varables for dfferent possble adverse events encountered by the ndvdual pror to flng, and e s an error term. he specfcaton n equaton () s smlar to the specfcaton n Fay, Hurst and Whte (00). 7 Accordng to these authors, f flng for bankruptcy s manly drven by a strategc behavor we should observe 0 and 0,.e. ndvduals are more lkely to fle when ther fnancal beneft from flng s hgher, all else equal. In contrast, f flng for bankruptcy s manly drven by a non-strategc behavor we should observe 0 and 0,.e. ndvduals are more lkely to fle when an adverse event occurs whch reduces ther ablty to repay. 7 he only dfference s the ncluson of fnancal beneft ( fb ) n logarthms whle Fay, Hurst and Whte (00) use ths varable n levels. We apply a log transformaton to fb because ths varable exhbts a dstrbuton that s smlar to a log-normal dstrbuton, although left-censored at zero (see, e.g., Arabmazar and Schmdt, 98; Powell, 984). We partcularly use ln( fb ) to capture the characterstcs of censored data at zero. 7

9 However, as noted by Zhang, Sabarwal and Gan (05), the fnancal beneft from flng may be jontly determned wth the flng decson such that fb could be endogenous n equaton (). For example, an ndvdual s credtworthness and atttude towards debt, whch s unobserved, may determne how they accumulate debt (and thus ther fnancal beneft) and whether they fle for bankruptcy or not. Addtonally, the fnancal beneft pror to flng for bankruptcy may ncrease rrespectve of whether an ndvdual s ntendng to take advantage of the bankruptcy law or not. A strategc consumer wll conscously ncrease her unsecured debt before flng n order to ncrease the beneft from flng; a non-strategc consumer may also rollover her debt (.e. through the use of credt cards) when faced, for example, wth an adverse event as long as there s a chance of future repayment, thus also ncreasng her unsecured debt and measured fnancal beneft pror to flng. Zhang, Sabarwal and Gan (05) test for the potental endogenety of the fnancal beneft by jontly modelng the flng and fnancal beneft decson usng an extended dscrete choce model and examnng f both decsons are correlated. In ther model, f the fnancal beneft s exogenous, the observed flngs n the data are consstent wth a non-strategc behavor whle f the fnancal beneft s endogenous, the flngs are consstent but not exclusve to a strategc behavor. We mplement an alternatve, more general fnte mxture specfcaton, whch allows for dfferent flng behavor types when modelng the fnancal beneft and bankruptcy decsons. he unobserved consumer types may result from a combnaton of factors, ncludng those assocated wth the flng and debt atttude of an ndvdual. he fnancal beneft and flng decsons are condtonal on the consumer type and may or may not be jontly determned. he personal characterstcs and adverse events drvng these choces are also allowed to vary by 8

10 type. he dentfed ndvdual types can be assocated to a partcular flng behavor based on testable model mplcatons. Smlarly, the types can be correlated to a set of observable characterstcs. We redefne the decson to fle for bankruptcy as fle ln( fb ) X u 0 () where s the unobserved consumer type whch can be correlated wth fb and u s the new error term. Snce the type s unobserved t can only be determned wth a probablty. We can assume that ndvduals can be one of two possble types wth a partcular probablty such that Pr W and Pr W dstrbuton functon and ndvduals and, where s the normal cumulatve W s a set of type-determnant varables. We can thnk of as ype as ype ndvduals, and of W as varables that help descrbe the flng and debt atttude of an ndvdual. Certanly, we can allow for a wder set of types but our dataset supports a two-type model. We consdered, for example, a three-type model but the two-type model shows a lower Schwarz-Bayesan nformaton crteron than the three-type model; smlarly, a Lkelhood Rato test ndcates that the three-type model does not provde a better ft than the two-type model. 8 he flng decson s then gven by 8 Further detals are avalable upon request. 9

11 fle ( ln( fb ) X u 0) ( ln( fb ) X u 0) f f. (3) In the specfcaton above the effect of s absorbed by the constant terms and. he coeffcents further vary across types, whch permts to capture dfferentated effects of ndvdual characterstcs and other factors on the flng decson by type. 9 Wthout loss of generalty, we normalze the varances of the error terms of both types to one,.e. Var( u ) Var( u ). he behavor n accumulatng debt or fnancal beneft s also allowed to dffer across types. he fnancal beneft for or ype consumers s modeled as fb fb f fb 0 ln( fb ) X AE v t, (4a) fb 0 f fb 0 and for or ype consumers s modeled as fb fb f fb 0 ln( fb ) X AE v,. (4b) fb 0 f fb 0 where fb s the latent fnancal beneft. he adverse events AE help n ths case to model the fnancal beneft of flng. Snce adverse events are lkely exogenous to a household s bankruptcy 9 hs flexblty s smlar to Gan and Hernandez (03) that use a mxture specfcaton to model hotels behavor across dfferent demand regmes. 0

