Documentation: various LaTeX modernizations
- Use UTF8-encoding - Remove useless options and packages - Use doi where possiblemr#1894
Johannes Pfeifer
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c00307c8cc
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3ba57f497f
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295C1FE89E17EB3C
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@ -21,7 +21,7 @@
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at: \url{https://www.gnu.org/licenses/fdl.txt}
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\newline
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\indent Many thanks to Christopher Sims for providing his BVAR
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MATLAB\textregistered~routines, to St\'ephane Adjemian and Michel Juillard
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MATLAB\textsuperscript{\textregistered}~routines, to St\'ephane Adjemian and Michel Juillard
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for their helpful support, and to Marek Jaroci\'nski for reporting a bug.
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}}
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163
doc/dr.bib
163
doc/dr.bib
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@ -1,81 +1,73 @@
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% Encoding: UTF-8
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@techreport{adjemian/al:2011,
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author = {Adjemian, St\'ephane and Bastani, Houtan and Juillard, Michel and Mihoubi, Ferhat and Perendia, George and Ratto, Marco and Villemot, S\'ebastien},
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title = {Dynare: Reference Manual, Version 4},
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institution = {CEPREMAP},
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year = {2011},
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type = {Dynare Working Papers},
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number = {1}
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@TechReport{adjemian/al:2011,
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author = {Adjemian, St\'ephane and Bastani, Houtan and Juillard, Michel and Karam\'e, Fr\'ederic and Maih, Junior and Mihoubi, Ferhat and Mutschler, Willi and Perendia, George and Pfeifer, Johannes and Ratto, Marco and Villemot, S\'ebastien},
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institution = {CEPREMAP},
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title = {Dynare: Reference Manual Version 4},
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year = {2011},
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number = {1},
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type = {Dynare Working Papers},
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}
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@article{blanchard/kahn:1980,
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author = {Blanchard, Olivier Jean and Kahn, Charles M.},
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title = {The Solution of Linear Difference Models under Rational Expectations},
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journal = {Econometrica},
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year = 1980,
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volume = {48},
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number = {5},
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pages = {1305-11},
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month = {July},
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keywords = { Macromodels Yield curve Persistence},
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abstract = {Many have questioned the empirical relevance of the Calvo-Yun model. This paper adds a term structure to three widely studied macroeconomic models (Calvo-Yun, hybrid and Svensson). We back out from observations on the yield curve the underlying macroeconomic model that most closely matches the level, slope and curvature of the yield curve. With each model we trace the response of the yield curve to macroeconomic shocks. We assess the fit of each model against the observed behaviour of interest rates and find limited support for the Calvo-Yun model in terms of fit with the observed yield curve, we find some support for the hybrid model but the Svensson model performs best.},
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url = {http://ideas.repec.org/a/ecm/emetrp/v48y1980i5p1305-11.html}
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@Article{blanchard/kahn:1980,
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author = {Blanchard, Olivier Jean and Kahn, Charles M.},
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journal = {Econometrica},
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title = {The Solution of Linear Difference Models under Rational Expectations},
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year = {1980},
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month = {7},
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number = {5},
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pages = {1305-11},
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volume = {48},
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abstract = {Many have questioned the empirical relevance of the Calvo-Yun model. This paper adds a term structure to three widely studied macroeconomic models (Calvo-Yun, hybrid and Svensson). We back out from observations on the yield curve the underlying macroeconomic model that most closely matches the level, slope and curvature of the yield curve. With each model we trace the response of the yield curve to macroeconomic shocks. We assess the fit of each model against the observed behaviour of interest rates and find limited support for the Calvo-Yun model in terms of fit with the observed yield curve, we find some support for the hybrid model but the Svensson model performs best.},
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doi = {10.2307/1912186},
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keywords = {Macromodels Yield curve Persistence},
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}
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@article{klein:2000,
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author = {Klein, Paul},
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title = {Using the generalized Schur form to solve a multivariate linear rational expectations model},
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journal = {Journal of Economic Dynamics and Control},
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year = 2000,
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volume = {24},
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number = {10},
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pages = {1405-1423},
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month = {September},
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keywords = {},
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abstract = {},
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url = {http://ideas.repec.org/a/eee/dyncon/v24y2000i10p1405-1423.html}
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@Article{klein:2000,
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author = {Klein, Paul},
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journal = {Journal of Economic Dynamics and Control},
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title = {Using the generalized {Schur} form to solve a multivariate linear rational expectations model},
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year = {2000},
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month = {September},
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number = {10},
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pages = {1405-1423},
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volume = {24},
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doi = {10.1016/s0165-1889(99)00045-7},
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}
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@article{schmitt-grohe/uribe:2004,
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author = {Schmitt-Groh\'{e}, Stephanie and Ur\'{i}be, Martin},
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title = {Solving dynamic general equilibrium models using a second-order approximation to the policy function},
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journal = {Journal of Economic Dynamics and Control},
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year = 2004,
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volume = {28},
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number = {4},
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pages = {755-775},
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month = {January},
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keywords = {},
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url = {http://ideas.repec.org/a/eee/dyncon/v28y2004i4p755-775.html}
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@Article{schmitt-grohe/uribe:2004,
