Working Paper Preventing systemic crises through bank transparency

econsto www.econsto.eu De Oen-Access-Publkatonsseve de ZBW Lebnz-Infomatonszentum Wtschaft The Oen Access Publcaton Seve of the ZBW Lebnz Infomaton Cente fo Economcs Hyytnen, A; Takalo, Tuomas Wokng Pae Peventng systemc cses though bank tansaency ETLA Dscusson Paes, The Reseach Insttute of the nnsh Economy (ETLA), No. 776 Povded n Cooeaton wth: Reseach Insttute of the nnsh Economy (ETLA), Helsnk Suggested Ctaton: Hyytnen, A; Takalo, Tuomas (2001) : Peventng systemc cses though bank tansaency, ETLA Dscusson Paes, The Reseach Insttute of the nnsh Economy (ETLA), No. 776 Ths Veson s avalable at: htt://hdl.handle.net/10419/63965 Nutzungsbedngungen: De ZBW äumt Ihnen als Nutzen/Nutze das unentgeltlche, äumlch unbeschänkte und zetlch auf de Daue des Schutzechts beschänkte enfache Recht en, das ausgewählte Wek m Rahmen de unte htt://www.econsto.eu/dsace/nutzungsbedngungen nachzulesenden vollständgen Nutzungsbedngungen zu vevelfältgen, mt denen de Nutzen/de Nutze sch duch de este Nutzung envestanden eklät. Tems of use: The ZBW gants you, the use, the non-exclusve ght to use the selected wok fee of chage, tetoally unestcted and wthn the tme lmt of the tem of the oety ghts accodng to the tems secfed at htt://www.econsto.eu/dsace/nutzungsbedngungen By the fst use of the selected wok the use agees and declaes to comly wth these tems of use. zbw Lebnz-Infomatonszentum Wtschaft Lebnz Infomaton Cente fo Economcs

ETLA ELINKEINOELÄMÄN TUTKIMUSLAITOS THE RESEARCH INSTITUTE O THE INNISH ECONOMY Lönnotnkatu 4 B 00120 Helsnk nland Tel. 358-9-609 900 Telefax 358-9-601 753 Wold Wde Web: htt://www.etla.f/ Keskusteluaheta Dscusson aes No. 776 A Hyytnen Tuomas Takalo PREVENTING SYSTEMIC CRISES THROUGH BANK TRANSPARENCY We thank Abjht Banejee, Sudto Bhattachaya, Esa Jokvuolle, Klaus Kultt, abzo Lóez-Gallo, Davd Mayes, Juha-Pekka Nnmäk, Oz Shy, Otto Tovanen, Jukka Vauhkonen and semna atcants n the Swedsh School of Economcs, Åbo Akadem Unvesty, and the 27th E.A.R.I.E confeence n Lausanne fo ecetve comments. Takalo acknowledges fnancal suot fom the Academy of nland and the Yjö Jahnsson oundaton. Much of ths eseach was comleted when Hyytnen was afflated wth the Bank of nland and Takalo was vstng the Deatments of Economcs at the MIT and Boston Unvesty. ISSN 0781-6847 20.11.2001

HYYTINEN, A TAKALO, Tuomas. PREVENTING SYSTEMIC CRISES THROUGH BANK TRANSPARENCY. Helsnk: ETLA, Elnkenoelämän Tutkmuslatos, The Reseach Insttute of the nnsh Economy, 2001, 17. (Keskusteluaheta, Dscusson Paes, ISSN 0781-6847; No. 776). ABSTRACT: Bankng system s known to be vulneable to self-fulfllng cses that ae caused by deostos coodnaton falue. We show that tansaency egulaton may event systemc cses by elmnatng the ossblty of the coodnaton falue. In ncle, tansaency egulaton n ou model woks lke the deost nsuance n the nfluental atcles by Damond and Dybvg (1983) and Matutes and Vves (1996), whee the deost nsuance may event systemc confdence cses. KEYWORDS: bankng, dsclosue, bank tansaency, deost nsuance, fnancal safety net HYYTINEN, A TAKALO, Tuomas. PREVENTING SYSTEMIC CRISES THROUGH BANK TRANSPARENCY. Helsnk: ETLA, Elnkenoelämän Tutkmuslatos, The Reseach Insttute of the nnsh Economy, 2001, 17 s. (Keskusteluaheta, Dscusson Paes, ISSN 0781-6847; No. 776). TIIVISTELMÄ: Pankkjäjestelmät saattavat olla eävakata, koska ne ovat alttta tsensä toteuttavlle kselle, jota tallettajen koodnaato-ongelmat ja eäluottamus ankkjäjestelmää kohtaan saattavat saada akaan. Tässä tutkmuksessa osotetaan, että ankken tedonantovelvollsuusääntelyllä vodaan estää tämän tyysten ksen syntymnen, sllä ankktomnnan avomuudella vodaan vähentää tlanteta, jossa tallettajen koodnaato-ongelmat ja odotukset vakuttavat ankkjäjestelmän tomntaan. Tedonantovelvollsuusääntely tom mallssamme eaatteessa vastaavast kun talletusvakuutus Damondn ja Dybvgn (1983) ja Matutesn ja Vvesn (1996) tutkmuksssa, jossa talletusvakuutus vähentää tallettajen luottamuksen omahduksesta syntyvä ksejä. AVAINSANAT: ankktomnta, tedonantovelvollsuus, ankktomnnan avomuus, talletusvakuutus, ankkjäjestelmän tuvavekko

