arXiv 7 Feb 2026 · Econometrics
arXiv:2602.07377 · PDF · DOI · OpenAlex · Extracted main text
We study inference in models where a transformation of parameters exhibits first-order degeneracy -- that is, its gradient is zero or close to zero, making the standard delta method invalid. A leading example is causal mediation analysis, where the indirect effect is a product of coefficients and the gradient degenerates near the origin. In these local regions of degeneracy the limiting behaviors of plug-in estimators depend on nuisance parameters that are not consistently estimable. We show that this failure is intrinsic -- around points of degeneracy, both regular and quantile-unbiased estimation are impossible. Despite these restrictions, we develop minimum-distance methods that deliver uniformly valid confidence intervals. We establish sufficient conditions under which standard chi-square critical values remain valid, and propose a simple bootstrap procedure when they are not. We demonstrate favorable power in simulations and in an empirical application linking teacher gender attitudes to student outcomes.
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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 | Andrews, I. and A. Mikusheva (2016) A geometric approach to nonlinear econometric models | 1.000 | 11 | 4 | 100% |
| 2 | Dufour, J.-M., E. Renault, and V. Zinde-Walsh (2025) Wald tests when restrictions are locally singular | 1.000 | 11 | 4 | 100% |
| 3 | van Garderen, K. J. and N. P. van Giersbergen (2024) A nearly similar powerful test for mediation | 1.000 | 8 | 4 | 100% |
| 4 | Alan, S., S. Ertac, and I. Mumcu (2018) Gender stereotypes in the classroom and effects on achievement | 0.874 | 6 | 2 | 100% |
| 5 | Hirano, K. and J. R. Porter (2012) Impossibility results for nondifferentiable functionals | 0.866 | 20 | 3 | 65% |
| 6 | Le Cam, L (1972) Limits of experiments | 0.737 | 3 | 2 | 100% |
| 7 | Le Cam, L (1970) On the assumptions used to prove asymptotic normality of maximum likelihood estimates | 0.737 | 3 | 2 | 100% |
| 8 | van der Vaart, A. W (1998) Asymptotic Statistics | 0.644 | 4 | 2 | 50% |
| 9 | Ganics, G., A. Inoue, and B. R. and (2021) Confidence intervals for bias and size distortion in iv and local projections-iv models | 0.511 | 2 | 1 | 100% |
| 10 | Stock, J. and M. Yogo (2005) Testing for Weak Instruments in Linear IV Regression | 0.511 | 2 | 1 | 100% |
Showing the top 10 of 91 scored citations.