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author = {Schmitt-Groh\'{e}, Stephanie and Ur\'{i}be, Martin},
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journal = {Journal of Economic Dynamics and Control},
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title = {Solving dynamic general equilibrium models using a second-order approximation to the policy function},
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year = {2004},
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month = {January},
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number = {4},
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pages = {755-775},
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volume = {28},
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doi = {10.1016/s0165-1889(03)00043-5},
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}
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@article{sims:2001,
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author = {Sims, Christopher A},
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title = {Solving Linear Rational Expectations Models},
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journal = {Computational Economics},
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year = 2002,
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volume = {20},
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number = {1-2},
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pages = {1-20},
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month = {October},
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keywords = {},
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abstract = {},
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url = {http://ideas.repec.org/a/kap/compec/v20y2002i1-2p1-20.html}
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@Article{sims:2001,
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author = {Sims, Christopher A},
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journal = {Computational Economics},
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title = {Solving Linear Rational Expectations Models},
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year = {2002},
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month = {October},
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number = {1-2},
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pages = {1-20},
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volume = {20},
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doi = {10.1023/A:1020517101123},
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}
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@incollection{uhlig:1999,
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author = {Uhlig, Harald},
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title = {A toolkit for analysing nonlinear dynamic stochastic models easily},
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booktitle = {Computational Methods for the Study of Dynamic Economics},
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publisher = {Oxford University Press},
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year = {1999},
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editor = {Marimon, Ramon and Scott, Androw},
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pages = {30-61}
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@InCollection{uhlig:1999,
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author = {Uhlig, Harald},
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booktitle = {Computational Methods for the Study of Dynamic Economies},
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publisher = {Oxford University Press},
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address = {Oxford},
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title = {A toolkit for analysing nonlinear dynamic stochastic models easily},
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year = {1999},
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editor = {Marimon, Ramon and Scott, Andrew},
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pages = {30-61},
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}
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@ -86,26 +78,25 @@
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year = {2003}
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}
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@article{collard/juillard:2001:compecon,
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author = {Collard, Fabrice and Juillard, Michel},
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title = {A Higher-Order Taylor Expansion Approach to Simulation of Stochastic Forward-Looking Models with an Application to a Nonlinear Phillips Curve Model},
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journal = {Computational Economics},
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year = {2001},
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volume = {17},
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number = {2-3},
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pages = {125-39},
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month = {June},
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keywords = {},
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url = {http://ideas.repec.org/a/kap/compec/v17y2001i2-3p125-39.html}
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@Article{collard/juillard:2001:compecon,
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author = {Collard, Fabrice and Juillard, Michel},
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journal = {Computational Economics},
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title = {A Higher-Order {Taylor} Expansion Approach to Simulation of Stochastic Forward-Looking Models with an Application to a Nonlinear {Phillips} Curve Model},
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year = {2001},
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month = {6},
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number = {2-3},
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pages = {125-139},
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volume = {17},
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doi = {10.1023/A:1011624124377},
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}
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@book{golub/van-loan:1996,
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author = {Golub, Gene H. and Van Loan, Charles F.},
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title = {Matrix Computations},
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publisher = {The John Hopkins University Press},
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year = {1996},
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edition = {third}
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@Book{golub/van-loan:1996,
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author = {Golub, Gene H. and Van Loan, Charles F.},
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publisher = {The John Hopkins University Press},
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title = {Matrix Computations},
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year = {2013},
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address = {Baltimore},
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edition = {4},
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}
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@Comment{jabref-meta: databaseType:bibtex;}
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@ -3,7 +3,7 @@
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\usepackage{amssymb}
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\usepackage{amsmath}
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\usepackage{hyperref}
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\hypersetup{breaklinks=true,pagecolor=white,colorlinks=true,linkcolor=blue,citecolor=blue,urlcolor=blue}
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\hypersetup{breaklinks=true,colorlinks=true,linkcolor=blue,citecolor=blue,urlcolor=blue}
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\usepackage{natbib}
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\usepackage{fullpage}
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@ -36,7 +36,7 @@
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computing the first order approximated solution of a nonlinear rational
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expectations model. The core of the algorithm is a generalized Schur
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decomposition (also known as the QZ decomposition), as advocated by several
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authors in the litterature. The contribution of the present paper is to focus
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authors in the literature. The contribution of the present paper is to focus
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on implementation details that make the algorithm more generic and more
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efficient, especially for large models.
