Inference on a Structural Parameter in Instrumental Variables Regression with Weak Instruments

1996 ◽  
Author(s):  
Jiahui Wang ◽  
Eric Zivot
Keyword(s):  
Instrumental Variables ◽  
Structural Parameter ◽  
Weak Instruments

Implementing Valid Two-Step Identification-Robust Confidence Sets for Linear Instrumental-Variables Models

2018 ◽  
Vol 18 (4) ◽  
pp. 803-825 ◽  
Author(s):  
Liyang Sun
Keyword(s):  
Monte Carlo ◽  
Instrumental Variables ◽  
Projection Method ◽  
Econometric Models ◽  
Confidence Sets ◽  
Weak Instruments ◽  
Wald Tests ◽  
Endogenous Variables ◽  
Married Female ◽  
F Statistics

In this article, we consider inference in the linear instrumental-variables models with one or more endogenous variables and potentially weak instruments. I developed a command, twostepweakiv, to implement the two-step identification-robust confidence sets proposed by Andrews (2018, Review of Economics and Statistics 100: 337–348) based on Wald tests and linear combination tests (Andrews, 2016, Econometrica 84: 2155–2182). Unlike popular procedures based on first-stage F statistics (Stock and Yogo, 2005, Testing for weak instruments in linear IV regression, in Identification and Inference for Econometric Models: Essays in Honor of Thomas Rothenberg), the two-step identification-robust confidence sets control coverage distortion without assuming the data are homoskedastic. I demonstrate the use of twostepweakiv with an example of analyzing the effect of wages on married female labor supply. For inference on subsets of parameters, twostepweakiv also implements the refined projection method (Chaudhuri and Zivot, 2011, Journal of Econometrics 164: 239–251). I illustrate that this method is more powerful than the conventional projection method using Monte Carlo simulations.

scholarly journals ADMISSIBLE INVARIANT SIMILAR TESTS FOR INSTRUMENTAL VARIABLES REGRESSION

2009 ◽  
Vol 25 (3) ◽  
pp. 806-818 ◽  
Author(s):  
Victor Chernozhukov ◽  
Christian Hansen ◽  
Michael Jansson
Keyword(s):  
Likelihood Ratio ◽  
Instrumental Variables ◽  
Degrees Of Freedom ◽  
Average Power ◽  
Weighted Average ◽  
Likelihood Ratio Tests ◽  
Weak Instruments ◽  
Working Paper ◽  
Statistical Sense ◽  
Limiting Case

This paper studies a model widely used in the weak instruments literature and establishes admissibility of the weighted average power likelihood ratio tests recently derived by Andrews, Moreira, and Stock (2004, NBER Technical Working Paper 199). The class of tests covered by this admissibility result contains the Anderson and Rubin (1949, Annals of Mathematical Statistics 20, 46–63) test. Thus, there is no conventional statistical sense in which the Anderson and Rubin (1949) test “wastes degrees of freedom.” In addition, it is shown that the test proposed by Moreira (2003, Econometrica 71, 1027–1048) belongs to the closure of (i.e., can be interpreted as a limiting case of) the class of tests covered by our admissibility result.

OPTIMAL INFERENCE WITH MANY INSTRUMENTS

2002 ◽  
Vol 18 (1) ◽  
pp. 140-168 ◽  
Author(s):  
Jinyong Hahn
Keyword(s):  
Sample Size ◽  
Asymptotic Distribution ◽  
Instrumental Variables ◽  
Asymptotic Approximation ◽  
Simultaneous Equations ◽  
Convolution Theorem ◽  
Structural Parameter ◽  
Simultaneous Equations Model ◽  
Many Instruments ◽  
Bayesian Estimators

In this paper, I derive the efficiency bound of the structural parameter in a linear simultaneous equations model with many instruments. The bound is derived by applying a convolution theorem to Bekker's (1994, Econometrica 62, 657–681) asymptotic approximation, where the number of instruments grows to infinity at the same rate as the sample size. Usual instrumental variables estimators with a small number of instruments are heuristically argued to be efficient estimators in the sense that their asymptotic distribution is minimal. Bayesian estimators based on parameter orthogonalization are heuristically argued to be inefficient.

THE IMPACT OF A HAUSMAN PRETEST ON THE ASYMPTOTIC SIZE OF A HYPOTHESIS TEST

2009 ◽  
Vol 26 (2) ◽  
pp. 369-382 ◽  
Author(s):  
Patrik Guggenberger
Keyword(s):  
Least Squares ◽  
Hypothesis Test ◽  
Ordinary Least Squares ◽  
Reduced Form ◽  
Structural Parameter ◽  
Ratio Test ◽  
Two Stage ◽  
Weak Instruments ◽  
Asymptotic Size ◽  
The Impact

