Timothy B. Armstrong, Michal Kolesár
arXiv 22 Aug 2018 · Econometrics · 29 citations (OpenAlex)
arXiv:1808.07387 · PDF · DOI · OpenAlex · Extracted main text
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.
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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., Gentzkow, M., and Shapiro, J. M (2017) Measuring the sensitivity of parameter estimates to sample statistics | 1.000 | 12 | 5 | 100% |
| 2 | Conley, T. G., Hansen, C. B., and Rossi, P. E (2012) Plausibly exogenous | 1.000 | 5 | 3 | 100% |
| 3 | Kitamura, Y., Otsu, T., and Evdokimov, K (2013) Robustness, infinitesimal neighborhoods, and moment restrictions | 0.874 | 7 | 2 | 100% |
| 4 | Newey, W. K. and McFadden, D. L (1994) Large sample estimation and hypothesis testing | 0.843 | 4 | 4 | 75% |
| 5 | van der Vaart, A. W (1998) Asymptotic Statistics | 0.843 | 5 | 4 | 60% |
| 6 | Donoho, D. L (1994) Statistical estimation and optimal recovery | 0.843 | 3 | 3 | 100% |
| 7 | Imbens, G. W. and Manski, C. F (2004) Confidence intervals for partially identified parameters | 0.737 | 3 | 3 | 67% |
| 8 | Newey, W. K (1985) Generalized method of moments specification testing | 0.737 | 3 | 3 | 67% |
| 9 | DiTraglia, F. J (2016) Using invalid instruments on purpose: Focused moment selection and averaging for GMM | 0.737 | 3 | 2 | 100% |
| 10 | Armstrong, T. B. and Kolesár, M (2018) Optimal inference in a class of regression models self | 0.659 | 14 | 3 | 29% |
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