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Instrumental Variables Two-Stage Least Squares (2SLS) vs. Maximum Likelihood Structural Equation Modeling of Causal Effects in Linear Regression Models

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Abstract
In the presence of omitted variables or similar validity threats, regression estimates are biased. Unbiased estimates (the causal effects) can be obtained in large samples by fitting instead the Instrumental Variables Regression (IVR) model. The IVR model can be estimated using structural equation modeling (SEM) software or using Econometric estimators such as two-stage least squares (2SLS). We describe 2SLS using SEM terminology, and report a simulation study in which we generated data according to a regression model in the presence of omitted variables and fitted (a) a regression model using ordinary least squares, (b) an IVR model using maximum likelihood (ML) as implemented in SEM software, and (c) an IVR model using 2SLS. Coverage rates of the causal effect using regression methods are always unacceptably low (often 0). When using the IVR model, accurate coverage is obtained across all conditions when N = 500. Even when the IVR model is misspecified, better coverage than regression is generally obtained. Differences between 2SLS and ML are small and favor 2SLS in small samples (N <= 100).
Keywords
GENERALIZED-METHOD, Causal inference, structural equation modeling, econometrics, regression, observational data

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MLA
Maydeu-Olivares, Alberto, et al. “Instrumental Variables Two-Stage Least Squares (2SLS) vs. Maximum Likelihood Structural Equation Modeling of Causal Effects in Linear Regression Models.” STRUCTURAL EQUATION MODELING-A MULTIDISCIPLINARY JOURNAL, vol. 26, no. 6, Routledge Journals, Taylor & Francis Ltd, 2019, pp. 876–92.
APA
Maydeu-Olivares, A., Shi, D., & Rosseel, Y. (2019). Instrumental Variables Two-Stage Least Squares (2SLS) vs. Maximum Likelihood Structural Equation Modeling of Causal Effects in Linear Regression Models. STRUCTURAL EQUATION MODELING-A MULTIDISCIPLINARY JOURNAL, 26(6), 876–892.
Chicago author-date
Maydeu-Olivares, Alberto, Dexin Shi, and Yves Rosseel. 2019. “Instrumental Variables Two-Stage Least Squares (2SLS) vs. Maximum Likelihood Structural Equation Modeling of Causal Effects in Linear Regression Models.” STRUCTURAL EQUATION MODELING-A MULTIDISCIPLINARY JOURNAL 26 (6): 876–92.
Chicago author-date (all authors)
Maydeu-Olivares, Alberto, Dexin Shi, and Yves Rosseel. 2019. “Instrumental Variables Two-Stage Least Squares (2SLS) vs. Maximum Likelihood Structural Equation Modeling of Causal Effects in Linear Regression Models.” STRUCTURAL EQUATION MODELING-A MULTIDISCIPLINARY JOURNAL 26 (6): 876–892.
Vancouver
1.
Maydeu-Olivares A, Shi D, Rosseel Y. Instrumental Variables Two-Stage Least Squares (2SLS) vs. Maximum Likelihood Structural Equation Modeling of Causal Effects in Linear Regression Models. STRUCTURAL EQUATION MODELING-A MULTIDISCIPLINARY JOURNAL. 2019;26(6):876–92.
IEEE
[1]
A. Maydeu-Olivares, D. Shi, and Y. Rosseel, “Instrumental Variables Two-Stage Least Squares (2SLS) vs. Maximum Likelihood Structural Equation Modeling of Causal Effects in Linear Regression Models,” STRUCTURAL EQUATION MODELING-A MULTIDISCIPLINARY JOURNAL, vol. 26, no. 6, pp. 876–892, 2019.
@article{8642364,
  abstract     = {In the presence of omitted variables or similar validity threats, regression estimates are biased. Unbiased estimates (the causal effects) can be obtained in large samples by fitting instead the Instrumental Variables Regression (IVR) model. The IVR model can be estimated using structural equation modeling (SEM) software or using Econometric estimators such as two-stage least squares (2SLS). We describe 2SLS using SEM terminology, and report a simulation study in which we generated data according to a regression model in the presence of omitted variables and fitted (a) a regression model using ordinary least squares, (b) an IVR model using maximum likelihood (ML) as implemented in SEM software, and (c) an IVR model using 2SLS. Coverage rates of the causal effect using regression methods are always unacceptably low (often 0). When using the IVR model, accurate coverage is obtained across all conditions when N = 500. Even when the IVR model is misspecified, better coverage than regression is generally obtained. Differences between 2SLS and ML are small and favor 2SLS in small samples (N <= 100).},
  author       = {Maydeu-Olivares, Alberto and Shi, Dexin and Rosseel, Yves},
  issn         = {1070-5511},
  journal      = {STRUCTURAL EQUATION MODELING-A MULTIDISCIPLINARY JOURNAL},
  keywords     = {GENERALIZED-METHOD,Causal inference,structural equation modeling,econometrics,regression,observational data},
  language     = {eng},
  number       = {6},
  pages        = {876--892},
  publisher    = {Routledge Journals, Taylor & Francis Ltd},
  title        = {Instrumental Variables Two-Stage Least Squares (2SLS) vs. Maximum Likelihood Structural Equation Modeling of Causal Effects in Linear Regression Models},
  url          = {http://dx.doi.org/10.1080/10705511.2019.1607740},
  volume       = {26},
  year         = {2019},
}

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