Bulat Gafarov, Matthias Meier, José Luis Montiel Olea
arXiv 18 Apr 2025 · Econometrics
arXiv:2504.14106 · PDF · Extracted main text
We study the properties of projection inference for set-identified Structural Vector Autoregressions. A nominal $1-\alpha$ projection region collects the structural parameters that are compatible with a $1-\alpha$ Wald ellipsoid for the model's reduced-form parameters (autoregressive coefficients and the covariance matrix of residuals). We show that projection inference can be applied to a general class of stationary models, is computationally feasible, and -- as the sample size grows large -- it produces regions for the structural parameters and their identified set with both frequentist coverage and robust Bayesian credibility of at least $1-\alpha$. A drawback of the projection approach is that both coverage and robust credibility may be strictly above their nominal level. Following the work of \cite{Kaido_Molinari_Stoye:2014}, we `calibrate' the radius of the Wald ellipsoid to guarantee that -- for a given posterior on the reduced-form parameters -- the robust Bayesian credibility of the projection method is exactly $1-\alpha$. If the bounds of the identified set are differentiable, our calibrated projection also covers the identified set with probability $1-\alpha$. %eliminating the excess of robust Bayesian credibility also eliminates excessive frequentist coverage. We illustrate the main results of the paper using the demand/supply-model for the U.S. labor market in Baumeister_Hamilton(2015)
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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 | Baumeister, Christiane and Hamilton, James D (2015) Sign restrictions, structural vector autoregressions, and useful prior information | 1.000 | 9 | 4 | 100% |
| 2 | Giacomini, Raffaella and Kitagawa, Toru (2021) Robust Bayesian inference for set-identified models | 1.000 | 6 | 4 | 100% |
| 3 | Lütkepohl, Helmut (2013) Introduction to multiple time series analysis | 0.928 | 5 | 3 | 80% |
| 4 | Kaido, Hiroaki and Molinari, Francesca and Stoye, Jörg (2019) Confidence Intervals for Projections of Partially Identified Parameters | 0.928 | 4 | 4 | 100% |
| 5 | Uhlig, Harald (2005) What are the effects of monetary policy on output? Results from an agnostic identification procedure | 0.909 | 12 | 6 | 75% |
| 6 | Arias, Jonas E and Rubio-Ram\'irez, Juan F and Waggoner, Daniel F (2018) Inference based on structural vector autoregressions identified with sign and zero restrictions: Theory and applications | 0.644 | 3 | 2 | 67% |
| 7 | Dufour, Jean-Marie and Taamouti, Mohamed (2005) Projection-based statistical inference in linear structural models with possibly weak instruments | 0.644 | 2 | 2 | 100% |
| 8 | Dufour, Jean-Marie and Taamouti, Mohamed (2007) Further results on projection-based inference in IV regressions with weak, collinear or missing instruments | 0.644 | 2 | 2 | 100% |
| 9 | Inoue, Atsushi and Kilian, Lutz (2016) Joint confidence sets for structural impulse responses | 0.644 | 2 | 2 | 100% |
| 10 | Inoue, Atsushi and Kilian, Lutz (2013) Inference on impulse response functions in structural VAR models | 0.644 | 2 | 2 | 100% |
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