The paper presents a general solution method for rational expectations models that can be represented by systems of. deterministic first order linear differential equations with constant coefficients. It is the continuous time adaptation of the method of Blanchard and Kahn. To obtain a unique solution there must be as many linearly independent boundary conditions as there are linearly independent state variables. Three slightly different versions of a well-known small open economy macroeconomic model were used to illustrate three fairly general ways of specifying the required boundary conditions. The first represents the standard case in which the number of stable characteristic roots equals the number of predetermined variables. The second represents the case where the number of stable roots exceeds the number of predetermined variables but equals the number of predetermined variables plus the number of "backward-looking" but non-predetermined variables whose discontinuities are linear functions of the discontinuities in the forward-looking variables. The third represents the case where the number of unstable roots is less than the number of forward-looking state variables. For the last case, boundary conditions are suggested that involve linear restrictions on the values of the state variables at a future date. The method of this paper permits the numerical solution of models with large numbers of state variables. Any combination of anticipated or unanticipated, current or future and permanent or transitory shocks can be analyzed.
{"title":"Saddlepoint Problems in Contifuous Time Rational Expectations Models: A General Method and Some Macroeconomic Ehamples","authors":"W. Buiter","doi":"10.2307/1913470","DOIUrl":"https://doi.org/10.2307/1913470","url":null,"abstract":"The paper presents a general solution method for rational expectations models that can be represented by systems of. deterministic first order linear differential equations with constant coefficients. It is the continuous time adaptation of the method of Blanchard and Kahn. To obtain a unique solution there must be as many linearly independent boundary conditions as there are linearly independent state variables. Three slightly different versions of a well-known small open economy macroeconomic model were used to illustrate three fairly general ways of specifying the required boundary conditions. The first represents the standard case in which the number of stable characteristic roots equals the number of predetermined variables. The second represents the case where the number of stable roots exceeds the number of predetermined variables but equals the number of predetermined variables plus the number of \"backward-looking\" but non-predetermined variables whose discontinuities are linear functions of the discontinuities in the forward-looking variables. The third represents the case where the number of unstable roots is less than the number of forward-looking state variables. For the last case, boundary conditions are suggested that involve linear restrictions on the values of the state variables at a future date. The method of this paper permits the numerical solution of models with large numbers of state variables. Any combination of anticipated or unanticipated, current or future and permanent or transitory shocks can be analyzed.","PeriodicalId":11754,"journal":{"name":"ERN: Other Macroeconomics: Aggregative Models (Topic)","volume":"192 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"1984-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79630057","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper is a review of rational expectations models used in macroeconomic research. The purpose is to examine in some detail the differences between the models, the advantages and disadvantages of alternative models the empirical support for the models and their policy implications. The main theme is that there os a wide diversity among rational expectations models in macroeconomics, despite their common expectational assumptions and methods of analysis. Information-based and contast-based theories are reviewed as alternative models of aggregate supply. A brief review od rational expectations models of the demand side is also provided, along with a discusion of some problems with the rational expextations assumption.
{"title":"Rational Expectations Models in Macroeconomics","authors":"John B. Taylor","doi":"10.3386/W1224","DOIUrl":"https://doi.org/10.3386/W1224","url":null,"abstract":"This paper is a review of rational expectations models used in macroeconomic research. The purpose is to examine in some detail the differences between the models, the advantages and disadvantages of alternative models the empirical support for the models and their policy implications. The main theme is that there os a wide diversity among rational expectations models in macroeconomics, despite their common expectational assumptions and methods of analysis. Information-based and contast-based theories are reviewed as alternative models of aggregate supply. A brief review od rational expectations models of the demand side is also provided, along with a discusion of some problems with the rational expextations assumption.","PeriodicalId":11754,"journal":{"name":"ERN: Other Macroeconomics: Aggregative Models (Topic)","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"1983-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88666617","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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