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@ -4,15 +4,15 @@
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\documentclass[12pt,a4paper]{article}
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\usepackage{amssymb,amsmath}
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\usepackage[dvips]{graphicx}
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\usepackage{natbib}
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\usepackage{psfrag}
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\usepackage{setspace}
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\usepackage{rotating}
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\usepackage{hyperref}
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\hypersetup{breaklinks=true,pagecolor=white,colorlinks=true,linkcolor=blue,citecolor=blue,urlcolor=blue}
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\hypersetup{breaklinks=true,colorlinks=true,linkcolor=blue,citecolor=blue,urlcolor=blue}
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%\singlespacing (interlinea singola)
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%\onehalfspacing (interlinea 1,5)
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%\doublespacing (interlinea doppia)
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\usepackage{doi,natbib}
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%\bibpunct{(}{)}{;}{a}{,}{,}
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@ -1,19 +1,24 @@
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@ARTICLE{Ratto_CompEcon_2008,
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author = {Ratto, M.},
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title = {Analysing DSGE Models with Global Sensitivity Analysis},
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journal = {Computational Economics},
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year = {2008},
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volume = {31},
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pages = {115--139},
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% Encoding: UTF-8
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@Article{Ratto_CompEcon_2008,
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author = {Ratto, M.},
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journal = {Computational Economics},
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title = {Analysing DSGE Models with Global Sensitivity Analysis},
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year = {2008},
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pages = {115--139},
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volume = {31},
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doi = {10.1007/s10614-007-9110-6},
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}
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@ARTICLE{Iskrev2010,
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author = {Nikolay Iskrev},
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title = {Local Identification in {DSGE} Models},
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@Article{Iskrev2010,
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author = {Nikolay Iskrev},
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journal = {Journal of Monetary Economics},
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year = {2010},
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volume = {57},
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pages = {189-202}
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title = {Local Identification in {DSGE} Models},
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year = {2010},
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number = {2},
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pages = {189-202},
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volume = {57},
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doi = {10.1016/j.jmoneco.2009.12.007},
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}
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@UNPUBLISHED{Iskrev2011,
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@ -23,3 +28,5 @@
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note = {mimeo},
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year = {2011}
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}
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@Comment{jabref-meta: databaseType:bibtex;}
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@ -1,23 +1,23 @@
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\documentclass[11pt,a4paper]{article}
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\usepackage{bibmad,graphicx,latexsym,amssymb,times}
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\usepackage[cp850]{inputenc}
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\usepackage{graphicx,latexsym,amssymb,times}
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\usepackage[utf8]{inputenc}
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\begin{document}
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\title{Stochastic simulations with {\sc Dynare}. \\ A practical guide.}
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\author{Fabrice Collard (GREMAQ, University of Toulouse)\\Adapted for Dynare 4.1\\ by Michel Juillard and S\'ebastien Villemot (CEPREMAP)}
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\author{Fabrice Collard (GREMAQ, University of Toulouse)\\Adapted for Dynare 4.x\\ by Michel Juillard and S\'ebastien Villemot (CEPREMAP)}
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\date{First draft: February 2001\hspace{10mm}This draft: December 2009.}
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\maketitle
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This document describes a model involving both endogenous and exogenous state variable. We first describe the theoretical model, before showing how the perturbation method is implemented in {\sc Dynare}.
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\section{A theoretical model}
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We consider an economy that consists of a large number of dynastic households and a large number of firms. Firms are producing a homogeneous final 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 firms. In each and every period three perfectly competitive markets open --- the markets for consumption goods, labor services, and financial capital in the form of firms' shares.
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\section{A theoretical model}
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We consider an economy that consists of a large number of dynastic households and a large number of firms. Firms are producing a homogeneous final 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 firms. In each and every period three perfectly competitive markets open --- the markets for consumption goods, labor services, and financial capital in the form of firms' shares.
