Inference in Instrumental Variable Models With Heteroskedasticity and Many Instruments

Crudu, Federico; Mellace, Giovanni; Sándor, Zsolt

doi:10.1017/s026646662000016x

Cited by 11 publications

(12 citation statements)

References 42 publications

(78 reference statements)

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“…We note that the standard estimators proposed by Crudu et al (2021) are equal to Chao et al's (2012) estimators with their residual êi replaced by e i (β 0 ). Specifically, let…”

Section: Verifying Assumption 2 I1 Standard Estimatorsmentioning

confidence: 88%

“…It is possible to compute γ(β 0 ) based on Chao et al's (2012) argument with their JIVE-based residuals êi from the structure equation replaced by e i (β 0 ). The consistency of such an estimator Φ 1 (β 0 ) for Φ 1 (β 0 ) has been established by Crudu et al (2021) under weak identification and β 0 = β. Similar arguments can be used to show the consistency of rest of the elements in γ(β 0 ) under both weak and strong identifications.…”

Section: Setup and Limit Problemsmentioning

confidence: 99%

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A Conditional Linear Combination Test with Many Weak Instruments

Lim¹,

Wang²,

Zhang³

2022

Preprint

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We consider a linear combination of jackknife Anderson-Rubin (AR) and orthogonalized Lagrangian multiplier (LM) tests for inference in IV regressions with many weak instruments and heteroskedasticity. We choose the weight in the linear combination based on a decisiontheoretic rule that is adaptive to the identification strength. Under both weak and strong identifications, the proposed linear combination test controls asymptotic size and is admissible. Under strong identification, we further show that our linear combination test is the uniformly most powerful test against local alternatives among all tests that are constructed based on the jackknife AR and LM tests only and invariant to sign changes.

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“…We note that the standard estimators proposed by Crudu et al (2021) are equal to Chao et al's (2012) estimators with their residual êi replaced by e i (β 0 ). Specifically, let…”

Section: Verifying Assumption 2 I1 Standard Estimatorsmentioning

confidence: 88%

Section: Setup and Limit Problemsmentioning

confidence: 99%

A Conditional Linear Combination Test with Many Weak Instruments

Lim¹,

Wang²,

Zhang³

2022

Preprint

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“…This is motivated by the recent increase in popularity of penalisation-based approaches to the (very) many IV problem is sufficient for the case of independent data. Recently, fully weak-identification robust AR-type statistics have been developed that allow for the number of IVs to be of the order of magnitude of T (Anatolyev and Gospodinov, 2010;Crudu, Mellace, and Sándor, 2020;Mikusheva and Sun, 2020). However, all of these approaches treat the IVs as fixed, and are hence not applicable in the context of time series.…”

Section: Ad-hoc Selection Of Instrumental Variablesmentioning

confidence: 99%

“…Contrarily to other approaches in the literature, this statistic requires no assumption on the factor structure of the IVs, nor does it make any sparsity-type assumption that requires only a few of the very many IVs to be relevant, while allowing for a number of IVs that increases exponentially with the sample size. This test directly contributes to the (very) many weak IVs literature predominantly restricted to the cross-sectional case (see Anatolyev and Gospodinov (2010), Belloni et al (2012), Crudu, Mellace, and Sándor (2020), and Mikusheva and Sun ( 2020)), and can find application well beyond the example of NKPCs considered in this paper.…”

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confidence: 93%

Inference on the New Keynesian Phillips Curve with Very Many Instrumental Variables

Dovì¹

2021

Preprint

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Limited-information inference on New Keynesian Phillips Curves (NKPCs) and other singleequation macroeconomic relations is characterised by weak and high-dimensional instrumental variables (IVs). Beyond the efficiency concerns previously raised in the literature, I show by simulation that ad-hoc selection procedures can lead to substantial biases in post-selection inference. I propose a Sup Score test that remains valid under dependent data, arbitrarily weak identification, and a number of IVs that increases exponentially with the sample size.Conducting inference on a standard NKPC with 359 IVs and 179 observations, I find substantially wider confidence sets than those commonly found. * I thank Sophocles Mavroeidis and Anna Mikusheva for very helpful comments and suggestions. All errors and omissions are my own.

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“…Crudu et al . () design a hybrid parameter and specification test based on the Anderson–Rubin statistic and Bekker and Crudu () symmetric jackknife objective function. In a way, this is a generalization of the Anatolyev and Gospodinov's () test robust to conditional heteroskedasticity and asymptotically unbalanced instrument design.…”

Section: Heteroskedastic Model With Many Instrumentsmentioning

confidence: 99%

Many Instruments and/or Regressors: A Friendly Guide

Anatolyev

2018

Journal of Economic Surveys

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This paper surveys the state of the art in the econometrics of regression models with many instruments or many regressors based on alternative -namely, dimension -asymptotics. We list critical results of dimension asymptotics that lead to better approximations of properties of familiar and alternative estimators and tests when the instruments and/or regressors are numerous. Then, we consider the problem of estimation and inference in the basic linear instrumental variables regression setup with many strong instruments. We describe the failures of conventional estimation and inference, as well as alternative tools that restore consistency and validity. We then add various other features to the basic model such as heteroskedasticity, instrument weakness, etc., in each case providing a review of the existing tools for proper estimation and inference. Subsequently, we consider a related but different problem of estimation and testing in a linear mean regression with many regressors. We also describe various extensions and connections to other settings, such as panel data models, spatial models, time series models, and so on. Finally, we provide practical guidance regarding which tools are most suitable to use in various situations when many instruments and/or regressors turn out to be an issue.Most recent theoretical literature tends to deal with all of the possible complications involved, and thus the degree of sophistication can become a stumbling block for applied researchers. The survey is structured so that complications are gradually scaffolded on an easily comprehensible skeleton model -a linear homoskedastic IVs model. In this section, we describe a road map for how the survey is organized.Section 3 presents the statistical foundations for many instrument/regressor asymptotics; an uninterested reader may skip this section during a first reading and jump to Section 4. First, we reiterate the idea of alternative asymptotic approximations, in particular, dimension asymptotics. Second, the historical evolution of limit theorems for bilinear forms -the main building block of many instrument/regressor MANY INSTRUMENTS AND/OR REGRESSORS: A FRIENDLY GUIDE 691 asymptotics -is shown, starting with an example of a simplest quadratic form, to show the differences between the approaches -the traditional asymptotics and dimension asymptotics -and how they interlock. Third, a certain important asymptotic property of the diagonal of the projection matrix is discussed.In Section 4, a linear homoskedastic IVs model is considered in detail. The reasons why 2SLS estimation fails and various remedies for such failures (bias correction, jackknifing, and LIML) are discussed. The alternative asymptotic distributions of consistent estimators are presented, initially for the case of normal errors. Then, we relax error normality to examine the arising complications and discuss how they can be handled. In addition to inferential procedures regarding parameter restrictions, the issues of asymptotic efficiency and specification testing ar...

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Inference in Instrumental Variable Models With Heteroskedasticity and Many Instruments

Cited by 11 publications

References 42 publications

A Conditional Linear Combination Test with Many Weak Instruments

A Conditional Linear Combination Test with Many Weak Instruments

Inference on the New Keynesian Phillips Curve with Very Many Instrumental Variables

Many Instruments and/or Regressors: A Friendly Guide

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