Chiara ratton-lavoi Chaptr Chaptr : rivatization Diusion o har wnrship an olitics. Introuction inc th 980s many national govrnmnts hav pursu privatization programs. Although th wor "privatization" ncompasss a varity o govrnmnt policis rom rgulation policis to th sal o stat-own ntrpriss to th privat sctor a cntral atur o privatization policis is th chang rom public to privat ownrship. Th scal o ths programs varis across countris but th trn towar privatization is worlwi. Th biggst privatization program in a capitalist country to at was implmnt by th consrvativ Thatchr govrnmnt in Britain primarily in th 980s. In 979 at th bginning o th privatization procss stat-own ntrpriss account or about 0.5 prcnt o th country's D. Toay almost vrything has bn privatiz rom uasi-comptitiv activitis li transportation automobil manuacturing stl an port oprations to public utilitis li tlcommunication gas lctricity an watr. ith th xcption o postal srvics which ar still in public hans all British public utilitis ar now privat ntrpriss. Th British Consrvativ govrnmnt aopt its privatization plans with at last thr intn an clar goals: - improv th conomic icincy o th ntrpris For a tail stuy an valuation o th British privatization program s icrs an Yarrow 988. 37
Chiara ratton-lavoi Chaptr - ruc th ublic ctor Borrowing Ruirmnt BR or mor gnrally rais rvnus or th govrnmnt - win shar ownrship among small invstors mploys an th gnral public ncouraging thm to buy an hol shars o privatiz companis through various spcial arrangmnts installmnt paymnts loyalty bonuss spcial iscounts an low shar prics. hthr th chang in ownrship structur is in itsl suicint to improv icincy is th subjct o continual bat. hat is not controvrsial is that th sal o public ntrpriss can rais signiicant rvnu. rivatization programs in th Unit Kingom hav rais tns o billions o pouns or th Trasury. Nvrthlss ths rvnus coul hav bn much highr. In act mpirical vinc shows that th British govrnmnt runtly unrpric shars o th nwly privatiz irms whn it sol thm to th public. For xampl Jninson an Mayr 988 an icrs an Yarrow 988 show that th avrag iscount on ors or sal o stat ntrpriss in Britain has bn much highr as a prcntag o gross procs than th iscount usually obsrv in Initial ublic rings o privat issus. Tabl lists th major sals carri out by th British govrnmnt rom 977 to 99. For ach sal th tabl rports th prcntag o th stoc sol th gr o unrpricing as masur by th prcntag irnc btwn th or pric pr shar an its mart valu at th n o th irst ay o traing an th man multipl. Most companis wr sol using a ix-pric or whn th govrnmnt sts th pric o th shars whil only w sals us a tnr or whn applicants bi a pric abov a stanar minimum st by th govrnmnt. Typically prmiums wr high an th issus wr ovrsubscrib. Jninson an Mayr also rport similar vinc or privatizations in Franc. 38
Chiara ratton-lavoi Chaptr Tabl. rivatizations in Th Unit Kingom: 977-99. Company Dat o sal ta sol prcntag Discount prcntag Dman multipl* British trolum Jun 977 7.7 4.7 Novmbr 979 5.5 ptmbr 983 7 a.7 ctobr 987 36.8 3 b --- c British Arospac Fbruary 98 50 4 3.5 May 985 --- c 5.4 Cabl an irlss Novmbr 98 49 7.3 5.6 Dcmbr 983 3 - a 0.7 Dcmbr 985 0.0 a Amrsham Fbruary 98 00 3.4 5.6 Associat British orts Fbruary 983 5.5 3. 35 April 984 48.5 0. a.6 Jaguar August 984 00 8.5 8.3 British Tlcom Dcmbr 984 50. 33 5 Dcmbr 99 3.9 4..5 July 993 --- c --- c Entrpris il July 984 00 0 a 0.7 Britoil Novmbr 98 5-8.8 a 0.3 August 985 49 0 Trust avings Ban ctobr 986 00 35.5 8 British as Dcmbr 986 00 9. 4 British Airways Fbruary 987 00 35. 3 Rolls Royc May 987 00 36.5 9.4 BAA July 987 00 8.8 8 British tl Dcmbr 988 00 3.3 3.3 Anglian atr Dcmbr 989 00 48.5. N.. atr roup Dcmbr 989 00 35.6 Northumbria atr Dcmbr 989 00 57 9.0 vrn Trnt Dcmbr 989 00 3.8.. atr Dcmbr 989 00 47.8 outhrn atr Dcmbr 989 00 4 3.4 Thams atr Dcmbr 989 00 36 4.3 lsh atr Dcmbr 989 00 4. ssx atr Dcmbr 989 00 54 4.0 Yorshir atr Dcmbr 989 00 49.6 East Milans Elctric Dcmbr 990 00 50.5 9.5 Eastrn Elctric Dcmbr 990 00 48 9. Lonon Elctric Dcmbr 990 00 4 8. Manwb Dcmbr 990 00 66 5.4 Milans Elctric Dcmbr 990 00 50 9.5 Norwb Dcmbr 990 00 5.7 Northrn Elctric Dcmbr 990 00 4.5 3.7 aboar Dcmbr 990 00 3. outh als Elctric Dcmbr 990 00 64 5.8 outh strn Elctric Dcmbr 990 00 50. outhrn Elctric Dcmbr 990 00 50.6 Yorshir Elctric Dcmbr 990 00 59.5 7.7 National owr March 99 60 37.5 5.4 owrn March 99 60 37 5.4 cottish Hyro-Elctric Jun 99 00 3.0 cottish owr Jun 99 00 5.5 3.0 ourc: Enrico C. rotti 995. * Ratio o man to supply o stoc. a Tnr sal. b Issu uring th ctobr 987 stoc crash. Th pric all o th issu was lss than th gnral pric clin. c Inormation not availabl. 39
Chiara ratton-lavoi Chaptr Evn in th long trm prmiums on nw issus wr high conirming that shars o nwly privatiz irms wr a goo long-trm invstmnt. This suggsts a poor pricing cision by th govrnmnt. Th vry w cass in which th valu o shars o privatiz ntrpriss ll or i not incras wr thos that wr in th mist o an inustry wi crisis Britoil Entrpris il an th partial sal o Cabl an irlss in 983. n th on han th unrpricing phnomnon apparntly contraicts th clar objctiv o raising rvnus. n th othr han i th govrnmnt wants small invstors to buy shars thn low prics might b justii. But why woul th govrnmnt car about iusion o shar ownrship in th irst plac? This papr provis on xplanation o th govrnmnt s sir or wi shar ownrship an it shows that high iusion o asst ownrship an low shar pric can b chosn by a govrnmnt that wants to maximiz rvnus. Consir a ynamic gam o complt inormation in which a govrnmnt irst privatizs a company an thn compts or vots against an opposition party. Th govrnmnt s objctiv is to choos th pric o shars an th lvl o promotional ort to maximiz its xpct nt rvnus. Ris nutral votrs ci how many shars to buy i any. Thy hav intical xognous incom but ar irntiat by thir transaction costs. Altrnativly th govrnmnt can ci to sll th company to a non voting orign invstor who has an unlimit bugt an woul buy th ntir company or any pric that os not xc its tru valu. Atr th sal o th company to th public th two partis announc what xpropriation rat thy woul implmnt i thy win th upcoming lction. High promotional ort gnrats iusion o asst ownrship which in turn lowrs th xpropriation rat that th two partis will simultanously announc in uilibrium in th political gam. I show that it is optimal or th incumbnt party to unrpric th stoc with rspct 40
Chiara ratton-lavoi Chaptr to its tru valu. This is on to incras th siz o th sharholrs intrst group which will avor th party announcing a lowr xpropriation rat in th scon prio; invstors anticipation o a low xpropriation rat allows th govrnmnt to sll th company at a highr pric. Th govrnmnt is willing to sacriic utur rvnus rom xpropriation bcaus it may not b in powr whn thos rvnus ar collct. Typically th optimal policy is charactriz by unrpricing o shars a positiv lvl o promotional ort an wi shar ownrship. Th xisting litratur on privatization appars not to hav analyz privatization an unrpricing in such a political ramwor. al mthos an shar prics in privatization hav bn analyz by Branco an Mllo 99 an rotti 995 in th contxt o a signaling gam btwn th govrnmnt an invstors. Thy or th ollowing xplanation o unrpricing an graual or complt sals obsrv in privatization programs 3. A govrnmnt that cis to sll a irm to privat invstors can b o two typs: a typ committ to avoiing intrrnc atr th sal or an uncommitt typ which cannot rsist aopting x-post policis that will ruc th valu o th privat stoc. Th govrnmnt's typ is privat inormation. Both typs striv to maximiz sal procs an th typ that intrvns also gains rom intrrnc. inc invstors ar willing to pay mor i thr is no intrrnc th committ typ wants to signal its commitmnt whil th intrvning typ has an incntiv to imitat th othr typ's stratgy. Using a two-prio signaling mol th authors show that or crtain rangs o valus o th paramtrs a sparating uilibrium xists in which th committ govrnmnt slls only a raction o th irm 3 Thr is a major irnc btwn th two analyss. hil Branco an Mllo assum that proits ar xognously givn ual to zro unr public ownrship an growing at a constant rat whn th irm is privatiz rotti nognously rivs proits rom spciic assumptions concrning managrs' incntivs unr th irnt ownrship structurs. rotti mas also th rathr rstrictiv assumption that managrs o th irm ar also th utur privat ownrs. 4
