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Kenneth L Judd - One of the best experts on this subject based on the ideXlab platform.
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lower bounds on approximation errors to numerical solutions of dynamic Economic Models
Econometrica, 2017Co-Authors: Kenneth L Judd, Lilia Maliar, Serguei MaliarAbstract:We propose a novel methodology for evaluating the accuracy of numerical solutions to dynamic Economic Models. It consists in constructing a lower bound on the size of approximation errors. A small lower bound on errors is a necessary condition for accuracy: If a lower error bound is unacceptably large, then the actual approximation errors are even larger, and hence, the approximation is inaccurate. Our lower‐bound error analysis is complementary to the conventional upper‐error (worst‐case) bound analysis, which provides a sufficient condition for accuracy. As an illustration of our methodology, we assess approximation in the first‐ and second‐order perturbation solutions for two stylized Models: a neoclassical growth model and a new Keynesian model. The errors are small for the former model but unacceptably large for the latter model under some empirically relevant parameterizations.
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smolyak method for solving dynamic Economic Models lagrange interpolation anisotropic grid and adaptive domain
Journal of Economic Dynamics and Control, 2014Co-Authors: Kenneth L Judd, Lilia Maliar, Serguei Maliar, Rafael ValeroAbstract:We show how to enhance the performance of a Smolyak method for solving dynamic Economic Models. First, we propose a more efficient implementation of the Smolyak method for interpolation, namely, we show how to avoid costly evaluations of repeated basis functions in the conventional Smolyak formula. Second, we extend the Smolyak method to include anisotropic constructions that allow us to target higher quality of approximation in some dimensions than in others. Third, we show how to effectively adapt the Smolyak hypercube to a solution domain of a given Economic model. Finally, we argue that in large-scale Economic applications, a solution algorithm based on Smolyak interpolation has substantially lower expense when it uses derivative-free fixed-point iteration instead of standard time iteration. In the context of one- and multi-agent optimal growth Models, we find that the proposed modifications to the conventional Smolyak method lead to substantial increases in accuracy and speed.
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smolyak method for solving dynamic Economic Models lagrange interpolation anisotropic grid and adaptive domain
National Bureau of Economic Research, 2013Co-Authors: Kenneth L Judd, Lilia Maliar, Serguei Maliar, Rafael ValeroAbstract:First, we propose a more efficient implementation of the Smolyak method for interpolation, namely, we show how to avoid costly evaluations of repeated basis functions in the conventional Smolyak formula. Second, we extend the Smolyak method to include anisotropic constructions; this allows us to target higher quality of approximation in some dimensions than in others. Third, we show how to effectively adapt the Smolyak hypercube to a solution domain of a given Economic model. Finally, we advocate the use of low-cost fixed-point iteration, instead of conventional time iteration. In the context of one- and multi-agent growth Models, we find that the proposed techniques lead to substantial increases in accuracy and speed of a Smolyak-based projection method for solving dynamic Economic Models.
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numerically stable and accurate stochastic simulation approaches for solving dynamic Economic Models
Quantitative Economics, 2011Co-Authors: Kenneth L Judd, Lilia Maliar, Serguei MaliarAbstract:We develop numerically stable and accurate stochastic simulation approaches for solving dynamic Economic Models. First, instead of standard least-squares methods, we examine a variety of alternatives, including least-squares methods using singular value decomposition and Tikhonov regularization, least-absolute deviations methods, and principal component regression method, all of which are numerically stable and can handle ill-conditioned problems. Second, instead of conventional Monte Carlo integration, we use accurate quadrature and monomial integration. We test our generalized stochastic simulation algorithm (GSSA) in three applications: the standard representative agent neoclassical growth model, a model with rare disasters and a multi-country Models with hundreds of state variables. GSSA is simple to program, and MATLAB codes are provided.
Serguei Maliar - One of the best experts on this subject based on the ideXlab platform.
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lower bounds on approximation errors to numerical solutions of dynamic Economic Models
Econometrica, 2017Co-Authors: Kenneth L Judd, Lilia Maliar, Serguei MaliarAbstract:We propose a novel methodology for evaluating the accuracy of numerical solutions to dynamic Economic Models. It consists in constructing a lower bound on the size of approximation errors. A small lower bound on errors is a necessary condition for accuracy: If a lower error bound is unacceptably large, then the actual approximation errors are even larger, and hence, the approximation is inaccurate. Our lower‐bound error analysis is complementary to the conventional upper‐error (worst‐case) bound analysis, which provides a sufficient condition for accuracy. As an illustration of our methodology, we assess approximation in the first‐ and second‐order perturbation solutions for two stylized Models: a neoclassical growth model and a new Keynesian model. The errors are small for the former model but unacceptably large for the latter model under some empirically relevant parameterizations.
