arXiv 5 Jun 2026 · Econometrics
arXiv:2606.07871 · PDF · DOI · OpenAlex · Extracted main text
Traditional inference on the coefficient in an instrumental variables regression does not retain size when the instrument set is weak. With constant treatment effects or one instrument, the Anderson and Rubin (1949) AR test, the Klieibergen (2002)-Moreira (2003) LM test, and the Moreira CLR test provide robust alternatives which retain validity. Under treatment effect heterogeneity, no valid inference procedure exists in the overidentified setting. This paper develops the TSLS likelihood ratio (TLR) statistic, for performing inference on the TSLS estimand. When combined with a two-step procedure in the spirit of Berger and Boos (1994), it retains uniform validity across both the weak- and strong-instrument regimes. The procedure retains power with small choices of first-step level, hence the test can be constructed to numerically coincide with the Wald test in the strong-instrument limit.
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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 | Moreira, M. J (2003) A conditional likelihood ratio test for structural models | 1.000 | 6 | 3 | 100% |
| 2 | Anderson, T. W. and Rubin, H (1949) Estimation of the parameters of a single equation in a complete system of stochastic equations | 1.000 | 5 | 3 | 100% |
| 3 | Berger, R. L. and Boos, D. D (1994) P values maximized over a confidence set for the nuisance parameter | 0.928 | 4 | 3 | 100% |
| 4 | Kleibergen, F (2002) Pivotal statistics for testing structural parameters in instrumental variables regression | 0.928 | 4 | 3 | 100% |
| 5 | Staiger, D. and Stock, J. H (1997) Instrumental variables regression with weak instruments | 0.874 | 6 | 2 | 100% |
| 6 | Stern, R. J. and Wolkowicz, H (1995) Indefinite trust region subproblems and nonsymmetric eigenvalue perturbations | 0.737 | 3 | 3 | 67% |
| 7 | Angrist, J. D. and Imbens, G. W (1995) Two-stage least squares estimation of average causal effects in models with variable treatment intensity | 0.737 | 3 | 2 | 100% |
| 8 | Lee, D. S., McCrary, J., Moreira, M. J., Porter, J. R., and Yap, L (2023) What to do when you can't use '1.96' confidence intervals for IV | 0.737 | 3 | 2 | 100% |
| 9 | Angrist, J. D., Graddy, K., and Imbens, G. W (2000) The interpretation of instrumental variables estimators in simultaneous equations models with an application to the demand for f… | 0.644 | 2 | 2 | 100% |
| 10 | Andrews, I., Stock, J. H., and Sun, L (2019) Weak instruments in instrumental variables regression: Theory and practice | 0.511 | 2 | 1 | 100% |
Showing the top 10 of 41 scored citations.