Economic Growth with Bubbles

 Jewel Agnes Hines
 4 months ago
 Views:
Transcription
1 Economic Growh wih Bubbles AlberoMarin,andJaumeVenura March 2010 Absrac We develop a sylized model of economic growh wih bubbles. In his model, financial fricions lead o equilibrium dispersion in he raes of reurn o invesmen. During bubbly episodes, unproducive invesors demand bubbles while producive invesors supply hem. Because of his, bubbly episodes channel resources owards producive invesmen raising he growh raes of capial and oupu. The model also illusraes ha he exisence of bubbly episodes requires some invesmen o be dynamically inefficien: oherwise, here would be no demand for bubbles. This dynamic inefficiency, however, migh be generaed by an expansionary episode iself. JEL classificaion: E32, E44, O40 Keywords: bubbles, dynamic inefficiency, economic growh, financial fricions, pyramid schemes Marin: CREI and Universia Pompeu Fabra, Venura: CREI and Universia Pompeu Fabra, CREI, Universia Pompeu Fabra, Ramon Trias Fargas 2527, Barcelona, Spain. We hank Vasco Carvalho for insighful commens. We acknowledge suppor from he Spanish Minisry of Science and Innovaion(grans ECO and CSD ), he Generalia de CaalunyaDIUE(gran 2009SGR1157), and he Barcelona GSE Research Nework. In addiion, Venura acknowledges suppor from he ERC (Advanced Gran FP ), and Marin from he Spanish Minisry of Science and Innovaion (gran Ramon y Cajal RYC ) and from he Lamfalussy Fellowship Program sponsored by he ECB. Any views expressed are only hose ofheauhorsanddononecessarilyrepresenheviewsofheecborheeurosysem.
2 1 Inroducion Modern economies ofen experience episodes of large movemens in asse prices ha canno be explained by changes in economic condiions or fundamenals. I is commonplace o refer o hese episodes as bubbles popping up and bursing. Typically, hese bubbles are unpredicable and generae subsanial macroeconomic effecs. Consumpion, invesmen and produciviy growh all endosurgewhenabubblepopsup,andhencollapseorsagnaewhenhebubbleburss. Here, we address he following quesions: Wha is he origin of hese bubbly episodes? Why are hey unpredicable? How do bubbles affec consumpion, invesmen and produciviy growh? In a nushell, he goal of his paper is o develop a sylized view or model of economic growh wih bubbles. The heory presened here feaures wo idealized asse classes: producive asses or capial andpyramidschemesor bubbles. Bohassesareusedasasoreofvalueorsavingsvehicle,bu hey have differen characerisics. Capial is cosly o produce bu i is hen useful in producion. Bubbles play no role in producion, bu iniiaing hem is cosless. 1 We consider environmens wih raional, informed and risk neural invesors ha hold only hose asses ha offer he highes expeced reurn. The heoreical challenge is o idenify siuaions in which hese invesors opimally choose o hold bubbles in heir porfolios and hen characerize he macroeconomic consequences of heir choice. Our research builds on he seminal papers of Samuelson(1958) and Tirole(1985) who viewed bubbles as a remedy o he problem of dynamic inefficiency. Their argumen is based on he dual role of capial as a producive asseand a sore of value. Tosaisfy he need for a sore of value, economies someimes accumulae so much capial ha he invesmen required o susain i exceeds he income ha i produces. This invesmen is inefficien and lowers he resources available for consumpion. In his siuaion, bubbles can be boh aracive o invesors and feasible from a macroeconomic perspecive. For insance, a pyramid scheme ha absorbs all inefficien invesmens in each period is feasible and is reurn exceeds ha of he invesmens i replaces. This explains he origins and he effecs of bubbles. Since bubbles do no have inrinsic value, heir size depends on he marke s expecaion of heir fuure size. In a world of raional invesors, his opens he door for 1 Iisdifficulofindheseidealizedasseclassesinfinancialmarkes,ofcourse,asexisingassesbundleorpackage ogehercapialandbubbles. Yewehinkhamuchcanbelearnedbyworkingwihhesebasicasses. Toprovide a simple analogy, we have surely learned much by sudying heoreical economies wih a full se of ArrowDebreu securiies, even hough only a few bundles or packages of hese basic securiies are raded in he real world. 1
3 selffulfilling expecaions o play a role in bubble dynamics and accouns for heir unpredicabiliy. The SamuelsonTirole model provides an elegan and powerful framework o hink abou bubbles. However, he picure ha emerges from his heory is hard o reconcile wih hisorical evidence. In his model, bubbly episodes are consumpion booms financed by a reducion in inefficien invesmens. During hese episodes boh he capial sock and oupu conrac. In he real world, bubbly episodes end o be associaed wih consumpion booms indeed. Bu hey also end o be associaed wih expansions in boh he capial sock and oupu. A successful model of bubbles mus come o grips wih hese correlaions. Thispapershowshowobuildsuchamodelbyexendingheheoryofraionalbubblesohe case of imperfec financial markes. In he SamuelsonTirole model, fricionless financial markes eliminae raeofreurn differenials among invesmens making hem eiher all efficien or all inefficien. Inroducing financial fricions is crucial because hese creae raeofreurn differenials and allow efficien and inefficien invesmens o coexis. Our key observaion is quie simple: bubbles no only reduce inefficien invesmens, bu hey also increase efficien ones. In our model, bubbly episodes are booms in consumpion and efficien invesmens financed by a reducion in inefficien invesmens. If he increase in efficien invesmens is sizable enough, bubbly episodes expand he capialsockandoupu. Thisurnsouobehecaseunderawiderangeofparameervalues. Toundersandheseeffecsofbubblyepisodes,iisusefuloanalyzeheseofransfersha bubbles implemen. Remember ha a bubble is nohing bu a pyramid scheme by which he buyer surrenders resources oday expecing ha fuure buyers will surrender resources o him/her. The economy eners each period wih an iniial disribuion of bubble owners. Some of hese owners bough heir bubbles in earlier periods, while ohers jus creaed hem. When he marke for bubbles opens, on he demand side we find invesors who canno obain a reurn o invesmen abovehaofbubbles; whileonhesupplysidewefindconsumersandinvesors whocanobain a reurn o invesmen above ha of bubbles. When he marke for bubbles closes, resources have been ransferred from inefficien invesors o consumers and efficien invesors, leading o an increase in consumpion and efficien invesmens a he expense of inefficien invesmens. Akeyaspecofheheoryishowhedisribuionofbubbleownersisdeermined. Asinhe SamuelsonTirole model, our economy is populaed by overlapping generaions ha live for wo periods. The young inves and he old consume. The economy eners each period wih wo ypes ofbubbleowners: heoldwhoacquiredbubblesduringheiryouh,andheyoungwhoarelucky enough o creae hem. Since he old only consume, bubble creaion by efficien young invesors 2
4 plays a crucial role in our model: i allows hem o finance addiional invesmen by selling bubbles. Inroducing financial fricions also solves a nagging problem of he heory of raional bubbles, which was firs poined ou by Abel e al. (1989). In he SamuelsonTirole model, bubbles can only exis if he invesmen required o susain he capial sock exceeds he income ha i produces. Abel e al. (1989) examined a group of developed economies and found ha, in all of hem, invesmen falls shor of capial income. This finding has ofen been considered evidence ha raional bubbles canno exis in real economies. Inroducing financial fricions ino he heory shows ha his conclusion is unwarraned. The observaion ha capial income exceeds invesmen only implies ha, on average, invesmens are dynamically efficien. Bu his does no exclude he possibiliy ha he economy conains pockes of dynamically inefficien invesmens ha could suppor a bubble. Nor does i exclude he possibiliy ha an expansionary bubble, by lowering he reurn o invesmen, creaes iself he pockes of dynamically inefficien invesmens ha suppor i. Insuchsiuaions,heesofAbeleal. wouldwronglyconcludehabubblesarenopossible. Besides building on he seminal conribuions of Samuelson (1958) and Tirole (1985), his paper is closely relaed o previous work on bubbles and economic growh. SainPaul (1992), Grossman and Yanagawa(1993), and King and Ferguson(1993) exend he SamuelsonTirole model o economies wih endogenous growh due o exernaliies in capial accumulaion. In heir models, bubbles slow downhe growhraeof heeconomy. Olivier (2000) uses asimilar model o show how, if ied o R&D firms, bubbles migh foser echnological progress and growh. The model developed in his paper sresses he relaionship beween bubbles and fricions in financial markes. Azariadis and Smih(1993) were, o he bes of our knowledge, he firs o show ha conracing fricions could relax he condiions for he exisence of raional bubbles. More recenly, Caballero and Krishnamurhy (2006), Kraay and Venura (2007), and Farhi and Tirole (2009) conain models in which he exisence and economic effecs of raional bubbles are closely linked o financial fricions. Whereas we derive our resuls in a sandard growh model, hese papers sudy economies wih linear producion funcions or sorage echnology. The paper is organized as follows: Secion 2 presens he SamuelsonTirole model, provides condiions for he exisence of equilibrium bubbles and discusses heir macroeconomic effecs. Secion 3 inroduces financial fricions and conains he main resuls of he paper. Secion 4 exends hese resuls o an economy wih longrun growh. Finally, Secion 5 concludes. 3