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smolyak method for solving dynamic Economic Models lagrange interpolation anisotropic grid and adaptive domain
Journal of Economic Dynamics and Control, 2014Co-Authors: Kenneth L Judd, Lilia Maliar, Serguei Maliar, Rafael ValeroAbstract:We show how to enhance the performance of a Smolyak method for solving dynamic Economic Models. First, we propose a more efficient implementation of the Smolyak method for interpolation, namely, we show how to avoid costly evaluations of repeated basis functions in the conventional Smolyak formula. Second, we extend the Smolyak method to include anisotropic constructions that allow us to target higher quality of approximation in some dimensions than in others. Third, we show how to effectively adapt the Smolyak hypercube to a solution domain of a given Economic model. Finally, we argue that in large-scale Economic applications, a solution algorithm based on Smolyak interpolation has substantially lower expense when it uses derivative-free fixed-point iteration instead of standard time iteration. In the context of one- and multi-agent optimal growth Models, we find that the proposed modifications to the conventional Smolyak method lead to substantial increases in accuracy and speed.
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smolyak method for solving dynamic Economic Models lagrange interpolation anisotropic grid and adaptive domain
National Bureau of Economic Research, 2013Co-Authors: Kenneth L Judd, Lilia Maliar, Serguei Maliar, Rafael ValeroAbstract:First, we propose a more efficient implementation of the Smolyak method for interpolation, namely, we show how to avoid costly evaluations of repeated basis functions in the conventional Smolyak formula. Second, we extend the Smolyak method to include anisotropic constructions; this allows us to target higher quality of approximation in some dimensions than in others. Third, we show how to effectively adapt the Smolyak hypercube to a solution domain of a given Economic model. Finally, we advocate the use of low-cost fixed-point iteration, instead of conventional time iteration. In the context of one- and multi-agent growth Models, we find that the proposed techniques lead to substantial increases in accuracy and speed of a Smolyak-based projection method for solving dynamic Economic Models.
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numerically stable and accurate stochastic simulation approaches for solving dynamic Economic Models
Quantitative Economics, 2011Co-Authors: Kenneth L Judd, Lilia Maliar, Serguei MaliarAbstract:We develop numerically stable and accurate stochastic simulation approaches for solving dynamic Economic Models. First, instead of standard least-squares methods, we examine a variety of alternatives, including least-squares methods using singular value decomposition and Tikhonov regularization, least-absolute deviations methods, and principal component regression method, all of which are numerically stable and can handle ill-conditioned problems. Second, instead of conventional Monte Carlo integration, we use accurate quadrature and monomial integration. We test our generalized stochastic simulation algorithm (GSSA) in three applications: the standard representative agent neoclassical growth model, a model with rare disasters and a multi-country Models with hundreds of state variables. GSSA is simple to program, and MATLAB codes are provided.
Lilia Maliar - One of the best experts on this subject based on the ideXlab platform.
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lower bounds on approximation errors to numerical solutions of dynamic Economic Models
Econometrica, 2017Co-Authors: Kenneth L Judd, Lilia Maliar, Serguei MaliarAbstract:We propose a novel methodology for evaluating the accuracy of numerical solutions to dynamic Economic Models. It consists in constructing a lower bound on the size of approximation errors. A small lower bound on errors is a necessary condition for accuracy: If a lower error bound is unacceptably large, then the actual approximation errors are even larger, and hence, the approximation is inaccurate. Our lower‐bound error analysis is complementary to the conventional upper‐error (worst‐case) bound analysis, which provides a sufficient condition for accuracy. As an illustration of our methodology, we assess approximation in the first‐ and second‐order perturbation solutions for two stylized Models: a neoclassical growth model and a new Keynesian model. The errors are small for the former model but unacceptably large for the latter model under some empirically relevant parameterizations.
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smolyak method for solving dynamic Economic Models lagrange interpolation anisotropic grid and adaptive domain
Journal of Economic Dynamics and Control, 2014Co-Authors: Kenneth L Judd, Lilia Maliar, Serguei Maliar, Rafael ValeroAbstract:We show how to enhance the performance of a Smolyak method for solving dynamic Economic Models. First, we propose a more efficient implementation of the Smolyak method for interpolation, namely, we show how to avoid costly evaluations of repeated basis functions in the conventional Smolyak formula. Second, we extend the Smolyak method to include anisotropic constructions that allow us to target higher quality of approximation in some dimensions than in others. Third, we show how to effectively adapt the Smolyak hypercube to a solution domain of a given Economic model. Finally, we argue that in large-scale Economic applications, a solution algorithm based on Smolyak interpolation has substantially lower expense when it uses derivative-free fixed-point iteration instead of standard time iteration. In the context of one- and multi-agent optimal growth Models, we find that the proposed modifications to the conventional Smolyak method lead to substantial increases in accuracy and speed.