12 decson, they act more as a negatve shock to an ndvdual s wealth. Consstent wth ths vew, we may dstngush between dfferent flng behavors by testng whether consumers make ther debt and flng decson jontly or not. Emprcally, ths s mplemented by testng whether fnancal beneft s endogenous to the flng decson n equaton (3). In partcular, we let u v and u v, where Var( ) and s s vs Var( v s ) for s,. A drect test of the correlaton between the error terms n equatons (3) vs and (4) provdes key nsghts about the potental flng behavor of the dentfed consumer types. More specfcally, f Cov( us, vs ) 0, s, or, alternatvely, s 0, we can conclude that the fnancal beneft s exogenous to the flng decson n equaton (3). hus f 0, the correspondng s-type ndvduals are consumers who do not jontly manpulate ther debt and flng decsons; f 0, consumers jontly manpulate ther debt and flng decsons. he test s s then crtcal to lnk the modeled types to partcular flng behavors lke strategc (f 0) and non-strategc ( 0 ), at least partally. s he varables consdered n the X vector nclude age, educaton, household sze, f ndvdual s self-employed or owns a busness and f she s a home owner, as well as regonal dummes to control for dfferences across locatons. he adverse events accounted for nclude health problems, dvorce, job loss and unemployment spell. hese varables are generally smlar to the control varables used n other prevous emprcal studes on consumer bankruptcy (e.g., Chakravarty and Rhee, 999; Fay, Hurst and Whte, 00; Zhang, Sabarwal and Gan, 05). Note also that dfferent adverse events may have a dfferent mpact on the modeled fnancal beneft and potental flng behavor. For example, a dvorce may be more predctable than a health shock, and may have a dfferent effect on debt and bankruptcy decsons. s s

13 Smlarly, as ndcated above, we can assocate the dentfed consumer types to specfc observable characterstcs through W. he types ntend to capture potental dfferences among ndvduals n, for example, ther credtworthness and debt atttude, whch shape ther flng behavor. We nclude n W the household ncome, number of credt cards, the shoppng atttude of the household head, a measure of rsk averson, and the gender and race of the head. Gven that the flng and fnancal beneft decsons are condtonal on the consumer type, all the varables ncluded n the type-equaton stll affect these decsons, although ndrectly, through the lkelhood of beng of a certan type. Whle several of these varables serve as proxes of an ndvdual s debt atttude, t s not clear a pror whether they wll be postvely or negatvely correlated wth a partcular flng behavor and the lkelhood of flng for bankruptcy. For nstance, whle a person wth a hgher ncome s generally more prudent, cares more about her reputaton and s less lkely to take debts and plan for bankruptcy, a person wth several credt cards may sgnal ether a hgh credtworthness and low probablty of abusng the law or, n contrast, may be more lkely to fle for bankruptcy gven the hgher number of credt cards (debts) she holds. Women are also consdered to be more rsk averse than men (Croson and Gneezy, 009), but they are not necessarly more or less lkely to fle for bankruptcy. Rsk-averseness tself may be assocated wth a lower or hgher probablty of flng (Athreya, 006; Gan and Mosquera, 008). Overall, n the proposed model the vector of ndvdual characterstcs and other observable factors X help us to model both the lkelhood of an ndvdual to fle for bankruptcy and her behavor n accumulatng debt or fnancal beneft. he occurrence of adverse events AE n the prevous perod drectly affect an ndvduals fnancal beneft and ndrectly her