5 2 The SamuelsonTirole model Samuelson (1958) and Tirole (1985) showed ha bubbles are possible in economies ha are dynamically inefficien, i.e. ha accumulae oo much capial. Bubbles crowd ou capial and raise he reurn o invesmen. We reformulae his heory in erms of bubbly episodes and provide a quick refresher of is macroeconomic implicaions. 2.1 Basic seup Consider a counry inhabied by overlapping generaions of young and old, all wih size one. Time sarsa=0andhengoesonforever. Allgeneraionsmaximizeheexpecedconsumpionwhen old: U =E c +1 ;whereu andc +1 arehewelfareandheoldageconsumpionofgeneraion. The oupu he counry is given by a CobbDouglas producion funcion of labor and capial: F(l,k )=l 1 k wih (0,1),and l andk arehecounry slaborforceandcapialsock, respecively. All generaions have one uni of labor which hey supply inelasically when hey are young,i.e. l =1. Thesockofcapialinperiod+1equalsheinvesmenmadebygeneraion duringisyouh. 2 Thismeansha: k +1 =s k, (1) where s is he invesmen rae, i.e. he fracion of oupu ha is devoed o capial formaion. Markes are compeiive and facors of producion are paid he value of heir marginal produc: w =(1 ) k and r = k 1, (2) wherew andr arehewageandherenalrae,respecively. Tosolvehemodel, weneedofindheinvesmenrae. Theolddonosaveandheyoung save all heir income. Wha do he young do wih heir savings? A his poin, i is cusomary o assume ha hey use hem o build capial. This means ha he invesmen rae equals he savings of he young. Since he laer equal labor income, which is a consan fracion 1 of oupu, he invesmen rae is consan as in he classic Solow(1956) model: s =1. (3) 2 Thais,weassumeha(i)producingoneuniofcapialrequiresoneuniofconsumpion,andha(ii)capial fully depreciaes in producion. We also assume ha he firs generaion found some posiive amoun of capial o workwih,i.e. k 0 >0. 4
6 Therefore,helawofmoionofhecapialsockis: k +1 =(1 ) k. (4) Equaion(4) consiues a very sylized version of a sandard workhorse of modern macroeconomics. A lo of progress has been made by adding more sophisicaed formulaions of preferences and echnology, various ypes of shocks, a few marke imperfecions, and a role for money. We shall nodoanyofhisherehough. 2.2 Equilibria wih bubbles Insead, we follow he pahbreaking work of Samuelson(1958) and Tirole(1985), and assume he young have he addiional opion of purchasing bubbles or pyramid schemes. These are inrinsically uselessasses,andheonlyreasonopurchasehemisoresellhemlaer. Leb behesockof old bubbles in period, i.e. already exising before period or creaed by earlier generaions; and leb N behesockofnewbubbles,i.e. addedinperiodorcreaedbygeneraion. Weassume hahereisfreedisposalofbubbles. Thisimplieshab 0andb N 0. Wealsoassumeha bubbles are creaed randomly and wihou cos. This implies ha new bubbles consiue a pure profiorrenforhosehacreaehem. 3 Raionaliy imposes wo resricions on he ype of bubbles ha can exis. Firs, bubbles mus grow fas enough or oherwise he young will no be willing o purchase hem. Second, he aggregae bubblecannogrowoofasoroherwiseheyoungwillnobeableopurchasehem. Therefore, ifb >0,hen E { b+1 b +b N } = k 1 +1, (5) b (1 ) k. (6) Equaion(5)saysha,forbubblesobearacive,heymusdeliverhesamereurnascapial. 4 Thereurnohebubbleconsissofisgrowhoverheholdingperiod. Thepurchasepriceofhe bubbleisb +b N,andhesellingpriceisb +1. Thereurnocapialequalsherenalraesinceeach 3 Noe ha new bubbles canno be linked o he ownership of objecs ha can be raded before he dae he bubbles appear. Oherwise he bubble would have already apppeared in he firs dae in which he objec can be raded. The reason issimple: a raionalindividual would be willing o pay a posiiveprice for an objec if hereis some probabiliy ha his objec commands a posiive price in he fuure. See Diba and Grossman(1987). 4 Wecanruleouhepossibiliyhabubblesdeliverahigherreurnhancapial. Asssumenoandlehereurn ohebubbleobesriclyhigherhan hereurnocapial. Then, nobodywouldinvesandhereurn ocapial wouldbeinfiniy. Buhismeanshahebubblemusgrowaaraeinfiniyandhisisnopossible. 5
7 uni of capial coss one uni of consumpion and i fully depreciaes in one period. Equaion(6) says ha, for bubbles o be feasible, hey canno ougrow he economy s savings. The savings of he youngconsisoflaborincomeandhevalueofnewbubblescreaedbyhem,i.e. (1 ) k +b N. Sinceheolddonosave,heyoungmusbepurchasinghewholeaggregaebubble,i.e. b +b N. The invesmen rae equals he income lef afer purchasing he bubbles as a share of oupu: and his implies he following law of moion for he capial sock: s =1 b k, (7) k +1 =(1 ) k b. (8) Equaion(8) shows he key feaure of he SamuelsonTirole model: bubbles crowd ou invesmen and slow down capial accumulaion. Foragiveniniialcapialsockandbubble,k 0 >0andb 0 0,acompeiiveequilibriumisa sequence { k,b,b N } =0 saisfyingequaions(5),(6)and(8). Theassumpionhaheyoungonly buildcapialisequivalenoaddingheaddiionalequilibriumresricionhab =b N =0forall. This resricion canno be jusified on a priori grounds, bu we noe ha here always exiss oneequilibriuminwhichiissaisfied. 5 There are a couple of imporan differences beween he model described here and he original ones of Samuelson (1958) and Tirole (1985). Unlike us, Samuelson analyzed an economy wih a linear producion funcion or sorage echnology. Tirole analyzed insead a sandard growh model like he one we sudy. Unlike us, however, he made weak assumpions on preferences and echnology. Inparicular, heonly assumedheexisenceofuiliyandproducionfuncions, U =u(c,c +1 ) andf(l,k )wihsandardproperies. Unlikeus,bohSamuelsonandTiroleresricedheanalysis o he subse of equilibria ha are deerminisic and do no involve bubble creaion or desrucion. Thais,heyimposedheaddiionalresricionshaE b +1 =b +1 andb N =0forall. 6,7 Despie hese differences, we label he model described above as he SamuelsonTirole model o give due credi o heir seminal conribuions. 5 Thisequilibriummighnoexisinhepresenceofrens. SeeTirole(1985)andCaballeroeal. (2010). 6 Underheseresricions,any bubblemushaveexised from heverybeginning of imeand ican neverburs, i.e. isvaluecanneverbezero. 7 Tohebesofourknowledge,Weil(1987)washefirsoconsidersochasicbubblesingeneralequilibrium. 6
8 2.3 Bubbly episodes An imporan payoff of analyzing sochasic equilibria wih bubble creaion and desrucion is ha his allows us o rigorously capure he noion of a bubbly episode. Generically, he economy flucuaes beween periods in which b = b N = 0 and periods in which b > 0 and/or b N > 0. We say ha he economy is in he fundamenal sae if b = b N = 0. We say insead ha he economyisexperiencingabubbly episode ifb >0and/orb N >0. Abubblyepisodesarswhen he economy leaves he fundamenal sae and ends he firs period in which he economy reurns o he fundamenal sae. The following proposiion provides he condiions for he exisence of bubbly episodes in he SamuelsonTirole model: Proposiion1 Bubblyepisodesarepossibleifandonlyif<0.5. Theproofofhisproposiionexploisausefulrickhamakeshemodelrecursive. Lex be heaggregaebubbleasashareofhelaborincome,i.e. x (1 ) k Then,wecanrewrieEquaions(5)and(6)assayinghaifx >0,hen b b N andx N (1 ) k. E x +1 = 1 x+x N 1 x, (9) x 1. (10) Equaions(9) and(10) describe bubble dynamics. There are wo sources of randomness in hese dynamics: shocksobubblecreaion,i.e. x N ;andshocksohevalueofheexisingbubble,i.e. x. Anyadmissiblesochasicprocessforx N andx saisfyingequaions(9)and(10)isanequilibrium of he model. By admissible, we mean ha he sochasic process mus ensure ha x 0 and x N 0 for all. Conversely, any equilibrium of he model can be expressed as an admissible sochasicprocessforx N andx. To prove Proposiion 1 we ask if, among all sochasic processes for x N and x ha saisfy Equaion (9), here is a leas one ha also saisfies Equaion (10). I is useful o examine firs hecaseinwhichhereisnobubblecreaionaferabubblyepisodessars. Figure1plosE x +1 againsx, usingequaion(9)wihx N =x N s andx N =0forall >s, where sis heperiodin whichheepisodesars. Thelefpanelshowshecaseinwhich 0.5andheslopeofE x +1 aheoriginisgreaerhanorequaloone. Anyiniialbubblewouldbedemandedonlyifiwere 7
9 expecedoconinuouslygrowasashareoflaborincome,i.e. E x +1 >x inallperiods. Buhis meanshainsomescenarioshebubbleougrowshesavingsofheyounginfinieime, i.e. i violaes Equaion(10). Therefore, bubbly episodes canno happen if 0.5. The righ panel of Figure1showsinseadhecaseinwhich<0.5. Anyiniialbubblex s+1 > canberuled ouwihhesameargumen. Buanyiniialbubblex s canbeparofanequilibrium asiispossibleofindaprocessforx hasaisfiesequaions(9)and(10)simulaneously E x 1 E x 1 x x Figure 1 Allowing for bubble creaion does no relax he condiions for exisence of bubbly episodes. To seehis,noehabubblecreaionshifsupwardsheschedulee x +1 infigure1. Theinuiionis clear: new bubbles compee wih old bubbles for he income of nex period s young, reducing heir reurn and making hem less aracive. This complees he proof of Proposiion 1. This proof is insrucive and helps us undersand he connecion beween bubbles and dynamic inefficiency. To deermine wheher a bubbly episodes can exis, we have asked: Is i possible o consruc a pyramid scheme ha is aracive wihou exploding as a share of labor income? We haveseenhaheanswerisaffirmaiveifandonlyifhereexissochasicprocessesforx N and x suchha: E x +1 <x. Theseprocessesexisifandonlyif<0.5. To deermine wheher he economy is dynamically inefficien, we ask: Is he economy accumulaingoomuchcapial? Theanswerisaffirmaiveifandonlyifheinvesmenrequiredosusainhe 8
10 capialsockexceedsheincomehahiscapialproduces. Invesmenequals(1 x ) (1 ) k, while capial income is given by k. Therefore, he economy is dynamically inefficien if and only if (1 x ) (1 ) k > k. (11) Sraighforward algebra shows ha his condiion is equivalen o asking wheher here exis sochasicprocessesforforx N andx suchha: E x +1 <x +x N. These processes exis if and only if < 0.5. Therefore, in he SamuelsonTirole model he condiions for he exisence of bubbly episodes and dynamic inefficiency coincide. 2.4 The macroeconomic effecs of bubbles To deermine he macroeconomic consequences of bubbly episodes, we rewrie he law of moion of hecapialsockusinghedefiniionofx : k +1 =(1 x ) (1 ) k. (12) Equaion(12) describes he dynamics of he capial sock for any admissible sochasic process for hebubble, i.e. x N andx ; saisfyingequaions(9)and(10). This consiues afull soluiono he model. Ineresingly, bubbly episodes can be lierally inerpreed as shocks o he law of moion of he capial sock of he Solow model. To beer undersand he naure of hese shocks, consider he following example: Example 1((n, p) episodes) Consider he subse of bubbly episodes ha are characerized by(i) a consan probabiliy of ending, i.e. Pr (b +1 =0 b >0)=p and (ii) an iniial bubble x N s and henaconsanraeofnewbubblecreaion,i.e. x N =n x. ThelefpanelofFigure2showsa(n,p)episode. ThesolidlinerepresensEquaion(9),i.e. he valueofx +1 haleavesheyoungindifferenbeweenbuyinghebubbleorinvesingincapial. Afeaureof(n,p)episodesishahebubbledeclinesasashareoflaborincomehroughouhe episode,i.e. x +1 x forallandx 0. Onlyifheiniialbubbleismaximal,i.e. x s+1 x 1, 9
