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A Geometric Approach to Nonlinear Econometric Models

Author

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  • Isaiah Andrews
  • Anna Mikusheva

Abstract

Conventional tests for composite hypotheses in minimum distance models can be unreliable when the relationship between the structural and reduced‐form parameters is highly nonlinear. Such nonlinearity may arise for a variety of reasons, including weak identification. In this note, we begin by studying the problem of testing a “curved null” in a finite‐sample Gaussian model. Using the curvature of the model, we develop new finite‐sample bounds on the distribution of minimum‐distance statistics. These bounds allow us to construct tests for composite hypotheses which are uniformly asymptotically valid over a large class of data generating processes and structural models.

Suggested Citation

  • Isaiah Andrews & Anna Mikusheva, 2016. "A Geometric Approach to Nonlinear Econometric Models," Econometrica, Econometric Society, vol. 84, pages 1249-1264, May.
    • Handle: RePEc:wly:emetrp:v:84:y:2016:i::p:1249-1264
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    Cited by:

    1. Simon Freyaldenhoven & Christian Hansen & Jesse M. Shapiro, 2019. "Pre-event Trends in the Panel Event-Study Design," American Economic Review, American Economic Association, vol. 109(9), pages 3307-3338, September.
    2. Xiaohong Chen & Timothy Christensen & Keith O’Hara & Elie Tamer, 2016. "MCMC Confidence sets for Identified Sets," Cowles Foundation Discussion Papers 2037R, Cowles Foundation for Research in Economics, Yale University, revised Jul 2016.
    3. Antoine, Bertille & Lavergne, Pascal, 2023. "Identification-robust nonparametric inference in a linear IV model," Journal of Econometrics, Elsevier, vol. 235(1), pages 1-24.
    4. Jean-Jacques Forneron, 2019. "Detecting Identification Failure in Moment Condition Models," Papers 1907.13093, arXiv.org, revised Oct 2023.
    5. Patrick Kline & Raffaele Saggio & Mikkel Sølvsten, 2020. "Leave‐Out Estimation of Variance Components," Econometrica, Econometric Society, vol. 88(5), pages 1859-1898, September.
    6. Allen, David, 2022. "Asset Pricing Tests, Endogeneity issues and Fama-French factors," MPRA Paper 113610, University Library of Munich, Germany.
    7. Gregory Cox, 2020. "Weak Identification with Bounds in a Class of Minimum Distance Models," Papers 2012.11222, arXiv.org, revised Dec 2022.
    8. Patrik Guggenberge & Frank Kleibergen & Sophocles Mavroeidis, 2021. "A Powerful Subvector Anderson Rubin Test in Linear Instrumental Variables Regression with Conditional Heteroskedasticity," Economics Series Working Papers 960, University of Oxford, Department of Economics.
    9. Gregory Cox, 2022. "Weak Identification in Low-Dimensional Factor Models with One or Two Factors," Papers 2211.00329, arXiv.org, revised Mar 2024.
    10. Xiaohong Chen & Timothy M. Christensen & Keith O'Hara & Elie Tamer, 2016. "MCMC confidence sets for identified sets," CeMMAP working papers 28/16, Institute for Fiscal Studies.
    11. Frank Kleibergen & Zhaoguo Zhan, 2021. "Double robust inference for continuous updating GMM," Papers 2105.08345, arXiv.org.
    12. Christis Katsouris, 2023. "Optimal Estimation Methodologies for Panel Data Regression Models," Papers 2311.03471, arXiv.org, revised Nov 2023.
    13. Tetsuya Kaji, 2021. "Theory of Weak Identification in Semiparametric Models," Econometrica, Econometric Society, vol. 89(2), pages 733-763, March.
    14. Han, Sukjin & Vytlacil, Edward J., 2017. "Identification in a generalization of bivariate probit models with dummy endogenous regressors," Journal of Econometrics, Elsevier, vol. 199(1), pages 63-73.

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