14 lkelhood of flng. hat s, we can recover the effect of adverse events on the flng probablty through the channel of fnancal beneft. Smlarly, the varables ncluded n the type equaton ( W ) ndrectly affect the flng and fnancal beneft choces through the lkelhood of beng of a certan type. Certanly, there can be some dscusson regardng whch varables should be ncluded n the dfferent modeled equatons, smlar to the dscusson when estmatng a selecton model. Yet, the specfcaton above provdes the best ft for the data and ultmately we can recover margnal effects (condtonal or uncondtonal) of all the control varables on the flng decson. he resultng jont densty of the flng decson and fnancal beneft, ( fle,ln( )) wth two consumer types, and, s equal to fb f fle,ln( fb ) X, AE, W f fle,ln( fb ), X, AE, W Pr( X, AE, W ) f fle,ln( fb ), X, AE, W Pr( X, AE, W ) (5) where we omt the subscrpts to save space. hs jont densty conssts of four observed cases: ( fle,ln( fb ) 0), ( fle 0,ln( fb ) 0), ( fle,ln( fb )) and ( fle 0,ln( fb )), where ln( fb ) s postve and contnuous n the last two cases. he proposed model belongs to the class of fnte mxture densty models. he dentfcaton of these models has been extensvely studed n recent years (see, e.g., Mahajan, 006; Lewbel, 007; Fox and Gandh, 008; Henry, Ktamura and Salané, 04; Gan, Huang and Mayer, 05). A necessary dentfcaton condton of the model requres an excluson restrcton,.e. that the set W s dfferent from X and AE. Henry, Ktamura and Salané (04) 3

15 show that the model s fully dentfable f W s correlated wth and W s condtonally ndependent of the error terms ( u and u ) n equaton (3). Intutvely, the model dentfcaton s smlar to that underlyng a two-stage least squares (SLS) procedure. Formally, the key dentfyng assumpton n the proposed model s gven by f fle,ln( fb ), X, AE, W f fle,ln( fb ), X, AE. (6) W only affects the probablty of beng of a certan type, but s not related to the condtonal jont densty ( fle,ln( fb ) ). When W ncludes more than one varable, Henry, Ktamura, and Salané (04) and Gan, Huang, and Mayer (05) further show that ether usng the full set of W or a subset of W wll produce consstent estmates of the parameters n the flng equaton. A drect mplcaton of the type-varyng model s that we requre some but not full nformaton about the factors descrbng ndvdual heterogenety ( ) to dentfy the parameters n the flng equaton. A Hausman-type specfcaton test can be then mplemented comparng the estmated coeffcents n equaton (4) usng the full set of W versus the estmates usng a subset of W. hs test s smlar to an overdentfcaton test n an nstrumental varables approach. Falng to reject the null hypothess of no systematc dfferences between the estmated coeffcents provdes supportng evdence for the approprateness of the model specfcaton. Overall, the jont denstes for each of the four observed cases are gven by 4

16 5 ) ( ) ( ) ( Pr 0 ),ln( Pr Pr 0 ),ln( Pr 0) ),ln( Pr( v AE X v v v AE X X W dv v v X W fb fle fb fle fb fle, (7a) ) ( Pr 0 ) 0,ln( Pr Pr 0 ) 0,ln( Pr 0 ) 0,ln( Pr v AE X v v v AE X X W dv v v X W fb fle fb fle fb fle, (7b) ) ln( )) ln( ( ) ( ) ln( ) ln( ) ln( ) ( Pr ),ln( Pr Pr ),ln( Pr )),ln( Pr( v v v v v AE X fb fb X W AE X fb AE X fb fb X W fb fle fb fle fb fle,(7c) and

17 Pr( fle 0,ln( fb )) Pr Pr fle 0,ln( fb ) Pr fle 0,ln( fb ) Pr X ln( fb ) ln( fb ) X AE ( W) v v ( W) ( X ln( fb )) v ln( fb ) X AE v ln( fb ) X AE v (7d) where s the normal densty functon. 3. Data he data used n the analyss s obtaned from the Survey of Consumer Fnances (SCF), whch s a natonal survey sponsored by the Federal Reserve Board n cooperaton wth the Department of reasury and collected by NORC at the Unversty of Chcago. Whle ths cross-sectonal survey s generally conducted every three years, key nformaton such as the locaton (regon) of the respondents has not been released to the publc after 998. We work wth the 998 dataset, whch provdes all the necessary varables to carry out the analyss. he SCF s the most representatve survey of household fnances n the US. 0 he dataset has detaled nformaton on households balance sheets and ther use of fnancal servces, labor force partcpaton, pensons and demographc characterstcs. hs ncludes data on bankruptcy 0 For further detals on the 998 SCF refer to Kennckell, Starr-McCluer and Surette (998). 6