11 his rae of decline becomes zero. This paern of behavior is no generic, however, as he following example shows: Example 2((x N,p)episodes) Consider he subse of bubbly episodes ha are characerized by (i)aconsanprobabiliyofending,i.e. Pr (b +1 =0 b >0)=pand(ii)aniniialbubblex N s and henaconsanamounofbubblecreaionx N =x N. The righ panel of Figure 2 shows an (x N,p) episode. Any iniial bubbleconverges o x 2. If x s+1 <x 2,hebubblegrowshroughouheepisode. Ifx s+1>x 2,hebubbledeclineshroughou he episode. Once again, if he iniial bubble is maximal, i.e. x s+1 x 2, his rae of decline becomeszeroandhebubbleneverconvergesox 2. x 1 x 1 x 1 x 2 x 2 x x Figure 2 The only randomness in hese examples refers o he periods in which hey sar and end. Throughou he bubbly episode, he bubble moves deerminisically unil he episodes ends. This need no be, of course. Assume, for insance, ha bubble creaion randomly swiches beween being a fracion of he exising bubble, i.e. x N = n x ; and being a consan amoun, i.e. x N = x N. Thais,helawsofmoionofhebubbleinherighandlefpanelsofFigure2operaeadifferen (andrandom)imesduringagivenbubblyepisode. Then,x willconvergeoheinerval(0,x 2 ), and hen randomly flucuae wihin i unil he episode ends. Figure 3 shows he macroeconomic effecs of one of hese bubbly episodes. Assume iniially ha heeconomyisinhefundamenalsaesohaheappropriaelawofmoionisheonelabeled k F +1. SinceheiniialcapialsockisbelowheSolowseadysae,i.e. k <k F (1 ) 1 1,he 10
12 economy is growing a a posiive rae. When a bubbly episode sars, he invesmen rae falls and helawofmoionshifsbelowhefundamenalone. Inhefigure,k B +1 represenshelawofmoion when he bubbly episode begins. The picure has been drawn so ha he capial sock is above heseadysaeassociaedok B +1,i.e. k >k B. Asaresul,growhurnsnegaive. Throughou heepisode,k B +1 mayshifupordownashebubblegrowsorshrinks,alhoughialwaysremains below he original law of moion k+1 F. Evenually, he episode ends and he economy reurns o k F +1. k 1 F k 1 B k 1 k B k k F k Figure 3 Afirssigh,onecouldhinkofbubblyepisodesasakinonegaiveshocksoheinvesmen rae. Bu his would no be quie righ. Bubbles also affec consumpion direcly as passing he bubble across generaions increases he share of oupu ha he old receive and consume: c =[+(1 ) x ] k. (13) The relaionship beween bubbles and consumpion has herefore wo differen aspecs o i. Pas bubbles reduce he capial sock and, ceeris paribus, his lowers consumpion. Bu presen bubbles raiseheshareofoupuinhehandsofheoldand,ceerisparibus,hisraisesconsumpion. 2.5 Discussion Bubbles affec allocaions hrough wo channels: (i) by implemening a se of inergeneraional ransfers, and (ii) by creaing wealh shocks. The firs channel is a cenral feaure of a pyramid scheme, by which buyers surrender resources oday expecing fuure buyers o surrender resources o 11
13 hem. These inergeneraional ransfers are feasible because he economy is dynamically inefficien. The second channel are he wealh shocks associaed wih bubble creaion and desrucion. When bubbles appear, hose lucky individuals who creae hem receive a windfall or ransfer from he fuure. This is anoher cenral feaure of a pyramid scheme whereby he iniiaor claims ha, bymakinghim/herapaymennow, heoherparyearns herighoreceiveapaymenfrom a hird person laer. By successfully creaing and selling a bubble, young individuals have assigned hemselvesandsoldhe righs oheincomeofageneraionlivinginheveryfarfuureor,o be more exac, living a infiniy. This appropriaion of righs is a pure windfall or posiive wealh shock for he generaion ha creaes hem. Naurally, he opposie happens when bubbles burs since his consiues a negaive wealh shock for hose ha are holding hem and see heir value collapse. Once exended o allow for random bubbles and random bubble creaion and desrucion, he SamuelsonTirole model provides an elegan and powerful framework o hink abou bubbly episodes. Unforunaely, he macroeconomic implicaions of he SamuelsonTirole model are a odds wih he facs along wo key dimensions: 1. The model predics ha bubbles can only appear in dynamically inefficien economies, i.e However, Abeleal. (1989)examinedagroupofdevelopedeconomiesandfound ha,inallofhem,aggregaeinvesmen,i.e. (1 x ) (1 ) k,fallsshorofaggregae capialincome,i.e. k. 2. The model predics ha bubbles lead o simulaneous drops in he sock of capial and oupu. Hisorical evidence suggess however ha bubbly episodes are associaed wih increases in he capial sock and oupu. We nex show ha hese discrepancies beween he heory and he facs res on one imporan assumpion: financial markes are fricionless. 3 Inroducing financial fricions We exend he model by inroducing a moive for inrageneraional rade and a financial fricion ha impedes his rade. We show ha his relaxes he condiions for he exisence of bubbly episodes. Moreover, hese episodes can lower he reurn o invesmen and lead o expansions in he capial sock. 12
14 3.1 Seup wih financial fricions Assumehaafracionε [0,1]ofheyoungofeachgeneraioncanproduceoneuniofcapial wih one uni of he consumpion good. We refer o hem as producive invesors. The remaining young are unproducive invesors, as hey only have access o an inferior echnology ha produces δ<1unisofcapialwihoneuniofheconsumpiongood. Thisheerogeneiycreaesgainsfrom borrowing and lending. If markes worked well, unproducive invesors would lend heir resources o producive ones and hese would inves on everyone s behalf. This would bring us back o he SamuelsonTirole model. We shall however assume ha his is no possible because of some unspecified marke imperfecion. The goal here is o analyze how his financial fricion affecs equilibrium oucomes. Now he evoluion of he capial sock depends no only on he level of invesmen bu also on is composiion. Le A be heaverageefficiency of invesmen. Then, Equaion (1)mus be replaced by k +1 =s A k. (14) For insance, inhe benchmark case in which he young use all heir savings obuild capial we have ha: A =ε+(1 ε) δ A. (15) Since all individuals inves he same amoun, he average efficiency of invesmen is deermined by he populaion weighs of boh ypes of invesors. The invesmen rae is sill deermined by Equaion(3)andhedynamicsofhecapialsockaregivenby k +1 =(1 ) A k. (16) SinceA<1,financialfricionslowerhelevelofhecapialsockbuheydonoaffechenaure ofisdynamics. Thisresuldoesnogohroughonceweallowforbubbles. 3.2 Equilibria wih bubbles The inroducion of financial fricions forces us o make an assumpion abou he disribuion of rens from bubble creaion. In he SamuelsonTirole model, all invesmen is carried ou by producive invesors and he disribuion of rens is inconsequenial. Wih financial fricions, his isnolongerhecasesincehedisribuionofwealh andhenceofheserens affecsheaverage 13
15 efficiency of invesmen. We use b NP and b NU o denoe he sock of new bubbles creaed by produciveandunproduciveinvesors,respecively. Naurally,b NP +b NU =b N. Recall ha raionaliy imposes wo resricions on he ype of bubbles ha can exis. Firs, bubbles mus grow fas enough or oherwise he young will no be willing o purchase hem. Second, heaggregaebubblecannogrowoofasoroherwiseheyoungwillnobeableopurchasehem. While he second of hese resricions sill implies Equaion(6), he firs of hem now implies ha ifb >0,hen E { b +1 b +b NP +b NU =δ k 1 +1 if } [ δ k+1 1 ], k 1 +1 = k 1 +1 if if b +b NP (1 ε) (1 ) k b +b NP (1 ε) (1 ) k b +b NP (1 ε) (1 ) k <1 =1 >1. (17) Equaion (17) is nohing bu a generalizaion of Equaion (5) ha recognizes ha he marginal buyerofhebubblechangesashebubblegrows. Ifhebubbleissmall,hemarginalbuyerisan unproducive invesor and he expeced reurn o he bubble mus equal he reurn o unproducive invesmens. If he bubble is large, he marginal buyer is an producive invesor and he expeced reurn o he bubble mus be he reurn o producive invesmens. Bubbles affec boh he level of invesmen and is composiion. As in he SamuelsonTirole model, he bubble reduces he invesmen rae and Equaion(7) sill holds. Unlike he Samuelson Tirole model, he bubble now affecs he average efficiency of invesmen as follows: (1 ) A k +(1 δ) b NP δ b (1 ) k A = b if 1 if b +b NP (1 ε) (1 ) k b +b NP (1 ε) (1 ) k <1 1. (18) To undersand Equaion(18), noefirs ha inhe fundamenal saeb =b NP =b NU =0and he average efficiency of invesmen equals he populaion average A. Bubbles raise he efficiency of invesmen hrough wo channels. Firs, exising bubbles displace a disproporionaely high share of unproducive invesmens. This is why A is increasing in b. Second, bubble creaion byproduciveinvesorsraisesheirincomeandexpands heirinvesmen. Thisiswhy A isalso increasinginb NP. When all unproducive invesmens have been eliminaed, he average efficiency of invesmen reaches one. 14
16 Wecanhusrewriehedynamicsofhecapialsockasfollows: (1 ) A k +(1 δ) bnp δ b if k +1 = (1 ) k b if b +b NP (1 ε) (1 ) k b +b NP (1 ε) (1 ) k <1 1. (19) Bubbles now have conflicing effecs on capial accumulaion and oupu. On he one hand, exising bubbles reduce he invesmen rae. On he oher hand, new bubbles raise he efficiency of invesmen. Ifhefirseffecdominaes,i.e. b NP < 1 δ b δ,bubblesareconracionaryandcrowd oucapial. Ifinseadhesecondeffecdominaes,i.e. b NP > δ 1 δ b,bubblesareexpansionary and crowd in capial. We are ready o define a compeiive equilibrium for he modified model. For a given iniial capial sock and bubble, k 0 > 0 and b 0 0, a compeiive equilibrium is a sequence { k,b,b NP saisfying Equaions (6), (17) and (19). As we show nex, here are many,b NU } =0 such equilibria. 3.3 Bubbly episodes wih financial fricions The following proposiion provides he condiions for he exisence of bubbly episodes in he model wih financial fricions: Proposiion 2 Bubbly episodes are possible if and only if: A < A+δ { } A max A+δ, (1 ε) δ ifa>1 ε ifa 1 ε. Proposiion 2 generalizes Proposiion 1 o he case of financial fricions. Once again, we use he rickofmakinghemodelrecursivehroughachangeofvariables. Definenowx NP b NP (1 ) k and x NU b NU (1 ) k. Then, we can rewrie Equaions (6) and (17) as saying ha if x >0, 15