Chiara ratton-lavoi Chaptr in prio on an complts th sal in prio two whil th uncommitt typ slls th ntir stoc in th irst prio. Thr is a crucial valu o th raction sol in prio on at an blow which th uncommitt govrnmnt's payo rom intrrnc woul b largr than th gains rom avoiing intrrnc in th irst prio an obtaining a highr pric in th sason or. For som paramtr valus a sparating uilibrium through partial sal only os not xist. In this cas th authors show that th committ govrnmnt can combin unrpricing with a partial sal or to inuc sparation 4. Unrpricing is a issipativ signal an it acts th two typs' payos in th sam way. Thror unrpricing alon cannot gnrat sparation. Also an or or sal must b chosn by th govrnmnt to stratgically manipulat th pric o shars. I th govrnmnt is a committ typ th mol pricts that w shoul obsrv ithr tnr ors with partial sals an no unrpricing or a ix-pric or with partial sals an unrpricing. Th optimal uilibrium stratgy or an uncommitt typ is always to sll all at onc through tnr. Th prsnt mol irs in thr unamntal ways rom th signaling mols o privatization. First this mol os not ruir that political partis hav hin charactristics: all actors in th mol hav complt inormation about th two partis objctivs. In act th two partis ar intical with rspct to thir prrncs an th cisions that thy ma in this mol although on party has th avantag o incumbncy. con th rat o xpropriation is trmin nognously in th contxt o th lctoral comptition whn ach party chooss to announc th rat o utur xpropriation that maximizs its chancs o winning th lction 4 Ths rsults ar similar to thos obtain in th inanc litratur to xplain unrpricing in Is o privat issus s or xampl Alln an Faulhabr 989 rinblatt an Hwang 989 an lch 989. In that cas th asymmtry o inormation btwn invstors an issur rgars th tru valu o th irm. As mntion in th introuction th avrag iscount obsrv or th sals o stat ntrpriss has bn much highr than th iscount obsrv or privat issus. 4
Chiara ratton-lavoi Chaptr an its utur xpct inancial gains rom xpropriation. Thir th signaling mols o privatization prict unrpricing only whn thr is a partial sal o th stat-own company but this rsult cannot xplain th historical vinc as prsnt in Tabl o complt sals at prics lowr than th companis tru valus. Th prsnt mol gnrats xactly this priction an it provis a rational or unrpricing an iusion o shar ownrship as outcoms o a privatization policy aim at maximizing inancial an political gains. ction scribs th timing o th mol th partis objctivs an th votrs bhavior both as invstors in th irst prio an as votrs in th scon prio. ction 3 solvs th lction subgam an sction 4 stuis th NE o th whol gam. ction 5 contains inal commnts.. Timing an playrs objctivs Consir a two-party mocracy. Th partis ar inx by { } whr an not th party in powr an th opposition party rspctivly. Th votrs ar inx by i I [0]. Each votr i is charactriz by c i b [ 0 c] [ r r ] whr c an r ar xognous c i masurs votr i s cost o ngaging in transactions an b i masurs votr i s prsonal bias towar on party or th othr which xists or rasons outsi th mol. Th votrs ar istribut uniormly ovr [ 0 c] [ r r] ; thror c i an b i ar statistically inpnnt o ach othr an across votrs. Th transaction cost c i trmins votr i s invstmnt bhavior whil b i trmins votr i s tnncy to vot or on party or th othr. Each ininitsimal votr is initially now with th sam amount o xognous i 43
Chiara ratton-lavoi Chaptr incom or walth. Th total mass o th population is normaliz to on; thror is th iniviual incom as wll as th total aggrgat incom in th conomy. A ris nutral orignr now with an unlimit bugt ss to maximiz his xpct walth. Altrnativly on can thin o a rich omstic invstor who has only an ininitsimal an thror irrlvant impact on th lctoral procss. Thr ar two prios. In th irst prio th govrnmnt slls to th public a singl stat-own ntrpris. Th govrnmnt slls th ntir irm oring to privat invstors a crtain total numbr o shars hr normaliz to on or simplicity. Th govrnmnt announcs a shar pric an it xrts promotional ort [0 with total cost A. inc th total numbr o shars is normaliz to on rprsnts th sal valu o th ntir oring as wll as th pric o a singl shar. Assum that <. Each votr cis how many shars o th irm to buy i any an no votr is willing to pay mor than th stoc s air valu. I also assum that or a pric that os not xc th stoc s air valu th govrnmnt can sll any numbr o shars to th orign invstor. inc no potntial invstor is willing to pay or th shars mor than thir air valu an sinc or a pric not xcing th air valu th orignr is always willing to purchas all unsol shars in uilibrium th govrnmnt nvr sts a pric xcing th stoc s air valu an at th chosn pric it slls th ntir oring. In th scon prio th govrnmnt an th opposition party compt or vots in an lction. Lt not th raction o th population that bought shars in th irst prio. Th votrs ar partition into two intrst groups: th sharholr group an th nonsharholr raction N -. Th two partis simultanously announc thir platorms. In particular thy announc th xpropriation rat that thy woul impos on privat proits i 44
Chiara ratton-lavoi Chaptr thy win th lction. Th xpropriation rat can b intrprt broaly as any coniscatory policy or proit tax that rucs th valu o th privat company. Th xtrm cas o govrnmnt intrrnc is th r-nationalization o th privat company i... Atr th platorm announcmnts th lction is hl an ach votr i vots or on o th two partis. Th nwly privatiz company mas proits ual to with >0. Finally th winning party xpropriats th privat proits at th promis rat. I assum that th nwly lct govrnmnt ulills its commitmnt. cours this assumption ignors th ralistic issu o whthr th lct party woul actually p its promiss. Th implicit assumption is that votrs rmmbr lction promiss an ach party acs prohibitivly larg political losss i it viats rom its announc platorm whn in powr. Th tim at which th govrnmnt announcs its choic o is a moling assumption that ruirs som xplanation. Although in prio on th govrnmnt is abl to anticipat its optimal stratgy in prio two I assum that it cannot prcommit itsl in th irst prio to a particular gr o utur intrrnc. This choic o th timing o commitmnt rlcts a spciic assumption about votrs bhavior: votrs in this mol rmmbr an punish viations rom lction promiss only an thy ignor promiss ma bor th lction campaign 5. Although xognously givn in th mol this choic o th timing o commitmnt capturs an important aspct o rality: in rality promiss o count but thy tn to count lss whn thy ar ma much in avanc. It otn happns that unxpct vnts an nw 5 Altrnativly on coul assum that privat proits ar ranom an that in th irst prio som proxy o th proitability o th company is privat inormation o th govrnmnt. In such a mol th timing o th commitmnt o th govrnmnt to implmnt a crtain rat o xpropriation woul b riv nognously. 45
Chiara ratton-lavoi Chaptr circumstancs caus ol promiss an ol commitmnts to thos promiss to los cribility ovr tim... Th partis objctivs Th govrnmnt an th opposition ar sl-intrst maximizing agnts. Thy car only about thir own inancial gains an about thir chancs o winning th lction. hn both partis play thir uilibrium stratgis in th scon prio lction gam µ nots th govrnmnt s probability o winning th lction an nots th rat o xpropriation that th govrnmnt announcs in uilibrium just bor th lction an which it woul implmnt i rlct. Th objctiv o th govrnmnt is to choos th shar pric an th lvl o promotional ort that maximiz [ A ] µ β [] Th xognous paramtr 0 rprsnts th raction o nt rvnus rom th sal A an latr xpropriation that irctly bnits th govrnmnt. n intrprtation o is that it is th prcntag o inancial arnings rom th privatization policy that th party in powr is abl to us or its own prsonal bnit: mony that th party holing oic is abl to invst on activitis an/or goos that bnit only th party or its supportrs. Altrnativly can b intrprt as a masur o th gr o corruption in th political systm. 46