18 flngs, debts, assets, ncome, household sze, as well as characterstcs of the household head lke age, sex, educaton, martal status and employment condton. wo key varables n our analyss are bankruptcy flngs and the net fnancal beneft from flng. he flng rate n the 998 SCF sample s.8% (55 out of 4,305 surveyed households). hs fgure s close to the.6% natonal bankruptcy flng rate reported by the US Courts n the correspondng year. We cannot dstngush, however, between Chapter 7 and Chapter 3 flngs as the SCF survey does not provde nformaton on the chapter choce. Whle flng under Chapter 7 s a lqudaton bankruptcy that usually takes between 3 and 5 months to receve a dscharge, flng under Chapter 3 s a reorganzaton bankruptcy that takes between 36 and 60 months to receve a dscharge. Stll, as noted by Fay, Hurst and Whte (00), households have a choce between the two flng procedures and the potental fnancal beneft from flng under Chapter 3 s related to that under Chapter 7. Followng Fay, Hurst and Whte (00), the net fnancal beneft from flng s defned as fb max d max w ex,0,0 (8) where d s the value of unsecured debt dscharged n bankruptcy by household, household wealth, and resdence. In ths equaton, w s the ex s the value of bankruptcy exempton n the household s state of d represents the gross benefts of flng whle max ex,0 w, he Panel Study of Income Dynamcs (PSID) also provdes nformaton on bankruptcy flngs, wealth, ncome and demographc characterstcs, but the wealth nformaton s less detaled than the SCF for some varables of nterest n ths study and t s collected n 5-year ntervals. here are, for example, only 54 bankruptcy flngs n the PSID over the perod , whch s roughly half of the natonal flng rate durng the same perod (Fay, Hurst and Whte, 00). 7

19 whch measures the nonexempt assets that a fler loses n bankruptcy, represents the fnancal costs of flng. If maxw ex,0 0 to yeld the formula above. d, not flng domnates flng, so fb s truncated at zero Note, however, that ths calculaton does not capture the full economc costs of flng. A more complete measure of costs would nclude the future costs from flng such as more restrcted (and costly) access to credt markets and the loss of proft streams from lqudated assets, as well as out-of-pocket flng costs. 3 Unfortunately, relable data on these measures s not avalable and s also a lmtaton of prevous related studes (e.g., Fay, Hurst and Whte, 00; Zhang, Sabarwal and Gan, 05). We nclude as unsecured debt d both credt card debts and nstallment loans. Credt card debts comprse both tradtonal credt card debts (e.g., Vsa, Mastercard, Dscover) and revolvng debts from credt cards ssued by stores (e.g., retal store cards, arlne cards, gasolne cards). Installment loans refer to those loans obtaned for purposes other than real estate and car purchases. he household wealth w s the total fnancal and non-fnancal assets net of secured debts lke mortgages and car loans. Fnancal assets nclude transacton accounts (checkng, savngs, money market and call accounts), depost certfcates, bonds, stocks, drectly-held mutual funds, cash-value of lfe nsurance, quas-lqud assets (ndvdual retrement accounts, thrft accounts and future pensons), and other managed assets (trust funds, annutes and management nvestment accounts wth equty nterest). 4 Non-fnancal assets nclude the value of all vehcles, prmary resdence, resdental real estate and busness nterests. 3 See, e.g., Berkowtz and Hynes (999), Musto (004) and Han and L (0). 4 Other fnancal assets comprse, for example, loans gven to other ndvduals, future proceeds, royaltes, deferred compensatons, non-publc stocks and cash not elsewhere classfed. 8

20 he constructon of the bankruptcy exempton ex requres certan adjustments as the SCF provdes the Census regon but not state where the household resdes. Frst, we obtan the 998 exempton levels for each state from Elas, Renauer and Leonard (999). We recover exempton levels for homestead equty n owner-occuped homes, equty n vehcles, personal property and wldcard exemptons, and use the sum of these exemptons as the exempton varable for each state. 5 We then calculate a regonal composte exempton measure based on the exemptons for each state n a regon and usng as weghts the relatve populaton of the state n the regon. 6 able presents descrptve statstcs of all the varables used n the analyss. We observe, for example, that the calculated fnancal beneft s on average around 3,99 dollars for the full sample, yet flers show a fnancal beneft whch s about fve tmes hgher than nonflers (8,680 versus 3,80 dollars). As noted above, the control varables nclude age and educaton of the household head, household sze, whether the head s self-employed or owns a busness, f the head s a homeowner, and regonal dummes to capture local fxed effects. he adverse events, whch are assumed to occur wth an exogenous probablty pror to the flng decson, nclude whether the household head (self-reported) health condton s poor, f the head s dvorced, f the head was unemployed at any tme durng the pror twelve months and the 5 We adjust the exemptons for each state whenever possble. For example, f a state doubles the exempton for marred households, we also double the exempton. When a state allows resdents to choose between state or federal exemptons, whch s the case of ffteen states, we consder the larger of the exemptons. For states wth unlmted homestead exemptons, we use as the homestead exempton the average of the home values n our sample. 6 he state populaton data s obtaned from Regonal Economc Informaton System (REIS) from the Bureau of Economc Analyss. 9