17 hen E x +1 = 1 δ (x +x NP +x NU ) [ A+(1 δ) x NP δ x δ (x +x NP +x NU ) 1 A+(1 δ) x NP δ x, +x NU = 1 x+x NP 1 x 1 x+x NU 1 x +x NP ] if x+xnp 1 ε if x +x NP 1 ε if x +x NP 1 ε <1 =1 >1, (20) x 1. (21) Equaions(20) and(21) describe bubble dynamics in he modified model. Any admissible sochasic process for x NP, x NU and x saisfying Equaions (20) and (21) is an equilibrium of he model. Conversely, any equilibrium of he model can be expressed as an admissible sochasic process for x NP,x NU andx. To prove Proposiion 2 we ask again if, among all sochasic processes for x NP, x NU and x ha saisfy Equaion (20), here is a leas one ha also saisfies Equaion (21). Consider firs hecaseinwhichhereisnobubblecreaionaferabubblyepisodesars. Figure4plosE x +1 againsx,usingequaion(20)wihx NP =x NP s,x NU =x NU s andx NP =x NU =0forall>s, wheresisonceagainheperiodinwhichheepisodesars. Thelefpanelshowshecaseinwhich A A+δ andheslopeofe x +1 aheoriginisgreaerhanorequaloone. Thismeansha anyiniialbubblewouldbedemandedonlyifiwereexpecedoconinuouslygrowasashareof laborincome,i.e. ifiviolaesequaion(21),andhiscanberuledou. TherighpanelofFigure 4showshecaseinwhich< A A+δ. NowheslopeofE x +1 aheoriginislesshanoneand, asaresul,e x +1 muscrosshe45degreelineonceandonlyonce. Lex behevalueofx a hapoin. Anyiniialbubblex s+1 >x canberuledou. Buanyiniialbubblex N s x canbe parofanequilibriumsinceiispossibleofindasochasicprocessforx hasaisfiesequaions (20) and(21). 16
18 E x 1 E x 1 1 x x 1 x Figure 4 Is i possible ha bubble creaion relaxes he condiions for he exisence of bubbly episodes? Consider firs bubble creaion by unproducive invesors, i.e. x NU. As in he SamuelsonTirole model,hisypeofbubblecreaionshifsheschedulee x +1 upwards. Theinuiionishesameas before: new bubbles compee wih old bubbles for he income of nex period s young, reducing heir reurn and making hem less aracive. Therefore, allowing for bubble creaion by unproducive invesors does no relax he condiions for he exisence of bubbly episodes. Considernexbubblecreaionbyproduciveinvesors,i.e. x NP. Thisypeofbubblecreaion shifs he schedule E x +1 upwards if x (0,A] (1 ε,1], bu i shifs i downwards if x (A,1 ε]. Toundersandhisresul,iisimporanorecognizehedoubleroleplayedbybubble creaion by producive invesors. On he one hand, new bubbles compee wih old ones for he income of nex period s young. This effec reduces he demand for old bubbles and shifs he schedulee x +1 upwards. Onheoherhand,produciveinvesorssellnewbubblesounproducive invesors and use he proceeds o inves, raising average invesmen efficiency and he income of nexperiod syoung. ThiseffecincreaseshedemandforoldbubblesandshifshescheduleE x +1 downwards. Thissecondeffecoperaeswheneverx 1 ε,andidominaeshefirseffeconly ifx A. Hence,ifA>1 ε,bubblecreaionbyproduciveinvesorscannorelaxhecondiion for he exisence of bubbly episodes. If A 1 ε, bubble creaion { does relax he condiion } for he exisence of bubbles. Namely, A hiscondiionbecomes<max A+δ, 1. Figure 5 provides some inuiion for 1+4 (1 ε) δ his resul by ploing E x +1 againsx, using Equaion (20)and assuminghax NU =0while 17
19 x NP =x NP s if=sand x NP = 0 ifx (0,A] (1 ε,1] 1 ε x ifx (A,1 ε], forall>s. Thelefpanelshowshecaseinwhichbubblecreaionbyproduciveinvesorsdoes no affec he condiions for he exisence of bubbly episodes. The righ panel shows insead he case in which bubble creaion by producive invesors weakens he condiions for he exisence of bubbly episodes. This complees he proof of Proposiion 2. E x 1 E x 1 A 1 x A 1 x Figure 5 Wih financial fricions, he connecion beween bubbles and dynamic inefficiency becomes more suble. To deermine wheher a bubbly episodes can exis, we asked again: Is i possible o consruc apyramidschemehaisaracivewihouexplodingasashareoflaborincome? Wehaveshown haheanswerisaffirmaiveifandonlyifhereexissochasicprocessesforx NP, x NU andx such ha: E x +1 <x. These processes exis if and only if saisfies he resricion in Proposiion 2. To deermine wheher he economy is dynamically inefficien, we ask again: Is he economy accumulaing oo much capial? This quesion is now ricky because here are wo ypes of invesmens. The condiion ha aggregae invesmen be higher han aggregae capial income, i.e. (1 x ) (1 ) k > k, 18
20 asks wheher he average invesmen exceeds he income i produces. Even if his were no he case, he economy migh sill be dynamically inefficien since i migh conain pockes of invesmens ha exceed he income hey produce. We need o check for his addiional possibiliy. Invesmens byunproduciveinvesorsequal ( 1 ε x x NP ) (1 ) k,whileheircapialincomeisgiven δ (1 ε x x NP ) by A+(1 δ) x NP k δ x. Therefore, hese invesors consiue a pocke of dynamic inefficiency if and only if: ( 1 ε x x NP ) (1 ) k δ (1 ε x x NP ) > A+(1 δ) x NP δ x. k (22) Sraighforward algebra shows ha his condiion holds if and only if here exis sochasic processes forforx NP andx suchha: E x +1 <x +x NP. A When A+δ < (1 ε) δ hisresricionisweakerhanhecondiionforheexisenceof bubbly episodes in Proposiion 2. The inuiion for his resul is ha someimes bubbly episodes can only exis if here is enough bubble creaion. This requires he economy o be no only dynamically inefficien, bu o be sufficienly so o suppor bubble creaion. This discussion sheds some ligh on he analysis of Abel e al. (1989). The finding ha aggregae invesmen falls shor of aggregae capial income sill implies ha > 0.5. Under his parameer resricion, financial fricions are crucial for bubbly episodes o exis and heir removal would eliminae hese episodes a once. Bu i does no follow ha, under his parameer resricion, bubblyepisodescannoexis. Thisisforworeasons: (i)if0.5<< A A+δ,inhefundamenal saeherearepockesofdynamicinefficiencyhawouldsupporabubbleifiwereopopup; A and (ii) if A+δ < 1, here are no pockes of dynamic inefficiency in he 1+4 (1 ε) δ fundamenal sae bu an expansionary bubble ha lowers he reurn o invesmen would creae such pockes iself. This second case brings a simple bu powerful poin home: wha is required for bubbly episodes o exis is ha he economy be dynamically inefficien during hese episodes and no in he fundamenal sae. Bubbles ha crowd in capial can conver a dynamically efficien economy ino a dynamically inefficien one. 3.4 The macroeconomic effecs of bubbles revisied We have shown ha financial fricions weaken he condiions for bubbly episodes o exis. We show nex ha hey also modify he macroeconomic effecs of bubbly episodes. To do his, we rewrie 19
21 helawofmoionofhecapialsockusinghedefiniionofx andx NP : [ A+(1 δ) x NP δ x ] (1 ) k if k +1 = (1 ) k x if x +x NP 1 ε x +x NP 1 ε <1 1. (23) Equaion (23) describes he dynamics of he capial sock for any admissible sochasic process forhebubble, i.e. x NP, x NU andx ; saisfyingequaions(20)and(21). Onceagain, noeha bubbly episodes are akin o shocks o he law of moion of capial. As in he SamuelsonTirole model, bubbles can grow, shrink or randomly flucuae hroughou hese episodes. The macroeconomic effecs of bubbly episodes depend on wheher x NP is smaller or greaer δ han x. If smaller, bubbly episodes are conracionary and hey lower he capial sock 1 δ and oupu. If greaer, bubbly episodes are expansionary and hey raise he capial sock and oupu. 8 Conracionary episodes are similar in all regards o hose analyzed in he Samuelson Tirole model. As for expansionary episodes, heir macroeconomic effecs are illusraed in Figure 6. Assume iniially ha he economy is in he fundamenal sae so ha he appropriae law of moion is he one labeled k+1 F. This law of moion for he fundamenal sae is ha of he sandard Solow model. Assume ha, iniially, he capial sock is equal o he Solow seady sae 1 sohak =k F [A (1 )] 1. Whenanexpansionarybubblepopsup,ireducesunproducive invesmens and uses par of hese resources o increase producive invesmens. As can be seen fromequaion(23),helawofmoionduringhebubblyepisodeliesabovek F +1 : inhefigure,kb +1 represens he iniial law of moion when he episode begins. As a resul, growh urns posiive. Throughou he episode, k B +1 may shif as he bubble grows or shrinks. The capial sock and oupu, however, unambiguously increase relaive o he fundamenal sae. Evenually, he bubble burssandheeconomyreurnsoheoriginallawofmoionk F. 8 Evenwihinasingleepisode,heeffecsonhecapialsockandoupumighvaryhroughimeoracrosssaes of naure. 20
22 k 1 B k 1 F k 1 k F k Figure 6 Expansionary and conracionary episodes differ also in heir implicaions for consumpion. In his model, consumpion is sill expressed by Equaion (13). Therefore, regardless of heir ype, allpresenbubblesraiseheincomeinhehandsofheoldandhusconsumpion. However,he effec of pas bubbles depends on heir ype. If hey were conracionary, he curren capial sock and herefore consumpion are lower. If insead hey were expansionary, he curren capial sock and herefore consumpion are higher. 3.5 Discussion The SamuelsonTirole model has been criicized because he condiions for he exisence of bubbly episodes and heir macroeconomic effecs seem boh unrealisic. We have shown ha hese criicisms do no apply o he model wih financial fricions. In paricular, (i) bubbly episodes are possible even if aggregae invesmen falls shor of capial income and; (ii) bubbly episodes can be expansionary. The criiques o he SamuelsonTirole model herefore sem from he assumpion ha financial markes are fricionless and raes of reurn o invesmen are equalized across invesors. We can summarize our findings on he connecion beween bubbles and financial fricions wih hehelpoffigure7. Thelinelabeled C provides,foreachδ,helargeshaisconsisenwih heexisenceofconracionaryepisodes. 9 Thelinelabeled E provides, foreachδ, helarges 9 Theseepisodesarepossibleifandonlyifheeconomyisdynamicallyinefficieninhefundamenalsae. Therefore, C = A A+δ. 21
23 ha is consisen wih he exisence of expansionary episodes. 10 These lines pariion he (,δ) spaceinofourregions IV I C III II E 1 Figure 7 BubblyepisodesarepossibleinRegionsIIIV,bunoinRegionI.InRegionsIIandIII,< C andconracionaryepisodesarepossible. InRegionIIIandIV,< E andexpansionaryepisodes arepossible. Wecanhinkofδasameasureofhecossoffinancialfricions. Thehigherisδ,he smaller are he gains from borrowing and lending and he smaller are he coss of financial fricions. In he limiing case of δ 1, he SamuelsonTirole model applies: only conracionary episodes arepossibleandhisrequires<0.5. Asδ decreases,hecondiionsforexisencearerelaxedfor bohypesofbubblyepisodes. Inhelimiingcaseofδ 0,financialfricionsareverysevereand all ypes of bubbly episodes are possible regardless of. 10 Fomally,heexisenceofaexpansionarybubblyepisoderequiresheexisenceofariple { x,x NP } saisfyinge x +1 <x andx δ 1 δ <xnp,wheree x +1 isasinequaion(20). Thismeansha: (1 ε) δ E = A (1 δ) δ+a (1 δ) when δ 0.5 ε 1 ε when δ> 0.5 ε 1 ε,x NU 11 Figure7hasbeendrawnunderheassumpionhaε<0.5. ThisguaraneeshaRegionIVexiss. 22
