We develop a concept of weak identification in linear IV models in which the number of instruments can grow at the same rate or slower than the sample size. We propose a jackknifed version of the classical weak identification-robust Anderson-Rubin (AR) test statistic. Large-sample inference based on the jackknifed AR is valid under heteroscedasticity and weak identification. The feasible version of this statistic uses a novel variance estimator. The test has uniformly correct size and good power properties. We also develop a pre-test for weak identification that is related to the size property of a Wald test based on the Jackknife Instrumental Variable Estimator (JIVE). This new pre-test is valid under heteroscedasticity and with many instruments.
We propose and implement an approach to inference in linear instrumental variables models which is simultaneously robust and computationally tractable. Inference is based on self-normalization of sample moment conditions, and allows for (but does not require) many (relative to the sample size), weak, potentially invalid or potentially endogenous instruments, as well as for many regressors and conditional heteroskedasticity. Our coverage results are uniform and can deliver a small sample guarantee. We develop a new computational approach based on semidefinite programming, which we show can equa…
Instrumental variables estimation has gained considerable traction in recent decades as a tool for causal inference, particularly amongst empirical researchers. This paper makes three contributions. First, we provide a detailed theoretical discussion on the properties of the standard two-stage least squares estimator in the presence of weak instruments and introduce and derive two alternative estimators. Second, we conduct Monte-Carlo simulations to compare the finite-sample behavior of the different estimators, particularly in the weak-instruments case. Third, we apply the estimators to a rea…
In this note, we offer an approach to estimating causal/structural parameters in the presence of many instruments and controls based on methods for estimating sparse high-dimensional models. We use these high-dimensional methods to select both which instruments and which control variables to use. The approach we take extends BCCH2012, which covers selection of instruments for IV models with a small number of controls, and extends BCH2014, which covers selection of controls in models where the variable of interest is exogenous conditional on observables, to accommodate both a large number of co…
Limited-information inference on New Keynesian Phillips Curves (NKPCs) and other single-equation 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 …
The identification of the network effect is based on either group size variation, the structure of the network or the relative position in the network. I provide easy-to-verify necessary conditions for identification of undirected network models based on the number of distinct eigenvalues of the adjacency matrix. Identification of network effects is possible; although in many empirical situations existing identification strategies may require the use of many instruments or instruments that could be strongly correlated with each other. The use of highly correlated instruments or many instrument…
This paper presents a simple method for carrying out inference in a wide variety of possibly nonlinear IV models under weak assumptions. The method is non-asymptotic in the sense that it provides a finite sample bound on the difference between the true and nominal probabilities of rejecting a correct null hypothesis. The method is a non-Studentized version of the Anderson-Rubin test but is motivated and analyzed differently. In contrast to the conventional Anderson-Rubin test, the method proposed here does not require restrictive distributional assumptions, linearity of the estimated model, or…
Weak-instrument-robust subvector inference in instrumental variables regression: A subvector Lagrange multiplier test and properties of subvector Anderson-Rubin confidence sets
Instrumental variables (IV) regression is widely used to estimate causal treatment effects in settings where receipt of treatment is not fully random, but there exists an instrument that generates exogenous variation in treatment exposure. While IV can recover consistent treatment effect estimates, they are often noisy. Building upon earlier work in biostatistics (Joffe and Brensinger, 2003) and relating to an evolving literature in econometrics (including Abadie et al., 2019; Huntington-Klein, 2020; Borusyak and Hull, 2020), we study how to improve the efficiency of IV estimates by exploiting…
This paper develops a new specification test for the instrument weakness when the number of instruments $K_n$ is large with a magnitude comparable to the sample size $n$. The test relies on the fact that the difference between the two-stage least squares (2SLS) estimator and the ordinary least squares (OLS) estimator asymptotically disappears when there are many weak instruments, but otherwise converges to a non-zero limit. We establish the limiting distribution of the difference within the above two specifications, and introduce a delete-$d$ Jackknife procedure to consistently estimate the as…
In this paper, I show that classic two-stage least squares (2SLS) estimates are highly unstable with weak instruments. I propose a ridge estimator (ridge IV) and show that it is asymptotically normal even with weak instruments, whereas 2SLS is severely distorted and un-bounded. I motivate the ridge IV estimator as a convex optimization problem with a GMM objective function and an L2 penalty. I show that ridge IV leads to sizable mean squared error reductions theoretically and validate these results in a simulation study inspired by data designs of papers published in the American Economic Revi…
University of British Columbia（不列颠哥伦比亚大学）；Google（谷歌）；Columbia University（哥伦比亚大学）
Instrumental variable methods provide a powerful approach to estimating causal effects in the presence of unobserved confounding. But a key challenge when applying them is the reliance on untestable "exclusion" assumptions that rule out any relationship between the instrument variable and the response that is not mediated by the treatment. In this paper, we show how to perform consistent IV estimation despite violations of the exclusion assumption. In particular, we show that when one has multiple candidate instruments, only a majority of these candidates---or, more generally, the modal candid…
Empirical researchers are increasingly faced with rich data sets containing many controls or instrumental variables, making it essential to choose an appropriate approach to variable selection. In this paper, we provide results for valid inference after post- or orthogonal $L_2$-Boosting is used for variable selection. We consider treatment effects after selecting among many control variables and instrumental variable models with potentially many instruments. To achieve this, we establish new results for the rate of convergence of iterated post-$L_2$-Boosting and orthogonal $L_2$-Boosting in a…
This paper is concerned with the findings related to the robust first-stage F-statistic in the Monte Carlo analysis of Andrews (2018), who found in a heteroskedastic grouped-data design that even for very large values of the robust F-statistic, the standard 2SLS confidence intervals had large coverage distortions. This finding appears to discredit the robust F-statistic as a test for underidentification. However, it is shown here that large values of the robust F-statistic do imply that there is first-stage information, but this may not be utilized well by the 2SLS estimator, or the standard G…
