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Bayesian Approaches to Shrinkage and Sparse Estimation

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  • Dimitris Korobilis

    (University of Glasgow, UK; Rimini Centre for Economic Analysis)

  • Kenichi Shimizu

    (University of Glasgow, UK)

Abstract

In all areas of human knowledge, datasets are increasing in both size and complexity, creating the need for richer statistical models. This trend is also true for economic data, where high-dimensional and nonlinear/nonparametric inference is the norm in several fields of applied econometric work. The purpose of this paper is to introduce the reader to the world of Bayesian model determination, by surveying modern shrinkage and variable selection algorithms and methodologies. Bayesian inference is a natural probabilistic framework for quantifying uncertainty and learning about model parameters, and this feature is particularly important for inference in modern models of high dimensions and increased complexity. We begin with a linear regression setting in order to introduce various classes of priors that lead to shrinkage/sparse estimators of comparable value to popular penalized likelihood estimators (e.g. ridge, lasso). We explore various methods of exact and approximate inference, and discuss their pros and cons. Finally, we explore how priors developed for the simple regression setting can be extended in a straightforward way to various classes of interesting econometric models. In particular, the following case-studies are considered, that demonstrate application of Bayesian shrinkage and variable selection strategies to popular econometric contexts: i) vector autoregressive models; ii) factor models; iii) time-varying parameter regressions; iv) confounder selection in treatment effects models; and v) quantile regression models. A MATLAB package and an accompanying technical manual allow the reader to replicate many of the algorithms described in this review.

Suggested Citation

  • Dimitris Korobilis & Kenichi Shimizu, 2022. "Bayesian Approaches to Shrinkage and Sparse Estimation," Working Paper series 22-02, Rimini Centre for Economic Analysis.
    • Handle: RePEc:rim:rimwps:22-02
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    Cited by:

    1. Gary Koop & Dimitris Korobilis, 2023. "Bayesian Dynamic Variable Selection In High Dimensions," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 64(3), pages 1047-1074, August.
    2. Dimitris Korobilis & Maximilian Schröder, 2023. "Monitoring multicountry macroeconomic risk," Working Papers No 06/2023, Centre for Applied Macro- and Petroleum economics (CAMP), BI Norwegian Business School.
    3. Dimitris Korobilis & Maximilian Schröder, 2023. "Monitoring multicountry macroeconomic risk," Working Paper 2023/9, Norges Bank.
    4. Dimitris Korobilis & Maximilian Schroder, 2023. "Monitoring multicountry macroeconomic risk," Papers 2305.09563, arXiv.org.
    5. Francesco Ravazzolo & Luca Rossini, 2023. "Is the Price Cap for Gas Useful? Evidence from European Countries," Working Papers 2023.23, Fondazione Eni Enrico Mattei.
    6. Maximilian Schroder, 2024. "Mixing it up: Inflation at risk," Papers 2405.17237, arXiv.org, revised May 2024.
    7. Donald J. Lacombe & Nasima Khatun, 2023. "What are the determinants of financial well‐being? A Bayesian LASSO approach," American Journal of Economics and Sociology, Wiley Blackwell, vol. 82(1), pages 43-59, January.
    8. Dimitris Korobilis & Maximilian Schroder, 2022. "Probabilistic Quantile Factor Analysis," Papers 2212.10301, arXiv.org, revised Aug 2024.

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    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C20 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - General
    • C30 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - General
    • C45 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Neural Networks and Related Topics
    • C46 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Specific Distributions
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection

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