24 4 Bubbles and longrun growh The SamuelsonTirole model predaes he developmen of endogenous growh models. To maximize comparabiliy, he model wih financial fricions used he same producion srucure. No surprisingly, i has lile o say abou he relaionship beween bubbles and longrun growh. We now generalize he producion srucure and allow for he possibiliy of consan or increasing reurns o capial. We show ha he condiions for exisence of bubbly episodes do no change. However, even ransiory episodes have permanen effecs and can even lead he economy ino or ou of negaivegrowh raps. 4.1 Seup wih longrun growh We assume ha he producion of he final good consiss of assembling a coninuum of inermediae inpus,indexedbym [0,m ]. Thisvariable,whichcanbeinerpreedashelevelofechnology in period, will be obained endogenously as par of he equilibrium. The producion funcion of he final good is given by he following symmeric CES funcion: m 1 y =η µ q m dm 0 µ, (24) where q m denoes unis of he variey m of inermediae inpus and µ > 1. The consan η is a normalizaion parameer ha will be chosen laer. Throughou, we assume ha final good producersarecompeiive,andwenormalizehepriceofhefinalgoodoone. Producion of inermediae inpus requires labor and capial. In paricular, each ype of inermediaeinpum [0,m ]isproducedaccordingohefollowingproducionfuncion, q m =(l m,v ) 1 (k m,v ) a, (25) wherel m,v andk m,v respecivelydenoeheuseoflaborandcapialocoverhevariablecossof producing variey m. Besides his use of facors, he producion of any given variey requires he paymenofafixedcosf m givenby 1=(l m,f ) 1 (k m,f ) a ifq m >0 f m = 0 ifq m =0, (26) 23
25 where l m,f and k m,f respecively denoe he use of labor and capial o cover he fixed coss of producing variey m. To simplify he model, we assume ha inpu varieies become obsolee in one generaion and, as a resul, all generaions mus incur hese fixed coss. I is naural herefore o assume ha he producion of inermediae inpus akes place under monopolisic compeiion and free enry. Thisproducionsrucureisaspecial caseofhaconsideredby Venura(2005). 12 Heshows ha, under he assumpions made, i is possible o rewrie Equaion(24) as y =k µ, (27) where we have chosen unis such ha η = (µ) µ (1 µ) µ 1. Mainaining he assumpion of compeiive facor markes, facor prices can now be expressed as follows w =(1 ) k µ and r = k µ 1. (28) Equaion(27) shows ha here are wo opposing effecs of increasing he sock of physical capial. On he one hand, such increases make capial abundan and hey have he sandard effec of decreasing is marginal produc. The srengh of his diminishingreurns effec is measured by. On he oher hand, increases in he sock of capial expand he varieies of inpus produced in equilibrium, which has an indirec and posiive effec on he marginal produc of capial. The srengh of his markesize effec is measured by µ. If diminishing reurns are srong and markesizeeffecsareweak( µ<1)increasesinphysicalcapialreducehemarginalproducofcapial. Ifinseaddiminishingreurnsareweakandmarkesizeeffecsaresrong( µ 1)increasesin physical capial raise he marginal produc of capial. 4.2 Equilibria wih bubbles How does his generalizaion of he producion srucure affec he dynamics of bubbles and capial? Forabubbleobearacive,isexpecedreurnmusbealeasequalohereurnoinvesmen. 12 TheAppendixconainsaformalderivaionofheequaionshafollow. 24
26 Formally, his requiremen mus now be wrien as follows, E { b +1 b +b NP +b NU } =δ k µ 1 [ δ k µ 1 = k µ 1, k µ 1 ] if if if b +b NP (1 ε) (1 ) k µ b +b NP (1 ε) (1 ) k µ b +b NP (1 ε) (1 ) k µ <1 =1 >1, (29) which is a generalizaion of Equaion (17). The dynamics of he capial sock, in urn, are now given by, k +1 = (1 ) A k µ +(1 δ) b NP δ b if (1 ) k µ b if b +b NP (1 ε) (1 ) k µ b +b NP (1 ε) (1 ) k µ <1 1, (30) whichisageneralizaionofequaion(19). Foragiveniniialcapialsockandbubble,k 0 >0and b 0 0,acompeiiveequilibriumisasequence { k,b,b NP } =0 saisfyingequaions(6),(29) and(30).,b NU 4.3 Bubbly episodes wih longrun growh This generalizaion of he producion srucure expands he se of economies ha can be analyzed wih he model. I does no, however, affec he condiions for he exisence of bubbly episodes. Thais, Proposiion 2 applies for any valueof µ. Toseehis, definex b NP b NU b (1 ) k µ, x NP (1 ) k µ andx NU (1 ) k µ. OnceweapplyourrecursiverickoEquaion(29), we recover Equaion(20). Hence, bubble dynamics are sill described by Equaions(20) and(21). I is useful a his poin o provide an addiional characerizaion of he condiion for dynamic inefficiency. Combining Equaions(22) and(30) we find ha he economy has pockes of dynamic inefficiency if and only if he growh rae exceeds he reurn o unproducive invesmens, G +1 ( k+1 k ) µ δ k µ 1 +1 R U +1. (31) This condiion is quie inuiive. Remember ha, for a bubble o exis, i mus grow fas enough obearacivebunooofasoougrowisdemand,i.e. isgrowhmusbebeweeng +1 and R U +1. WhenhecondiioninEquaion(31)failshereisnoroomforsuchabubble. Considerfirshecaseinwhich µ<1. ConracionarybubblesreduceG +1 andincreaser U
27 This is why conracionary episodes areonly possibleif, in hefundamenal sae, G +1 >R U +1. Expansionarybubbles,however,increaseG +1 andlowerr U +1. Thisiswhyexpansionaryepisodes aresomeimespossibleevenif,inhefundamenalsae,g +1 <R U +1. Consider nex he case in which µ 1. Now, markesize effecs dominae diminishing reurns and he relaionship beween he capial sock and he reurn o invesmen is reversed. Conracionary bubbles sill reduce G +1 bu now hey also reduce R U +1. Despie his, we sill find ha conracionary episodes are only possible if, in he fundamenal sae, G +1 > R U +1. The reason, of course, is ha he decrease in R U +1 is small relaive o he decrease in G +1. Expansionary bubbles sill increase G +1 bu now hey also increase R+1 U. Despie his, we sill findhaexpansionaryepisodesmighbepossibleevenif,inhefundamenalsae,g +1 <R U +1. Thereason,onceagain,ishaheincreaseinR U +1 issmallrelaiveoheincreaseing The macroeconomic effecs of bubbles Wecanrewriehelawofmoionofhecapialsockusinghedefiniionsofx andx NP : k +1 = [ A+(1 δ) x NP δ x ] (1 ) k µ (1 ) k µ x if if x +x NP 1 ε x +x NP 1 ε <1 1. (32) Equaion(32) describes he dynamics of he capial sock for any admissible sochasic process for hebubble,i.e. x NP,x NU andx ;saisfyingequaions(20)and(21). Onceagain,noehabubbly episodes are akin o shocks o he law of moion of capial. As in previous models, bubbles can grow, shrink or randomly flucuae hroughou hese episodes. If diminishing reurns are srong andmarkesizeeffecsareweak,i.e. µ<1,allheanalysisofsecion3applies. Therefore,we resric he analysis o he new case in which diminishing reurns are weak and markesize effecs aresrong,i.e. µ 1. An ineresing feaure of bubbly episodes when µ 1is ha, even if hey are ransiory, hey can have permanen effecs on he levels and growh raes of capial and oupu. We illusrae hiswihhehelpoffigure9. Thelefpaneldepicshecaseofanexpansionarybubble. Iniially, heeconomyisinhefundamenalsaesohaheappropriaelawofmoionisheonelabeled k F +1. Since he iniial capial sock is below he seady sae, i.e. k < k F [(1 ) A] 1 1 µ, growh is negaive. We hink of his economy as being caugh in a negaivegrowh rap. When an expansionary bubble pops up, i reduces unproducive invesmens and uses par of hese re 26
28 sources o increase producive invesmens. During he bubbly episode, he law of moion of capial lies above k+1 F : in he figure, kb +1 represens he iniial law of moion when he episode begins. Throughouheepisode,k+1 B mayshifashebubblegrowsorshrinks. Growhmaybeposiive if, during he bubbly episode, he capial sock lies above is seadysae value as shown in he figure. Evenually, he bubble burss bu he economy migh keep on growing if he capial sock aheimeofbursingexceedsk F. Thebubblyepisode,houghemporary,leadsheeconomyou of he negaivegrowh rap and i has a permanen effec on longrun growh. k 1 B k 1 F k 1 k 1 kf 1 kb 1 k B k k F k k F k k B k Figure 8 Naurally, i is also possible for bubbles o lead he economy ino a negaive growh rap hereby having permanen negaive effecs on longrun growh. The righ panel of Figure 9 shows an example of a conracionary bubble ha does his. This secion has exended he model o allow for endogenous growh. This does no affec he condiions for he exisence of bubbly episodes. I does, however, affec some of heir macroeconomic effecs. Firs, he behavior of he reurn o invesmen during bubbly episodes is reversed. Second, bubbly episodes can have longrun effecs on economic growh. 5 Furher issues and research agenda We have developed a sylized model of economic growh wih bubbles. In his model, financial fricions lead o equilibrium dispersion in he raes of reurn o invesmen. During bubbly episodes, unproducive invesors demand bubbles while producive invesors supply hem. Because of his, bubbly episodes channel resources owards producive invesmen raising he growh raes of capial and oupu. The model also illusraes ha he exisence of bubbly episodes requires some 27
Morningstar Investor Return
Morningsar Invesor Reurn Morningsar Mehodology Paper March 3, 2009 2009 Morningsar, Inc. All righs reserved. The informaion in his documen is he propery of Morningsar, Inc. Reproducion or ranscripion by
More informationKEY CONCEPTS AND PROCESS SKILLS. 1. An allele is one of the two or more forms of a gene present in a population. MATERIALS AND ADVANCE PREPARATION
Gene Squares 61 40 o 2 3 50minue sessions ACIVIY OVERVIEW P R O B L E M S O LV I N G SUMMARY Sudens use Punne squares o predic he approximae frequencies of rais among he offspring of specific crier crosses.
More informationBetting Against Beta
Being Agains Bea Andrea Frazzini and Lasse H. Pedersen * This draf: Ocober 5, 2010 Absrac. We presen a model in which some invesors are prohibied from using leverage and oher invesors leverage is limied
More informationStock Return Expectations in the Credit Market
Sock Reurn Expecaions in he Credi Marke Hans Bysröm * Sepember 016 In his paper we compue longerm sock reurn expecaions (across he business cycle) for individual firms using informaion backed ou from
More informationWhat the Puck? an exploration of TwoDimensional collisions
Wha he Puck? an exploraion of TwoDimensional collisions 1) Have you ever played 8Ball pool and los he game because you scrached while aemping o sink he 8Ball in a corner pocke? Skech he sho below: Each
More informationMarket timing and statistical arbitrage: Which market timing opportunities arise from equity price busts coinciding with recessions?