Chiara ratton-lavoi Chaptr Th rmaining raction - o th inancial rvnus is spnt by th party in oic to provi a uantity o public goo. How is in will b iscuss latr whn th iniviual invstmnt cision is analyz. Th xognous paramtr β 0 rprsnts th intrinsic i.. noninancial bnit that th party rcivs rom holing oic. Th utur in this mol is not iscount thror th iscount rat is assum to b zro. A masurs total costs o th promotional ort [ 0 unrtan by th govrnmnt whn it slls th company to th public. Th promotion o th sal rucs th transaction costs o th potntial invstors thror incrasing th raction o popl who buy shars. I assum that lim A with A0 A' 0 0 an A A >0 or all 0 6. In th irst prio th govrnmnt chooss a privatization pacag that maximizs its objctiv in [] subjct to on constraint: to sll th company to any omstic or orign invstors th govrnmnt must choos a shar pric that os not xc th utur nt xpct valu o th irm. Thror th govrnmnt must choos: - * [] whr * µ µ is th xpct rat o xpropriation. Th platorms an pn on both an. Th govrnmnt is othrwis unconstrain: in particular th govrnmnt will always b abl to sll th ntir company bcaus it can always choos to sll all th shars to th orign invstor at thir tru valu. Th opposition party obsrvs th govrnmnt s choics o an in th irst prio an in th scon prio bor th lction it compts or vots against th party in powr. Th 6 Hratr singl an oubl prims not irst an scon rivativs o unctions o on variabl. 47
Chiara ratton-lavoi Chaptr partis announc thir platorms simultanously. pciically th opposition announcs th valu o that maximizs: β µ [3] whr µ is th opposition party s probability o winning th lction. For simplicity assum that th valus o th paramtrs an β ar th sam or both partis. Th uilibrium o th political gam as shown in ction 3 o th papr will b a symmtric uilibrium in which both partis announc th sam xpropriation rat an ar ually lily to win th lction... Th votrs prrncs In th irst prio ach votr i i [0] cis how many shars o th stat-own company to buy i any at th announc stoc pric. In th scon prio votrs vot givn th partis platorm announcmnts. th ctions that ollow ction... stuis th iniviual invstmnt cision an ction... stuis iniviual voting bhavior. Finally ction..3. rivs th uations that scrib ach party s xpct margin o victory as wll as its probability o winning th lction.... Th invstmnt cision At th bginning o th irst prio ach votr is now with th sam amount o incom. Each votr i also has an iiosyncratic transaction cost paramtr c i. Ths 48
Chiara ratton-lavoi Chaptr transaction charactristics ar uniormly istribut ovr th ral intrval [ 0 c]; thror or any c [0c] th raction o th population having a transaction paramtr not xcingc is c c. Each votr must ci how many shars o th irm to buy. Lt i not th numbr o shars man by votr i. In maing th invstmnt cision ach votr consirs his privat payo. pciically votrs riv utility rom th consumption o a public goo an rom prsonal incom that thy spn on privat goos. Thy consum th uantity o th public goo which is provi by th party in powr using th raction - o th rvnus rom th sal an rom th xpropriation. Th unit pric o th public goo is normaliz to on. otr i also has a crtain amount o isposabl incom y i which is th sum o his initial nowmnt an any nt inancial gains that rsult rom th iniviual invstmnt cision. Th utility that votr i rivs rom consumption is y i. Assum 7 a uasilinar utility unction o th orm y i y i. Quasilinarity implis that: yi y y i i y i 0 0 [4] In aition assum that 000 >0 an <0. Finally i votr i buys any strictly positiv numbr o shars h will incur a utility loss rom participating in th transaction. Ths transaction costs ar highr or popl having a highr valu o th prsonal transaction charactristic c i an thy ar lowr or highr lvls o promotional ort xrt by th govrnmnt. This assumption rlcts th ia that th party in powr wants th inormation concrning th sal to b asily an chaply availabl to all 7 From now on subscripts not partial rivativs o unctions o svral variabls. 49
Chiara ratton-lavoi Chaptr votrs an that to ma th sal attractiv to potntial buyrs it aopts spcial promotional campaigns 8. otr i s transaction costs T i ual: T i ci i ci 0 i ci < otr i s total utility is: u i yi Ti i > 0 i i 0 i i [0] whr y i [ A ] [ ] i i i i i i > i [5] Hr nots th uantity o th public goo purchas by th govrnmnt y i nots votr i s iniviual isposabl incom rprsnts th actual raliz xpropriation rat an i nots th numbr o shars actually rciv by votr i. For a chosn pric an a givn lvl o promotional ort th issu can b ovrsubscrib in which cas th govrnmnt uss a rationing schm that rucs ach iniviual s man by th sam proportion. I is th total raction o th population that buys th stoc thn i > implis ovrsubscription an ach invstor will rciv / shars. otrs anticipat this possibility whn taing thir invstmnt cision. 8 Th British Consrvativ ovrnmnt or xampl istribut vouchrs that coul b us to ruc bills such as phon bills or lctricity bills by all thos who bought shars o th privatiz public utilitis. 50
Chiara ratton-lavoi Chaptr Each votr i chooss i to maximiz his utility in [5] subjct to th constraint impos by his limit incom: 0 i. Assum that changs in th iniviual ininitsimal man i o not inlunc th choic o in th scon prio. Hnc 0 implying 0. This assumption is i i rasonabl in this ramwor. inc votrs ar istribut uniormly ovr [ 0 c] [ r r] ach votr is too small or his bhavior to act aggrgat outcoms. Inspction o th maximization problm rvals that only y i is act by th choic o i. Furthrmor sinc - y i is non-crasing in i. Thror i votr i mans any shars h woul man as many shars as possibl i.. i * /. can conclu that thos votrs who man shars man th sam numbr / whil votrs with suicintly high transaction costs o not man any shars: thror th iniviual man or shars i * is ithr zro or /. Th total man or shars is. Th rationing rul bcoms: i i [6] with whn th issu is xactly subscrib. I th issu is unrsubscrib thn th govrnmnt slls th rmaining shars to th orign buyr at pric. 5
Chiara ratton-lavoi Chaptr Th analysis o th invstmnt cision conclus by riving or ach pric an lvl o promotional ort th thrshol valu o th transaction paramtr c i that charactrizs th marginal invstor. an only i: Aopting an arbitrary ti-braing rul whn c i votr i buys shars o th company i y i ci [7] Thror givn th pric an th lvl o promotional ort an givn th anticipat rat o xpropriation th thrshol valu o c i that charactrizs th marginal invstor is c y i From conition [7] an using th initions o y i an it ollows that or any > 0 thr is always a positiv raction o votrs that has zro transaction costs an consuntly buys shars vn whn th govrnmnt chooss to pric th stoc at. n th othr han i thr is no promotional ort 0 thn only or a pric lowr than th stoc s valu will votrs buy shars o th stat-own company. Th proportion o th total population with a valu o th transaction paramtr blow th thrshol is givn by: prob ci c prob c y c i i y i Thror rcalling that 0 th raction o sharholrs is in as ollows: 0 c c y or y i i or c y < < i [8] 5
Chiara ratton-lavoi Chaptr Th xprssion abov ins th raction o sharholrs as a unction o th lvl o promotional ort th govrnmnt cis to unrta [ 0 9 an it hols or any pric smallr thn or ual to th air valu o th company -.... Iniviual voting bhavior Atr th Initial ublic ring th population o votrs is partition into th raction o sharholrs scrib by uation [8] an th raction o non-sharholrs N with N -. In th scon prio atr th govrnmnt an th opposition announc thir platorms an ach votr vots or th party h prrs. otrs avor th party that givs thm th highst total utility. This pns on th announc xpropriation rat bcaus th rat o xpropriation will act th uantity suppli o th public goo an i th votr is a sharholr th votr s isposabl incom. I assum that iniviual utility an so voting bhavior is also act by a bias trm ε i which is th sum o a prsonal iiosyncratic bias b i an a systmatic bias δ: ε i δ i [0] [9] bi Th iiosyncratic bias b i is uniormly istribut ovr [ r r] R an δ is uniormly istribut ovr [ λ λ] R. Thror th total bias ε i is istribut ovr th intrval [ λ r λ r ]. Th bias trm capturs th ia that th voting cision is inlunc by nonpolicy rlat mattrs an iology as wll as by policy issus othr than th rat o 9 inc [ [ ] 0 it has to b c y i 0 which implis y i c. 53
