Estimation With Many Instrumental Variables

By Christian Hansen, Jerry A. Hausman, Whitney K. Newey. Journal of Business & Economic Statistics, 2006

350 citations recorded by the source corpus.

Using many valid instrumental variables has the potential to improve efficiency but makes the usual inference procedures inaccurate. We give corrected standard errors, an extension of Bekker to nonnormal disturbances, that adjust for many instruments. We find that this adjustment is useful in empirical work, simulations, and in the asymptotic theory. Use of the corrected standard errors in t-ratios leads to an asymptotic approximation order that is the same when the number of instrumental variables grows as when the number of instruments is fixed. We also give a version of the Kleibergen weak instrument statistic that is robust to many instruments.

Subfields: Finance, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/eb1612b5fc43697abbd42cdd75b97fc31415f2bf

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Citations in the corpus

Two-Sample Instrumental Variable Analyses Using Heterogeneous Samples (2017, background): “In this regime, LIML-like estimators are asymptotically unbiased but the asymptotic variance needs to be carefully derived (Hansen et al., 2008).”
Criminal Networks: Who is the Key Player? (2012, background): “The 2SLS could be asymptotic biased when the number of IVs increases too fast relative to the sample size (see, e.g., Bekker, 1994; Bekker and van der Ploeg, 2005; Hansen et al., 2008).”
ESTIMATION IN AN INSTRUMENTAL VARIABLES MODEL WITH TREATMENT EFFECT HETEROGENEITY (2012, background): “The choice Ŝ = I2 leads to the symmetrically normalized two-stage least squares estimator studied in Keller (1975), Hillier (1990) and Alonso-Borrego and Arellano (1999).”
On the Asymptotic Optimality of the LIML Estimator with Possibly Many Instruments (2010, background): “Some of these results are improvements on Anderson (1976), Kunitomo (1980), Morimune (1983) and Bekker (1994), Chao and Swanson (2005, 2006), Van Hasselt (2006), Hansen, Hausman, and Newey (2008), several of which are in the literature, and they are presented in a uniform notation.”
The reduced form: A simple approach to inference with weak instruments (2008, neutral): “Both Rothenberg (1984) and Hansen, Hausman, and Newey (2005) suggest that a useful rule of thumb is to not use the usual asymptotic approximation if the Wald statistic is not in the mid-thirties or higher when there is one instrument and one endogenous variable, and this cutoff value is increasing…”
Instrumental variables estimation with many weak instruments using regularized JIVE (2014, methodology): “As an illustration, consider the class of estimators used in Hansen, Hausman, and Newey (2008) which include all the so-called k-class estimators except for OLS: δ = (X P X − αX X) −1 (X P Y − αX Y ) where P = Z(Z Z) − Z , A − denotes a generalized inverse of A, X is an n × G matrix formed by…”
Statistical inference in two-sample summary-data Mendelian randomization using robust adjusted profile score (2018, methodology): “In the one-sample IV literature, this many weak IV setting (p → ∞) has been considered by Bekker [5], Stock and Yogo [49], Hansen, Hausman and Newey [25] among many others in econometrics.”
ALTERNATIVE ASYMPTOTICS AND THE PARTIALLY LINEAR MODEL WITH MANY REGRESSORS (2015, background): “Kunitomo (1980) and Morimune (1983) derived asymptotic variances that are larger than the usual formulae when the number of instruments and sample size grow at the same rate, and Bekker (1994) and others provided consistent estimators of these larger variances.”
Empirical Evidence on Inflation Expectations in the New Keynesian Phillips Curve (2014, methodology): “There is a large econometric literature on this issue; see, e.g., Hansen, Hausman, and Newey (2008).”
Massachusetts Institute of Technology Department of Economics Working Paper Series Sparse Models and Methods for Optimal Instruments with an Application to Eminent Domain Sparse Models and Methods for Optimal Instruments with an Application to Eminent Domain (positive): “In terms of estimation risk, it outperforms both LIML and its modification due to [25] (FULL) 5 which have been advocated as procedures that are robust to using many instruments (e.g. [27]).”
Child Care Choices and Children’s Cognitive Achievement: The Case of Single Mothers (2011, methodology): “(See, e.g., Stock and Yogo 2004; Anderson, Kunitomo, and Matsushita 2005; Andrews and Stock 2006; and Hansen, Hausman, and Newey 2008.)”
Educational mismatch, wages, and wage growth: Overeducation in Sweden, 1974-2000 (2009, methodology): “However, it has been suggested that the bias in the point estimates may be dealt with by estimating the model using Fuller LIML (Andrews and Stock 2005, Hahn et al. 2004, Hansen et al. 2005).”