21 number of weeks unemployed over the pror twelve months. 7 he controls n the type equaton comprse the household ncome, number of credt cards mantaned by the household head, whether the head shops around for the best term, a measure of rsk averson, and the gender and race of the head. 8 [Insert able ] 4. Results hs secton presents and dscusses the estmaton results. For comparson purposes we frst present the results of the Probt or pooled model, whch does not account for unobserved flng types when modelng the bankruptcy decson. We then turn to our two-type model. We dscuss the estmaton results, test the model dentfcaton and evaluate the out-of-sample performance of the model. 4. Pooled model able reports the estmaton results of modelng the decson of flng for bankruptcy usng a standard Probt model. he model specfcaton n the frst two columns s smlar to the specfcaton n Fay, Hurst and Whte (00). he dfference between the two columns s that n column () we nclude fnancal beneft n levels plus ts squared term whle n column () we 7 he results are qualtatvely smlar when accountng nstead for the poor health condton of ether the head or partner. 8 he shop around varable can take values between and 5 after the ndvdual s asked When makng major savng and nvestment decsons, some people shop around for the very best terms whle others don't. What number would you be on the scale, where the hgher the number the greater the shoppng around. he rsk averse varable takes a value of one f the ndvdual smply responds not wllng to take any fnancal rsks when drectly asked about the amount of fnancal rsk that you are wllng to take when you save or make nvestments. 0

22 nclude fnancal beneft n logarthms. In column (3) we add the varables used to model the type equaton. [Insert able ] We fnd that the drecton of the effects of the control varables are generally comparable to those reported n Fay, Hurst and Whte (00), when applcable. In partcular, fnancal beneft affects the flng decson postvely and at a decreasng rate n column (). In columns () and (3) we also observe a postve correlaton between fnancal beneft and the probablty of flng. On average, a,000 dollars ncrease n the fnancal beneft (roughly a 5% ncrease n the sample mean) ncreases the lkelhood of flng n 0.06 percentage ponts, whch s equvalent to a 4.7% ncrease n the flng rate. 9 Among the adverse events, only beng dvorced s postvely correlated wth the decson to fle. Famly sze s postvely assocated wth flng across all specfcatons, whle the number of credt cards seems negatvely correlated wth the flng decson n column (3). As n Fay, Hurst and Whte (00), usng a standard Probt model provdes lttle support for a non-strategc behavor snce the fnancal beneft s postvely correlated wth the decson to fle and among the adverse events only dvorce s sgnfcantly correlated wth the flng decson. As dscussed above, however, ths model does not account for dfferent flng types and the potental endogenety of fnancal beneft. 4. wo-type model 9 Fay, Hurst and Whte (00) fnd a 7% ncrease n the flng rate after a,000 dollars ncrease n the fnancal beneft.

23 able 3 presents the estmaton results of the type-varyng model, whch allows for two flng types (ype and ype ) and formally tests the exogenety of fnancal beneft n the flng decson for each type. In the model, the effects of the varables ncluded n the flng and fnancal beneft equatons are allowed to vary by consumer type, whle the adverse events are assumed to act as a negatve shock to the household wealth and help to model the fnancal beneft of flng. We further correlate the probablty of beng of a certan type wth specfc observable characterstcs. [Insert able 3] Several mportant patterns emerge from the table. Frst, smlar to the Probt or pooled model, we observe a postve correlaton between the fnancal beneft and the lkelhood of flng among the two consumer types. However, the fnancal beneft s exogenous to the bankruptcy decson for the frst type and endogenous for the second type, as nferred from the reported correlatons between the error terms n the flng and fnancal beneft equatons. More specfcally, = -0.8 (0.30) s statstcally dfferent from zero at conventonal levels whle = (0.6) s not. In addton, the condtonal probablty of flng, reported at the bottom of the table, s consderably dfferent between the two types. he chances of flng for bankruptcy s more than 4.5 tmes hgher among ype consumers relatve to ype consumers (3.5% versus 0.75%). Hence, the model clearly dstngushes between two flng types wth dfferent probabltes of flng and dfferent behavor n terms of the fnancal beneft and flng decsons. ype ndvduals, who do not jontly manpulate ther fnancal beneft and flng decsons and are less lkely to fle for bankruptcy, can be assocated wth non-strategc ndvduals who do not ntend to abuse the law and who would repay ther debt n the absence of an adverse event.