Chiara ratton-lavoi Chaptr xpropriation. Th total bias ε i can b in avor o whn positiv or against whn ngativ th govrnmnt. For clarity o xposition th analysis hncorth uss th oubl subscript ij to inicat th intity i [0] an th typ j { N} o ach votr rspctivly an u ij with { } to inicat votr ij s utility as unction o th rat o xpropriation implmnt by th party that wins th lction. Finally U ij tas votr ij s bias trm into account an thror it rprsnts th total utility votr ij rivs rom th victory o party. U with w 0 otr ij s utility i party wins is thror: u uij ε b δ i ij i ij wε y T i i wins th lction i wins th lction i i [0] {} j { N} or or j j N [0] whr [ ] A y [ ] i ovrsubscription i no ovrsubscription ithin ach intrst group all votrs hav intical prrncs ovr. It is immiat that th non-sharholrs utility is strictly incrasing in. Thror th non-sharholrs always prr ull xpropriation o privat proits: th highr is th 54
Chiara ratton-lavoi Chaptr xpropriation rat th biggr is th amount o public goo an th highr is th utility o a votr who os not own shars. For a sharholr a highr xpropriation rat rsults in mor public goo but it also rucs th sharholr s isposabl incom. This trao implis that th optimal rat o xpropriation or a sharholr can b smallr than on Appnix contains th analysis concrning th optimal xpropriation rat or th rprsntativ sharholr. How o votrs cast thir vot? Each will vot or th party whos announc platorm i implmnt woul giv him th highr utility givn his voting bias. pciically votr ij vots or th opposition i an only i: U ij U ij Thror aopting an arbitrary ti-braing rul th probability σ ij that votr i in group j vots or th opposition is givn by 0 : σ ij i ε u - u 0 i ε > u - u i ij ij i ij ij [] In th sam way votr ij vots or th govrnmnt i an only i U ij ij an th probability that votr i in group j vots or th govrnmnt is g ij ij σ ij. 0 oting is assum to b costlss. 55
Chiara ratton-lavoi Chaptr..3. Th plurality an th probability o winning th lction. Rcalling that ε i δ it is asy to calculat th probability that a givn votr bi supports th opposition. Lt t b th valu o th iiosyncratic bias b i that mas votr ij inirnt btwn voting or th govrnmnt or or th opposition: t u - u δ ij ij Th istribution unction o th iiosyncratic bias trm b i is uniorm ovr th intrval [ r r ]. Thror: probb i t or - r < t < r r t r whr r is b i s uniorm nsity. Thn th probability that votr ij avors th opposition is: [ ] i t ij ij σ ij prob b u - u δ r r [] an th probability that votr ij vots or th govrnmnt is g ij σ. ij Th total raction o vots cast or th opposition is th sum o th proportions o vots pro-opposition in th two intrst groups: r u u r N r u u r i i δ δ imilarly r u u r N r u u r i i δ δ is th raction o th population that avors th govrnmnt. 56
Chiara ratton-lavoi Chaptr Th plurality or ithr party as a unction o th announc platorms an is simply th irnc btwn th raction o th population that vots in avor o th party an th rmaining raction that avors th political opponnt. pciically th pluralitis or th opposition party an th govrnmnt ar rspctivly: L L [ ] r z δ L whr z ui ui N u u [3] is th valu o th systmatic bias δ at which th pluralitis ar zro an th lction rsults in a ti. inc thr ar only two partis an vryon in th population vots a party wins th lction whnvr its plurality is positiv. Thror th partis probability o winning th political comptition is a iscontinuous unction o thir pluralitis. Lt µ inicat th probability that party wins. Thn: i L > 0 µ i L 0 0 i L < 0 { } Th pluralitis pn on th ralization o th systmatic bias δ which is uniormly istribut ovr [ λ λ ] with nsity ual to λ. Th nxt stp is to riv th probability that party wins th lction. From th istribution o δ: prob δ < z z λ or - λ < z < λ λ 57
Chiara ratton-lavoi Chaptr an thror: µ prob L > 0 prob δ < z z λ λ µ prob L > 0 prob δ > z z λ λ [4] Each party s probability o winning th lction as xprss in [4] tas valus btwn zro an on i: λ < u u < λ [ 0 ] i [ 0 ] N [5] ij ij I assum that th valu o λ is big nough to nsur that conition [5] is satisi. hat this assumption mans is th ollowing. hn th utility irntials or both sharholrs an non-sharholrs ta valus in th support o th systmatic bias thn not only is thr a positiv probability that votr ij vots or ithr party but also thr is always a positiv probability that within ach intrst group th plurality o ithr party is positiv. Thror nithr th govrnmnt nor th opposition can guarant thmslvs an ovrall majority rgarlss o th othr party s promis. This implis that ach votr s probability o voting or on party is a irntiabl unction o that party s promis K implying that ach party s probability o winning is a irntiabl unction o its campaign promis. Th rivation o th partis probability o winning th lction conclus th scription o th mol. In th ctions that ollow th gam is solv by bacwar inuction. inc at ach stag o th gam vry playr has xactly th sam inormation th gam is a ynamic gam o complt inormation an th appropriat uilibrium concpt is subgam prction. ction 3 analyzs th subgam. ction 4 loos at th ruc gam in th irst prio an iscusss th uilibrium o th mol. 58
Chiara ratton-lavoi Chaptr 3. Th subgam In prio two atr th sal o th stat-own company to th privat sctor th party in powr an th opposition compt or vots simultanously announcing thir choics o an. In oing so ach party commits itsl to implmnt th announc rat o xpropriation i it wins th lction. ivn th othr party s choic party chooss th rat o xpropriation that solvs th ollowing: max [ µ β ] subjct to 0 [6] whr µ is in by uation [4]. Th unconstrain vrsion o this maximization problm ruirs th ollowing irstorr conition at any critical point: µ β µ 0 [7] K y K To simpliy notation rom now on y K an K K From th initions in [3] an [4] an rcalling rom [4] that y : µ i u N u λ [8] with using [4] [5] an [0]: u y i y [ ] u [ ] 59
Chiara ratton-lavoi Chaptr whr an thror ar trmin in th irst prio with ithr / i th issu is unrsubscrib or / i thr is ovrsubscription. Bcaus by assumption 0 β 0 > 0 an 0 < µ < conitions [7] an [8] ruir that at any critical point: µ i u N u < 0 λ simpliis to: Rcalling that N - an irctly rom substitution th ncssary conition abov < K [9] which must hol at any critical point in th unconstrain problm. Conition [9] tlls us somthing about th marginal impact o xpropriation valuat at th point impli by th policy that satisis th irst-orr conition [7]. Rcall that y : thn < implis that th aggrgat marginal utility losss or K y omstic sharholrs rom lost incom o xc th aggrgat marginal utility gains rom incras consumption o th public goo. I conition [9] hols thn th optimal platorm announcmnt or party i it xists xcs th rprsntativ sharholr s prrr rat o xpropriation. Formally any that satisis conition [9] also satisis < : this implis that or th rprsntativ K sharholr u i < 0 at th uilibrium s Appnix uation A. I 0 thn 60
Chiara ratton-lavoi Chaptr conition [9] cannot hol or [ 0 ] implying µ 0 an thror th bst choic or party is to announc. From [7] an using [8] th suicint scon-orr conition or an unconstrain global maximum or party is: µ β µ λ β i i u N u u N u 0 λ < [0] I [0] is satisi at vry critical point thn th objctiv unction is strictly concav an thror i a critical point xists it is th uniu maximum. Rwriting th irst-orr conition as u N u i λµ β an thn substituting it togthr with u ij j { N} K into [0] th scon-orr conition valuat at th critical point bcoms: λ β [ N N ] λ λ λµ β < 0 K K K β λ λµ β [] Rcall that yy 0 y 0 an that -N. 6
