In the early literature, adaptive learning was applied either to adhoc models or to models with repeated, finite horizons such as the muth model. E44 abstract we develop a variation of the macroeconomic model with banking in gertler and kiyotaki 2011 that allows for liquidity mismatch and bank runs as in diamond and dybvig 1983. Notice that it is a discounted innite horizon utility budget constaints k. Banking, liquidity, and bank runs in an infinite horizon economy by mark gertler and nobuhiro kiyotaki. Determinacy of equilibrium in infinite horizon economics. What is an infinite horizon economy economics job market. In the following i apply this analysis to the setting of monetary policy.
We had previously in our initial development of dynamic optimization using the cal culus of. Difference between model predictive control and rolling horizon optimization. As we have discussed in the solows model, it is the standard bearer, through which other growth models. There is a unitmeasure continuum of workers and another continuum of singlevacancy rms with endogenous measure pinned down by the free entry condition. Behavioral macroeconomics american economic association. I also show how the hamiltonian approach works and why the first order condition are. Romer presents the major theories concerning the central questions of macroeconomics. Economics 5118 advanced macroeconomics ii lakehead university. The ramseycasskoo pmans model differs from the sol owswan model in that the choice of consumption is exp licitly micr ofounded at a point in time and so endogenizes the. The task is to develop a plan that minimizes the expected cost or maximize expected reward over some number of stages.
Infinite horizon model short term fluctuations grasp economics. Advanced macroeconomics i 3 the armington model of international trade. Infinite horizon model short term fluctuations youtube. Economics 200e, professor bergin, spring 1998 adapted from lecture notes of kevin salyer and from stokey, lucas and prescott 1989 outline 1 a typical problem 2 a deterministic finite horizon problem 2. Foundations of neoclassical growth lecture notes 5. As in the twoperiod model, the consumer faces periodbyperiod budget constraints. Infinite horizon optimization and dynamic programming lecture.
For a formal treatment of euler equation approach on the infinite horizon. The ramseycasskoopmans mode l, or ramsey growt h mo del, is a neoclassi cal m odel of economic growth based primarily on the work of fr a nk p. An excellent textbook presentation of this model is given by david romer, advanced macroeconomics, chapters 1 and 2. Focus on progression of international economic relationships 1.
Banking, liquidity, and bank runs in an infinite horizon. The fifth edition of romers advanced macroeconomics continues its tradition as the standard text and the starting point for graduate macroeconomics courses and helps lay the groundwork for students to begin doing research in macroeconomics and monetary economics. Here we begin with the basics of this model, which will already be familiar to many of you. George mccandless spring 2007 1 innitely lived agents innitely lived agents why do we use this kind of model do we believe people plan over innite horizons. In contrast, to the ramseycasskoopmans neoclassical growth model in which individuals are infinitelylived, in the olg model individuals live a finite length of time, long enough to overlap with at least one period of another agents life. Solution method for infinitehorizon maximization problem. Price equilibrium for infinite horizon economic models by david gale 1. Most modern dynamic models of macroeconomics build on the framework described in solows 1956 paper. In the solow growth model, when a household saves in period t, the return to saving in period t 1 comes from rental of capital, at a rate r t 1.
Dynamic means that a model following the dsge approach is expected to be an infinite horizon model it is socially unacceptable to call a stochastic. Longrun models with full employment 2 weeks the solowswan model. Introduction to dynamic programming applied to economics. We present general conditions under which the reducedform model can possess estable sunspot equilibria and apply these conditions. In the subsequent section we present a stylized integrated assessment model and define fh and ih solution approaches. Theorem means that the extension from a long but finite to an infinite horizon. In other macroeconomic topics, such as monetary economics, labor. The model implies that the choice of time period matters e. Lectures notes on deterministic dynamic programming. A model of output and factor prices given factor stocks 1. Ramsey, with significant extensions by david cass and tjalling koopmans. Banking, liquidity, and bank runs in an infinite horizon economy by mark gertler and nobuhiro kiyotaki we develop an infinite horizon macroeconomic model of banking that allows for liquidity mismatch and bank runs. The overlapping generations olg model is one of the dominating frameworks of analysis in the study of macroeconomic dynamics and economic growth. Thats why the chicago school often uses infinite horizon economy models.