Table of Contents 1 Intoducton 1 2 The Model 4 3 A Ratonale fo Tansaency 8 4 Conclusons and Polcy Imlcatons 11 Refeences 12 Aendx: Poof of Remak 16

1 Intoducton Bankng secto s known to be vulneable to systemc cses. Ths concen about the systemc cses has led to the ceaton of extensve safety nets. Howeve, the exstence of a safety net entals a wdely ecognzed moal hazad oblem. Safety nets n geneal, and deosto nsuance schemes n atcula, ovde ncentves fo excessve sk takng by banks. 1 The am of ths ae s to demonstate that systemc cses can be evented wthout the safety net by enhancng bank tansaency. Thee s abundant evdence that weak tansaency makes banks asset sks oaque. Stock maket atcants ncludng the ofessonal analysts, such as Moody s and Standad and Poo s, encounte dffcultes n measung banks' cedtwothness and sk exosues (Poon, th, and ung 1999, Mogan 1999, and Jodan, Peek and Rosengen 2000). And academcs face the same oblems. 2 It s not easy to nteet banks accountng data (Beatty, Chambelan and Maglolo 1995, Collns, and Shackelfod and Wahlen 1995) no dsclosues of banks cedt losses (Ahmed, Takeda and Thomas 1999, and US Geneal Accountng Offce 1994). Rochet and Tole (1996) note that ntebank lendng comlcates assessment of banks actual lqudty and solvency atos. A bank can be tansaent to maket atcants both befoe and afte nvestments ae made n the bank. In the ex ost sense, the degee of a bank's tansaency detemnes the degee of nfomaton avalable to ts clam-holdes on the bank s fnancal condton. If t tanses that the value of a bank s assets s low, the bank s cedtos, and atculaly ts unnsued deostos, may wthdaw the funds. The theat of a bank un can then dsclne bankes n the sk-takng (see e.g., Caloms and Khan 1991, Chen 1999, and Nnmäk 2001). 1 Thee s a szeable lteatue on the economcs of bank egulaton and desgn of safety nets. See Dewatont and Tole (1994) and Bhattachaya, Boot and Thako (1998) fo geneal evews. The lnk between moal hazad oblems and the DIS s also well documented. Kane (1989), fo nstance, egads the US safety net and fxed-ate DIS as man easons fo the Savngs and Loan css of the 1980s. Beln et al (1991) ovde a concse evew of emcal lteatue on the DIS and bankng oblems. The concluson s that 'the moal hazad oblem s oeatve and sgnfcant' (. 738). Demguc-Kunt and Detagache (1998) fnd that an exlct DIS has nceased the faglty of the bankng system aound the wold. 2 As Kamnsky and Renhat (1999,. 476) ut t, 'Indcatos of busness falues and nonefomng loans ae also usually avalable only at low fequences, f at all; the latte ae also made less nfomatve by banks dese to hde the oblems fo as long as ossble.' 1

