Bayesian Models for Causal Analysis with Many Potentially Weak Instruments

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Date

2015

Authors

Jiang, Sheng

Advisors

Tokdar, Surya Tapas

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Abstract

This paper investigates Bayesian instrumental variable models with many instruments. The number of instrumental variables grows with the sample size and is allowed to be much larger than the sample size. With some sparsity condition on the coefficients on the instruments, we characterize a general prior specification where the posterior consistency of the parameters is established and calculate the corresponding convergence rate.

In particular, we show the posterior consistency for a class of spike and slab priors on the many potentially weak instruments. The spike and slab prior shrinks the number of instrumental variables, which avoids overfitting and provides uncertainty quantifications on the first stage. A simulation study is conducted to illustrate the convergence notion and estimation/selection performance under dependent instruments. Computational issues related to the Gibbs sampler are also discussed.

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Citation

Jiang, Sheng (2015). Bayesian Models for Causal Analysis with Many Potentially Weak Instruments. Master's thesis, Duke University. Retrieved from https://hdl.handle.net/10161/10020.

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