Inverting the indirect—The ellipse and the boomerang: Visualizing the confidence intervals of the structural coefficient from two-stage least squares (original) (raw)
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2009
This paper considers the problem of estimating model parameters in the case of endogenous regressors when the problem involves a large number of weak and/or invalid instruments. A Latent generalized method of moments estimator in a data rich environment (LGMM) is presented in the broader context of the generalized method of moments estimators (GMM), and a nonlinear simultaneous latent-factors GMM estimation routine is described that provides estimates of both the latent instruments and the structural parameters. The potential weak instruments are allowed to be highly correlated with the innovation of the regression equation. Consistency of the single equation LGMM estimator is established. We show that this estimator is consistent even if the observed instruments are invalid. A Monte Carlo experiment, that compares the relative performance of this estimator with some other estimators, is reviewed. Simulations indicate that the method outperforms OLS and other estimators when the instruments are both valid and invalid and, the idiosyncratic errors may be weakly cross-correlated and heteroskedastic.
Time to Demystify Endogeneity Bias
SSRN Electronic Journal, 2015
This study exposes the flaw in defining endogeneity bias by correlation between an explanatory variable and the error term of a regression model. Through dissecting the links which have led to entanglement of measurement errors, simultaneity bias, omitted variable bias and self-selection bias, the flaw is revealed to stem from a Utopian mismatch of reality directly with single explanatory variable models. The consequent estimation-centred route to circumvent the correlation is shown to be committing a type III error. Use of single variable based 'consistent' estimators without consistency of model with data can result in significant distortion of causal postulates of substantive interest. This strategic error is traced to a loss in translation of those causal postulates into multivariate conditional models appropriately designed through an efficient combination of substantive knowledge with data information. Endogeneity bias phobia will be uprooted once applied modelling research is centred on such designs.
2009
In this paper, we propose a procedure based on projection techniques for building exact confidence sets for covariances between errors and endogenous regressors in linear structural models. This procedure is robust to weak instruments and can be used as exogeneity test for endogenous regressors. We characterize the necessary and sufficient conditions under which these confidence sets are bounded. We also show that the procedure is asymptotically valid even in presence of heteroskedasticity or autocorrelation.
Credible Two-Stage Least Squares Inference With Possibly-Flawed Instruments
Two-stage least squares (2SLS) is commonly used to obtain consistent structural parameter inferences and asymptotically-valid inference results where one or more explanatory variables is -due to endogeneity, measurement error, etc.-correlated with the model error term. But the validity of 2SLS rests on an assumption that each of the instruments used is itself is unflawed -i.e., uncorrelated with the model error. Here we finesse the untestability of this assumption by quantifying the sensitivity of any particular 2SLS inference result to failures of this assumption. Our results make it feasible to determine which 2SLS inference results are robust to instrument flaws and which are not, thereby making it possible to obtain 'credible' 2SLS inferences.
Resurgence of Instrument Variable Estimation and Fallacy of Endogeneity
2014
This paper provides a critical “rational reconstruction”of the evolution of attitudes to the use of the instrumental variable, IV, estimator in different parts of econometrics. The author, like many statisticians, is sceptical about the usefulness of the technique and in particular about the resurgence of its use in micro-econometrics. Both the critique and the detailed, nicely documented, history of the way that interest in instrumental variables has waxed and waned are very interesting. While the paper is polemical and is likely to be controversial, it raises some relevant questions and should engender some debate, hopefully prompting some interesting responses. I think the paper might be more effective were it less polemical, but I think that with some revision the paper is worth publishing. Below I discuss some of the issues and make a few suggestions.
Structural equation modeling, 2019
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).
Industrial Marketing Management, 2020
Endogeneity issues in empirical research have received increasing academic attention. Tackling endogeneity problems effectively and using the appropriate estimation techniques are important quality benchmarks in the publication process of many academic journals. In this paper, we discuss the use of instrumental variables (IVs) in business and marketing research, with a particular focus on its implementation in STATA. We discuss several pre-and postestimation tests that researchers can use to implement various versions of IVs in STATA, including two-stage least squares regression, limited information maximum likelihood estimation, and generalized method of moments.