James A. Duffy, Sophocles Mavroeidis
arXiv 9 Apr 2026 · Econometrics
arXiv:2604.07718 · PDF · DOI · OpenAlex · Extracted main text
We study identification in structural vector autoregressions (SVARs) in which the endogenous variables enter nonlinearly on the left-hand side of the model, a feature we term endogenous nonlinearity, to distinguish it from the more familiar case in which nonlinearity arises only through exogenous or predetermined variables. This class of models accommodates asymmetric impact multipliers, endogenous regime switching, and occasionally binding constraints. We show that, under weak regularity conditions, the model parameters and structural shocks are (nonparametrically) identified up to an orthogonal transformation, exactly as in a linear SVAR. Our results have the powerful implication that most existing identification schemes for linear SVARs extend directly to our nonlinear setting, with the number of restrictions required to achieve exact identification remaining unchanged. We specialise our results to piecewise affine SVARs, which provide a convenient framework for the modelling of endogenous regime switching, and their smooth transition counterparts. We illustrate our methodology with an application to the nonlinear Phillips curve, providing a test for the presence of nonlinearity that is robust to the choice of identifying assumptions, and finding significant evidence for state-dependent inflation dynamics.
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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 | Benigno, P. and G. B. Eggertsson (2023) It's baaack: The surge in inflation in the 2020s and the return of the non-linear Phillips curve, National Bureau of Economic Re… | 1.000 | 17 | 4 | 100% |
| 2 | Beaudry, P., C. Hou, and F. Portier (2025) On the fragility of the nonlinear Phillips curve view of recent inflation, National Bureau of Economic Research, Working Paper 3… | 0.928 | 4 | 3 | 100% |
| 3 | Mavroeidis, S (2021) Identification at the zero lower bound self | 0.874 | 5 | 2 | 100% |
| 4 | Matzkin, R. L (2008) Identification in nonparametric simultaneous equations models | 0.830 | 7 | 3 | 57% |
| 5 | Aruoba, S. B., M. Mlikota, F. Schorfheide, and S. Villalvazo (2022) SVARs with occasionally-binding constraints | 0.811 | 4 | 2 | 100% |
| 6 | Berry, S. T. and P. A. Haile (2018) Identification of nonparametric simultaneous equations models with a residual index structure | 0.737 | 3 | 2 | 100% |
| 7 | Ball, L., D. Leigh, and P. Mishra (2022) Understanding US inflation during the COVID-19 era | 0.737 | 3 | 2 | 100% |
| 8 | Kilian, L. and H. Lütkepohl (2017) Structural Vector Autoregressive Analysis | 0.737 | 3 | 2 | 100% |
| 9 | Auerbach, A. J. and Y. Gorodnichenko (2012) Measuring the output responses to fiscal policy | 0.644 | 2 | 2 | 100% |
| 10 | Duffy, J. A. and S. Mavroeidis (2024) Common trends and long-run identification in nonlinear structural VARs, arXiv:2404.05349 self | 0.644 | 2 | 2 | 100% |
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