Ex ante tansaency mles that otental deostos and othe cedtos can aecate a bank s fnancal condton o to lacng funds n t. Ths stengthens maket dsclne, because the bette nvestos ae able to evaluate banks' sk ostons, the moe sk-senstve the banks fundng costs should be. The suly of funds to a bank s also dectly elated to the eceved soundness of the bank. The contenton that lowe qualty banks attact fewe unnsued deosts than hghe qualty banks has sound emcal suot (see e.g., Pak 1995, Bllet, Gafnkel, O Neal 1998, Pak and Pestan 1998, Matnez Pea and Schmukle 1998, and Jagtan and Lemeux 2000). Deste ts motance, the ex ante tansaency and ts effect on maket dsclne ae elatvely seldom addessed n a concetual famewok. o ths eason, we equate tansaency to ts ex ante dmenson, although the key nsghts n ths ae ae ndeendent of the tye of tansaency. To enhance the tansaency of bankng sectos, vaous ntenatonal nsttutons, such as the Basel Commttee on Bankng Suevson, G7 nance Mnstes, Intenatonal Monetay und and the Wold Bank, have camagned fo moved accountng and dsclosue actces (see e.g., Basel Commttee 1998, 1999a, 1999b). Numeous scholas, such as Beln, Saundes and Udell (1991), Edwads and Mshkn (1995), Bhattachaya, Boot and Thako (1998), Mayes and Vesala (1998), Rosengen (1998), and Jodan, Peek and Rosengen (1999, 2000), also advocate a tansaent bankng system. The calls fo nceased tansaency seem to be well-founded gven the exeence of ecent bankng cses aound the wold. o nstance, Rosengen (1998) agues that tansaency educes the cost of cses, Jodan et al (1999) suggest that tansaency moves maket dsclne n cses, Summes (2000) consde tansaency the best way to event cses and an effectve olcy esonse to cses, and Vshwanath and Kaufmann (2001) egad tansaency egulaton as a at of the nsttutonal stuctue that enhance fnancal stablty. Pehas the most goous agument fo the nceased tansaency s ovded by Gannett (2001) who shows how asymmetc nfomaton between nvestos and banks exlans contagous bankng cses both wthn a county and acoss countes. 2

Buldng on the dea n Matutes and Vves (1996) we oose a novel justfcaton fo tansaency egulaton. We show that when banks sk ofles ae unobsevable, deostos self-fulfllng exectatons lead to multle equlba. Possble equlba nclude a comlete collase of the bankng secto stemmng fom deostos coodnaton falue. Ths s consstent wth the celebated model by Damond and Dybvg (1983) whee the banks lqudty sevce endes them suscetble to uns n whch deostos anc and attemt to wthdaw the deosts smultaneously. A bank un may also be caused by the ex ost tansaency, n whch case the un s tggeed by advese nfomaton about the qualty of the bank s loan otfolo (Cha and Jagannathan 1988). In ou model, thee can be a systemc collase that s caused by lack of the ex ante tansaency. The tansaency equement woks lke the deost nsuance n Damond and Dybvg (1983) and Matutes and Vves (1996) n emovng the 'bad' equlbum,.e., the collase of the bankng secto. Ou analyss s also elated to the lteatue dealng wth the moal hazad oblem caused by a DIS. The oosed emedes nclude sk-based nsuance emums, catal adequacy equements, ncentve-comatble DISs, banks equty nvestments, and ntetemoal asset dvesfcaton (see e.g., Chan, Geenbaum and Thako 1992, Cane 1995, Santos 1999, and Nnmäk 2001). We comlement these effots by studyng how the tansaency equement can be substtuted fo the DIS. The est of the atcle oceeds as follows. In secton 2, we set out a model of hozontal dffeentaton whee banks comete fo deostos on the bass of asset qualty. To kee ou analyss as smle and comaable wth the evous lteatue as ossble, we adot the standad model of satal cometton develoed by Salo (1979). Ths model - and ts cousn, the Hotellng lne - has been used extensvely n the bankng lteatue, e.g., n Besanko and Thako (1992), Chao, Peez-Castllo and Vede (1995), Matutes and Vves (1996), and Vllas-Boas and Schmdt-Moh (1999). In atcula, the setu n Codella and Levy Yeyat (1998a) s qute smla to ous. In secton 3 we ove ou man fndng. Tansaency egulaton may move welfae by eventng the collase of the bankng secto. Concludng emaks ae gven n secton 4. 3