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Household preferences are characterized by the lifetime utility function:
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\begin{equation}
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E_t\sum_{\tau=t}^{\infty}{\beta^\star}^{\tau-t} \left(\log(c_t)-\theta\frac{h_t^{1+\psi}}{1+\psi}\right)
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\label{eq:ut}
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\end{equation}
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\noindent where $0<\beta^\star<1$ is a constant discount factor, $c_t$ is consumption in period
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$t$, $h_t$ is the fraction of total available time devoted to productive activity in period $t$, $\theta>0$ and $\psi\geqslant 0$. 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
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$t$, $h_t$ is the fraction of total available time devoted to productive activity in period $t$, $\theta>0$ and $\psi\geqslant 0$. 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
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\begin{equation}
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c_t+i_t=y_t
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\label{eq:bud}
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@ -44,7 +44,7 @@ a_t\\b_t
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\left(
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\begin{array}{cc}
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\rho&\tau\\
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\tau&\rho\\
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\tau&\rho\\
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\end{array}
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\right)\left(
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\begin{array}{c}
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@ -57,7 +57,7 @@ a_{t-1}\\b_{t-1}
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\end{array}
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\right) \label{eq:process}
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\end{equation}
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where $|\rho+\tau|<1$ and $|\rho-\tau|<1 $ for sake of stationarity and
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where $|\rho+\tau|<1$ and $|\rho-\tau|<1 $ for sake of stationarity and
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\begin{eqnarray*}
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E(\varepsilon_t)&=& 0,\\
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E(\nu_t)&=& 0,\\
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@ -65,7 +65,7 @@ E(\varepsilon_t\varepsilon_s)&=&\left\{
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\begin{array}{lcl}
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\sigma^2_\varepsilon & \mbox{ if } & t=s \\
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0 & \mbox{ if } & t\neq s \\
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\end{array}\right. \mbox{, }\\
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\end{array}\right. \mbox{, }\\
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E(\nu_t\nu_s)&=&\left\{
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\begin{array}{lcl}
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\sigma^2_\nu & \mbox{ if } & t=s \\
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@ -75,24 +75,24 @@ E(\varepsilon_t\nu_s)&=&\left\{
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\begin{array}{lcl}
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\varphi\sigma_\varepsilon\sigma_\nu & \mbox{ if } & t=s \\
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0 & \mbox{ if } & t\neq s \\
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\end{array}\right. \mbox{. }
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\end{array}\right. \mbox{. }
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\end{eqnarray*}
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\section{Dynamic Equilibrium}
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The dynamic equilibrium of this economy follows from the first order conditions for optimality:
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The dynamic equilibrium of this economy follows from the first order conditions for optimality:
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\begin{eqnarray*}
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&&c_t \theta h_t^{1+\psi}=(1-\alpha) y_t \\
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&&\beta E_t\left[\left(\frac{\exp(b_t) c_t}{\exp(b_{t+1})c_{t+1}}\right)\left(\exp(b_{t+1})\alpha \frac{y_{t+1}}{k_{t+1}}+1-\delta\right)\right]=1\\
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&&y_t=\exp(a_t) k_t^\alpha h_t^{1-\alpha} \\
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&&k_{t+1}=\exp(b_t)(y_t-c_t)+(1-\delta)k_t \\
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&&a_t=\rho a_{t-1}+\tau b_{t-1}+\varepsilon_t \\
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&&b_t=\tau a_{t-1}+\rho b_{t-1}+\nu_t
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&&b_t=\tau a_{t-1}+\rho b_{t-1}+\nu_t
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\end{eqnarray*}
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\section{The {\sc dynare} code}
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The {\sc dynare} code is straightforward to write, as the equilibrium is written in the natural way. The whole code is reported at the end of the section. Before that we proceed step by step.
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\paragraph{Preamble}
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The preamble consists of the some declarations to setup the endogenous and exogenous variables, the parameters and assign values to these parameters.
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The preamble consists of the some declarations to setup the endogenous and exogenous variables, the parameters and assign values to these parameters.
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\begin{enumerate}
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\item {\tt var y, c, k, h, a, b;} specifies the endogenous variables in the model since we have output ({\tt y}), consumption ({\tt c}), capital ({\tt k}), hours ({\tt h}) and the two shocks ({\tt a, b}).
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\item {\tt varexo e, u;} specifies the exogenous variables in the model --- namely the innovations of the shocks, since we have the innovation of the non--incorporated shock ({\tt e}), and the innovation of the incorporated shock ({\tt u}).