24 hese are probably consumers who place a lot of value n ther reputaton as well as consumers who may smply exhbt ratonal nattenton to a rare event. ype ndvduals who seem to jontly manpulate ther fnancal beneft (unsecured debt) and flng decsons and are more lkely to fle may comprse, n turn, strategc consumers who conscously ncrease ther debt before flng to beneft from t. However, t may also nclude non-strategc consumers who do not ntend to beneft from the law but smply rollover ther debt when faced wth an adverse event n the hope of future repayng t. hat s, ndvduals who may appear strategc due to a non-strategc run-up of debt before flng. he nature of our data does not permt us to further dsentangle between these potental opposte behavors among ype consumers, but the role of adverse events n the estmated model can provde some gudance on ths matter as dscussed next. We observe a sgnfcant correlaton between several adverse events and the fnancal beneft among ype ndvduals, as opposed to ype ndvduals. In partcular, among ype consumers, reportng beng dvorced and unemployment spell have a postve effect on the fnancal beneft whle havng been unemployed has a negatve effect; among ype consumers, only havng been unemployed s negatvely correlated wth fnancal beneft. Intutvely, beng dvorced may lead to a larger amount of debt and a hgher fnancal beneft, potentally ncludng more debt beng dscharged such that both (ex) partners get a fresh start. 0 ranston to unemployment at some pont over the past months may lower the access to credt markets, decreasng the potental fnancal beneft. Yet, condtonal on beng unemployed, an ncrease n 0 raczynsk (0) shows that hgher exempton levels can lead to hgher dvorce rates as the ncome protecton (rsk-sharng) offered by marrage s replaced by that offered by bankruptcy laws. hs s smlar to Mahoney (05) who explot multple varatons n asset exempton laws and shows that bankruptcy can serve as mplct health nsurance gven that most medcal care s provded on credt, whch can be dscharged on bankruptcy. 3

25 the number of weeks under ths condton may result n reachng credt lmts on exstng debt lnes or an ncrease n outstandng debts (due to the non-servcng of the debt), whch wll ncrease the fnancal beneft. Hence, the varyng role of adverse events by type support the assocaton of ype consumers wth ndvduals who do not ntend to abuse the law n the absence of an adverse event; certan adverse events affect ther potental fnancal beneft, whch may (or not) result n flng, but the fnancal beneft s not jontly manpulated wth the flng decson. Smlarly, whle we cannot unravel strategc and non-strategc behavors among ype ndvduals, the lack of correlaton between most of the adverse events and the fnancal beneft provde some support for a strategc behavor among ype consumers relatve to a non-strategc run-up of debt before flng. We further dscuss below the (ndrect) effect of adverse events on the flng decson by type, whch s channeled through ther mpact on the fnancal beneft. he varables ncluded n the type equaton permt, n turn, to correlate the lkelhood of beng of a certan flng type wth partcular characterstcs. We fnd that ncome s postvely correlated wth the lkelhood of beng a ype consumer. We nterpret ths fndng n lne wth the fact that households wth a hgher ncome are generally more prudent and care more about ther reputaton, such that they are less lkely to jontly manpulate ther fnancal beneft and flng decson and fle for bankruptcy. he costs of the socal dsapproval (socal stgma) assocated wth flng, for example, can be relatvely hgher among rcher than poorer households. Our proxy of rsk averson s, n contrast, negatvely correlated wth the probablty Agarwal and Lu (003) fnd that county unemployment rates n the US are sgnfcantly correlated wth credt card delnquency and bankruptcy rates. Athreya and Smpson (006) also argue that ncome nterruptons, the recept of publc nsurance lke unemployment assstance and the ncdence of personal bankruptcy are all closely related; the authors show that ncreases n the generosty of publc nsurance can lead to more bankruptcy. 4

