Asymptotics of Diagonal Elements of Projection Matrices Under Many Instruments/Regressors

Anatolyev, Stanislav; Yaskov, Pavel

doi:10.1017/s0266466616000165

Cited by 20 publications

(7 citation statements)

References 31 publications

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“…Assumption 3.2(b) requires the mean square approximation error of the f (x) and g(x) by the linear combination of instruments ψ K (x) goes to 0 as the number of instrument increases. Assumption 3.3 also imposes homoskedasticity and restricts the growth rate of K. For example, K = O(N ) is not allowed under 3.3(c), see van Hasselt (2010), Anatolyev and Yaskov (2017), and references therein.…”

Section: Assumptions and Higher-order Mse Resultsmentioning

confidence: 99%

Higher-Order Approximation of Iv Estimators With Invalid Instruments

Kang¹

2022

Econom. Theory

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This paper analyzes the higher-order approximation of instrumental variable (IV) estimators in a linear homoskedastic IV regression model when a large set of instruments with potential invalidity is present. We establish theoretical results on the higher-order mean-squared error (MSE) approximation of the two-stage least-squares (2SLS), the limited information maximum likelihood (LIML), the Fuller (FULL), the bias-adjusted 2SLS, and jackknife version of the LIML and FULL estimators by allowing for local violations of the instrument exogeneity conditions. Based on the approximation to the higher-order MSE, we consider the instrument selection criteria that can be used to choose among the set of available instruments. We demonstrate the asymptotic optimality of the instrument selection procedure proposed by Donald and Newey (2001, Econometrica 69, 1161–1191) in the presence of locally (faster than $N^{-1/2}$ ) invalid instruments in the sense that the dominant term in the MSE with the chosen instrument is asymptotically equivalent to the infeasible optimum. Furthermore, we propose instrument selection procedures to choose instruments among the sets of conservative (known) valid instruments and potentially locally ( $N^{-1/2}$ ) invalid instruments based on the higher-order MSE of the IV estimators by considering the bias-variance trade-off.

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Section: Assumptions and Higher-order Mse Resultsmentioning

confidence: 99%

Higher-Order Approximation of Iv Estimators With Invalid Instruments

Kang¹

2022

Econom. Theory

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“…Let us consider the Monte Carlo setup of Hausman et al (2012). One of the features of this experiment is that the sum of the diagonal elements of P does not converge to λ = lim k n , as shown in Anatolyev and Yaskov (2017). The DGP is given by where γ = β = 1, while π = 0.1 in the analysis of size and π ∈ {0.1,1} in the analysis of power.…”

Section: Data Generating Processesmentioning

confidence: 99%

Inference in Instrumental Variable Models With Heteroskedasticity and Many Instruments

2020

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This paper proposes novel inference procedures for instrumental variable models in the presence of many, potentially weak instruments that are robust to the presence of heteroskedasticity. First, we provide an Anderson–Rubin-type test for the entire parameter vector that is valid under assumptions weaker than previously proposed Anderson–Rubin-type tests. Second, we consider the case of testing a subset of parameters under the assumption that a consistent estimator for the parameters not under test exists. We show that under the null, the proposed statistics have Gaussian limiting distributions and derive alternative chi-square approximations. An extensive simulation study shows the competitive finite sample properties in terms of size and power of our procedures. Finally, we provide an empirical application using college proximity instruments to estimate the returns to education.

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“…Note that the instrument vector is such that the diagonal of P is asymptotically heterogeneous (see Anatolyev and Yaskov 2017). In the homoskedastic case, simplifications due to error normality pertaining to variance estimation and specification testing (see sections 3.2 and 3.3) are applicable.…”

Section: Simulationsmentioning

confidence: 99%

Many instruments: Implementation in Stata

Anatolyev

Skolkova

2019

The Stata Journal

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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.

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Asymptotics of Diagonal Elements of Projection Matrices Under Many Instruments/Regressors

Cited by 20 publications

References 31 publications

Higher-Order Approximation of Iv Estimators With Invalid Instruments

Higher-Order Approximation of Iv Estimators With Invalid Instruments

Inference in Instrumental Variable Models With Heteroskedasticity and Many Instruments

Many instruments: Implementation in Stata

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