3 edition of **Solving nonlinear stochastic growth models** found in the catalog.

Solving nonlinear stochastic growth models

John B. Taylor

- 87 Want to read
- 15 Currently reading

Published
**1989** by National Bureau of Economic Research in Cambridge, MA .

Written in English

- Stochastic processes.,
- Rational expectations (Economic theory),
- Time and economic reactions.

**Edition Notes**

Statement | John B. Taylor, Harald Uhlig. |

Series | NBER working paper series -- working paper no. 3117, Working paper series (National Bureau of Economic Research) -- working paper no. 3117. |

Contributions | Uhlig, Harald. |

The Physical Object | |
---|---|

Pagination | 22 p. : |

Number of Pages | 22 |

ID Numbers | |

Open Library | OL22437652M |

Numerical solution of nonlinear stochastic integral equation by stochastic operational matrix based on Bernstein polynomials M Asgari, E Hashemizadeh, M Khodabin, K Maleknejad Bull. Math. Soc. Sci. Math. Roumanie 57 (), , Recursive utility models of the type suggested by ref. 1 and featured in the asset-pricing literature by ref. 2 and others represent preferences as the solution to a nonlinear forward-looking difference equation with a terminal condition. Such preferences are used in economic dynamics because seemingly simple parametric versions provide a convenient device to change risk aversion while.

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Solving Nonlinear Stochastic Growth Models: A Comparison of Alternative Solution Methods John B. Taylor, Harald Uhlig. NBER Working Paper No. (Also Reprint No. r) Issued in September NBER Program(s):Economic Fluctuations and GrowthCited by: Solving Nonlinear Stochastic Growth Models: A Comparison of Alternative Solution Methods John B.

Taylor Department of Economics, Stanford University, Stanford, CA 0 Harald Uhlig Department of Economics, University of Minnesota, Minneapolis, MN The purpose of this article is to report on a comparison of several alternative.

Solving Nonlinear Stochastic Growth Models: A Comparison of Alternative Solution Methods. February ; Journal of Business and Economic Statistics 8(1); DOI: / This paper presents an algorithm for solving nonlinear dynamic stochastic models that computes value function by simulations.

We argue that the proposed algorithm can be a useful alternative to the existing methods in some Consider a version of the two-sector neoclassical growth model with four types of exogenous shocks. Solving Nonlinear Stochastic Growth Models: an Algorithm Computing Value Function by Simulations.

Maliar, L. and S. Maliar Economic Letters – 87 () – Keywords: Nonlinear stochastic models,Value function,Parameterized expectations,Monte Carlo simulations,Numerical Methods. As a comparison, we also apply the algorithm for solving the one-sector neoclassical model where there are shocks only to technology.

Table 1 provides the simulation results under three values of simulation length, T∈{,10 }.Observe that the expense for the two-sector model is about three times as high as that for the one-sector model.

This article presents the stochastic growth model. The stochastic growth model is a stochastic version of the neoclassical growth model with microfoundations,1 and provides the backbone of a lot of macroeconomic models that are used in modern macroeconomic research.

The most popular way to solve the stochastic growth model, is to linearize the. Stochastic numerical approach for solving second order nonlinear singular functional differential equation. some of them are population growth models, Cohesive GA-IPA strength is used to find the design variable of the networks for solving the nonlinear second order singular DDEs.

The purpose of this article is to report on a comparison of several alternative numerical solution techniques for nonlinear rational-expectations models. The comparison was made by asking individual researchers to apply their different solution techniques to a simple representative-agent, optimal, stochastic growth model.

Decision rules as well as simulated time series are compared. The model presented in these notes is the main workhorse for the study of business cycles.

Matlab codes for solving and simulating this model are available on the course web page. 2 Stochastic NGM Just as with the deterministic NGM, we can prove that stochastic NGM is Pareto e¢ cient. 4 Non-stochastic growth model In the non-stochastic growth model, the problem of the representative agent is to allocate resources between consumption and investment in capital, as in the continuous time Ramsey model.

Capital is completely malleable, being able to be transformed into consumption at a rate of one-to-one. Since the model is. Solving the Stochastic Growth Model by Policy-Function Iteration.