26 of beng a ype consumer. hs can be lnked to the fact that less rsk-averse consumers are more lkely to exhbt ratonal nattenton to rare events such that they choose ther debt level wthout fully accountng for the occurrence of an adverse event. ype ndvduals are assumed to both not abuse the law and pay ther debts n the absence of adverse events. If we further segment our sample based on the lkelhood of the household of beng of a certan type, we can obtan addtonal nsghts about observed flng and fnancal beneft patterns wthn each type. able 4 dvdes the sample between consumers wth an estmated ype - probablty of 0.5 or greater and consumers wth a probablty less than Accordng to ths crteron,,66 (6%) of the households are consdered as ype and,689 (39%) as ype. hs ndcates a hgher prevalence of ype households n the data. Notably, the sample average probablty of flng among ype consumers s 0.7% versus.% among ype consumers. More nterestng, the potental fnancal beneft s sgnfcantly hgher among ype consumers and, on average, 36.6% of them have a strctly postve fnancal beneft relatve to 3.7% of ype. hs s consstent wth the vew of ype consumers as ndvduals who conscously (or not) ncrease ther debt before flng. hese patterns also suggest that the types n the model are not purely dentfed by the functonal form. We formally evaluate n the next secton the model dentfcaton. [Insert able 4] Fnally, the estmated model s nformatve n terms of the effects of dfferent control varables on the flng decson, whch can vary by flng type. o better apprecate ths, able 5 shows the effects of hypotheszed changes n partcular varables on the probablty of flng, hs measure of rsk averson, however, may be mperfect as t s not based on a standard lottery choce experment. 3 he sample average probablty of beng ype s 58.9%. 5

27 evaluated at the sample means. We calculate both condtonal and total (uncondtonal) margnal effects as the effects of these varables are allowed to vary by type; n the case of adverse events, the effect s channeled through the effect on fnancal beneft. 4 he table also reports the correspondng percentage changes n the flng rate. 5 [Insert able 5] For example, f fnancal beneft ncreases by,000 dollars, the probablty of flng ncreases by 0.3 percentage ponts among ype consumers and by 0.6 percentage ponts among ype consumers. Hence, the margnal effect of fnancal beneft on the flng decson s slghtly smaller among the non-strategc ndvduals. Relatve to the flng rate, the ncrease s equvalent to a 3.8% rse n the probablty of flng for ype ndvduals and.4% for ype ndvduals. he total ncrease n the flng rate s 9.%, whch s much hgher than the 4.7% ncrease estmated wth the pooled Probt model. Smlarly, an ncrease n famly sze by one member decreases the flng rate by 3.3% among ype consumers, but ncreases the flng rate by.% among ype consumers. Regardng the adverse events, beng dvorced, whch has a postve effect on the fnancal beneft, ncreases the lkelhood of flng among ype ndvduals by more than four tmes whle t has a margnal effect among ype ndvduals. One more week of unemployment spell also has a postve effect on the probablty of flng among ype consumers (.6%) and a close to zero effect among ype consumers. Recall 4 he margnal effect for each type s the change n the condtonal probablty of flng. he total margnal change s the weghted average change usng as weghts the estmated average probabltes of beng ype and ype (0.59 and 0.4). 5 he change n the flng rate results from dvdng the margnal effects by the correspondng average flng probabltes (0.0073, 0.03 and 0.08). 6

28 that ype households, who do not seem to jontly manpulate ther debt and fnancal beneft decson, are not expected to fle for bankruptcy n the absence of facng an adverse event. In sum, the results obtaned show the mportance of havng a flexble, type-consstent model, whch dentfy two dfferent bankruptcy behavor patterns. he results permt to assocate the dentfed types to specfc characterstcs and provdes some nsghts about the possble factors drvng the flng decson, whch can dffer by type. hs s crtcal n a context where nformaton asymmetres seem to play a crtcal role n bankruptcy. 4.3 Model dentfcaton We now evaluate the dentfcaton of the estmated two-type model. As ndcated above, when estmatng a dscrete mxture specfcaton we requre only partal nformaton about the factors descrbng the consumer types ( ) to dentfy the parameters n the flng equaton (3). A subset of the varables ncluded n W used to model the type equaton should stll produce consstent estmates of the parameters n the flng equaton. able 6 reports the correspondng Hausman test results when comparng our base (benchmark) model that uses the full set of varables n W versus alternatve specfcatons that exclude dfferent varables n W. We observe that the sgn and magntude of the coeffcents are generally not senstve to the excluson of dfferent varables n the type equaton. In all but one case there are no systematc dfferences at conventonal statstcal levels between the estmated coeffcents across the models. hs exercse supports the robustness of the mplemented mxture model. [Insert able 6] 7

