Jens Klooster, Mikhail Zhelonkin
arXiv 25 Mar 2024 · Econometrics
arXiv:2403.16844 · PDF · DOI · OpenAlex · Extracted main text
The classical tests in the instrumental variable model can behave arbitrarily if the data is contaminated. For instance, one outlying observation can be enough to change the outcome of a test. We develop a framework to construct testing procedures that are robust to weak instruments, outliers and heavy-tailed errors in the instrumental variable model. The framework is constructed upon M-estimators. By deriving the influence functions of the classical weak instrument robust tests, such as the Anderson-Rubin test, K-test and the conditional likelihood ratio (CLR) test, we prove their unbounded sensitivity to infinitesimal contamination. Therefore, we construct contamination resistant/robust alternatives. In particular, we show how to construct a robust CLR statistic based on Mallows type M-estimators and show that its asymptotic distribution is the same as that of the (classical) CLR statistic. The theoretical results are corroborated by a simulation study. Finally, we revisit three empirical studies affected by outliers and demonstrate how the new robust tests can be used in practice.
appendix boundary found by appendix_titled_section at “Appendix” · 83% of the source is main text. Read the extracted text to check this.
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 | Angrist, J. D. and Krueger, A. B (1991) Does Compulsory School Attendance Affect Schooling and Earnings? | 1.000 | 10 | 3 | 100% |
| 2 | Klooster, J. and Zhelonkin, M (2024) Outlier Robust Inference in the Instrumental Variable Model With Applications to Causal Effects self | 1.000 | 5 | 3 | 100% |
| 3 | Alesina, A. and Zhuravskaya, E (2011) Segregation and the Quality of Government in a Cross Section of Countries | 0.874 | 11 | 2 | 100% |
| 4 | Ananat, E. O (2011) The Wrong Side(s) of the Tracks: The Causal Effects of Racial Segregation on Urban Poverty and Inequality | 0.874 | 9 | 2 | 100% |
| 5 | Staiger, D. and Stock, J. H (1997) Instrumental Variables Regression With Weak Instruments | 0.874 | 8 | 2 | 100% |
| 6 | Andrews, I., Stock, J. H., and Sun, L (2019) Weak Instruments in Instrumental Variables Regression: Theory and Practice | 0.874 | 6 | 2 | 100% |
| 7 | Moreira, M. J (2003) A Conditional Likelihood Ratio Test for Structural Models | 0.874 | 6 | 2 | 100% |
| 8 | Heritier, S. and Ronchetti, E (1994) Robust Bounded-Influence Tests in General Parametric Models | 0.811 | 5 | 2 | 80% |
| 9 | Hampel, F. R., Ronchetti, E. M., Rousseeuw, P. J., and Stahel, W. A (1986) Robust Statistics: The Approach Based on Influence Functions | 0.644 | 4 | 1 | 100% |
| 10 | Bound, J., Jaeger, D. A., and Baker, R. M (1995) Problems With Instrumental Variables Estimation When the Correlation Between the Instruments and the Endogeneous Explanatory Var… | 0.644 | 2 | 2 | 100% |
Showing the top 10 of 57 scored citations.