Journal of Business & Economic Statistics: Vol. 8, No. 1, pp. Nonlinear Stochastic Operator Equations deals with realistic solutions of the nonlinear stochastic equations arising from the modeling of frontier problems in many fields of science.

This book also discusses a wide class of equations to provide modeling of problems concerning physics, engineering, operations research, systems analysis, biology. "Solving Nonlinear Stochastic Growth Models: A Comparison of Alternative Solution Methods," NBER Working PapersNational Bureau of Economic Research, Inc.

Judd, Kenneth L., " Projection methods for solving aggregate growth models," Journal of Economic Theory, Elsevier, vol. 58(2), pagesDecember. In this paper, we introduce a stochastic population model in a closed system. This model is a nonlinear stochastic integro-differential equation.

At first, we solve this problem via the stochastic θ-method. Then we solve it by using the Bernstein polynomials and collocation method. This method reduces integro-differential equation to a system of nonlinear algebraic equations. The stochastic growth model, which is a version of the neoclassical growth model with microfoundations, provides the basis for many macroeconomic models which are used in contemporary macroeconomic research.

This article, available for free download, is intended for readers with advanced knowledge of macroeconomics and related equations. Taylor, J, Uhlig, H. (): Solving Nonlinear Stochastic Growth Models: A Comparison of Alternative Solution Methods. Journal of Business and Economics Statistics, Vol., 8 No.

1 CrossRef Google Scholar. this connection explicit, we introduce rst the stochastic neoclassical growth model, the ancestor of all modern DSGE models, and then show how we can derive a functional equation problem that solves for the equilibrium dynamics of the model in terms of either a value function, an Euler equation, or a conditional expectation.

stochastic models and also new models are provided along with a related bibliogra-phy. Stochastic models included are the Gompertz, Linear models with multiplicative noise term, the Revised Exponential and the Generalized Logistic.

Emphasis is given in the presentation of stochastic models with a sigmoid form for the mean value. Book. Mar ; Tsutomu Harada Solving Nonlinear Stochastic Growth Models: A Comparison of Alternative Solution Methods This paper argues that a clear understanding of the stochastic.

Stochastic Growth Models Stochastic Growth Models Stochastic Growth Models Brock and Mirman (): generalization of neoclassical growth and starting point of Real Business Cycle models Baseline neoclassical growth: complete markets, households and –rms can.

Abstract: MATLAB program solving one- and two-sector neoclassical stochastic growth models by computing value function by simulation as described in the article "Solving Nonlinear Dynamic Stochastic Models: An Algorithm Computing Value Function by Simulations" by Lilia Maliar and Serguei Maliar, Economic Lett pp, CiteSeerX - Document Details (Isaac Councill, Lee Giles, Pradeep Teregowda): Associate Editor's Note: The following 11 articles summarize the efforts to date of a group that has been working on the new and exciting topic of solution strategies for nonlinear rational-expectations models.

The members of the group wish to thank the National Bureau of Economic Research, the Institute for Empirical. Solving the Stochastic Growth Model by Linear-Quadratic Approximation and by Value-Function Iteration.

Journal of Business & Economic Statistics: Vol. 8, No. 1, pp. the maximum proﬂt $of the stochastic decision program (). The diﬁerence $ 1, is called the Value of the Stochastic Solu-tion (VSS) re°ecting the possible gain by solving the full stochastic model.

Two-stage stochastic program with recourse For a stochastic decision program, we denote by x 2 lRn1;x ‚ 0; the. By David Edward Robinson, Published on 05/01/ Recommended Citation. Robinson, David Edward, "Solving Nonlinear Stochastic Growth Models: The Projection and the Finite Element Methods of.

Sims, Christopher. “Solving the Stochastic Growth Model by Backsolving with a Particular Nonlinear Form for the Decision Rule.” Journal of Business and Economic Statistics 8.

The models that you have seen thus far are deterministic models. For any time t, there is a unique solution X(t). On the other hand, stochastic models result in a distribution of possible values X(t) at a time t. To understand the properties of stochastic models, we need to use the language of probability and random variables.

