Gregor Steiner, Mark Steel
arXiv 18 Apr 2025 · Statistics — Methodology
arXiv:2504.13520 · PDF · Extracted main text
Instrumental variables are a popular tool to infer causal effects under unobserved confounding, but choosing suitable instruments is challenging in practice. We propose gIVBMA, a Bayesian model averaging procedure that addresses this challenge by averaging across different sets of instrumental variables and covariates in a structural equation model. Our approach extends previous work through a scale-invariant prior structure and accommodates non-Gaussian outcomes and treatments, offering greater flexibility than existing methods. The computational strategy uses conditional Bayes factors to update models separately for the outcome and treatments. We prove that this model selection procedure is consistent. By explicitly accounting for model uncertainty, gIVBMA allows instruments and covariates to switch roles and provides robustness against invalid instruments. In simulation experiments, gIVBMA outperforms current state-of-the-art methods. We demonstrate its usefulness in two empirical applications: the effects of malaria and institutions on income per capita and the returns to schooling. A software implementation of gIVBMA is available in Julia.
appendix boundary found by appendix_command · 47% of the source is main text. Read the extracted text to check this.
The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Steel, M. F. J. and Zens, G (2026) Model uncertainty in latent Gaussian models with univariate link function self | 1.000 | 5 | 4 | 100% |
| 2 | Karl, A. and Lenkoski, A (2012) Instrumental Variable Bayesian Model Averaging via Conditional Bayes Factors | 0.909 | 16 | 8 | 75% |
| 3 | Kang, H., Zhang, A., Cai, T. T., and Small, D. S (2016) Instrumental Variables Estimation With Some Invalid Instruments and its Application to Mendelian Randomization | 0.874 | 6 | 3 | 67% |
| 4 | Lee, J. and Lenkoski, A (2022) Incorporating Model Uncertainty in Market Response Models with Multiple Endogenous Variables by Bayesian Model Averaging | 0.843 | 4 | 3 | 75% |
| 5 | Kuersteiner, G. and Okui, R (2010) Constructing Optimal Instruments by First-Stage Prediction Averaging | 0.794 | 6 | 3 | 50% |
| 6 | Fernández, C., Ley, E., and Steel, M. F. J (2001) Benchmark priors for Bayesian model averaging self | 0.754 | 7 | 4 | 43% |
| 7 | DiTraglia, F. J (2016) Using invalid instruments on purpose: Focused moment selection and averaging for GMM | 0.737 | 3 | 2 | 100% |
| 8 | Card, D (1995) Using geographic variation in college proximity to estimate the return to schooling | 0.644 | 10 | 2 | 40% |
| 9 | Lopes, H. F. and Polson, N. G (2014) Bayesian Instrumental Variables: Priors and Likelihoods | 0.644 | 2 | 2 | 100% |
| 10 | Windmeijer, F., Farbmacher, H., Davies, N., and Davey Smith, G (2019) On the Use of the Lasso for Instrumental Variables Estimation with Some Invalid Instruments | 0.644 | 2 | 2 | 100% |
Showing the top 10 of 50 scored citations.
arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.
| Citing paper | Intensity | Mentions | Sections | |
|---|---|---|---|---|
| 1 | Possibilistic Instrumental Variable Regression | 0.644 | 2 | 2 |