A Conditional Likelihood Ratio Test for Structural Models
Abstract
This paper develops a general method for constructing exactly similar tests based on the conditional distribution of nonpivotal statistics in a simultaneous equations model with normal errors and known reduced-form covariance matrix. These tests are shown to be similar under weak-instrument asymptotics when the reduced-form covariance matrix is estimated and the errors are non-normal. The conditional test based on the likelihood ratio statistic is particularly simple and has good power properties. Like the score test, it is optimal under the usual local-to-null asymptotics, but it has better power when identification is weak.
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This result is loosely parallel to results in the weak identification literature showing that certain procedures control size under weak identification but are efficient under strong identification.
“We view this result as loosely parallel to results in the weak identification literature showing that certain procedures control size under weak identification but are efficient under strong identification (e.g.Moreira, 2003).”
From A More Credible Approach to Parallel Trends (2023) · cites this paper as Moreira, 2003
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- Authors
- Moreira, M. J.
- Affiliations
- Harvard University (US)
- Corresponding author
- Moreira, Marcelo J.
- Venue
- Econometrica
- Publisher
- The Econometric Society
- Published
- 2003-07
- Volume
- 71
- Issue
- 4
- Pages
- 1027-1048
- ISSN
- 0012-9682 (ISSN-L)
- 1468-0262
- OpenAlex
- W2123750251
- Cited by
- 796
- References
- 28
- Citations by year
- 2026: 22 · 2025: 31 · 2024: 24 · 2023: 22 · 2022: 29 · 2021: 34 · 2020: 34 · 2019: 37 · 2018: 35 · 2017: 50 · 2016: 38 · 2015: 40 · 2014: 39 · 2013: 47 · 2012: 46
- FWCI
- 29.09
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Econometrica (publishedVersion)
- LA Referencia (Red Federada de Repositorios Institucionales de Publicaciones Científicas) (publishedVersion)
- Americanae (AECID Library) (submittedVersion)
- Topics
- Physical Sciences › Mathematics › Statistics and Probability › Advanced Causal Inference Techniques
- Social Sciences › Economics, Econometrics and Finance › General Economics, Econometrics and Finance › Monetary Policy and Economic Impact
- Physical Sciences › Mathematics › Statistics and Probability › Advanced Statistical Methods and Models
- Keywords
- conditional likelihood ratio test, structural equation modeling, simultaneous equations model, weak instruments, score test, weak identification, statistical power, non-normal errors
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