This paper investigates the asymptotic size properties of a two-stage test in the linear instrumental variables model when in the first stage a Hausman (1978) specification test is used as a pretest of exogeneity of a regressor. In the second stage, a simple hypothesis about a component of the structural parameter vector is tested, using a t-statistic that is based on either the ordinary least squares (OLS) or the two-stage least squares estimator (2SLS), depending on the outcome of the Hausman pretest. The asymptotic size of the two-stage test is derived in a model where weak instruments are ruled out by imposing a positive lower bound on the strength of the instruments. The asymptotic size equals 1 for empirically relevant choices of the parameter space. The size distortion is caused by a discontinuity of the asymptotic distribution of the test statistic in the correlation parameter between the structural and reduced form error terms. The Hausman pretest does not have sufficient power against correlations that are local to zero while the OLS-based t-statistic takes on large values for such nonzero correlations. Instead of using the two-stage procedure, the recommendation then is to use a t-statistic based on the 2SLS estimator or, if weak instruments are a concern, the conditional likelihood ratio test by Moreira (2003).

Many instruments: Implementation in Stata

2019 ◽  
Vol 19 (4) ◽  
pp. 849-866
Author(s):  
Stanislav Anatolyev ◽  
Alena Skolkova
Keyword(s):  
Instrumental Variables ◽  
Instrumental Variable ◽  
Simulation Experiment ◽  
Real Data ◽  
Projection Matrix ◽  
Consistent Estimation ◽  
Specification Tests ◽  
Weak Instruments ◽  
Many Instruments

In recent decades, econometric tools for handling instrumental-variable regressions characterized by many instruments have been developed. We introduce a command, mivreg, that implements consistent estimation and testing in linear instrumental-variables regressions with many (possibly weak) instruments. mivreg covers both homoskedastic and heteroskedastic environments, estimators that are both nonrobust and robust to error nonnormality and projection matrix limit, and parameter tests and specification tests both with and without correction for existence of moments. We also run a small simulation experiment using mivreg and illustrate how mivreg works with real data.

ON THE ASYMPTOTIC SIZE DISTORTION OF TESTS WHEN INSTRUMENTS LOCALLY VIOLATE THE EXOGENEITY ASSUMPTION

2011 ◽  
Vol 28 (2) ◽  
pp. 387-421 ◽  
Author(s):  
Patrik Guggenberger
Keyword(s):  
Instrumental Variables ◽  
Alternative Measure ◽  
Inference Procedure ◽  
Size Distortion ◽  
Weak Instruments ◽  
Testing Procedures ◽  
Generalized Empirical Likelihood ◽  
Asymptotic Size ◽  
Nominal Size ◽  
Distortion Reduction

In the linear instrumental variables model with possibly weak instruments we derive the asymptotic size of testing procedures when instruments locally violate the exogeneity assumption. We study the tests by Anderson and Rubin (1949, The Annals of Mathematical Statistics 20, 46–63), Moreira (2003, Econometrica 71, 1027–1048), and Kleibergen (2005, Econometrica 73, 1103–1123) and their generalized empirical likelihood versions. These tests have asymptotic size equal to nominal size when the instruments are exogenous but are size distorted otherwise. While in just-identified models all the tests that we consider are equally size-distorted asymptotically, the Anderson-Rubin type tests are less size-distorted than the tests of Moreira (2003) and Kleibergen in over-identified situations. On the other hand, we also show that there are parameter sequences under which the former test asymptotically overrejects more frequently. Given that strict exogeneity of instruments is often a questionable assumption, our findings should be important to applied researchers who are concerned about the degree of size distortion of their inference procedure. We suggest robustness of asymptotic size under local model violations as a new alternative measure to choose among competing testing procedures. We also investigate the subsampling and hybrid tests introduced in Andrews and Guggenberger (2010a, Journal of Econometrics 158, 285–305) and show that they do not offer any improvement in terms of size-distortion reduction over the Anderson-Rubin type tests.

Weak Instruments in Instrumental Variables Regression: Theory and Practice

2019 ◽  
Vol 11 (1) ◽  
pp. 727-753 ◽  
Author(s):  
Isaiah Andrews ◽  
James H. Stock ◽  
Liyang Sun
Keyword(s):  
Instrumental Variables ◽  
Clustered Data ◽  
Practical Importance ◽  
American Economic Review ◽  
Theory And Practice ◽  
Confidence Sets ◽  
Weak Instruments ◽  
Endogenous Regressors ◽  
Conventional Methods ◽  
Regression Theory

When instruments are weakly correlated with endogenous regressors, conventional methods for instrumental variables (IV) estimation and inference become unreliable. A large literature in econometrics has developed procedures for detecting weak instruments and constructing robust confidence sets, but many of the results in this literature are limited to settings with independent and homoskedastic data, while data encountered in practice frequently violate these assumptions. We review the literature on weak instruments in linear IV regression with an emphasis on results for nonhomoskedastic (heteroskedastic, serially correlated, or clustered) data. To assess the practical importance of weak instruments, we also report tabulations and simulations based on a survey of papers published in the American Economic Review from 2014 to 2018 that use IV. These results suggest that weak instruments remain an important issue for empirical practice, and that there are simple steps that researchers can take to better handle weak instruments in applications.

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