Lecture 8, overlapping generations daron acemoglu mit november 22, 2011. Equilibrium growth with infinite horizon households 1. Both rms and workers are riskneutral and discount future at the same rate r0. It is most often used to model the economy of kansas, though it also works for nebraska, north dakota, and parts of texas. Infinite horizon continuous time optimization youtube. I was looking at some lecture notes online and i thought that when they said the solution solved the last equation i have above, they were speaking about the solution of the infinite horizon transversality condition. Basic accountingpe worldge worldgovt interventionin nite horizon international macroeconomics macroeconomics is all about dynamics distinguishes this course from international trade, international relations, etc. Rubinstein 1982, however, shows that the solution has a. Growth model, dynamic optimization in discrete time. We develop an infinite horizon macroeconomic model of banking that allows for liquidity mismatch a. Lectures notes on deterministic dynamic programming craig burnsidey october 2006 1 the neoclassical growth model 1. Differences between rhc and control horizon in mpc.
Setup of the model as in previous models barro and gordon 1983a, b, costs for period t depend on actual and unexpected inflation. Its immediate aim is to give further results on infinite horizon or open ended equi librium models of the type first studied by samuelson c 7 and later. Its an economy where you look at the horizon and its infinite. The solow growth model is a workhorse for many macroeconomic applications, and it is the starting place for the modern theory of economic growth.
Model risk by itself is not a direct source of losses, which is the reason why we do not classify it as a position or inherent risk. Constant growth dividend model with an infinite horizon known as the gordon model after its developer, myron gordon. Therefore, there are no associated termination actions. Lecture notes for macroeconomics i, 2004 yale economic. Optimal control of infinitehorizon growth models fep working. Finite horizon bargaining in nite horizon bargaining. The basic analytical tools for dynamic macroeconomics or recursive macro economics are.
Thetotal population is l t, so each household has l th members. Consider a basic dmp twosided search model in continuous time. This paper examines the stability of sunspot equilibria in onesector rbc models under infinite horizon learning. The most common dynamic optimization problems in economics and. This model was set up to study a closed economy, and we will assume that there is a constant population. This day will concern the neoclassical growth model with an infinite horizon behavior of saving. Macroeconomics i charles engel and menzie chinn spring 2020 lecture 8. Penman columbia business school, columbia university the last 20 years has seen a significant development in valuation models. Production constant returns, decreasing returns, and inada. Estimate is based on the discounted value of an infinite stream of future dividends that grow at a constant rate, g.
The infinite horizon model o the ramsey model the overlapping generations model o the diamond model endogenous growth models. Econ 702 macroeconomics i charles engel and menzie chinn. The rubinstein model if t is in nity, the game is much harder since we cannot use backward induction. The infinite horizon idea, which is meant as a standin for a many, many, many time period framework, is sketched in figure 43. The first chapter discusses economic growth facts pdf and the second chapter discusses the ramseycass koomans infinite horizon model in continuous time as well as the two period overlapping generations model in discrete time pdf. Up to the 1990s, the premier model, in both text books and practice, was the discounted cash flow model. Analysis of saving and investment required reading. Necessity of transversality conditions for infinite horizon problems. Please keep in mind that the readings, exercises, and course packet materials for this years econ 502 may differ in various ways from the materials assigned for econ 502 in previous years, and these differences may be reflected in differences in the form and content of the exams. We then present a new solution method for solving ih problems growth models with or without an environmental sector. In the ramsey model, agents or the dictator choose consumption and investment optimally so as to maximize their individual utility or. Banking, liquidity and bank runs in an infinite horizon economy mark gertler and nobuhiro kiyotaki nber working paper no. An excellent textbook presentation of this model is given by david romer, advanced macroeconomics.
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