EconBase
← All papers

Inference on the TSLS Estimand with Weak Instruments and Treatment Effect Heterogeneity

Arnstein Vestre

arXiv 5 Jun 2026 · Econometrics

arXiv:2606.07871 · PDF · DOI · OpenAlex · Extracted main text

Abstract

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.

Citation extraction

41
references
71
in-text mentions
41
distinct cited
0
self-citations
8,202
main-text words

appendix boundary found by appendix_command · 47% of the source is main text. Read the extracted text to check this.

Most heavily cited references

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.

ReferenceIntensityMentionsSectionsMain text
1Moreira, M. J (2003) A conditional likelihood ratio test for structural models1.00063100%
2Anderson, T. W. and Rubin, H (1949) Estimation of the parameters of a single equation in a complete system of stochastic equations1.00053100%
3Berger, R. L. and Boos, D. D (1994) P values maximized over a confidence set for the nuisance parameter0.92843100%
4Kleibergen, F (2002) Pivotal statistics for testing structural parameters in instrumental variables regression0.92843100%
5Staiger, D. and Stock, J. H (1997) Instrumental variables regression with weak instruments0.87462100%
6Stern, R. J. and Wolkowicz, H (1995) Indefinite trust region subproblems and nonsymmetric eigenvalue perturbations0.7373367%
7Angrist, J. D. and Imbens, G. W (1995) Two-stage least squares estimation of average causal effects in models with variable treatment intensity0.73732100%
8Lee, 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 IV0.73732100%
9Angrist, 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…0.64422100%
10Andrews, I., Stock, J. H., and Sun, L (2019) Weak instruments in instrumental variables regression: Theory and practice0.51121100%

Showing the top 10 of 41 scored citations.