Journal of Applied Finance & Banking, vol.1, no.1, 2011, 5381 ISSN: 17926580 (prin version), 17926599 (online) Inernaional Scienific Press, 2011 Marke iming and saisical arbirage: Which marke iming
More informationFORECASTING TECHNIQUES ADE 2013 Prof Antoni Espasa TOPIC 1 PART 2 TRENDS AND ACCUMULATION OF KNOWLEDGE. SEASONALITY HANDOUT
FORECASTING TECHNIQUES ADE 2013 Prof Anoni Espasa TOPIC 1 PART 2 TRENDS AND ACCUMULATION OF KNOWLEDGE. SEASONALITY HANDOUT February 2013 MAIN FACTORS CAUSING TRENDS Increases in populaion. Seady inflaion.
More informationRolling ADF Tests: Detecting Rational Bubbles in Greater China Stock Markets
Singapore Managemen Universiy Insiuional Knowledge a Singapore Managemen Universiy Disseraions and Theses Collecion (Open Access) Disseraions and Theses 2008 Rolling ADF Tess: Deecing Raional Bubbles in
More informationQUANTITATIVE FINANCE RESEARCH CENTRE. Optimal Time Series Momentum QUANTITATIVE FINANCE RESEARCH CENTRE QUANTITATIVE F INANCE RESEARCH CENTRE
QUANTITATIVE FINANCE RESEARCH CENTRE QUANTITATIVE F INANCE RESEARCH CENTRE QUANTITATIVE FINANCE RESEARCH CENTRE Research Paper 353 January 15 Opimal Time Series Momenum XueZhong He, Kai Li and Youwei
More informationEconomics 487. Homework #4 Solution Key Portfolio Calculations and the Markowitz Algorithm
Economics 87 Homework # Soluion Key Porfolio Calculaions and he Markowiz Algorihm A. Excel Exercises: (10 poins) 1. Download he Excel file hw.xls from he class websie. This file conains monhly closing
More informationKINEMATICS IN ONE DIMENSION
chaper KINEMATICS IN ONE DIMENSION Secion 2.1 Displacemen Secion 2.2 Speed and Velociy 1. A paricle ravels along a curved pah beween wo poins P and Q as shown. The displacemen of he paricle does no depend
More informationWORLD GROWTH AND INTERNATIONAL CAPITAL FLOWS IN THE XXI st CENTURY
CEPREMAP WORLD GROWTH AND INTERNATIONAL CAPITAL FLOWS IN THE XXI s CENTURY A prospecive analysis wih he INGENUE 2 model by he INGENUE TEAM Michel AGLIETTA and Vladimir BORGY (Cepii), Jean CHATEAU (Ocde),
More informationMeasuring Potential Output and Output Gap and Macroeconomic Policy: The Case of Kenya
Universiy of Connecicu DigialCommons@UConn Economics Working Papers Deparmen of Economics Ocober 2005 Measuring Poenial Oupu and Oupu Gap and Macroeconomic Policy: The Case of Kenya Angelica E. Njuguna
More informationINSTRUCTIONS FOR USE. This file can only be used to produce a handout master:
INSTRUCTIONS OR USE This file can only be used o produce a handou maser: Use Prin from he ile menu o make a prinou of he es. You may no modify he conens of his file. IMPORTNT NOTICE: You may prin his es
More informationDYNAMIC portfolio optimization is one of the important
, July 24, 2014, London, U.K. A Simulaionbased Porfolio Opimizaion Approach wih Leas Squares Learning Chenming Bao, Geoffrey Lee, and Zili Zhu Absrac This paper inroduces a simulaionbased numerical
More informationDynamics of market correlations: Taxonomy and portfolio analysis
Dynamics of marke correlaions: Taxonomy and porfolio analysis J.P. Onnela, A. Chakrabori, and K. Kaski Laboraory of Compuaional Engineering, Helsinki Universiy of Technology, P.O. Box 9203, FIN02015
More informationSources of OverPerformance in Equity Markets: Mean Reversion, Common Trends and Herding
The Universiy of Reading THE BUSINESS SCHOOL FOR FINANCIAL MARKETS Sources of OverPerformance in Equiy Markes: Mean Reversion, Common Trends and Herding ISMA Cenre Discussion Papers in Finance 200308
More informationOverreaction and Underreaction :  Evidence for the Portuguese Stock Market 
Overreacion and Underreacion :  Evidence for he Poruguese Sock Marke  João Vasco Soares* and Ana Paula Serra** March 2005 * Faculdade de Economia da Universidade do Poro ** (corresponding auhor) CEMPRE,
More informationTime & Distance SAKSHI If an object travels the same distance (D) with two different speeds S 1 taking different times t 1
www.sakshieducaion.com Time & isance The raio beween disance () ravelled by an objec and he ime () aken by ha o ravel he disance is called he speed (S) of he objec. S = = S = Generally if he disance ()
More informationInstruction Manual. Rugged PCB type. 1 Terminal Block. 2 Function. 3 Series Operation and Parallel Operation. 4 Assembling and Installation Method
Rugged PCB ype Insrucion Manual 1 Terminal Block Funcion.1...4.5.6.7 Inpu volage range Inrush curren limiing Overcurren proecion Overvolage proecion Oupu volage adjusmen range Isolaion Remoe ON/OFF E9
More informationMachine Learning for Stock Selection
Machine Learning for Sock Selecion Rober J. Yan Compuer Science Dep., The Uniersiy of Wesern Onario jyan@csd.uwo.ca Charles X. Ling Compuer Science Dep., The Uniersiy of Wesern Onario cling@csd.uwo.ca
More informationGuidance Statement on Calculation Methodology
Guidance Saemen on Calculaion Mehodology Adopion Dae: 28 Sepember 200 Effecive Dae: January 20 Reroacive Applicaion: No Required www.gipssandards.org 200 CFA Insiue Guidance Saemen on Calculaion Mehodology
More informationPerformance Attribution for Equity Portfolios
PERFORMACE ATTRIBUTIO FOR EQUITY PORTFOLIOS Performance Aribuion for Equiy Porfolios Yang Lu and David Kane Inroducion Many porfolio managers measure performance wih reference o a benchmark. The difference
More informationRealtime Stochastic Evacuation Models for Decision Support in Actual Emergencies
Realime Sochasic Evacuaion Models for Decision Suppor in Acual Emergencies ARTURO CUESTA, DANIEL ALVEAR, ORLANDO ABREU and DELFÍN SILIÓ Transpors and echnology projecs and processes Universiy of Canabria
More informationThe safe ships trajectory in a restricted area
Scienific Journals Mariime Universiy of Szczecin Zeszyy Naukowe Akademia Morska w Szczecinie 214, 39(111) pp. 122 127 214, 39(111) s. 122 127 ISSN 1733867 The safe ships rajecory in a resriced area Zbigniew
More informationName Class Date. Step 2: Rearrange the acceleration equation to solve for final speed. a v final v initial v. final v initial v.
Skills Workshee Mah Skills Acceleraion Afer you sudy each sample problem and soluion, work ou he pracice problems on a separae shee of paper. Wrie your answers in he spaces provided. In 1970, Don Big Daddy
More informationCentre for Investment Research Discussion Paper Series. Momentum Profits and TimeVarying Unsystematic Risk
Cenre for Invesmen Research Discussion Paper Series Discussion Paper # 080* Momenum Profis and TimeVarying Unsysemaic Risk Cenre for Invesmen Research O'Rahilly Building, Room 3.0 Universiy College Cork
More informationAn Alternative Mathematical Model for Oxygen Transfer Evaluation in Clean Water
An Alernaive Mahemaical Model for Oxygen Transfer Evaluaion in Clean Waer Yanjun (John) He 1, PE, BCEE 1 Kruger Inc., 41 Weson Parkway, Cary, NC 27513 Email: john.he@veolia.com ABSTRACT Energy consumpion
More informationFlow Switch LABOVHZS
Flow Swich S Volumeric flow swiching Almos no effec from differing viscosiies Versaile, configurable swiching oupu in pushpull design Robus consrucion Compac design Characerisics he VHZ gearwheel flow
More informationMethods for Estimating Term Structure of Interest Rates
Mehods for Esimaing Term Srucure of Ineres Raes Iskander Karibzhanov Absrac This paper compares differen inerpolaion algorihms for consrucing yield curves: cubic splines, linear and quadraic programming,
More informationEXAMINING THE FEASIBILITY OF PAIRED CLOSELYSPACED PARALLEL APPROACHES
EXAMINING THE FEASIBILITY OF PAIRED CLOSELYSPACED PARALLEL APPROACHES Seven J. Landry and Amy R. Priche Georgia Insiue of Technology Alana GA 303320205 ABSTRACT Paired closelyspaced parallel approaches
More informationDevelopment of Urban Public Transit Network Structure Integrating MultiClass Public Transit Lines and Transfer Hubs
Developmen of Urban Public Transi Nework Srucure Inegraing MuliClass Public Transi Lines and Transfer Hubs Zhenbao Wang 1, Anyan Chen 2 1College of Civil Engineering, Hebei Universiy of Engineering Handan,
More informationWhat is a Practical (ASTM C 618) SAIStrength Activity Index for Fly Ashes that can be used to Proportion Concretes Containing Fly Ash?
