Guide pdf 4 Stochastic simulations with DYNARE A practical guide Fabrice Collard GREMAQ University of Toulouse Adapted for Dynare by Michel Juillard and Se ?bastien Villemot CEPREMAP First draft February This draft December This document describes a model

Stochastic simulations with DYNARE A practical guide Fabrice Collard GREMAQ University of Toulouse Adapted for Dynare by Michel Juillard and Se ?bastien Villemot CEPREMAP First draft February This draft December This document describes a model involving both endogenous and exogenous state variable We ?rst describe the theoretical model before showing how the perturbation method is implemented in DYNARE A theoretical model We consider an economy that consists of a large number of dynastic households and a large number of ?rms Firms are producing a homogeneous ?nal product that can be either consumed or invested by means of capital and labor services Firms own their capital stock and hire labor supplied by the households Households own the ?rms In each and every period three perfectly competitive markets open ?? the markets for consumption goods labor services and ?nancial capital in the form of ?rms ? shares Household preferences are characterized by the lifetime utility function ? Et ? ??t log ct ?? ht ? ? t where ? is a constant discount factor ct is consumption in period t ht is the fraction of total available time devoted to productive activity in period t and ? We assume that there exists a central planner that determines hours consumption and capital accumulation maximizing the household ? s utility function subject to the following budget constraint ct it yt where it is investment and yt is output Investment is used to form physical capital which accumulates in the standard form as kt exp bt it ?? ? kt with ? where ? is the constant physical depreciation rate bt is a shock a ?ecting incorporated technological progress which properties will be de ?ned later COutput is produced by means of capital and labor services relying on a constant returns to scale technology represented by the following Cobb ??Douglas production function yt exp at kt h t ?? with at represents a stochastic shock to technology or Solow residual We assume that the shocks to technology are distributed with zero mean but display both persistence across time and correlation in the current period Let us consider the joint process at bt de ?ned as at bt ? ? at ?? bt ?? t t where ? and ? ?? for sake of stationarity and E t E t E t s ? if if t s t s E t s ? if if t s t s E t s ? ? if if t s t s Dynamic Equilibrium The dynamic equilibrium of this economy follows from the ?rst order conditions for optimality ct h t ? ?? yt ?Et exp bt ct exp bt ct yt exp at kt h t ?? exp bt yt kt ?? ? kt exp bt yt ?? ct ?? ? kt at ?at ?? bt ?? t bt at ?? ?bt ?? t The DYNARE code The DYNARE code is straightforward to write as the equilibrium is written in the natural way The whole code

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  • Publié le Jan 12, 2022
  • Catégorie Business / Finance
  • Langue French
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