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@ -133,9 +133,9 @@ theta = 2.95;
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\end{enumerate}
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\paragraph{Declaration of the model:}
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This step is done in a straightforward way. It starts with the instruction {\tt model;} and ends with {\tt end;}, in between all equilibrium conditions are written exactly the way we write it ``by hand''. However, there is a simple rule that should be kept in mind when the model is written. Let us consider a variable $x$:
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This step is done in a straightforward way. It starts with the instruction {\tt model;} and ends with {\tt end;}, in between all equilibrium conditions are written exactly the way we write it ``by hand''. However, there is a simple rule that should be kept in mind when the model is written. Let us consider a variable $x$:
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\begin{itemize}
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\item If $x$ is decided in period $t$ then we simply write ${\tt x}$.
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\item If $x$ is decided in period $t$ then we simply write ${\tt x}$.
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\item When the variable is decided in $t-1$, such as the capital stock in our simple model, we write ${\tt x(-1)}$. \item Finally, when a variable is decided in the next period, $t+1$, such as consumption in the Euler equation, we write ${\tt x(+1)}$.
|
||||
\end{itemize}
|
||||
Hence the required code to declare our model in {\sc Dynare} will be:
|
||||
|
|
@ -164,7 +164,7 @@ end;
|
|||
\end{verbatim}
|
||||
so that the level of consumption is actually given by ${\tt exp(c)}$.
|
||||
\paragraph{Solving the model}
|
||||
\begin{enumerate}
|
||||
\begin{enumerate}
|
||||
\item Now we need to provide numerical initial conditions for the computation of the deterministic steady state. This is done with the sequence between {\tt initval;} and {\tt end;}. Each variable, endogenous or exogenous, should be initialized. In our example, we give the exact values of the deterministic equilibrium in absence of shocks. This takes the form
|
||||
\begin{verbatim}
|
||||
initval;
|
||||
|
|
@ -206,12 +206,12 @@ Number of periods on which to compute the IRFs (default = 40)
|
|||
\item {\tt nofunctions}:
|
||||
Doesn't print the coefficients of the approximated solution
|
||||
\item {\tt nomoments}:
|
||||
Doesn't print moments of the endogenous variables
|
||||
Doesn't print moments of the endogenous variables
|
||||
\item {\tt order} = [1,2,3]:
|
||||
Order of Taylor approximation (default = 2)
|
||||
\item {\tt replic} = Integer:
|
||||
Number of simulated series used to compute the IRFs (default = 1, if order = 1, and 50 otherwise)
|
||||
\end{itemize}
|
||||
\end{itemize}
|
||||
|
||||
In our first example, we use simply:
|
||||
\begin{verbatim}
|
||||
|
|
@ -324,8 +324,8 @@ end;
|
|||
|
||||
stoch_simul(periods=2000, drop=200);
|
||||
\end{verbatim}
|
||||
\bibliographystyle{Usmad}
|
||||
\bibliography{/papers/biblio/michel}
|
||||
%\bibliographystyle{Usmad}
|
||||
%\bibliography{/papers/biblio/michel}
|
||||
|
||||
\end{document}
|
||||
|
||||
|
|
|
|||
|
|
@ -1,14 +1,15 @@
|
|||
% ----------------------------------------------------------------
|
||||
% AMS-LaTeX Paper ************************************************
|
||||
% **** -----------------------------------------------------------
|
||||
\documentclass[12pt,a4paper,pdftex,nofootinbib]{article}
|
||||
\usepackage[cp1252]{inputenc}
|
||||
\documentclass[12pt,a4paper,pdftex]{article}
|
||||
\usepackage[margin=2.5cm]{geometry}
|
||||
\usepackage[utf8]{inputenc}
|
||||
\usepackage{amssymb,amsmath}
|
||||
\usepackage[pdftex]{graphicx}
|
||||
\usepackage{graphicx}
|
||||
\usepackage{epstopdf}
|
||||
\usepackage{natbib}
|
||||
\usepackage{verbatim}
|
||||
\usepackage[pdftex]{color}
|
||||
\usepackage{xcolor}
|
||||
\usepackage{psfrag}
|
||||
\usepackage{setspace}
|
||||
\usepackage{rotating}
|
||||
|
|
@ -49,6 +50,15 @@
|
|||
\def \supp{{\rm supp}}
|
||||
\def \var{{\rm var}}
|
||||
|
||||
\usepackage[pdfpagelabels]{hyperref}
|
||||
\hypersetup{
|
||||
pdfproducer = {LaTeX},
|
||||
colorlinks,
|
||||
linkcolor=blue,
|
||||
filecolor=yellow,
|
||||
urlcolor=green,
|
||||
citecolor=green}
|
||||
|
||||
% ----------------------------------------------------------------
|
||||
\begin{document}
|
||||
|
||||
|
|
@ -349,7 +359,7 @@ Finally, the DYNARE command line options are:
|
|||
\item \verb"parallel": trigger the parallel computation using the first cluster specified in config file
|
||||
\item \verb"parallel=<clustername>": trigger the parallel computation, using the given cluster
|
||||
\item \verb"parallel_slave_open_mode": use the leaveSlaveOpen mode in the cluster
|
||||
\item \verb"parallel_test": just test the cluster, don’t actually run the MOD file
|
||||
\item \verb"parallel_test": just test the cluster, don't actually run the MOD file
|
||||
|
||||
\end{itemize}
|
||||
|
||||
|
|
@ -828,7 +838,7 @@ The modified \verb"random_walk_metropolis_hastings.m" is therefore:
|
|||
\noindent\begin{tabular}[b]{| p{\linewidth} |}
|
||||
\hline
|
||||
\begin{verbatim}
|
||||
function random_walk_metropolis_hastings(TargetFun,ProposalFun,…,varargin)
|
||||
function random_walk_metropolis_hastings(TargetFun,ProposalFun,\ldots,varargin)
|
||||
[...]