2017 World of Coal Ash (WOCA) Conference in Lexingon, KY  May 911, 2017 hp://www.flyash.info/ Wha is a Pracical (ASTM C 618) SAISrengh Aciviy Index for Fly Ashes ha can be used o Proporion Concrees
More informationA Dynamic Bioeconomic Model of Ivory Trade: Details and Extended Results
WORKING PAPER 200603 Resource Economics and Policy Analysis (REPA) Research Group Deparmen of Economics Universiy of Vicoria A Dynamic Bioeconomic Model of Ivory Trade: Deails and Exended Resuls G. Cornelis
More informationSIMULATION OF WAVE EFFECT ON SHIP HYDRODYNAMICS BY RANSE
1 h Inernaional Conference on Sabiliy of Ships and Ocean Vehicles 591 SIMULATION OF WAVE EFFECT ON SHIP HYDRODYNAMICS BY RANSE Qiuxin Gao, Universiy of Srahclyde, UK, Gao.q.x@srah.ac.uk Dracos Vassalos,
More informationZelio Control Measurement Relays RM4L Liquid Level Relays
Zelio Conrol Measuremen elays FNCTIONS These devices monior he levels of conducive liquids. They conrol he acuaion of pumps or valves o regulae levels; hey are also suiable for proecing submersible pumps
More informationUrban public transport optimization by bus ways: a neural networkbased methodology
Urban Transpor XIII: Urban Transpor and he Environmen in he 21s Cenury 347 Urban public ranspor opimizaion by bus ways: a neural neworkbased mehodology M. Migliore & M. Caalano Deparmen of Transporaion
More informationA Statistical, AgeStructured, LifeHistoryBased Stock Assessment Model for Anadromous Alosa
American Fisheries Sociey Symposium 35:275 283, 2003 2003 by he American Fisheries Sociey A Saisical, AgeSrucured, LifeHisoryBased Sock Assessmen Model for Anadromous Alosa A. JAMIE F. GIBSON 1 Acadia
More informationWHO RIDE THE HIGH SPEED RAIL IN THE UNITED STATES THE ACELA EXPRESS CASE STUDY
Proceedings of he 2010 Join Rail Conference JRC2010 April 2729, 2010, Urbana, Illinois, USA JRC201036236 WHO RIDE THE HIGH SPEED RAIL IN THE UNITED STATES THE ACELA EXPRESS CASE STUDY Zhenhua Chen The
More informationScienceDirect. Cycling Power Optimization System Using Link Models of Lower Limbs with CleatShaped Biaxial Load Cells
Available online a www.sciencedirec.com ScienceDirec Procedia Engineering 72 ( 20 ) 8 7 The 20 conference of he Inernaional Spors Engineering Associaion Cycling Power Opimizaion Sysem Using ink Models
More informationCHARACTERIZATION AND MODELING OF A PROPORTIONAL VALVE FOR CONTROL SYNTHESIS
CHARACTERIZATION AND MODELING OF A PROPORTIONAL VALVE FOR CONTROL SYNTHESIS Osama. OLABY, Xavier. BRN, Sylvie. SESMAT, Tanneguy. REDARCE and Eric. BIDEAX Laboraoire d Auomaique Indusrielle  hp://wwwlai.insalyon.fr
More informationDual Boost High Performances Power Factor Correction (PFC)
Dual Boos High Performances Power Facor Correcion (PFC) C. Aaianese, Senior Member, IEEE  V. Nardi, Member, IEEE  F. Parillo  G. Tomasso, Member, IEEE Deparmen of Auomaion, Elecromagneism, Compuer Science
More informationMaking Sense of Genetics Problems
Bio 101 Ms. Bledsoe Making Sense of Geneics roblems Monohbrid crosses Le s sar wih somehing simle: crossing wo organisms and waching how one single rai comes ou in he offsring. Le s use eas, as Mendel
More informationLSU RISK ASSESSMENT FORM Please read How to Complete a Risk Assessment before completion
Please read How o Complee a Risk Assessmen before compleion EVENT OR ACTIVITY BEING RISK ASSESSED (add name of even where relevan) NAME OF DEPARTMENT Squad Training Neball DATE OF COMPLETION OF RISK ASSESSMENT
More informationFIVE RISK FACTORS MODEL: PRICING SECTORAL PORTFOLIOS IN THE BRAZILIAN STOCK MARKET
Revisa Caarinense da Ciência Conábil, ISSN 18083781  eissn 22377662, Florianópolis, SC, Brazil, v. 16, n. 48, p. 8198, May/Aug. 2017 doi: 10.16930/22377662/rccc.v16n48.2376 Available a hp://revisa.crcsc.org.br
More informationCONTROL VALVES IN TURBOCOMPRESSOR ANTISURGE SYSTEMS
CONTROL VALVES IN TURBOCOMPRESSOR ANTISURGE SYSTEMS keninrol CONTROL VALVES IN TURBOCOMPRESSOR ANTISURGE SYSTEMS CONTROL VALVES IN TURBOCOMPRESSOR ANTISURGE SYSTEMS 0 KOSO KENT INTROL SUPPLIES A
More informationProceedings of the ASME 28th International Conference on Ocean, Offshore and Arctic Engineering OMAE2009 May 31  June 5, 2009, Honolulu, Hawaii
Proceedings of he ASME 28h Inernaional Conference on Ocean, Offshore and Arcic Engineering OMAE29 May 31  June 5, 29, Honolulu, Hawaii OMAE2979385 ANALYSIS OF THE TUNNEL IMMERSION FOR THE BUSANGEOJE
More informationAN ANALYSIS OF THE ECONOMIC EFFECT OF A ROAD DIET IN ELIZABETHTOWN AND GEORGETOWN, KENTUCKY
AN ANALYSIS OF THE ECOMIC EFFECT OF A ROAD DIET IN ELIZABETHTOWN AND GEORGETOWN, KENTUCKY MARCH 2014 This repor was produced a he reques of he Ron Sco, Ciy Manager for Danville, Kenucky, under he supervision
More informationReexamining SportsSentiment Hypothesis: Microeconomic Evidences from Borsa Istanbul
Reexamining SporsSenimen Hypohesis: Microeconomic Evidences from Borsa Isanbul Ka Wai Terence Fung +, Ender Demir, Chi Keung Marco Lau And Kwok Ho Chan * Absrac This paper examines he impac of inernaional
More informationWorld War 2 when Japan
Chaper 30 Reading Guide Chaper 30 Reading Guide A Second Global Conflic and he End of he European World Order A Second Global Conflic and he End of he European World Order Name: Name: Name: Due Dae: Wednesday,
More information2nd Regional Conference On Enhancing Transport Technology For Regional Competitiveness
nd Regional Conference On Enhancing Transpor Technology For Regional Compeiiveness SESSION C TBLE OF CONTENTS PREFCE... 4 ORGNISING COITTEE... 5 KEYNOTE DDRESS... 6 Session : UTOOTIE... 7 Session B : ERONUTICS...
More informationUS 9,615,553 B2 Apr. 11,2017
111111111111111111111111111111111111111111111111111111111111111111111111111 US009615553B2 (12) Unied Saes Paen Coniglio e al. (10) Paen No.: (45) Dae of Paen: US 9,615,553 B2 Apr. 11,2017 (54) ARTIFICIAL
More informationManaging the abundance of bison in Yellowstone National Park, winter Chris Geremia, P. J. White, and Rick Wallen September 12, 2011
Managing he abundance of bison in Yellowsone Naional Park winer 2012 Chris Geremia P. J. Whie and Rick Wallen Sepember 12 2011 EXECUTIVE SUMMARY Background Yellowsone Naional Park (YNP) developed a plan
More informationconnection Glen Smale discusses racing engine con rod technology with specialist manufacturers from around the world
Making he connecion Glen Smale discusses racing engine con rod echnology wih specialis manufacurers from around he world Making he connecion necessary beween he op end and he boom end of he racing engine
More informationPaul R. Drake Management School, University of Liverpool, Liverpool, UK
The curren issue and full ex archive of his journal is available a www.emeraldinsigh.com/09600035.hm Analysis of he bullwhip effec wih order baching in muliechelon supply chains Maloub Hussain College
More information29 B ROUTE Bus Times Summer NOTES a = Time at Vicarage Way. * = On Schooldays bus operates up to 5 minutes later.
Brighon Lewes Ringmer / Touris Aracions Lewes for Hisoric own wih Casle; Isfield for Lavender Line Railway; for Spa Valley Railway, Paniles CiySAVER ickes are only valid beween Brighon and Falmer. nework
More informationTHE PERSISTENCY OF INTERNATIONAL DIVERSIFICATION BENEFITS: THE ROLE OF THE ASYMMETRY VOLATILITY MODEL
ASIA ACADEMY of MAAGEMET JOURAL of ACCOUTIG and FIACE AAMJAF, Vol. 10, o. 1, 151 165, 014 THE PERSISTECY OF ITERATIOAL DIVERSIFICATIO BEEFITS: THE ROLE OF THE ASYMMETRY VOLATILITY MODEL Ung Sze ie 1*,
More informationCoefficients of Propellerhull Interaction in Propulsion System of Inland Waterway Vessels with Stern Tunnels
hp://www.ransnav.eu he Inernaional Journal on Marine Navigaion and Safey of Sea Transporaion Volume 8 Number 3 Sepember 214 DOI: 1.12716/11.8.3.8 Coefficiens of Propellerhull Ineracion in Propulsion Sysem
More informationSensors and Actuators A: Physical
Sensors and Acuaors A 144 (2008) 354 360 Conens liss available a ScienceDirec Sensors and Acuaors A: Physical journal homepage: www.elsevier.com/locae/sna A microrobo fish wih embedded SMA wire acuaed
More informationI t ' 4 ti. t ti. IQ:::: mass x heat of fusion (or heat of vaporization) I HEAT AND ITS MEASUREMENT. t t. t f I I I. Name
HEAT AND TS MEASUREMENT Name a (or energy) can be measured in unis of calories or joules. When here is a,,,,,,nperaure change (AT), hea (Q) can be calculaed using his formula: During a phase change, we
More informationImprovement of individual camouflage through background choice in groundnesting birds
This is he preproof acceped version of he manuscrip, he full version can be accessed for free here. Improvemen of individual camouflage hrough background choice in groundnesing birds Auhors: Marin Sevens*1,
More informationClemco Industries Corp. ISO 9001 Certified
Clemco Indusries Corp. ISO 9001 Cerified 6 cuf Classic Blas Machines Exclusively from... SIMPLE, RUGGED, RELIABLE More han 75 years of reliable field service have made Clemco blas machines he preferred
More informationSWIMMING POOL HEAT PUMP UNITS. Installation & Instruction Manual DURA  series
SWIMMIG POO HEAT PUMP UITS Insallaion & Insrucion Manual DUA  series ev. 1.12 29.07.2014 Conens SWIMMIG POO HEAT PUMP UITS... 1! Conens... 2! 1. Preface... 3! 2. Specificaions... 4! 2.1 Technical daa
More informationGenetic Mapping Exercise  Extra Credit. Do not work together  each person to do their own work.
Geneic Mapping Execise  Exa Cedi Name Secion # Do no ok ogehe  each peson o do hei on ok. hen loci of diffeen allelic goups ae on he same chomosome, linkage occus bu is no absolue. Cossingove alays
More informationPopulation size and exploitation of giant squid (Dosidicus gigas D Orbigny, 1835) in the Gulf of California, Mexico*
SCI. AR., 65 (): 758 SCIENIA ARINA 2 Populaion size and exploiaion of gian squid (Dosidicus gigas D Orbigny, 835) in he Gulf of California, exico* ENRIQUE ORALESBOJÓRQUEZ, AGUSÍN HERNÁNDEZHERRERA 2,
More informationEFFECTS OF WIND SPEED ON WIND TURBINE AVAILABILITY
EFFECTS OF WIND SPEED ON WIND TURBINE AVAILABILITY S. Faulsich 1, P. Lyding 1, P. J. Tavner 2 1 Fraunhofer Insiue for Wind Energy and Energy Sysem Technology (IWES) 2 Energy Group, School of Engineering,
More informationCal. 7T85 INSTRUCTIONS (P. 3) BEDIENUNGSANLEITUNG (S. 27) INSTRUCTIONS (P. 51) ISTRUZIONI (P. 75) INSTRUCCIONES (P. 99) INSTRUÇÕES (P.
Cal. 7T85 INSTRUCTIONS (P. 3) BEDIENUNGSANLEITUNG (S. 27) INSTRUCTIONS (P. 51) ISTRUZIONI (P. 75) INSTRUCCIONES (P. 99) INSTRUÇÕES (P. 123) (147 ) You are now he proud owner of a SEIKO Analogue Quarz Wach
More informationCOMPARATIVE STUDY OF VELOCITY REDUCTION ON FEATHER AND SYNTHETIC SHUTTLECOCKS USING CORRECTED INITIAL VELOCITY DURING OVERHEAD SMASH
Journal of Engineering Science and Technolog Special Issue on AASEC 6, Ocober (7) 95 School of Engineering, Talor s Uniersi COMPARATIVE STUDY OF VELOCITY REDUCTION ON FEATHER AND SYNTHETIC SHUTTLECOCKS
More informationAn Autonomous Blimp for the Wall Following Control.