2 The Model Consde a unvesally sk-neutal economy wth a hozontally dffeentated bankng ndusty whee thee ae n banks, ndexed by = 1,, n. The banks locate themselves symmetcally on a unt ccle. 3 Thee s a contnuum of otental deostos unfomly dstbuted along the ccle. All deostos ncu a 'tansotaton cost' (.e., tansacton o atcaton cost) when tavelng to a bank, and the cost e unt of 'dstance' s τ. We nomalze the sze of deosts to unty and denote bank s eayment oblgaton by. Because ou am of s to show how systemc cses can be evented wthout a safety net, thee s no deost nsuance scheme n ou model. The banks nvest the funds collected n sky ojects (loans). The obablty that a unt of deost funds nvested n bank s otfolo wll yeld a ostve etun s denoted by. The goss etun on the nvestment otfolo fo a unt of funds nvested s y, esultng n a oft magn e deost unt of etun s 1 y. The obablty of a zeo. If a bank s ojects fal, the bank tself also fals. We assume that the only cost of a bank falue s that ts deostos suffe the loss of the funds. Banks lendng and montong decsons affect the obablty of bank falues. The success obablty of a bank eflects the bank s sceenng and montong decsons and ultmately ts ablty to gathe nfomaton fo buldng a hgh-qualty loan otfolo. In the st of moden bankng theoy, nceasng s costly because of nfomaton gatheng costs such as ex ante, ntem and ex ost montong costs. Some of the nfomaton gatheng cost vaes wth the sze of the asset otfolo, but some at least s eodc. The costs that ae ndeendent of the otfolo cannot fully be conveyed to deost nteest ates and theefoe educe bank ofts. These costs mght eflect mantenance of sk management nfastuctue, ncludng nfomaton systems, basc databases and cedt scong models, as well as the eodc wages of montong esonnel and the cost of sustanng a banch netwok to gathe local nfomaton. 3 ollowng the usual actce we take the numbe of banks, n, as gven, and focus entely on symmetc equlba. 4

We buld a geneal model whee the cost of montong conssts of nfomaton gatheng costs c( ) that vay wth the sze of the otfolo, and the eodc costs of mantanng a montong nfastuctue C( ) that ae ndeendent of the sze of the otfolo. Both cost functons ae stctly nceasng and convex n the success obablty of a bank,.e., c/ > 0, 2 c/ 2 > 0, C/ > 0 and 2 C/ 2 > 0. Thoughout the ae we assume that these montong cost functons ae suffcently convex to satsfy the second-ode condtons and kee the model well-behaved. To ensue an nteo soluton, the usual bounday condtons ae also assumed: c(0) / =C(0) / = 0, and c(1) / =C(1) / =. A bank cometes fo deostos va ts nteest ate and montong decsons,.e., ts success obablty. In actce, t s easy to vefy the bank s nteest ate offe fom catalogs and advetsements, but the same does not necessaly aly to the montong decson. We thus assume the bank can commt tself to ts nteest ate announcements but encountes moal hazad temtatons egadng the montong decson (see also Codella and Levy Yeyat 1998b and Rochet and Tole 1996). As a esult, the level of s only mefectly known to deostos befoe they nvest the funds. In lne wth Boot and Schmets (2000), we assume that wth obablty α the deostos ae able to 'detect' the actual montong choce of banks. Wth the comlementay obablty, emans undetected. In such a case, the deostos atonally evaluate bank s asset sk ostons accodng to the exectaton E( ) = e. In equlbum, these belefs ae fulflled, as the deostos nfe that the banks falue obabltes ae those that eval n the Nash equlbum. The obsevablty of the montong level deends on the nfomaton dsclosue olcy of the banks. Wthout loss of genealty we nomalze the banks voluntay nfomaton dsclosue to zeo so that we can dentfy α as a tansaency equement mosed by the egulatoy authoty. The tmng of events s that deostos ae endowed wth a common assessment of the success oblem of each bank e. Po to lacng the funds, the deostos also obseve the catalog deost nteest ates and a eayment obablty (e.g., fom bank cedt atngs). The deostos then choose the banks, knowng that the banks can fully commt themselves ex ante only to the nteest ate offe. The moe tansaent the bankng secto s, the hghe the degee of the commtment to the 5

eayment obablty. nally, the banks smultaneously choose the montong effot and deost nteest ates. Let us now focus on the behavo of a deosto located at dstance x [0, 1/n] fom bank. Deostng n bank yelds an exected etun of E(R )=[α +(1-α) e ]. The bank s able to attact the deosto only f the exected etun coves the cost and f ts eayment contact s moe lucatve than those offeed by val banks,.e., f E(R )-1-τx E( R )-1-τ(1/n-x) whee E( R )=[α +(1-α) fo j. e ] wth = j and = j In the temnology of Vllas-Boas and Schmdt-Moh (1999), we focus on fullscale cometton,.e., we assume that τ s small enough to guaantee that the maket wll be coveed n equlbum. 4 Unde full-scale cometton, the total suly of funds fo bank s 1 1 e e D = α( ) (1 α)( ) n + τ +. (1) The ofts of the bank can then be wtten as π = A D - C( ). (2) whee A (y- )-c( ) catues the oft e deost unt. Bank chooses and so as to maxmze the ofts n (2). By usng symmety e e and atonal o belefs, = = = and =, the fst-ode condtons π/=0 and π/=0 can be smlfed to αa τ A C + n = 0 (3) 6