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smolyak method for solving dynamic Economic Models lagrange interpolation anisotropic grid and adaptive domain
National Bureau of Economic Research, 2013Co-Authors: Kenneth L Judd, Lilia Maliar, Serguei Maliar, Rafael ValeroAbstract:First, we propose a more efficient implementation of the Smolyak method for interpolation, namely, we show how to avoid costly evaluations of repeated basis functions in the conventional Smolyak formula. Second, we extend the Smolyak method to include anisotropic constructions; this allows us to target higher quality of approximation in some dimensions than in others. Third, we show how to effectively adapt the Smolyak hypercube to a solution domain of a given Economic model. Finally, we advocate the use of low-cost fixed-point iteration, instead of conventional time iteration. In the context of one- and multi-agent growth Models, we find that the proposed techniques lead to substantial increases in accuracy and speed of a Smolyak-based projection method for solving dynamic Economic Models.
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numerically stable and accurate stochastic simulation approaches for solving dynamic Economic Models
Quantitative Economics, 2011Co-Authors: Kenneth L Judd, Lilia Maliar, Serguei MaliarAbstract:We develop numerically stable and accurate stochastic simulation approaches for solving dynamic Economic Models. First, instead of standard least-squares methods, we examine a variety of alternatives, including least-squares methods using singular value decomposition and Tikhonov regularization, least-absolute deviations methods, and principal component regression method, all of which are numerically stable and can handle ill-conditioned problems. Second, instead of conventional Monte Carlo integration, we use accurate quadrature and monomial integration. We test our generalized stochastic simulation algorithm (GSSA) in three applications: the standard representative agent neoclassical growth model, a model with rare disasters and a multi-country Models with hundreds of state variables. GSSA is simple to program, and MATLAB codes are provided.
Robert John Evans - One of the best experts on this subject based on the ideXlab platform.
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Economic Models and Policy Advice: Theory Choice or Moral Choice?
Science in Context, 1999Co-Authors: Robert John EvansAbstract:This paper examines the interaction between Economic Models and policy advice through a case study of the U.K. government's Panel of Independent Forecasters. The Panel, which met for the first time in February 1993, was part of the government's response to the policy vacuum created by its departure from the European Exchange Rate Mechanism. The paper focuses on the policy recommendations made by the Panel and their foundation in Economic Models. It is argued that, because of their ambiguity, Economic Models do not provide an “objective” basis for policy making. Rather, they provide a level epistemological basis for debating the various social, political, and moral theories that can be used to frame Economic policy. The paper concludes that although Economic Models often serve to depoliticize Economic issues, they also have the potential to do exactly the opposite — namely, repoliticize them by connecting Economics to wider social and moral debates.
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Economic Models: the past, present and future?
Impact Assessment and Project Appraisal, 1998Co-Authors: Robert John EvansAbstract:This paper outlines a sociological perspective on the usefulness of Economic Models in assessment and policy-making. It combines an overview of the history of macro-Economic modelling research in the UK with insights drawn from the author's own research into the Economic forecasts and policy recommendations made by the Panel of Independent Forecasters to the UK Government during 1993. It argues that one of the most important achievements of the Panel was to communicate some of the diversity and excitement of its Economic (and econometric) Models. The more recent policy of giving operational responsibility for interest rate decisions to the Bank of England may have the opposite effect, and creates the potential for a ‘closed’ institutional space within which a particular Economic analysis may be uncritically accepted.
Rafael Valero - One of the best experts on this subject based on the ideXlab platform.
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smolyak method for solving dynamic Economic Models lagrange interpolation anisotropic grid and adaptive domain
Journal of Economic Dynamics and Control, 2014Co-Authors: Kenneth L Judd, Lilia Maliar, Serguei Maliar, Rafael ValeroAbstract:We show how to enhance the performance of a Smolyak method for solving dynamic Economic Models. First, we propose a more efficient implementation of the Smolyak method for interpolation, namely, we show how to avoid costly evaluations of repeated basis functions in the conventional Smolyak formula. Second, we extend the Smolyak method to include anisotropic constructions that allow us to target higher quality of approximation in some dimensions than in others. Third, we show how to effectively adapt the Smolyak hypercube to a solution domain of a given Economic model. Finally, we argue that in large-scale Economic applications, a solution algorithm based on Smolyak interpolation has substantially lower expense when it uses derivative-free fixed-point iteration instead of standard time iteration. In the context of one- and multi-agent optimal growth Models, we find that the proposed modifications to the conventional Smolyak method lead to substantial increases in accuracy and speed.
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smolyak method for solving dynamic Economic Models lagrange interpolation anisotropic grid and adaptive domain
National Bureau of Economic Research, 2013Co-Authors: Kenneth L Judd, Lilia Maliar, Serguei Maliar, Rafael ValeroAbstract:First, we propose a more efficient implementation of the Smolyak method for interpolation, namely, we show how to avoid costly evaluations of repeated basis functions in the conventional Smolyak formula. Second, we extend the Smolyak method to include anisotropic constructions; this allows us to target higher quality of approximation in some dimensions than in others. Third, we show how to effectively adapt the Smolyak hypercube to a solution domain of a given Economic model. Finally, we advocate the use of low-cost fixed-point iteration, instead of conventional time iteration. In the context of one- and multi-agent growth Models, we find that the proposed techniques lead to substantial increases in accuracy and speed of a Smolyak-based projection method for solving dynamic Economic Models.