An Auonomous Blimp for he Wall Following Conrol. SeungYong Oh *,**, Chi Won Roh *, Sung Chul Kang *, Eunai Kim ** * Inelligen Roboics Research Cener, Korea Insiue of Science an echnology, Seoul, Korea
More informationR410A Rotary Compressor Bearing Design Considerations
Prde Universiy Prde epbs Inernaional Compressor Engineering Conference School of Mechanical Engineering 1998 R41A Roary Compressor Bearing Design Consideraions J. R. Lenz Tecmseh Prodcs Company Follow
More informationOptimal Staged SelfAssembly of General Shapes
Opimal Saged SelAssemly o General Shapes Cameron Chalk, Eric Marinez, Roer Schweller 3, Luis Vega 4, Andrew Winslow 5, and im Wylie 6 Deparmen o Compuer Science, Universiy o eas Rio Grande Valley, Brownsville,
More informationA Simple Approach to Dynamic Material Balance in GasCondensate Reservoirs
Oil & Gas Science and Technology Rev. IFP Energies nouvelles, Copyrigh 23, IFP Energies nouvelles DOI:.256/ogs/2222 Vol. 69 (24), No. 2, pp. 3737 A Siple Approach o Dynaic Maerial Balance in GasCondensae
More informationHenry Kendall College Team (FIRST TEAM)
Henry Kendall College 1895 Team (FIRST TEAM) TULSA GOLDEN Hurricane fooball Tulsa s Fooball 1895: The Legacy Begins The legacy of Tulsa fooball began when he Bacone School for Indians and Henry Kendall
More informationINSTALLATION AND OPERATION MANUAL
IMPORTANT SAFETY INSTRUCTIONS SAVE THESE INSTRUCTIONS PLEASE READ THE ENTIRE CONTENTS OF THIS MANUAL PRIOR TO INSTALLATION AND OPERATION. BY PROCEEDING WITH LIFT INSTALLATION AND OPERATION YOU AGREE THAT
More informationOPTIMAL ENERGY SOURCE FOR AN ENVIRONMENTALLYFRIENDLY GOKART
Journal of Ecological Engineering Volume 17, Issue 5, Nov. 016, pages 90 95 DOI: 10.1911/998993/65454 Research Aricle OPTIMAL ENERGY SOURCE FOR AN ENVIRONMENTALLYFRIENDLY GOKART Pior Zbigniew Filip 1,
More informationVERTICAL DOUBLE TEAM TECHNIQUE ON POWER / COUNTER ( DUECE / TREY )
VERICAL DOUBLE EA ECHNIQUE ON POER / COUNER ( DUECE / REY ) COACHING POIN: GE HIP O HIP IH KNEES ORKING NORH & SOUH; 4 HANDS ON DL & 4 EYES ON LBer. I. POS (INSIDE BLOCKER): GAIN VERICAL LEVERAGE (YOUR
More informationOriginal Article. Physiological characteristics and physical fitness of girls at the beginning of classes at the volleyball sports school
Journal of Physical Educaion and Spor (JPES), 17(4), Ar 276, pp. 24672471, 2017 online ISSN: 2247806X; pissn: 2247 8051; ISSN  L = 22478051 JPES Original Aricle Physiological characerisics and physical
More informationDIMENSIONS AC Road travel
DIMENSIONS AC 10009 Road ravel 04 DIMENSIONS AC 10009 Lifing operaion OUTRIGGER BASES TO CHOOSE FROM: A 13.54m x 13.538m B 12.0m x 12.0m (NEW) C 9.671m x 9.885m 05 HA /SSL (HA50) AC 10009 AC 10009 17 HA
More informationINVERTER HEATPUMP FOR SWIMMING POOLS
IVE HEATPUMP FO SWIMMIG POOS Insallaion & Insrucion Manual hea pumps 000711611 Table of conens 1. Preface 3. Specificaions.1 Performance Daa. Dimensions 6 3. Insallaion and Connecion 3.1 Hea Pump ocaion
More informationSeriouslyFun! It s Business asunusual. Presented by CORAL HOSPITALITY. Contact our meeting and conference planners today.
DESTINATIONS Presened by CORAL HOSPITALITY I s Business asunusual I s all abou keeping ha compeiive edge. When you ravel for business, he independenlyowned and operaed desinaions under Coral managemen
More informationDIN, EN, ASTM. Металлопрокат и трубы по стандартам. Поставляем металлопрокат по стандарту ASME 16.48
Металлопрокат и трубы по стандартам DIN, EN, STM Поставляем металлопрокат по стандарту SME 16.48 Для заказа металлопроката или получения консультации обращайтесь по следующим контактам: Россия: +7 (495)
More informationDRINKING WATER PIPE SYSTEM. The blue line
DRINKING WATER PIPE SYSTEM The blue line Hanbook 2014 Inex The following coonly use abbreviaions are foun in his caalogue. Abbreviaion Descripion Uni A Crosssecional area 2 Ousie iameer of pipe i Insie
More informationA quantitative software testing method for hardware and software integrated systems in safety critical applications
A quantitative software testing method for hardware and software integrated systems in safety critical applications Hai ang a, Lixuan Lu* a a University of Ontario Institute of echnology, Oshawa, ON, Canada
More informationUNIVERSITY OF CALIFORNIA Economics 134 DEPARTMENT OF ECONOMICS Spring 2018 Professor David Romer
UNIVERSITY OF CALIFORNIA Economics 134 DEPARTMENT OF ECONOMICS Spring 2018 Professor David Romer LECTURE 2 OVERVIEW OF THE GREAT DEPRESSION January 22, 2018 I. THE 1920S A. GDP growth and inflation B.
More informationINSTALLATION AND OPERATION MANUAL
EUROPEN USERS 400V 0Hz SUPPLY DETILS RE IN CLUDED WITH ELECTRICL CONTROL BOX. DISREGRD SUPPLY WIRING DETILS IN THIS MNUL IMPORTNT SFETY INSTRUCTIONS SVE THESE INSTRUCTIONS PLESE RED THE ENTIRE CONTENTS
More informationOVERALL EVENT SPONSORS RACE SPONSORS SUPPORTING SPONSORS RETAIL PARTNER. Balmoral Road Races Ltd
OVERALL EVENT SPONSORS RACE SPONSORS SUPPORTING SPONSORS Balmoral Road Races Ld RETAIL PARTNER Board of Direcors: James Knowles (Chair) I Richard Gledson. RunBalmoral Managemen Team: Alasair Simpson I
More informationALT E R N AT I VE 1 C O R R I DO R  SHEET 2
xxvii Appendix C Pond Sree Revializaion Bus dolupa rae exceprovid u la apiduci officiandae ommo eium quae dolupain odi re corae si re, simusamus au dis au quian ven in conserae. Ima sediaem quam verem.
More informationDP2001/06. How much do import price shocks matter for consumer prices? Tim Hampton. November JEL classification: C22, E31
DP00/06 How uh do ior rie shoks aer for onsuer ries? Ti Haon Noveber 00 JEL lassifiaion: C, E3 Disussion Paer Series DP00/06 How uh do ior rie shoks aer for onsuer ries? Absra New Zealand and Ausralia
More informationTHE NINTH INFANTRY DIVISION ASSOCIATION
THE.'2 Gregory Ave., W...wk.n. N.J. 07087 THE NINTH INFANTRY DIVISION ASSOCIATION AriAinn Dues; $5.00 per year $ 1.50 wiii be earmarked o pay for he Oeofoil Voiume XXXIV NUMBER: MAYJUNE 1979 Commemoraion
More informationShelters. LeanTo Shelte. AFrame Shelte. The setup for a LeanTo shelter is very similar to an AFrame shelter.
Sheler plac/ fer o a pece of re ly al rm no r oppoed A Shele p wh rope. A ng r g n ee maeral. canva h e o of naral ad m a h y o a bv r AFrame Shele The mple heler he AFrame heler. We j e a rope beween
More informationArchitectural PORTFOLIO CALL FOR ENTRIES SCHOOLDESIGNS.COM. Presented by. See back page for photo credits.
rchiecural PORTFOLIO T H I R T Y  F I F T H N N U L 2017 CLL FOR ENTRIES See back page for phoo credis. Presened by SCHOOLDESIGNS.COM Receive naional acclaim for YOUR EDUCTION DESIGN PROJECTS WWW.SUMG.COM
More informationGame Theory (MBA 217) Final Paper. Chow Heavy Industries Ty Chow Kenny Miller Simiso Nzima Scott Winder
Game Theory (MBA 217) Final Paper Chow Heavy Industries Ty Chow Kenny Miller Simiso Nzima Scott Winder Introduction The end of a basketball game is when legends are made or hearts are broken. It is what
More informationWall Lot. Priority. Public Parking. Center. Vallejo St. P ac if ic Walton Square. Ja ck so n. Chinatown. B a tte r. M o n tg o K e ar n y G ra n t A
F ilb m b G re e n S ve Vallejo WORKSHOP #1 OUTOES Exploraorium Prioriy uodesk roadcas ener Prioriy roadw Fall 2014 Workshops Summy Law Offices ay The Waefron Resauran & afe oquea Golden Gaeway ommons
More informationbackstroke Published in associa on with swimteach.com
backstroke Backstroke Technique Made Easy backstroke swimming stroke broken down and explained Including 2 bonus exercises Published in associa on with swimteach.com Legal No ce Copyright 2010, swimteach.com
More informationMillSlicer PMC Phalaborwa AG Mill Ini4al Installa4on Trends and Results
MillSlicer PMC Phalaborwa AG Mill Ini4al Installa4on Trends and Results The following items obtained from the first couple days of system installaion are presented in the next several slides: I. PMC Single
More informationIntroduction to Pattern Recognition
Introduction to Pattern Recognition Jason Corso SUNY at Buffalo 12 January 2009 J. Corso (SUNY at Buffalo) Introduction to Pattern Recognition 12 January 2009 1 / 28 Pattern Recognition By Example Example:
More informationLean Against Bubbles versus Clean Up After. Bubbles Collapse in a RationalBubble Model
Lean Against Bubbles versus Clean Up After Bubbles Collapse in a RationalBubble Model Tomohiro Hirano y Jun Aoyagi Masaru Inaba First Version, April 2013 This Version, April 2015 Very Preliminary Abstract
More information(a) Advertised Jackpot Prize The estimated annuitized Jackpot Prize amount as determined by the Mega
53ER1770 MEGA MILLIONS. (1) Definitions. The following words and terms, when used in this rule, have the following meanings, unless the context clearly indicates otherwise: (a) Advertised Jackpot Prize
More informationPowerlaw distribution in Japanese racetrack betting
Powerlaw distribution in Japanese racetrack betting Takashi Ichinomiya Nonlinear Studies and Computation, Research Institute for Electronic Science, Hokkaido University, Sapporo 0600812, Japan. Abstract
More informationA Critical Analysis of the Technical Assumptions of the Standard Micro Portfolio Approach to Sovereign Debt Management
Please ce hs paper as: Blommesen, H. J. and A. Hubg (2012), A Crcal Analyss of he echncal Assumpons of he Sandard Mcro Porfolo Approach o Soveregn Deb Managemen, OECD Workng Papers on Soveregn Borrowng
More information