Chiara ratton-lavoi Chaptr inc K < 0 [] hols or any valu o. Thror thr xists a uniu optimal xpropriation rat that solvs party s scon prio unconstrain maximization problm. I th FC is not satisi or a valu o btwn zro an on thn th constrain optimum is ithr zro or on pning on th sign o th irst-orr conition at thos valus. It might b that conition [9] nvr hols or a valu o th xpropriation rat btwn zro an on in which cas th lt-han si o uation [7] is always positiv an thror th bounary solution is. I th raction o sharholrs is vry small it might b optimal or party to choos to announc ull xpropriation o privat proits this is always tru or 0. I this is th cas thn vryon woul anticipat th choic o an thror or any positiv pric noboy woul buy shars. For 0 a gnrat uilibrium o th gam may xist: in th irst prio th govrnmnt arns zro rvnus slling th ntir irm to th orignr invstor without any promotion o th sal an thn it ully xpropriats th privat company in th scon prio. This is uivalnt to not slling th irm at all. n th othr han i at 0 a marginal incras in th valu o th announc utur xpropriation gratly rucs th chancs that party wins th lction thn th optimal choic or party might b to promis a rat o xpropriation ual to zro. All ls ual this is mor lily to happn whn th group o sharholrs is larg. To conclu uation [7] ins th govrnmnt s optimal choic o as a unction o an as wll as th paramtrs o th mol. To riv th uilibria o th subgam it is convnint to xprss th govrnmnt s raction unction simply as. Euation [7] ins a symmtric solution to th opposition s problm an 6
Chiara ratton-lavoi Chaptr thror is th opposition party s raction unction. Th nxt ustions to b answr ar whthr thr xists a pur stratgy Nash uilibrium or this subgam an whthr that uilibrium is uniu. 3.. Existnc It is straightorwar to show that thr xists a Nash uilibrium in pur stratgis. Bcaus conition [] hols at th uniu optimum th implicit unction thorm guarants that thr xist wll in continuous raction unctions an. It ollows that th composit unction is continuous or [ 0 ] an it maps a compact convx st into itsl. Thror accoring to Brouwr s ix-point thorm thr xists a * such that * *. 3.. Uniunss Th subgam has a uniu Nash uilibrium i: { [0]: } 0 < < I < [] I [] hols thn th two raction unctions cross only onc in th intrval [0] an th uilibrium is uniu an symmtric. It is shown nxt that conition [] is always satisi. First o all to riv apply th implicit unction thorm to uation [7] which 63
Chiara ratton-lavoi Chaptr ins th raction unction an thn irntiat it with rspct to obtaining s th Appnix or th algbra: [ ] [ ] β [3] [ 0 ] inc solvs [7] it must satisy conition [9] namly < an thror with 0 β 0 > 0 an < 0 by assumption th nominator o [3] is ngativ or all [ 0 ]. Th sign o th numrator pns on th valu o. inc <0 is crasing in i.. crasing in. This amits th possibility that at low valus o > which implis that at thos valus o th numrator o [3] is positiv an th whol xprssion in [3] has a ngativ sign. But rcall conition [9] or th xistnc o an optimal intrior valu o : it ruirs < at th optimum. Thror any Nash uilibrium o th subgam must b in th upwar sloping part o th raction unctions whr or both an conition [9] is satisi: any optimal rspons is in I. inc I is a connct st i th slop o th raction unction is smallr than on or I thn th two raction unctions cross only onc in I an thror th uilibrium which has to b in I is uniu. From th symmtry o th two raction unctions it ollows that th subgam prct uilibrium is symmtric i.. at uilibrium. Hnc to conclu that conition [] 64
Chiara ratton-lavoi Chaptr hols or all I it suics to show that it is vrii at. Thror valuating [3] at conition [] is vrii whn: [ ] [ ] β < which bcoms: [ ] > [ ] β Th abov isuality always hols thror th subgam has a uniu Nash uilibrium with : th two partis will announc th sam xpropriation rat in uilibrium an thy will both hav ual chancs o winning th lction µ µ rom uation [4] an th inition o z. In th nxt ction o th papr th ubgam rct Nash uilibrium NE o th gam is riv. It is shown that through unrpricing an promotional ort th govrnmnt incrass shar ownrship an that wi shar ownrship is instrumntal in maximizing th govrnmnt s total payo. 4. Th irst prio: privatization promotional ort an unrpricing. In th irst prio th govrnmnt slls th stat-own company to th privat sctor. It chooss a shar-pric an a lvl o promotional ort to maximiz its own objctiv as givn by uation []. From th analysis o th subgam rcall that th rat o xpropriation 65
Chiara ratton-lavoi Chaptr announc by th govrnmnt in th scon prio is a unction o an th opposition s announcmnt * : * is. ymmtrically th opposition s announcmnt. Th raction o sharownrs as in by uations [8] [5] * an [6] is a unction g whn th issu is unrsubscrib an it is a unction g * whn thr is ovrsubscription. Thror bor th govrnmnt chooss an is itsl a unction o an th xpct rat o xpropriation * µ µ. inc vryon anticipats that an thror that th partis ar ually lily to win th lction µ µ th govrnmnt s optimization problm in [] bcoms: max subjct to [ A ] β 0 0 [4] Bsis imposing th stanar non-ngativity constraints on th choic variabls an th govrnmnt must choos a shar pric that os not xc th impli utur valu o th company i it wants to sll th company at all. n potntial gnrat uilibrium o th gam can b riv rom simpl inspction o th maximization problm in [4]: it is th possibl NE charactriz by * * * 0 * 0 * 0. From th analysis o th subgam rcall that th uilibrium announcmnt coul b * rgarlss o th siz o th sharholrs intrst group. In this cas th bst th govrnmnt can o is to pric th company at its tru valu *0 an to 66
Chiara ratton-lavoi Chaptr choos *0. This is an uilibrium at which thr is no unrpricing no promotion o th sal an ull xpropriation o privat proits an th ntir company is sol to th orign invstor *0 rom [8]. In this xtrm cas th privatization policy os not srv th purpos o incrasing th govrnmnt s inancial payo bcaus th sam rvnus can b obtain i th company rmains a stat-own company. Anothr possibl xtrm outcom is an uilibrium in which th announcmnt in th scon prio is always * 0. This is mor lily or high valus o o cours. But * 0 coul also b th outcom o th subgam at low valus o i citizns riv littl utility rom aitional consumption o th public goo vn whn vry w units o th public goo ar provi: in othr wors i th marginal utility riv rom consumption o th irst unit o th public goo is vry low thn th bst campaigning stratgy may b to announc zro xpropriation o utur privat proits s conition [9] rcalling that it is not a suicint conition or th xistnc o an intrior solution. To conclu thr is th possibility o an uilibrium such that th govrnmnt s optimal choics o * an * imply a valu o *0 that supports ithr * or * 0. * inc th most intrsting cas is an uilibrium with 0 < < th ollowing analysis assums that th optimal platorm announcmnts li btwn zro an on. * * Consir th maximization problm in [4]. It is straightorwar to show that som o th constraints ar not bining. First bcaus o th assumption lim A th govrnmnt will always choos *<. con it is asy to rul out any uilibrium with * 0. In act i 67
Chiara ratton-lavoi Chaptr th shars o th company ar givn away thn th govrnmnt can o at last as wll by * ping th irm: an uilibrium with * 0 * 0 an 0 < < is nvr optimal. Thror th maximization problm in [4] bcoms: max subjct to 0 [ A ] β [4 ] Using th Kuhn-Tucr ormulation th Lagrangian o th problm in [4 ] is: * * [ A ] β γ [ ] L γ [5] whr γ is th multiplir. Assum that * * is a solution o [4 ]. Thn thr xists a multiplirγ * 0 such that * * γ * satisis: L L L γ γ γ γ 0 L γ 0 0 L γ γ 0 0 γ Appli to [5] th conitions spcii abov bcom: Notic also that any uilibrium with zro promotional ort an ull pricing o th sal cannot b sustain by an xpropriation rat smallr than on: it cannot b that * * 0 an 0 < * < woul imply *0 rom [8] an so in th scon prio it is optimal to announc *. bcaus this 68
Chiara ratton-lavoi Chaptr 69 0 thn > 0 i 0 0 thn < 0 i 0 ' 0 * * γ γ γ γ γ γ γ A L L L [6] From [6] an uilibrium * * with unrpricing an positiv promotional ort has to satisy: 0 ' 0 * * * * * * * * A L L [7] with γ * 0. Assum that [7] charactrizs a global maximum in * *. Thn rom [7] it ollows: roposition Assum that thr xists a global maximum that solvs th maximization problm in [4 ]. Thn a ubgam rct Nash Euilibrium with 0 < < * < * an * > 0 xists i ' * * * * A [8] uch an uilibrium will hav * >0. Th ngativ an positiv signs o th total rivativs in [8] ar intuitiv. Ctris paribus th govrnmnt always prrs a high pric low promotional ort an a high