and A τ = 0, (4) n whee A=(y-)-c() s the equlbum oft e deost unt. Equatons (3) and (4) mlctly detemne the equlbum success obablty and the deost nteest ate as a functon of the model aametes. It s staghtfowad but tedous to solate the effect of the tansaency equement, α, on the success obablty,. 5 Remak. Inceasng the level of tansaency dscouages sk takng. Poof. In the aendx. The eason fo ths fndng s smly that enhancng bank tansaency stengthens maket dsclne. The suly of funds to a bank s dectly elated to the eceved soundness of the bank. Howeve, as we dscuss n detal n ou comanon ae (Hyytnen and Takalo 2001), ths agumentaton has a omnent defect, snce t gnoes dect and ndect comlance costs of tansaency. In the ae we ague that a oe evaluaton of ths maket-dsclne agument fo tansaency necesstates the ncooaton of these costs nto the model. The man ont of ths ae s to show that thee s anothe, evously ovelooked atonale fo tansaency. 4 An mlcaton of ths assumton s that we leave asde the local monooly and touchng makets cases. o a chaactezaton of such maket stuctues and the assocated equlba, see e.g., Salo (1979), Matutes and Vves (1996), Vllas-Boas and Schmdt-Moh (1999). A futhe estcton on the scoe of the esent analyss s that we focus on local nteactons between banks,.e., on local cometton, so that the otental maket shae of a bank conssts of deostos located between the bank and ts mmedate neghbous (see Stole 1995). 5 o bevty, we abstact fom analyzng the effects of aametes τ, and n n detal. Smlaly, we abstact fom analyzng the sgn of d/dα. These comaatve statcs execses ae avalable fom the authos on equest. 7

3 A Ratonale fo Tansaency It s often agued that deost nsuance s needed n ode to avod systemc cses asng fom the nheent faglty of the bankng ndusty. It tuns out that the same agument ales to the tansaency equement. Matutes and Vves (1996) show how the bankng secto may be vulneable to self-fulfllng cses f thee s a mnmum sze equement fo banks. If a bank does not obtan the mnmum maket shae, t cannot nvest and fals wth obablty one. Deostos exectatons then become self-fulfllng and the model theefoe exhbts multle equlba, one of whch s a collase of the ente bankng system. In Matutes and Vves (1996) the ntoducton of deost nsuance events fnancal collase by elmnatng the 'nobankng' equlbum. Let us now consde the ole of tansaency n a model whee a mnmum maket shae s needed to make a bank oeatve. The esence of the economes of scale n banks oducton technology mght gve a ase to such mnmum sze equement (Wllamson 1986, Matutes and Vves 1996). As we shall show at the end of ths secton, the mnmum sze equement can also emege fom the economes of scale ceated by a balance sheet constant. Suose ntally that no tansaency egulaton s n lace. Deostos then know that the banks cannot commt themselves ex ante to the eayment obablty. Because thee s no deost nsuance, the deostos can lose the amount deosted f the bank fals. As a esult, thee s a coodnaton game on the deostos. A coodnaton falue causng systemc css may occu. PROPOSITION 1. Wthout tansaency egulaton, a collase of the bankng system s ossble. Poof. When α = 0, all deostos atonally evaluate bank s asset sk ostons accodng to the exectaton E( ) = e and E(R )= e. If all deostos exect that e = 0,.e., that = 0, then E(R )=0, and bank has no customes fo any that t may choose. Because bank cannot acque the mnmum maket shae, t cannot cedbly choose a ostve eayment obablty. Bank s then cetan to fal. As s abtay, 8