|
||||
% here we wrap all local variables needed by the <*>_core function
|
||||
localVars = struct('TargetFun', TargetFun, ...
|
||||
|
|
@ -970,11 +980,11 @@ On the other hand, under the parallel implementation, a parallel monitoring plot
|
|||
|
||||
\section{Parallel DYNARE: testing}
|
||||
We checked the new parallel platform for DYNARE performing a number of tests, using different models and computer architectures. We present here all tests performed with Windows XP/MATLAB. However, similar tests were performed successfully under Linux/Ubuntu environment.
|
||||
In the Bayesian estimation of DSGE models with DYNARE, most of the computing time is devoted to the posterior parameter estimation with the Metropolis algorithm. The first and second tests are therefore focused on the parallelization of the Random Walking Metropolis Hastings algorithm (Sections \ref{s:test1}-\ref{s:test2}). In addition, further tests (Sections \ref{s:test3}-\ref{s:test4}) are devoted to test all the parallelized functions in DYNARE. Finally, we compare the two parallel implementations of the Metropolis Hastings algorithms, available in DYNARE: the Independent and the Random Walk (Section \ref{s:test5}).
|
||||
In the Bayesian estimation of DSGE models with DYNARE, most of the computing time is devoted to the posterior parameter estimation with the Metropolis algorithm. The first and second tests are therefore focused on the parallelization of the Random Walking Metropolis Hastings algorithm (Sections \ref{s:test1}-\ref{s:test2}). In addition, further tests (Sections \ref{s:test3}-\ref{s:test4}) are devoted to test all the parallelized functions in DYNARE. %Finally, we compare the two parallel implementations of the Metropolis Hastings algorithms, available in DYNARE: the Independent and the Random Walk (Section \ref{s:test5}).
|
||||
|
||||
\subsection{Test 1.}\label{s:test1}
|
||||
The main goal here was to evaluate the parallel package on a \emph{fixed hardware platform} and using chains of \emph{variable length}. The model used for testing is a modification of \cite{Hradisky_etal_2006}. This is a small scale open economy DSGE model with 6 observed variables, 6 endogenous variables and 19 parameters to be estimated.
|
||||
We estimated the model on a bi-processor machine (Fujitsu Siemens, Celsius R630) powered with an Intel(R) Xeon(TM) CPU 2.80GHz Hyper Treading Technology; first with the original serial Metropolis and subsequently using the parallel solution, to take advantage of the two processors technology. We ran chains of increasing length: 2500, 5000, 10,000, 50,000, 100,000, 250,000, 1,000,000.
|
||||
We estimated the model on a bi-processor machine (Fujitsu Siemens, Celsius R630) powered with an Intel\textsuperscript{\textregistered} Xeon\texttrademark CPU 2.80GHz Hyper Treading Technology; first with the original serial Metropolis and subsequently using the parallel solution, to take advantage of the two processors technology. We ran chains of increasing length: 2500, 5000, 10,000, 50,000, 100,000, 250,000, 1,000,000.
|
||||
|
||||
\begin{figure}[!ht]
|
||||
\begin{centering}
|
||||
|
|
@ -997,8 +1007,8 @@ Overall results are given in Figure \ref{fig:test_time_comp}, showing the comput
|
|||
The scope of the second test was to verify if results were robust over different hardware platforms.