Chiara ratton-lavoi Chaptr xpropriation rat s th objctiv unction in [4 ]. For any givn choic o i it was possibl or th govrnmnt to xpropriat mor at highr sal prics namly i * > 0 thn it woul pay to o so an < coul not b optimal. * Th sam rasoning hols i th ct on th platorm announcmnt o a cras in promotional ort is positiv i.. i < 0. For any givn valu o it woul pay to cras th ort xrt in prio on an thror to announc a highr xpropriation rat in th scon prio. Both cisions woul incras th govrnmnt s payo an consuntly * >0 coul not b optimal. * To analyz th uilibrium scrib by roposition w n to ocus on th two nognous variabls in th mol th raction o shar ownrship an th xpropriation rat. In th rmaining part o this analysis all th valus prsnt ar uilibrium valus although stars ar ropp or simplicity. Rcall that th govrnmnt's bst rply unction is a unction implicitly in by th FC in [7]. How os chang as changs ctris paribus? In gnral it is: Bcaus th uilibrium is symmtric in an th abov uation bcoms: 70
Chiara ratton-lavoi Chaptr Applying th Implicit Function Thorm to [7] using [3] an th initions in [3] [4] an [8] w obtain th ollowing rsults: roposition As shar ownrship changs th scon prio uilibrium announcmnt changs as ollows: β < 0 whn β unrsubscription an [9] 0 whn ovrsuscription Appnix or th proo For a givn an whn th issu is not ovrsubscrib an incras in shar ownrship causs a cras o th rat o xpropriation announc in th scon prio. This analytical rsult conirms th intuition that iusion o shar ownrship can b instrumntal in incrasing rvnus: highr shar ownrship implis lowr utur xpropriation an lowr xpropriation implis highr valu o th company that gos on sal. This in turn allows th govrnmnt to as a highr pric in th irst prio. 7
Chiara ratton-lavoi Chaptr nc th issu is ovrsubscrib any aitional incras in os not caus to cras. Th intuition bhin this rsult is simpl. Rcall rom th analysis o th subgam that th marginal impact o a chang in µ ui λ u N on th probability o winning th lction is givn by: [ ] λ with masuring th aggrgat marginal utility gains or th ntir population rom incras consumption o th public goo u to an incras in an y masuring th aggrgat marginal utility losss or omstic sharholrs rom lost incom u to any incras in. hn thr is ovrsubscription an thror th aggrgat impact on th sharholr group o any chang in is constant an ual to. In short onc th issu is ovrsubscrib any urthr incras in shar ownrship os not constitut an incntiv or th govrnmnt to announc a lowr xpropriation rat in th scon prio bcaus such an announcmnt woul not incras its chancs o winning th lction. Hnc th rsult in roposition. har ownrship as in by uations [8] [5] an [6] is a unction * g in cas o unrsubscription an a unction g * in cas o ovrsubscription whr * µ µ is th xpct rat o xpropriation. inc th scon prio uilibrium outcom is symmtric with an µ µ w can intrprt as a unction o. Thror using [8] [5] an [6] is xplicitly in as: 7
Chiara ratton-lavoi Chaptr c with y [ y ] [ A ] [ ] i unrsubscription i ovrsubscription [30] How os chang as th anticipat uilibrium announcmnt vrything ls constant? In gnral it is: changs holing g an i unrsubscription g g g which is i ovrsubscription. g Using [30] th rsults ar prsnt in th proposition blow. roposition 3 As th anticipat uilibrium valu o changs th chang in shar ownrship is givn by: [3] c < 0 whn unrsubscription c c [ ] < 0 whn ovrsubscription Appnix or th proo 73
Chiara ratton-lavoi Chaptr As th anticipat valu o utur xpropriation rat crass th anticipat valu o th irm F- incrass. For a givn an >0 mor invstors will man shars an thror incrass. Comparing th two uations in [3] th rsults inicat that or any givn ruction in xpropriation rat th incras in shar ownrship is proportionally lss whn th issu is ovrsubscrib than in cas o unrsubscription. This is simply xplain by consiring that i th issu is ovrsubscrib ach votr woul rciv proportionally wr shars. Thror th xpct rturns to iniviual invstmnt ar lowr than in th cas o unrsubscription an ctris paribus wr aitional votrs woul man shars. Th rsults prsnt in ropositions an 3 hlp to provi a graphical intrprtation o th gam an its possibl uilibria as prsnt in Figur. For a givn pric o th stoc an a givn lvl o promotional ort th igur combins th rsults o th lction gam in th scon prio th thin lin with a rprsntation o th irst prio invstmnt bhavior th thic lin. Th scon prio outcom is summariz by rprsnting th valu o th irm which is F- as a unction o shar ownrship. From roposition w now that holing an constant as incrass crass. Thror F incrass as incrass as inicat by th positiv slop o th thin lin in Figur. Th valu o th irm incrass with only whn th issu is unrsubscrib: or any givn >0 thr is always a positiv valu o / byon which th issu is ovrsubscrib i.. > 0 accoring to roposition an thror F os not chang with. Notic also that always implis ovrsubscription. 74
Chiara ratton-lavoi Chaptr Th irst prio rsults concrning th invstmnt cision ar summariz by uation [30] which ins th raction o sharholrs. Now consir rprsnting as a unction o F- th irnc btwn th valu o th company F- an its pric. is thror rprsnt as a unction o th gr o unrpricing as shown by th thic lin in Figur. ivn or any anticipat valu o such that F< th man or shars is zro i.. 0. As th anticipat valu o crass F incrass. For a valu o such that F givn >0 thr will b a raction o votrs with zro transaction costs who accoring to conition [7] ar intrst in buying shars. Thror will b positiv i.. >0 as inicat by th lat portion o th thic lin in Figur. As th anticipat valu o th rat o xpropriation gts smallr F incrass F->0 incrass an accoring to th rsults prsnt in roposition 3 incrass. At irst thr is unrsubscription </ an all votrs who want to buy shars ar abl to obtain as many shars as thy want. Evntually F incrass to whr /. At this point urthr incrass in F la to ovrsubscription an this changs th impact o an incras o F on crating th in shown in th iagram. As prviously xplain onc th issu is ovrsubscrib or th sam pric an th sam xpropriation rat thror or th sam valu F- o th stoc ach subscribr rcivs wr shars. This implis that th xpct rturns to th invstmnt ar lowr than thy woul othrwis b. It ollows that givn th promotional ort thror givn ach iniviual s transaction costs wr aitional votrs man shars: an incras in F has now a smallr ct on than it woul hav i th issu was not ovrsubscrib. 75
Chiara ratton-lavoi Chaptr F- F> E' F E F< high /< /> 0 / Figur : Th Euilibria o th am. 76
Chiara ratton-lavoi Chaptr Figur inicats th possibility o two uilibria 3 charactriz by unrpricing an activ promotion o th sal. n uilibrium point E in th iagram has rlativly low no ovrsubscription an high xpropriation: th govrnmnt prrs this uilibrium bcaus th highr rat o xpropriation incrass its rvnus. Th othr uilibrium point E in Figur is charactriz by rlativly high ovrsubscription an rationing an by rlativly low xpropriation thror low rvnus or th govrnmnt ctris paribus. Th actual ralization o on o th two possibl uilibria pns on th nognous trmination o an pns on which scon prio platorm announcmnt th invstors anticipat in th irst prio. Th govrnmnt may thror b abl to slct its prrr low -high uilibrium by maing a non-bining but cribl announcmnt o its utur platorm. Now consir th ct on an thror on th valu o th irm F- o a chang in holing an constant. Intuitivly or a givn pric highr implis lss public goo thror th utility votrs riv rom th consumption o any aitional unit o th public goo incrass an this in turn mans mor incntiv or th govrnmnt to xpropriat givn. Highr xpropriation rucs th irm's valu F. Mathmatically w hav to consir: 3 For simplicity th pictur rprsnts a linar rlationship btwn F an in th cas o unrsubscription. From roposition it is obvious that such rlationship will vry lily b non-linar. Thror aitional uilibria not shown in Figur ar possibl. 77