the same easonng ales to the ente ndusty,.e., f α = 0, a systemc collase e wth D = 0 and = = 0 ( = 1,2,,n) s ossble. Q.E.D Ths esult follows fom the deostos self-fulfllng exectatons leadng to systemc confdence css. Wthout tansaency, the deostos exectatons of = 0 ae ealzed n the equlbum, and no one fnds t oftable to unlateally e devate fom these stateges. The systemc-css equlbum coexsts wth the nteo symmetc equlbum chaactezed by full-scale cometton n (3)-(4). It s, howeve, ossble to elmnate the systemc-css equlbum by enhancng bank tansaency, PROPOSITION 2. A suffcently stngent tansaency egulaton elmnates the systemc-css equlbum. Poof. When α 1, thee s no oom fo moal hazad and theefoe deostos decsons cannot based on exectatons. Because the deostos exectatons lay no ole, bank can attact moe customes by nceasng. Bank can acque the mnmum maket shae unde the assumton of full-scale cometton and, accodngly, t can choose a ostve eayment obablty and the systemc css equlbum s elmnated. Q.E.D In ou model tansaency equement woks lke the deost nsuance n Damond and Dybvg (1983) and Matutes and Vves (1996) n emovng the 'bad' equlbum,.e., the collase of the bankng secto. A smla equvalence esult of tansaency and deost nsuance can be found n Codella and Levy Yeyat (1998b) and Matutes and Vves (2000) who ove that full tansaency and a sk-based deost nsuance scheme lead to an equal sk-takng ncentve. The advantage of tansaency egulaton ove the deost nsuance s that t does not cause moal-hazad oblems. In contast, t educes them, as oven n Remak. 9

In assessng the elablty of ths fndng, howeve, a caveat should be bone n mnd. Instead of moal hazad temtatons, tansaency egulaton may cause comlance costs fo banks. In Hyytnen and Takalo (2001) we consde both the dect costs of comlyng wth dsclosue equements and the ndect tansaency costs stemmng fom mefect oety ghts govenng nfomaton. Nonetheless, ou key agument hee emans obust even f achevng tansaency s costly fo banks. Tansaency egulaton s needed to avod self-fulfllng cses asng fom a mnmum sze equement fo banks. nally, we make the mnmum sze equement exlct. Thee ae vaous ways to ntoduce the economes of scale nto the model. We smly assume that the bank s balance sheet holds,.e., that a + C /D + c = 1, (5) whee a denotes bank s asset otfolo nvestments e deost unt. When the balance sheet constant s mosed, bank s deosts have to cove all ts nvestment exenses so that bank can lend only amount a. The funds nvested n montong dectly educe the amount of funds nvested n the ojects. The ofts of bank fom (2) can n ths case be ewtten as [ ( ya ) c ] D C π =. (6) Solvng (5) fo a and substtutng t fo (6) yelds [ ( y ) c ( 1+ y) ] D C ( y) π. (7) = 1+ Comang (7) wth (2) clealy demonstates the exstence of economes of scale. Deste ou assumton that c(0) / =C(0) / = 0, the devatve of (7) wth esect to when evaluated at = 0 (and at D = 0) s negatve. In othe wods, unde a bndng budget constant, t s otmal fo bank not to be oeatve. Ths s consstent wth the deostos exectatons. Thus, because of the costs caused by montong nvestments, bank needs a mnmum maket shae to oeate. 10

4 Conclusons and Polcy Imlcatons In ths ae we oose a novel justfcaton fo tansaency egulaton. It may event a comlete collase of the bankng secto asng fom the self-fulfllment of deostos exectatons. Tansaency egulaton n ou model woks lke the deost nsuance n the nfluental atcles by Damond and Dybvg (1983) and Matutes and Vves (1996), whee t may event systemc confdence cses. Deost nsuance, howeve, entals a wdely ecognzed moal hazad oblem. By enhancng bank tansaency, systemc cses can be avoded wthout the ceaton of the safety net. Hence, the advese ncentve effects of the nsuance can also be avoded. 11

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16 Aendx: Poof of Remak Let us fst exlctly wte the fst-ode-condtons as ( ) ( ) ( ) ( ) 0, = C n A c A τ α, (A1) ( ) ( ) 0, = n c A τ, (A2) whee A() = (y-)-c(). Equatons (A1) and (A2) detemne and as functons of α. The comaatve statcs can then be deved n a standad way: α α α d d d =. (A3) The, by usng Came s ule J d d = α α α 1 (A4) whee = J. (A5) By assumng that the cost-functons c and C ae suffcently convex n we know that / < 0 and J = > 0. By notng that /α. = 0, the sgn of d/dα s gven by the sgn of = α α 0. (A6)

Takng the atal devatves of and wth esect to α and fom (A1) and (A2) yelds αa =, (A7) α τ =, (A8) τ Substtutng (A7)-(A8) fo (A6) and smlfyng oves ou clam that d/dα > 0. Q.E.D 17

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