|
||||
We estimated the model with chain lengths of 1,000,000 runs on the following hardware platforms:
|
||||
\begin{itemize}
|
||||
\item Single processor machine: Intel(R) Pentium4(R) CPU 3.40GHz with Hyper Treading Technology (Fujitsu-Siemens Scenic Esprimo);
|
||||
\item Bi-processor machine: two CPU's Intel(R) Xeon(TM) 2.80GHz Hyper Treading Technology (Fujitsu-Siemens, Celsius R630);
|
||||
\item Single processor machine: Intel\textsuperscript{\textregistered} Pentium4\textsuperscript{\textregistered} CPU 3.40GHz with Hyper Treading Technology (Fujitsu-Siemens Scenic Esprimo);
|
||||
\item Bi-processor machine: two CPU's Intel\textsuperscript{\textregistered} Xeon\texttrademark 2.80GHz Hyper Treading Technology (Fujitsu-Siemens, Celsius R630);
|
||||
\item Dual core machine: Intel Centrino T2500 2.00GHz Dual Core (Fujitsu-Siemens, LifeBook S Series).
|
||||
\end{itemize}
|
||||
|
||||
|
|
@ -1042,7 +1052,7 @@ Unplugged network cable. &
|
|||
Given the excellent results reported above, we have parallelized many other DYNARE functions. This implies that parallel instances can be invoked many times during a single DYNARE session. Under the basic parallel toolbox implementation, that we call the `Open/Close' strategy, this implies that MATLAB instances are opened and closed many times by system calls, possibly slowing down the computation, specially for `entry-level' computer resources. As mentioned before, this suggested to implement an alternative strategy for the parallel toolbox, that we call the `Always-Open' strategy, where the slave MATLAB threads, once opened, stay alive and wait for new tasks assigned by the master until the full DYNARE procedure is completed. We show next the tests of these latest implementations.
|
||||
|
||||
\subsection{Test 3}\label{s:test3}
|
||||
In this Section we use the \cite{Lubik2003} model as test function\footnote{The \cite{Lubik2003} model is also selected as the `official' test model for the parallel toolbox in DYNARE.} and a very simple computer class, quite diffuse nowadays: Netbook personal Computer. In particular we used the Dell Mini 10 with Processor Intel® Atom™ Z520 (1,33 GHz, 533 MHz), 1 GB di RAM (with Hyper-trading). First, we tested the computational gain of running a full Bayesian estimation: Metropolis (two parallel chains), MCMC diagnostics, posterior IRF's and filtered, smoothed, forecasts, etc. In other words, we designed DYNARE sessions that invoke all parallelized functions. Results are shown in Figures \ref{fig:netbook_complete_openclose}-\ref{fig:netbook_partial_openclose}.
|
||||
In this Section we use the \cite{Lubik2003} model as test function\footnote{The \cite{Lubik2003} model is also selected as the `official' test model for the parallel toolbox in DYNARE.} and a very simple computer class, quite diffuse nowadays: Netbook personal Computer. In particular we used the Dell Mini 10 with Processor Intel\textsuperscript{\textregistered} Atom\texttrademark Z520 (1,33 GHz, 533 MHz), 1 GB di RAM (with Hyper-trading). First, we tested the computational gain of running a full Bayesian estimation: Metropolis (two parallel chains), MCMC diagnostics, posterior IRF's and filtered, smoothed, forecasts, etc. In other words, we designed DYNARE sessions that invoke all parallelized functions. Results are shown in Figures \ref{fig:netbook_complete_openclose}-\ref{fig:netbook_partial_openclose}.
