arXiv 3 Aug 2022 · Econometrics · 2 citations (OpenAlex)
arXiv:2208.01967 · PDF · DOI · OpenAlex · Extracted main text
This paper is concerned with the findings related to the robust first-stage F-statistic in the Monte Carlo analysis of Andrews (2018), who found in a heteroskedastic grouped-data design that even for very large values of the robust F-statistic, the standard 2SLS confidence intervals had large coverage distortions. This finding appears to discredit the robust F-statistic as a test for underidentification. However, it is shown here that large values of the robust F-statistic do imply that there is first-stage information, but this may not be utilized well by the 2SLS estimator, or the standard GMM estimator. An estimator that corrects for this is a robust GMM estimator, denoted GMMf, with the robust weight matrix not based on the structural residuals, but on the first-stage residuals. For the grouped-data setting of Andrews (2018), this GMMf estimator gives the weights to the group specific estimators according to the group specific concentration parameters in the same way as 2SLS does under homoskedasticity, which is formally shown using weak instrument asymptotics. The GMMf estimator is much better behaved than the 2SLS estimator in the Andrews (2018) design, behaving well in terms of relative bias and Wald-test size distortion at more standard values of the robust F-statistic. We show that the same patterns can occur in a dynamic panel data model when the error variance is heteroskedastic over time. We further derive the conditions under which the Stock and Yogo (2005) weak instruments critical values apply to the robust F-statistic in relation to the behaviour of the GMMf estimator.
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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 (2018) Valid Two-Step Identification-Robust Confidence Sets for GMM | 0.976 | 14 | 6 | 93% |
| 2 | Montiel Olea, J. L. and C. Pflueger (2013) A Robust Test for Weak Instruments | 0.928 | 4 | 3 | 100% |
| 3 | Stock, J. H. and M. Yogo (2005) Testing for Weak Instruments in Linear IV Regression, in | 0.860 | 11 | 5 | 64% |
| 4 | Staiger, D. and J. H. Stock (1997) Instrumental Variables Regression with Weak Instruments | 0.737 | 4 | 3 | 50% |
| 5 | Angrist, J. D (1991) Grouped-Data Estimation and Testing in Simple Labor-Supply Models | 0.405 | 1 | 1 | 100% |
| 6 | Angrist, J. D. and J.-S. Pischke (2009) Mostly Harmless Econometrics. An Empiricist's Companion | 0.405 | 1 | 1 | 100% |
| 7 | Arellano, M (2003) Panel Data Econometrics | 0.405 | 1 | 1 | 100% |
| 8 | Arellano, M. and O. Bover (1995) Another Look at the Instrumental Variable Estimation of Error-Components Models | 0.405 | 1 | 1 | 100% |
| 9 | Bekker, P. A. and J. Ploeg (2005) Instrumental Variable Estimation Based on Grouped Data | 0.405 | 1 | 1 | 100% |
| 10 | Bun, M. and M. de Haan (2010) Weak Instruments and the First-Stage F-Statistic in IV Models with a Nonscalar Error Covariance Structure, Tech | 0.405 | 1 | 1 | 100% |
Showing the top 10 of 11 scored citations.