Chiara ratton-lavoi Chaptr Th rsults ar prsnt in th ollowing roposition. roposition 4 ivn th pric an th raction o shar ownrship as avrtising ort changs th chang in uals: [3] A' β { [ ] β } > 0 i unrsubscription i ovrsubscription Appnix or th proo Th rsult in [3] conirms that thr xists a irct rlationship btwn lvl o avrtising ort chosn in th irst prio an rat o xpropriation announc in th scon prio givn an. Ctris paribus as incrass crass incrass crass thror th valu o th irm F crass incrass. For an incras in Figur illustrats this rsult graphically. Th thin lin rprsnting F as a unction o movs in th irction inicat by th ash lin in th igur. hat is th ct o a chang in on holing an constant? For a givn pric o shars an or a givn anticipat valu o utur xpropriation thror or a givn gr o unrpricing F- mor lss avrtising implis that mor wr invstors will buy th company's stoc. Again a ash lin in Figur illustrats this ct graphically or an incras in. This rsult is prsnt in roposition 5. 78
Chiara ratton-lavoi Chaptr F- F> F F< high /< /> 0 / Figur : Ect o an incras in avrtising ort. 79
Chiara ratton-lavoi Chaptr roposition 5 Holing an constant a chang in avrtising ort causs shar ownrship to chang as ollows: [33] g c > 0 i unrsubscription g g c c [ ] > 0 i ovrsubscription Appnix or th proo imilarly to what obtain in roposition 3 whn th issu is ovrsubscrib th rturns to iniviual invstmnt ar ruc by shar rationing an thror th incras in u to a givn incras in is proportionally lss than in th cas o unrsubscription. Figur suggsts that or both uilibria th ovrall ct on th uilibrium valu o o a chang in is uncrtain. hat th igur inicats is conirm by th comparativ statics rsults which ar prsnt in roposition 6. roposition 6 A I in uilibrium th issu is unrsubscrib an thror g th ct on o g g a chang in is masur by an it uals: [34] c - A' ith A'>0 < an c > 0 th sign is intrminat. B I in uilibrium th issu is ovrsubscrib an thror g th ct on o a chang in is masur by 80
Chiara ratton-lavoi Chaptr g g g which is g g g an it uals: A' c c [ ] [35] Again th sign is intrminat. Appnix or th proo Th uncrtainty concrning th ct o a chang in on th uilibrium valu o is xplain consiring th rsults prsnt in roposition an roposition 5. In uilibrium as incrass on th on han transaction costs ar lowr an mor votrs will buy shars roposition 5 on th othr han th govrnmnt will xpropriat mor in th scon prio i lct roposition. Highr anticipat xpropriation o proits will in turn ruc th invstors' incom rom shar ownrship an thror wr votrs will man shars. This tra-o trmins th ambiguity o th rsults prsnt in roposition 6 an it coul b liminat only introucing mor rstrictiv assumptions on som paramtrs in th mol. Now consir th ct on an thror on th valu o th irm F- o a chang in holing an constant. Mathmatically: 8
Chiara ratton-lavoi Chaptr Th rsults ar prsnt in roposition 7. roposition 7 For a givn lvl o avrtising ort an raction o shar ownrship th chang in u to a chang in shar pric is trmin as ollows: A Assum > Thn i th issu is unrsubscrib: [36] β β < 0 B I th issu is ovrsubscrib: [37] β { [ ] β } < 0 Appnix or th proo To unrstan th rsults prsnt in roposition 7 consir again th marginal impact o a chang in µ on th probability o winning th lction which is givn by: ui λ u N [ ] λ Rcall that masurs th aggrgat marginal utility gains or th ntir population rom incras consumption o th public goo u to an incras in an y masurs th aggrgat marginal utility losss or omstic sharholrs rom lost incom u to an incras in. Now consir th impact that a chang in th pric has on 8
Chiara ratton-lavoi Chaptr ach o ths componnts holing an constant. As incrass th amount o public goo incrass th utility riv rom th consumption o any aitional unit o th public goo crass at a rat masur by an thror th govrnmnt has an incntiv to announc lss xpropriation. This is th only ct o a chang in pric whn th issu is ovrsubscrib bcaus in cas o ovrsubscription th marginal impact o a chang in xpropriation rat on th sharholrs' utility as masur by is constant. Hnc th rsult in part B o roposition 7. n th othr han whn th issu is unrsubscrib th aggrgat marginal isutility o th sharholrs u to a chang in xpropriation as masur by is a unction o. As incrass th sharholrs' isutility incrass at a rat ual to. I assum that th aggrgat impact o a chang in pric on th marginal utility that th ntir population rivs rom consumption o th public goo is gratr than th impact has on th sharholrs' marginal utility. Hnc th rsult in part A o roposition 7. Ths rsults ar illustrat in Figur 3: or an incras in shar pric crass accoring to roposition 7 an thror th valu o th irm F- incrass ctris paribus ash thin lin in th igur. Figur 3 also shows th ct o a similar incras in pric on th raction o shar ownrship holing an an thror F constant: as incrass crass as inicat by th ash thic lin in th igur. Using th inition o in [30] roposition 8 prsnts this rsult mathmatically. 83
Chiara ratton-lavoi Chaptr F- F> F F< high /< /> 0 / Figur 3: Ect o an incras in shar pric. 84
Chiara ratton-lavoi Chaptr roposition 8 Holing an constant a chang in shar pric causs shar ownrship to chang as ollows: [38] g c < 0 i unrsubscription g g c c [ ] < 0 i ovrsubscription Appnix or th proo Th nxt proposition scribs th ovrall ct on th uilibrium valu o o a chang in pric whn th uilibrium valu o changs as wll accoring to th rsults prsnt in roposition. roposition 9 A I in uilibrium th issu is unrsubscrib an thror g th ct on o g g a chang in is masur by an it uals: [39] - c Th sign is intrminat. B I in uilibrium th issu is ovrsubscrib an thror g th ct on o a chang in is masur by g g g which is g g g an it uals: 85
Chiara ratton-lavoi Chaptr [40] c c [ ] > 0 Appnix or th proo To unrstan ths rsults consir roposition 8 togthr with roposition. Accoring to roposition 8 th ct o highr shar pric on shar ownrship is ngativ. This rsult is riv holing constant. But rom roposition w now that in uilibrium highr shar pric in th irst prio trmins lowr xpropriation rat in th scon prio. An anticipat lowr xpropriation translats in highr shar ownrship in th irst prio. Th combination o ths two opposit cts on o a chang in shar pric trmins th rsults prsnt in roposition 9. In cas o unrsubscription which o th two cts is strongr pns on th paramtr valus in th mol an without strictr assumptions on such valus th sign is uncrtain. In cas o ovrsubscription th uilibrium valu o incrass as incrass which inicats that th positiv ct on o a cras in th uilibrium xpropriation rat prvails. 5. Conclusions. Empirical vinc shows that govrnmnts aroun th worl hav otn sol companis to th privat sctor at big iscounts thror orgoing rvnus an that thy hav ngag in havy promotion an avrtising o th sal thror incurring high inancial costs. Thy also hav otn clar thir intrst in wi shar ownrship. 86
Chiara ratton-lavoi Chaptr This papr provis an xplanation or ths obsrvations. It shows that wi iusion o shar ownrship may maximiz govrnmnt rvnus rom privatization vn though this iusion must b achiv through xpnsiv promotional activitis an th unrpricing o shars. This rsult is obtain in a simpl two-prio mol o complt inormation with a govrnmnt that irst privatizs a company an thn compts or vots against a political opponnt. Th govrnmnt announcs a low sal pric an ngags in promotion o th sal in th irst prio an this gnrats iusion o shar ownrship among th population o votrs. In th scon prio th two partis compt or vots announcing simultanously thir choic o a utur rat o xpropriation taxation o privat proits. Th lowr is th pric o th stoc an th highr is th promotion xpnitur in th irst prio th biggr is th siz o th sharholr intrst group in th scon prio an thror th lowr is th announc utur rat o xpropriation. Th commitmnt to a low xpropriation rat thus allows th govrnmnt to st a highr pric in th irst prio. Th rsults show th possibility o two uilibria or a givn pric an lvl o promotional ort: on uilibrium occurs whn th issu is ovrsubscrib whil th othr charactrizs a sal with no ovrsubscription. Th govrnmnt always prrs th lattr uilibrium bcaus it proucs a highr rat o xpropriation an thror highr rvnus. Th mol can b xtn to inclu th possibility that privat proits which in th currnt analysis ar xognous pn on iusion o shar ownrship. In act any positiv ct on proitability o incras corporat control is ilut whn shars ar isprs among many small invstors. I this is th cas any incras o th pric o shars which coul b 87
