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Bayesian Factor Model Shrinkage for Linear IV Regression With Many Instruments

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  • P. Richard Hahn
  • Jingyu He
  • Hedibert Lopes

Abstract

A Bayesian approach for the many instruments problem in linear instrumental variable models is presented. The new approach has two components. First, a slice sampler is developed, which leverages a decomposition of the likelihood function that is a Bayesian analogue to two-stage least squares. The new sampler permits nonconjugate shrinkage priors to be implemented easily and efficiently. The new computational approach permits a Bayesian analysis of problems that were previously infeasible due to computational demands that scaled poorly in the number of regressors. Second, a new predictor-dependent shrinkage prior is developed specifically for the many instruments setting. The prior is constructed based on a factor model decomposition of the matrix of observed instruments, allowing many instruments to be incorporated into the analysis in a robust way. Features of the new method are illustrated via a simulation study and three empirical examples.

Suggested Citation

  • P. Richard Hahn & Jingyu He & Hedibert Lopes, 2018. "Bayesian Factor Model Shrinkage for Linear IV Regression With Many Instruments," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 36(2), pages 278-287, April.
    • Handle: RePEc:taf:jnlbes:v:36:y:2018:i:2:p:278-287
    DOI: 10.1080/07350015.2016.1172968
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    Cited by:

    1. Marcus L. Nascimento & Kelly C. M. Gonçalves & Mario Jorge Mendonça, 2023. "Spatio-Temporal Instrumental Variables Regression with Missing Data: A Bayesian Approach," Computational Economics, Springer;Society for Computational Economics, vol. 62(1), pages 29-47, June.
    2. Anindya Bhadra & Jyotishka Datta & Yunfan Li & Nicholas Polson, 2020. "Horseshoe Regularisation for Machine Learning in Complex and Deep Models," International Statistical Review, International Statistical Institute, vol. 88(2), pages 302-320, August.
    3. Cássio Roberto de Andrade Alves & Márcio Laurini, 2023. "Estimating the Capital Asset Pricing Model with Many Instruments: A Bayesian Shrinkage Approach," Mathematics, MDPI, vol. 11(17), pages 1-20, September.

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