|
||||
\begin{figure}[p]
|
||||
\begin{centering}
|
||||
% Requires \usepackage{graphicx}
|
||||
|
|
@ -1143,49 +1153,49 @@ The methodology identified for parallelizing MATLAB codes within DYNARE proved t
|
|||
\begin{figure}
|
||||
\begin{centering}
|
||||
% Requires \usepackage{graphicx}
|
||||
\epsfxsize=250pt \epsfbox{RWMH_quest1_PriorsAndPosteriors1Comp.pdf}
|
||||
\epsfxsize=300pt \epsfbox{RWMH_quest1_PriorsAndPosteriors1Comp.pdf}
|
||||
\caption{Prior (grey lines) and posterior density of estimated parameters (black = 100,000 runs; red = 1,000,000 runs) using the RWMH algorithm \citep[QUEST III model][]{Ratto_et_al_EconModel2009}.}\label{fig:quest_RWMH_comp1}
|
||||
\end{centering}
|
||||
\end{figure}
|
||||
\begin{figure}
|
||||
\begin{centering}
|
||||
% Requires \usepackage{graphicx}
|
||||
\epsfxsize=250pt \epsfbox{RWMH_quest1_PriorsAndPosteriors2Comp.pdf}
|
||||
\epsfxsize=300pt \epsfbox{RWMH_quest1_PriorsAndPosteriors2Comp.pdf}
|
||||
\caption{Prior (grey lines) and posterior density of estimated parameters (black = 100,000 runs; red = 1,000,000 runs) using the RWMH algorithm \citep[QUEST III model][]{Ratto_et_al_EconModel2009}.}\label{fig:quest_RWMH_comp2}
|
||||
\end{centering}
|
||||
\end{figure}
|
||||
\begin{figure}
|
||||
\begin{centering}
|
||||
% Requires \usepackage{graphicx}
|
||||
\epsfxsize=250pt \epsfbox{RWMH_quest1_PriorsAndPosteriors3Comp.pdf}
|
||||
\epsfxsize=300pt \epsfbox{RWMH_quest1_PriorsAndPosteriors3Comp.pdf}
|
||||
\caption{Prior (grey lines) and posterior density of estimated parameters (black = 100,000 runs; red = 1,000,000 runs) using the RWMH algorithm \citep[QUEST III model][]{Ratto_et_al_EconModel2009}.}\label{fig:quest_RWMH_comp3}
|
||||
\end{centering}
|
||||
\end{figure}
|
||||
\begin{figure}
|
||||
\begin{centering}
|
||||
% Requires \usepackage{graphicx}
|
||||
\epsfxsize=250pt \epsfbox{RWMH_quest1_PriorsAndPosteriors4Comp.pdf}
|
||||
\epsfxsize=300pt \epsfbox{RWMH_quest1_PriorsAndPosteriors4Comp.pdf}
|
||||
\caption{Prior (grey lines) and posterior density of estimated parameters (black = 100,000 runs; red = 1,000,000 runs) using the RWMH algorithm \citep[QUEST III model][]{Ratto_et_al_EconModel2009}.}\label{fig:quest_RWMH_comp4}
|
||||
\end{centering}
|
||||
\end{figure}
|
||||
\begin{figure}
|
||||
\begin{centering}
|
||||
% Requires \usepackage{graphicx}
|
||||
\epsfxsize=250pt \epsfbox{RWMH_quest1_PriorsAndPosteriors5Comp.pdf}
|
||||
\epsfxsize=300pt \epsfbox{RWMH_quest1_PriorsAndPosteriors5Comp.pdf}
|
||||
\caption{Prior (grey lines) and posterior density of estimated parameters (black = 100,000 runs; red = 1,000,000 runs) using the RWMH algorithm \citep[QUEST III model][]{Ratto_et_al_EconModel2009}.}\label{fig:quest_RWMH_comp5}
|
||||
\end{centering}
|
||||
\end{figure}
|
||||
\begin{figure}
|
||||
\begin{centering}
|
||||
% Requires \usepackage{graphicx}
|
||||
\epsfxsize=250pt \epsfbox{RWMH_quest1_PriorsAndPosteriors6Comp.pdf}
|
||||
\epsfxsize=300pt \epsfbox{RWMH_quest1_PriorsAndPosteriors6Comp.pdf}
|
||||
\caption{Prior (grey lines) and posterior density of estimated parameters (black = 100,000 runs; red = 1,000,000 runs) using the RWMH algorithm \citep[QUEST III model][]{Ratto_et_al_EconModel2009}.}\label{fig:quest_RWMH_comp6}
|
||||
\end{centering}
|
||||
\end{figure}
|
||||
\begin{figure}
|
||||
\begin{centering}
|
||||
% Requires \usepackage{graphicx}
|
||||
\epsfxsize=250pt \epsfbox{RWMH_quest1_PriorsAndPosteriors7Comp.pdf}
|
||||
\epsfxsize=300pt \epsfbox{RWMH_quest1_PriorsAndPosteriors7Comp.pdf}
|
||||
\caption{Prior (grey lines) and posterior density of estimated parameters (black = 100,000 runs; red = 1,000,000 runs) using the RWMH algorithm \citep[QUEST III model][]{Ratto_et_al_EconModel2009}.}\label{fig:quest_RWMH_comp7}
|
||||
\end{centering}
|
||||
\end{figure}
|
||||
|
|
|
|||
Loading…
Reference in New Issue