29 4.4 Predctve performance Lastly, we assess whether allowng for dfferent flng types offers a hgher predcatve performance on the lkelhood of flng than standard probablstc methods, whch can help to dentfy potental flers and non-flers. For the assessment, we follow a standard cross-valdaton procedure and randomly partton our sample nto a desgn subsample for estmaton purposes (80% of the observatons) and a test subsample for the out-of-sample predcton analyss (0% of the observatons). Both samples naturally mantan the full-sample proportons of flers and nonflers. he dea s to test how the model wll perform when usng new nformaton sets. 6 We acknowledge, however, that ths exercse may be subject to some lmtatons due to the already small number of flers n the full sample and the subsequent reducton of ths number n the data parttons. We use two dfferent procedures to calculate the probablty of flng of an ndvdual based on the two-type model estmates. he frst method or naïve approach smply uses the uncondtonal probablty of flng, whch s equvalent to the weghted sum of condtonal probabltes. he second method or conservatve approach uses both the condtonal and uncondtonal probablty of flng based on the lkelhood of beng of a partcular type. In partcular, the naïve approach s gven by f fle,ln( fb ) f fle,ln( fb ) Pr( ) f fle,ln( fb ) Pr( ) 6 An out-of-sample performance assessment s also more approprate when comparng between a models that account for latent types versus standard models wthout such types. 8

30 whle the conservatve approach s defned as f fle,ln( fb ) f f f f fle,ln( fb ) f Pˆr( ) n 5th quntle fle,ln( fb ) Pr( ) fle,ln( fb ) Pr( ) f Pˆr( ) n nd - fle,ln( fb ) f Pˆr( ) n st quntle 4th quntle where Pˆ r( ) s the estmated probablty of beng a ype ndvdual. able 7 presents dfferent performance ndcators for the Probt and two-type model. he results are based on 00 repeated 80-0% parttons. 7 he ndcators are the mean square predcted error and several performance ndcators, ncludng McFadden, Pug and Krschner (977) standard predctve performance measure and the correct flng and non-flng classfcaton rates. 8 We observe that the two-type model generally exhbts a hgher out-ofsample performance than the Probt model, although the pooled (Probt) model has a smaller mean square predcted error. In partcular, the two-type naïve and conservatve approach have an overall predctve performance of 78.4% and 78.8% versus 73.6% of the Probt model. Smlarly, the two-type model outperforms the Probt model by 3-4 percentage ponts n both correctly dentfyng flers (senstvty) and non-flers (specfcty). Hence, besdes beng more nformatve n terms of uncoverng dfferent flng behavor patterns and assocatng them to 7 he results are not senstve to alternatve data parttons (75-5% and 85-5%). 8 he performance and classfcaton rates are based on convertng the estmated flng probabltes to the standard 0/ bnary regme predcton. McFadden, Pug and Krschner (977) predctve performance measure s equal to p p p p where p j s the jth entry n the standard x confuson matrx of actual versus predcted (0,) outcomes n whch the entres are expressed as a fracton of the sum of all entres. 9

31 some observable characterstcs, the two-type model attans a margnally hgher predctve power than the pooled model. [Insert able 7] 5. Conclusons Personal bankruptcy has been extensvely studed n the US, but there s stll an ongong dscusson about the factors assocated wth flng. In a context where nformaton asymmetres play an mportant role, further understandng the elements and motvatons drvng the flng decson s crtcal to better desgn bankruptcy polces and provsons. If flers are manly conscously takng advantage of the law, then more strngent regulatons should be mplemented such as reducng the exempton levels, makng bankruptcy more expensve or lmtng the number of repeated flngs (debt dscharges). If flers are not delberately takng advantage of the law, then polces that attenuate the mpact of adverse events are recommended, ncludng mtgaton and preparedness strateges. hs paper examnes the exstence of dfferent flng types n the bankruptcy decson. he types n the model represent dfferent flng behavors, whch may result from a combnaton of factors. We fnd evdence of two flng types n the data. he fnancal beneft s exogenous to the flng decson among the frst type of consumers and endogenous among the second type. We nterpret the jont manpulaton of the debt and flng decson n the second group as consstent, although not exclusve, wth a strategc behavor, whle the frst group s n lne wth a non-strategc behavor or a ratonal nattenton to a rare event. We further observe that the second type has a hgher probablty of flng and shows a larger fnancal beneft. he proposed model s nformatve n that the factors correlated wth the flng decson seem to 30