[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-639000-105":59,"doc-detail-639000-en":130},{"code":4,"msg":5,"data":6},0,"success",[7,13,18,23,28,33,38,43,48,51,55],{"id":8,"doc_module":4,"doc_module_name":9,"category_name":10,"show_sort_weight":11,"slug":12},1,"Document","Story & Novel",90,"story-novel",{"id":14,"doc_module":4,"doc_module_name":9,"category_name":15,"show_sort_weight":16,"slug":17},2,"Literature",80,"literature",{"id":19,"doc_module":4,"doc_module_name":9,"category_name":20,"show_sort_weight":21,"slug":22},4,"Exam",70,"exam",{"id":24,"doc_module":4,"doc_module_name":9,"category_name":25,"show_sort_weight":26,"slug":27},5,"Comic",60,"comic",{"id":29,"doc_module":4,"doc_module_name":9,"category_name":30,"show_sort_weight":31,"slug":32},6,"Technology",50,"technology",{"id":34,"doc_module":4,"doc_module_name":9,"category_name":35,"show_sort_weight":36,"slug":37},7,"Healthcare",40,"healthcare",{"id":39,"doc_module":4,"doc_module_name":9,"category_name":40,"show_sort_weight":41,"slug":42},8,"Research & Report",30,"research-report",{"id":44,"doc_module":4,"doc_module_name":9,"category_name":45,"show_sort_weight":46,"slug":47},9,"Religion & Spirituality",20,"religion-spirituality",{"id":46,"doc_module":4,"doc_module_name":9,"category_name":49,"show_sort_weight":46,"slug":50},"World Cup","world-cup",{"id":52,"doc_module":4,"doc_module_name":9,"category_name":53,"show_sort_weight":52,"slug":54},10,"Lifestyle","lifestyle",{"id":56,"doc_module":4,"doc_module_name":9,"category_name":57,"show_sort_weight":24,"slug":58},19,"General","general",{"code":4,"msg":60,"data":61},"ok",{"site_id":62,"language":63,"slug":64,"title":65,"keywords":66,"description":67,"schema_data":68,"social_meta":123,"head_meta":125,"extra_data":127,"updated_unix":129},105,"en","collapsing-exchange-rate-regimes-paper","COLLAPSING EXCHANGE-RATE REGIMES - Paper","","Constructs two linear examples to analyze the collapse time of a fixed exchange-rate regime. The first is a continuous-time, perfect-foresight model that delivers an exact collapse time and reserve tracking. The second is a discrete-time, stochastic model with random collapse timing, generating an endogenous probability distribution over collapse time and producing a forward discount of the exchange rate even when the nominal exchange rate stays fixed. The framework supports timing analysis under fundamentals and speculative behavior.",{"@graph":69,"@context":122},[70,84,105],{"@type":71,"itemListElement":72},"BreadcrumbList",[73,77,79,82],{"item":74,"name":75,"@type":76,"position":8},"https://docshare.wps.com","Home","ListItem",{"item":78,"name":9,"@type":76,"position":14},"https://docshare.wps.com/document/",{"item":80,"name":40,"@type":76,"position":81},"https://docshare.wps.com/document/research-report/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/collapsing-exchange-rate-regimes-paper/639000/",{"url":83,"name":65,"@type":85,"image":86,"author":91,"headline":65,"publisher":94,"fileFormat":97,"inLanguage":63,"description":67,"dateModified":98,"datePublished":99,"encodingFormat":97,"isAccessibleForFree":100,"interactionStatistic":101},"DigitalDocument",{"url":87,"@type":88,"width":89,"height":90},"https://docshare.wps.com/thumbnails/collapsing-exchange-rate-regimes-paper/639000.png","ImageObject",300,407,{"name":92,"@type":93},"dawugda","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-28","2026-10-22",true,{"@type":102,"interactionType":103,"userInteractionCount":8},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"What are the two models used to study a fixed exchange-rate regime collapse?","Question",{"text":112,"@type":113},"One is a continuous-time, perfect-foresight linear model that allows exact collapse-time calculation. The other is a discrete-time stochastic model that generates an endogenous probability distribution over collapse timing.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"How does the perfect-foresight model determine collapse time?",{"text":117,"@type":113},"It uses a “shadow floating exchange rate” concept to connect the fixed-rate regime to the post-collapse floating regime, enabling explicit tracking of reserves until they are exhausted.",{"name":119,"@type":110,"acceptedAnswer":120},"Why can a forward discount arise in the stochastic model even if the exchange rate remains fixed?",{"text":121,"@type":113},"With a random collapse time, agents’ behavior generates an instantaneous forward discount on a weak currency despite the exchange rate staying fixed in the certainty-equivalent sense.","https://schema.org",{"og:url":83,"og:type":124,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":126,"canonical":83},"index,follow",{"doc_id":128,"site_id":62},639000,1792701057,{"code":4,"msg":5,"data":131},{"doc_id":128,"user_id":132,"nickname":92,"user_avatar":133,"doc_module":4,"category_id":39,"category_name":40,"doc_title":65,"doc_description":67,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":8,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":139,"language":140,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":141,"faqs":142,"seo_title":143,"seo_description":67,"update_tm":129,"read_time":144},3985747870947,"https://ap-avatar.wpscdn.com/davatar_3d24733baf745e90a7e4bdd5f77d97b2","# COLLAPSING EXCHANGE-RATE REGIMESSome linear examples*\n\nRobert P.FLOOD  \nNorthwestern University,Evanston IL60201,U.S.A.  \nPeter M.GARBER*  \nUniversity of Rochester,Rochester,NY 14627,U.S.A.Received May 1982,revised version received July 1983  \nWe construct a pair of linear examples to study the collapse time of a fixed exchange-rateregime.The first example is a perfect-foresight,continuous-time model which allows calculationof the exact collapse time and the tracking of reserves.The second example is a discrete time,stochastic model which yields an endogenous probability distribution over the collapse time andproduces a forward discount of the exchange rate.  \n## 1.Introduction\n\nIn this paper we construct a pair of simple linear examples to study thecollapse of a fixed exchange-rate regime.Introduced by Salant andHenderson(1978),the concepts we employ were extended to the foreignexchange market by Krugman(1979)and to gold standards by Flood andGarber(1984).  \nOur first example,a continuous-time,perfect-foresight model,allowsexplicit calculation of the collapse time while preserving essential elements ofKrugman's non-linear analysis.However,to perform the analysis we developthe concept of a 'shadow floating exchange rate'which allows easy extensionsto stochastic environments.We examine the timing of regime collapses eitherbased entirely on market fundamentals or based in part on arbitraryspeculative behavior.  \nA discrete time model,our second example,contains stochastic marketfundamentals which force the regime collapse.Hence,agents lack perfectforesight about the collapse time.The stochastic framework removes anunsatisfactory aspect of the perfect foresight example:under perfect foresight,a fixed exchange rate regime can collapse without ever producing a forward  \n*We have received financial support for this research from NSF Grant SES-7926807.  \ndiscount on the collapsing currency.¹In a stochastic model with a randomcollapse time,agents'behavior will produce a forward discount on a weakcurrency even when the exchange rate remains fixed.²  \nIn section 2 we develop the continuous-time,perfect-foresight example;insection 3 we develop the discrete-time,stochastic model.Section 4 containssome concluding remarks.  \n## 2.The continuous-time model with perfect foresight\n\nOur first examplc cmploys a small country modcl with purchasing powerparity.We assume that agents have perfect foresight and that the assetsavailable to domestic residents are domestic money,domestic bonds,foreignmoney,and foreign bonds.The domestic government holds a stock of foreigncurrency for use in fixing the exchange rate.Domestic money and domesticand foreign bonds dominate foreign money which yields no monetaryservices to domestic residents;therefore,private domestic residents will holdno foreign money.Domestic and foreign bonds are perfect substitutes.  \nWe build the model around five equations:  \nM(t)/P(t)=ao-a₁i(t),  a₁>0,  \n(1)  \nM(t)=R(t)+D(t),(2)  \nD(t)=μ,   μ>0,(3)  \nP(t)=P*(t)S(t),  \n(4)  \ni(t)=i*(t)+[S(t)/S(t)],(5)  \nwhere M(t),P(t),and i(t)are the domestic money stock,price level,andinterest rate,respectively.R(t)and D(t)represent the domestic governmentbook value of foreign money holdings and domestic credit,respectively.S(t)is the spot exchangc rate,i.e.the domestic money price of foreign money.Anasterisk(*)attached to a variable indicates 'foreign’,and a dot over avariable()indicates the time derivative.  \nEq.(1)reflects a money market equilibrium condition,the right-hand siderepresenting the demand for real balances.³Eq.(2)states that the money  \n'We are referring to the instantaneous forward discount,as in Krugman(1979).For longermaturities of forward contracts,the discount may become positive,even in the certainty case.  \n²We employ a discrete-time model purely as an analytical convenience.Our results can be  \nduplicated for some continuous-time processes.  \n³We interpret eq.(1)as the linear terms of a Taylor series expansion of some non-li","cbCaikQyfZf3AWLX","https://ap.wps.com/l/cbCaikQyfZf3AWLX","pdf",643078,13,"English","# 1. Introduction\n# 2. The continuous-time model with perfect foresight","[{\"question\":\"What are the two models used to study a fixed exchange-rate regime collapse?\",\"answer\":\"One is a continuous-time, perfect-foresight linear model that allows exact collapse-time calculation. The other is a discrete-time stochastic model that generates an endogenous probability distribution over collapse timing.\"},{\"question\":\"How does the perfect-foresight model determine collapse time?\",\"answer\":\"It uses a “shadow floating exchange rate” concept to connect the fixed-rate regime to the post-collapse floating regime, enabling explicit tracking of reserves until they are exhausted.\"},{\"question\":\"Why can a forward discount arise in the stochastic model even if the exchange rate remains fixed?\",\"answer\":\"With a random collapse time, agents’ behavior generates an instantaneous forward discount on a weak currency despite the exchange rate staying fixed in the certainty-equivalent sense.\"}]","COLLAPSING EXCHANGE-RATE REGIMES - Paper | PDF",33]