Sensitivity analysis using approximate moment condition models
By T. Armstrong, Michael J. Kolesar. Quantitative Economics, 2018
68 citations recorded by the source corpus.
We consider inference in models defined by approximate moment conditions. We show that near‐optimal confidence intervals (CIs) can be formed by taking a generalized method of moments (GMM) estimator, and adding and subtracting the standard error times a critical value that takes into account the potential bias from misspecification of the moment conditions. In order to optimize performance under potential misspecification, the weighting matrix for this GMM estimator takes into account this potential bias and, therefore, differs from the one that is optimal under correct specification. To formally show the near‐optimality of these CIs, we develop asymptotic efficiency bounds for inference in the locally misspecified GMM setting. These bounds may be of independent interest, due to their implications for the possibility of using moment selection procedures when conducting inference in moment condition models. We apply our methods in an empirical application to automobile demand, and show that adjusting the weighting matrix can shrink the CIs by a factor of 3 or more.
Subfields: Management Science and Operations Research, Statistics and Probability
View Paper: https://www.semanticscholar.org/paper/5cdf37f9b0964017c704a1a8a4a4f4807c991929
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In Management Science and Operations Research
In Statistics and Probability
Citations in the corpus
- Factorial Designs, Model Selection, and (Incorrect) Inference in Randomized Experiments (2019, unknown): “20This is because the one-sided long model t-tests are uniformly most powerful (e.g., Proposition 15.2 in van der Vaart, 1998) so that, for any β12, the maximal power is achieved by a one-sided ttest (e.g., Armstrong & Kolesar, 2015, 2021).”
- Minimizing Sensitivity to Model Misspecification (2018, background): “Consider the case where the square of the local dual norm defined in (6) can be written as ‖u‖2γ∗ = u >u, where u>w represents some inner product of elements u and w of the cotangent space T of Π at π(γ∗).”
- Counterfactual Sensitivity and Robustness (2019, background): “, Kitamura, Otsu, and Evdokimov (2013), Andrews, Gentzkow, and Shapiro (2017, 2020), Armstrong and Kolesár (2021), Bonhomme and Weidner (2021), and Mukhin (2018). Much of this literature is concerned with local misspecification of moment conditions, which is di↵erent from the setting we consider. Ou”