The Basic. This article describes three approximation methods I used to solve the growth model (Model 1) studied by the National Bureau of Economic Research's nonlinear rational-expectations-modeling group project, the results of which were summarized by Taylor and Uhlig ().

The methods involve computing exact solutions to models that approximate Model 1 in different ways. Motivation: Solow’s growth model Most modern dynamic models of macroeconomics build on the framework described in Solow’s () paper.1 To motivate what is to follow, we start with a brief description of the Solow model.

This model was set up to study a closed economy, and we will assume that there is a constant population. The model. Stochastic growth models. In this section, we describe several classical numerical stochastic growth models to show that they can be considered as extensions of above presented pseudo-random number generators and described in terms of nonlinear dynamic system composed of.

With J.T. Cox, Nonlinear voter models. Pages in Random Walks, Brownian Motion, and Interacting Particle Systems.() Edited by R. Durrett and H. Kesten. Birkhauser, Boston Stochastic models of growth and competition.

Pages in Proceedings of the International Congress of Math. Kyoto, Springer-Verlag, New York Stochastic growth model files as solved with Dynare: stochasticgrowth_stochasticgrowth _stochasticgrowth _stochasticgrowth _ Download Dynare programs and documentation files from here ; background reading: chapters and 7 of the Dynare User Guide, Dynare manual, Dynare tutorial.

A stochastic differential equation (SDE) is a differential equation in which one or more of the terms is a stochastic process, resulting in a solution which is also a stochastic are used to model various phenomena such as unstable stock prices or physical systems subject to thermal lly, SDEs contain a variable which represents random white noise calculated as.

In this paper, the stochastic growth logistic model with aftereffect for the cell growth of C. acetobutylicum P and Luedeking-Piret equations for solvent production in batch fermentation system is introduced.

The parameters values of the mathematical models are estimated via Levenberg-Marquardt optimization method of non. gradient-descent and genetic algorithm methods for solving these models of parameterized expectations.

Parameterized expectation methods, developed by Marcet () and Den Haan and Marcet (, ), work on the Euler equation that characterizes the solution to the stochastic growth model.

This approach involves approximation of the conditional. Solving stochastic diﬀerential equations Anders Muszta J Consider a stochastic diﬀerential equation (SDE) dX t = a(t,X t)dt+b(t,X t)dB t; X 0 = x 0.

(1) If we are interested in ﬁnding the strong solution to this equation then we are searching for a function f: [0,∞) × R → R such that X t = f(t,B t). This is so because. “Parameterized Expectations Algorithm: How to Solve for Labor Easily”, Computational Econom MATLAB code for the article by Lilia Maliar and Serguei Maliar, ().

“Solving Nonlinear Stochastic Growth Models: an Algorithm Computing Value Function by. Generally speaking, this two function are usually nonlinear, and very di cult to solve.

We may need to use some methods to approximate these two functions. Three widely used methods: Use a Simple stochastic growth model as the toy model to show how to implement these methods in Matlab or Dynare.

Jun YU (HKUST)AER April 6, 7. An inventory problem in which the stochastic demand rate in each period is considered. A model is presented to compute optimal order quantities and optimal delivery points in the planning period.

This model can also account for any anticipated price change that may occur from time to time. In addition the model can be used to compute volume discounts in accordance to the size of the order. The book covers basic theory as well as computational and analytical techniques to solve physical, biological, and financial problems.

It first presents classical concrete problems before proceeding to a unified theory of stochastic evolution equations and describing applications, such as turbulence in fluid dynamics, a spatial population.This new option allows modeling and optimization for models with uncertain elements via multistage stochastic linear, nonlinear and integer stochastic programming (SP).

Benders decomposition is used for solving large linear SP models. Deterministic equivalent method is used for solving nonlinear and integer SP models.In mathematics, the Kardar–Parisi–Zhang (KPZ) equation is a non-linear stochastic partial differential equation, introduced by Mehran Kardar, Giorgio Parisi, and Yi-Cheng Zhang in It describes the temporal change of a height field (→,) with spatial coordinate → and time coordinate: ∂ (→,) ∂ = ∇ + (∇) + (→,), Here (→,) is white Gaussian noise with average.