Machine learning for high-dimensional dynamic stochastic economies

Scheidegger, Simon; Bilionis, Ilias

doi:10.1016/j.jocs.2019.03.004

Cited by 51 publications

(15 citation statements)

References 45 publications

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“…Ratto (2008) employed first-order Sobol' indices to study the influence of structural parameters on reduced form estimation of linear or linearized DSGE models. More recently, Scheidegger and Bilionis (2017) proposed Gaussian process machine learning to solve economic models with very high-dimensional state spaces. They show how this framework lends itself naturally to uncertainty quantification.…”

Section: Introductionmentioning

confidence: 99%

Uncertainty quantification and global sensitivity analysis for economic models

Harenberg¹,

Marelli²,

Sudret³

et al. 2019

Quantitative Economics

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We present a global sensitivity analysis that quantifies the impact of parameter uncertainty on model outcomes. Specifically, we propose variance-decomposition-based Sobol' indices to establish an importance ranking of parameters and univariate effects to determine the direction of their impact. We employ the stateof-the-art approach of constructing a polynomial chaos expansion of the model, from which Sobol' indices and univariate effects are then obtained analytically, using only a limited number of model evaluations. We apply this analysis to several quantities of interest of a standard real-business-cycle model and compare it to traditional local sensitivity analysis approaches. The results show that local sensitivity analysis can be very misleading, whereas the proposed method accurately and efficiently ranks all parameters according to importance, identifying interactions and nonlinearities.

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Section: Introductionmentioning

confidence: 99%

Uncertainty quantification and global sensitivity analysis for economic models

Harenberg¹,

Marelli²,

Sudret³

et al. 2019

Quantitative Economics

View full text Add to dashboard Cite

show abstract

“…It is well known that, in most cases, closed form analytical solutions do not exist, and hence we need numerical solution methods. See for example Maliar and Maliar (2014), Aruoba et al (2006) and Christiano and Fisher (2000) for an overview and comparison studies of such methods or Norets (2012) and Scheidegger and Bilionis (2019) for more recent methods based on machine learning techniques such as articial neural networks.…”

Section: Introductionmentioning

confidence: 99%

Transformed Perturbation Solutions for Dynamic Stochastic General Equilibrium Models

Amaral

Nientker

2019

SSRN Journal

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Despite the recent introduction of novel solution methods for Dynamic Stochastic General Equilibrium (DSGE), perturbation methods are still among the most popular and widely used solution techniques for DSGE models. Unfortunately, nonlinear perturbation solutions produce paths with stochastic properties that invalidate econometric analysis. This paper proposes a correction that renders the econometric analysis valid and sound. The proposed correction is simple to implement in existing software packages such as Dynare, it does not add any signicant computational eort and, as a result, does not impact computational times. The corrected solution retains the same approximation properties as standard higher order perturbation methods and, in contrast to those methods, generates stable sample paths that are stationary, geometrically ergodic and absolutely regular. Additionally, moments are shown to be bounded. Transformed perturbation solutions are an alternative to the pruning method as proposed in Kim et al. (2008). The advantages of our approach are that, unlike pruning, we do not need to sacrice accuracy around the steady state by ignoring higher order eects, and furthermore, we also deliver a policy function. Moreover, the newly proposed solution is always more accurate globally than standard perturbation methods. We demonstrate the superior accuracy of our method in a range of simple examples. * We thank Michel Juillard, Sergey Ivashchenko and the attendants of the "Advances in solution methods" session of the 14th Dynare Conference for helpful comments and suggestions. We thank Martin Andreasen and Wouter Den Haan for making code available that aided the paper.

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“…There are methods to alleviate or even avoid the "curse of dimensionality" for some problems; see, for example,Rust (1997Rust ( , 2019,Judd et al (2014),Brumm and Scheidegger (2017),Cai (2019), andBilionis (2019).7 Note that VFI can be stable if it uses a shape-preserving approximation method(Cai and Judd (2013)). 8 For example, our DSICE example in Section 4.3 starts with a real world initial state that is far away from its steady state, which will take thousands of years to be reached, while policymakers want to compute an optimal carbon tax path in this century.…”

mentioning

confidence: 99%

“…66 There are methods to alleviate or even avoid the “curse of dimensionality” for some problems; see, for example, Rust (1997, 2019), Judd et al (2014), Brumm and Scheidegger (2017), Cai (2019), and Scheidegger and Bilionis (2019). …”

mentioning

confidence: 99%

A simple but powerful simulated certainty equivalent approximation method for dynamic stochastic problems

Cai

Judd

2023

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We introduce a novel simulated certainty equivalent approximation (SCEQ) method for solving dynamic stochastic problems. Our examples show that SCEQ can quickly solve high‐dimensional finite‐ or infinite‐horizon, stationary or nonstationary dynamic stochastic problems with hundreds of state variables, a wide state space, and occasionally binding constraints. With the SCEQ method, a desktop computer will suffice for large problems, but it can also use parallel tools efficiently. The SCEQ method is simple, stable, and can utilize any solver, making it suitable for solving complex economic problems that cannot be solved by other algorithms.

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Machine learning for high-dimensional dynamic stochastic economies

Cited by 51 publications

References 45 publications

Uncertainty quantification and global sensitivity analysis for economic models

Uncertainty quantification and global sensitivity analysis for economic models

Transformed Perturbation Solutions for Dynamic Stochastic General Equilibrium Models

A simple but powerful simulated certainty equivalent approximation method for dynamic stochastic problems

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