Asymptotic Distribution of Jive in a Heteroskedastic Iv Regression With Many Instruments

Chao, John C.; Swanson, Norman R.; Hausman, Jerry A.; Newey, Whitney K.; Woutersen, Tiemen

doi:10.1017/s0266466611000120

Cited by 67 publications

(42 citation statements)

References 25 publications

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“…Future research may extend to instrumental variables models with heteroskedasticity, with the literature for the many instrument case still being developed (e.g. Chao et al, 2012, and accommodate serial correlation in model errors.…”

Section: Resultsmentioning

confidence: 99%

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Instrumental variables estimation and inference in the presence of many exogenous regressors

Anatolyev

2013

The Econometrics Journal

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Summary We consider a standard instrumental variables model contaminated by the presence of a large number of exogenous regressors. In an asymptotic framework where this number is proportional to the sample size, we study the impact of their ratio on the validity of existing estimators and tests. When the instruments are few, the inference using the conventional 2SLS estimator and associated t and J statistics, as well as the Anderson–Rubin and Kleibergen tests, is still valid. When the instruments are many, the LIML estimator remains consistent, but the presence of many exogenous regressors changes its asymptotic variance. Moreover, the conventional bias correction of the 2SLS estimator is no longer appropriate. We provide asymptotically correct versions of bias correction for the 2SLS estimator, derive its asymptotically correct variance estimator, extend the Hansen–Hausman–Newey LIML variance estimator to the case of many exogenous regressors, and propose asymptotically valid modifications of the J overidentification tests based on the LIML and bias‐corrected 2SLS estimators.

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Section: Resultsmentioning

confidence: 99%

“…We heavily use the properties of M W such as |M Chao et al (2012), and the following and similar inequalities:…”

Section: Proofmentioning

confidence: 99%

Instrumental variables estimation and inference in the presence of many exogenous regressors

Anatolyev

2013

The Econometrics Journal

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“…The promised improvement in efficiency is appealing, but IV estimators based on many instruments may have poor properties. See, for example, Bekker (1994), Chao and Swanson (2005), Hansen, Hausman, and Newey (2008), and Chao, Swanson, Hausman, Newey, and Woutersen (2012), which proposed solutions for this problem based on "many-instrument" asymptotics. 2 In this paper, we contribute to the literature on IV estimation with many instruments by considering the use of Lasso and post-Lasso for estimating the first-stage regression of endogenous variables on the instruments.…”

Section: Introductionmentioning

confidence: 99%

Sparse Models and Methods for Optimal Instruments With an Application to Eminent Domain

et al. 2012

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We develop results for the use of Lasso and post-Lasso methods to form first-stage predictions and estimate optimal instruments in linear instrumental variables (IV) models with many instruments, p. Our results apply even when p is much larger than the sample size, n. We show that the IV estimator based on using Lasso or post-Lasso in the first stage is root-n consistent and asymptotically normal when the first stage is approximately sparse, that is, when the conditional expectation of the endogenous variables given the instruments can be well-approximated by a relatively small set of variables whose identities may be unknown. We also show that the estimator is semiparametrically efficient when the structural error is homoscedastic. Notably, our results allow for imperfect model selection, and do not rely upon the unrealistic "beta-min" conditions that are widely used to establish validity of inference following model selection (see also Belloni, Chernozhukov, and Hansen (2011b)). In simulation experiments, the Lasso-based IV estimator with a data-driven penalty performs well compared to recently advocated many-instrument robust procedures. In an empirical example dealing with the effect of judicial eminent domain decisions on economic outcomes, the Lassobased IV estimator outperforms an intuitive benchmark.Optimal instruments are conditional expectations. In developing the IV results, we establish a series of new results for Lasso and post-Lasso estimators of nonparametric conditional expectation functions which are of independent theoretical and practical interest. We construct a modification of Lasso designed to deal with non-Gaussian, heteroscedastic disturbances that uses a data-weighted 1 -penalty function. By innovatively using moderate deviation theory for self-normalized sums, we provide convergence rates for the resulting Lasso and post-Lasso estimators that are as sharp as the corresponding rates in the homoscedastic Gaussian case under the condition that log p = o(n 1/3 ). We also provide a data-driven method for choosing the penalty level that must be specified in obtaining Lasso and post-Lasso estimates and establish its asymptotic validity under non-Gaussian, heteroscedastic disturbances.KEYWORDS: Inference on a low-dimensional parameter after model selection, imperfect model selection, instrumental variables, Lasso, post-Lasso, data-driven penalty, heteroscedasticity, non-Gaussian errors, moderate deviations for self-normalized sums.

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“…Ashenfelter and Krueger use the simple regression framework while Behrman and Rosenzweig include control variables. Ashenfelter and Krueger (1992) is a preprint of their famous 1994-paper.3 Chao et al (2011) derive asymptotic results for jackknife-adjusted IV-estimators which are consistent for many instruments and allow for heteroskedasticity, see e.g. (Phillips and Hale, 1977).…”

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confidence: 99%

“…3 Chao et al (2011) derive asymptotic results for jackknife-adjusted IV-estimators which are consistent for many instruments and allow for heteroskedasticity, see e.g. (Phillips and Hale, 1977).…”

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A Simple Improvement of the IV‐estimator for the Classical Errors‐in‐Variables Problem

Andersson

Møen

2015

Oxf Bull Econ Stat

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Two measures of an error-ridden explanatory variable make it possible to solve the classical errors-in-variable problem by using one measure as an instrument for the other. It is well known that a second IV estimate can be obtained by reversing the roles of the two measures. We explore a simple estimator that is the linear combination of these two estimates, that minimizes the asymptotic mean squared error. In a Monte Carlo study we show that the gain in precision is significant compared to using only one of the original IV estimates. The proposed estimator also compares well with full information maximum likelihood under normality. Email: jonas.andersson@nhh.no and jarle.moen@nhh.no.We have received useful comments from Erik Biørn, Gernot Doppelhofer and Arngrim Hunnes. We are grateful to Anne Liv Scrase for proof-reading the manuscript.

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Asymptotic Distribution of Jive in a Heteroskedastic Iv Regression With Many Instruments

Cited by 67 publications

References 25 publications

Instrumental variables estimation and inference in the presence of many exogenous regressors

Instrumental variables estimation and inference in the presence of many exogenous regressors

Sparse Models and Methods for Optimal Instruments With an Application to Eminent Domain

A Simple Improvement of the IV‐estimator for the Classical Errors‐in‐Variables Problem

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