Chiara ratton-lavoi Chaptr obtain by incrasing iusion o asst ownrship an thror committing to lowr utur xpropriation might b partially ost by th ngativ ct that highr iusion woul hav on privat proits. 88
Chiara ratton-lavoi Chaptr Rrncs Alln F. an Faulhabr. R. 989 "ignaling by Unrpricing in th I Mart" Journal o Financial Economics vol. 3 pp. 303-3. Branco F. an Mllo A. 99 "A Thory o artial als an Unrpricing in rivatizations" MIT EFA oring apr #38. Coughlin. J. Mullr D. C. Murrl. 990 A Mol o Elctoral Comptition with Intrst roups Economics Lttrs vol. 3 pp. 307-3. Coughlin. J. Mullr D. C. Murrl. 990 Elctoral olitics Intrst roups an th iz o ovrnmnt Economic Inuiry vol. 8 pp. 68-705. rinblatt M. an Hwang Chuan Y. 989 "ignalling an th ricing o Nw Issus" Th Journal o Financ vol. 44 pp. 393-40. Jninson T. an Mayr C. 988 "Th rivatization rocss in Franc an th U.K." Europan Economic Rviw vol. 3 pp. 48-90. Linbc A. ibull J.. 987 Balanc-Bugt Ristribution as th utcom o olitical Comptition ublic Choic vol. 5 pp. 73-97. rotti E.C. 995 "Cribl rivatization" Th Amrican Economic Rviw ptmbr 995 vol. 85 pp.847-859. icrs J. 993 "rivatization an th Ris o Expropriation" in rivatization rocsss in Eastrn Europ it by Balassarri M. agantto L. an hlps E. II pp. 5-46. icrs J. an Yarrow. 988 rivatization. An Economic Analysis MIT rss. lch I. 989 "ason rings Imitation Costs an th Unrpricing o Initial ublic rings" Th Journal o Financ vol. 44 pp. 4-49. 89
Chiara ratton-lavoi Chaptr AENDIX Th sharholrs prrr xpropriation rat. In th scon prio th optimal platorm announcmnt or th rprsntativ sharholr solvs th problm blow: max y ci - {} c i [ 0 c] [ 0 with 0 [ ] A an subjct to [ ] i ovrsubscription y i no ovrsubscription Th irst orr conition o th unconstrain maximization problm is 0 K y whr or simplicity y K K K. By assumption y thror th abov conition simpliis to: - a 0 [A] K whr / i ovrsubscription / i no ovrsubscription Bcaus o th assumption o uasilinarity y y 0 an yy 0. Thror th scon orr conition or th xistnc o a uniu global maximum is always vrii. This 90
Chiara ratton-lavoi Chaptr provs th xistnc o a uniu solution o th unconstrain maximization problm but nothing xclus th possibility o a cornr solution o th constrain maximization program. nly imposing mor rstrictiv assumptions on th valus o th partial rivativs o th utility unction woul guarant an intrior valu or th sharholrs prrr rat o xpropriation. Th subgam: uniunss o th NE. Th solution o th govrnmnt s maximization problm is an it satisis th irst orr conition: i λµ β u N u 0 Dirntiating with rspct to w hav: λ µ u N u i Rmmbr that: u u i β N 0 [ λ] u u N u u µ λ i i an that ui K [ ] u K [ ] [A] 9
Chiara ratton-lavoi Chaptr with y. To simpliy th notation y y K K K an K K. Computing all th rivativs an substituting thm bac in [A]: N N [ ] β N N 0 which rcalling that N - simpliis to: β 0 Finally: [ ] [ ] β [ 0 ] which is uation [3] in ction 3.. o th papr. 9
Chiara ratton-lavoi Chaptr AENDIX roos o ropositions 3 5 6 8 an 9. as: From uation [30] in th papr in uilibrium shar ownrship is xplicitly in c with y [ y ] [ A ] [ ] i unrsubscription i ovrsubscription [A] > 0 < 0 A' > 0 Thror g in cas o unrsubscription an g i th issu is ovrsubscrib. In uilibrium as avrtising ort changs w hav: g g i unrsubscription g g g g g g A' > 0 From roposition in th papr: i ovrsubscription [A] [A3] 93
Chiara ratton-lavoi Chaptr 94 unrsubscription i g g ovrsubscription i g g g g g g < 0 From [A] w obtain: Th rsults prsnt in roposition 3 ollow rom [A4.] an [A4.3] th rsults in roposition 5 ollow rom [A4.] an [A4.3] an roposition 6 ollows rom [A3] an [A4]. Consir now a chang in th uilibrium shar pric. hav: [A5] From roposition in th papr: [A6] [ ] 0 3 ovrsubscription i unrsubscription i with 0 [A4] 0 < < > c y c y c g c y c y c g c y c g
Chiara ratton-lavoi Chaptr 95 Again using [A] w obtain: [A7] Th rsults prsnt in roposition 8 ollow rom [A7.] an [A7.3] an th rsults prsnt in roposition 9 ollow rom [A6] an [A7]. roos o ropositions 4 an 7. In orr to riv th rsults prsnt in ropositions 4 an 7 th Implicit Function Thorm has to b appli to th irst orr conition o th scon prio lction problm which implicitly ins : [ ] 0 3 ovrsubscription i unrsubscription i 0 ovrsubscription i 0 unrsubscription i 0 < < < < c y c y c g c y c y c g c c y c y c g
Chiara ratton-lavoi Chaptr 96 Also rcall that accoring to conition [9] in th papr it is: roo o roposition roposition trmins th ct o a chang in on th uilibrium valu o holing an constant. Rcalling that th uilibrium is symmtric an thror w hav: [ ] [ ] [ ] [ ] [ ] [ ] 0 ' 0 0 ovrsubscription i unrsubscription i othrwis 0 i [A8] 0 > < > A y A an u c c T T y u whr u u u u u u u u u u an u u with i i i i i i i i i i λ λ λ µ λ λ λ µ µ β µ <
Chiara ratton-lavoi Chaptr 97 Euation [3] in th papr ins 0 < < : [ ] [ ] β [A9] In irntiating th FC in [A8] with rspct to to calculat on has to consir th two possibilitis o unrsubscription an ovrsubscription sparatly. Unrsubscription Th ollowing pics o inormation ar riv rom th initions in [A8]: u u u u u u u u u u Thror y u u u u u u i i i i i i i i λ λ µ ] [ : [A0] 0 0;
Chiara ratton-lavoi Chaptr 98 An: Using th inormation in [A8] an [A0] th FC is irntiat with rspct to to obtain: Multiplying vry trm by an isolating th trms with : Using [A] an [A9] w inally obtain: which is th rsult prsnt in roposition. vrsubscription Again rom [A8] w can riv th ollowing pics o inormation: λ µ µ µ 0 λ λ β λ [A] 0 < β β β β 0 < β β
Chiara ratton-lavoi Chaptr 99 An: Using th inormation in [A8] an [A] th FC is irntiat with rspct to to obtain: which simpliis to: [ ] [ ] [ ] [ ] u u u u u u u u u u Thror y y u u u u y u u i i i i i i i i λ λ µ ] [ : [A] 0; λ µ µ µ [ ] [ ] [ ] 0 λ λ β λ
Chiara ratton-lavoi Chaptr 00 inc th trm in parnthsis is ngativ 4 it ollows: which is th rsult prsnt in roposition in cas o ovrsubscription. roo o roposition 4 roposition 4 stablishs th ct o a chang in avrtising ort on th uilibrium valu o holing an constant. Rcalling again that th uilibrium is symmtric an thror w hav: From [A8] th ollowing pics o inormation ar riv 4 This can b asily vrii rcalling that <0 an rrring to conition [9] in th papr. [ ] 0 λ λ λ β λ 0 an thror 0 ovrsubscription i unrsubscription i ' [A3] ' ' ; ' A T y y u A u A T y u A u i i i i
Chiara ratton-lavoi Chaptr 0 An: Using th inormation in [A8] an [A3] th FC is irntiat with rspct to to obtain: Multiplying vry trm by λ an isolating th trms with : ' A λ µ [ ] [ ] i i i i i A A A A A A u u u u u u u u u u Thror ' ' ' ' ' ' ] [ : λ λ µ [ ] 0 ' ' ' ' ' ' ' A A A A A A A λ λ β λ [ ] A β β '
Chiara ratton-lavoi Chaptr 0 which is: Thror using [A9] an [A4]: which is th rsult prsnt in roposition 4 in th papr. roo o roposition 7 roposition 7 spciis what is th ct o a chang in shar pric on th uilibrium valu o holing an constant. Hr w hav to riv: As or th proo o roposition w n to analyz th two cass o unrsubscription an ovrsubscription sparatly. Unrsubscription Th ollowing pics o inormation ar riv rom th initions in [A8]: [ ] [A4] 0 ' > A β β [ ] { } 0 ' > A β β - - [A5] - ; y y u u y u u i i
Chiara ratton-lavoi Chaptr 03 Thror: An: Using th inormation in [A8] an [A5] th FC is irntiat with rspct to. Atr som algbra w obtain: which is: An thror using [A9] an [A6]: which is th rsult prsnt in roposition 7. ] [ ] [ ] [ ] [ ] [ λ µ λ µ β β [A6] β β β β
Chiara ratton-lavoi Chaptr 04 vrsubscription Th ollowing pics o inormation ar riv rom th initions in [A8]: Thror: An: Using th inormation in [A8] an [A7] th FC is irntiat with rspct to. Atr som algbra w obtain: An thror using [A9] an [A8]: which is th rsult prsnt in roposition 7. y y u u y u u i i [A7] ; ] [ ] [ ] [ ] [ λ µ λ µ [ ] [ ] [A8] 0 < β β β β [ ] { } 0 < β β