More Like this

1. ASYMPTOTIC SIZE OF KLEIBERGEN’S LM AND CONDITIONAL LR TESTS FOR MOMENT CONDITION MODELS

   https://doi.org/10.1017/S0266466616000347  

   Andrews, Donald W.K.; Guggenberger, Patrik (October 2017, Econometric Theory)

   An influential paper by Kleibergen (2005, Econometrica 73, 1103–1123) introduces Lagrange multiplier (LM) and conditional likelihood ratio-like (CLR) tests for nonlinear moment condition models. These procedures aim to have good size performance even when the parameters are unidentified or poorly identified. However, the asymptotic size and similarity (in a uniform sense) of these procedures have not been determined in the literature. This paper does so. This paper shows that the LM test has correct asymptotic size and is asymptotically similar for a suitably chosen parameter space of null distributions. It shows that the CLR tests also have these properties when the dimension p of the unknown parameter θ equals 1. When p ≥ 2, however, the asymptotic size properties are found to depend on how the conditioning statistic, upon which the CLR tests depend, is weighted. Two weighting methods have been suggested in the literature. The paper shows that the CLR tests are guaranteed to have correct asymptotic size when p ≥ 2 when the weighting is based on an estimator of the variance of the sample moments, i.e., moment-variance weighting, combined with the Robin and Smith (2000, Econometric Theory 16, 151–175) rank statistic. The paper also determines a formula for the asymptotic size of the CLR test when the weighting is based on an estimator of the variance of the sample Jacobian. However, the results of the paper do not guarantee correct asymptotic size when p ≥ 2 with the Jacobian-variance weighting, combined with the Robin and Smith (2000, Econometric Theory 16, 151–175) rank statistic, because two key sample quantities are not necessarily asymptotically independent under some identification scenarios. Analogous results for confidence sets are provided. Even for the special case of a linear instrumental variable regression model with two or more right-hand side endogenous variables, the results of the paper are new to the literature. 

   more » « less
2. Inference for Iterated GMM Under Misspecification

   https://doi.org/10.3982/ECTA16274  

   Hansen, Bruce E.; Lee, Seojeong (January 2021, Econometrica)

   null (Ed.)

   This paper develops inference methods for the iterated overidentified Generalized Method of Moments (GMM) estimator. We provide conditions for the existence of the iterated estimator and an asymptotic distribution theory, which allows for mild misspecification. Moment misspecification causes bias in conventional GMM variance estimators, which can lead to severely oversized hypothesis tests. We show how to consistently estimate the correct asymptotic variance matrix. Our simulation results show that our methods are properly sized under both correct specification and mild to moderate misspecification. We illustrate the method with an application to the model of Acemoglu, Johnson, Robinson, and Yared (2008). 

   more » « less
3. Statistical and Causal Robustness for Causal Null Hypothesis Tests

   Yang, Junhui; Bhattacharya, Rohit; Lee, Youjin; Westling, Ted (April 2024, arXiv)

   Prior work applying semiparametric theory to causal inference has primarily focused on deriving estimators that exhibit statistical robustness under a prespecified causal model that permits identification of a desired causal parameter. However, a fundamental challenge is correct specification of such a model, which usually involves making untestable assumptions. Evidence factors is an approach to combining hypothesis tests of a common causal null hypothesis under two or more candidate causal models. Under certain conditions, this yields a test that is valid if at least one of the underlying models is correct, which is a form of causal robustness. We propose a method of combining semiparametric theory with evidence factors. We develop a causal null hypothesis test based on joint asymptotic normality of asymptotically linear semiparametric estimators, where each estimator is based on a distinct identifying functional derived from each of candidate causal models. We show that this test provides both statistical and causal robustness in the sense that it is valid if at least one of the proposed causal models is correct, while also allowing for slower than parametric rates of convergence in estimating nuisance functions. We demonstrate the effectiveness of our method via simulations and applications to the Framingham Heart Study and Wisconsin Longitudinal Study. 

   more » « less
4. Statistical and Causal Robustness for Causal Null Hypothesis Tests

   Yang, Junhui; Bhattacharya, Rohit; Lee, Youjin; Westling, Ted (July 2024, Proceedings of Machine Learning Research)

   Prior work applying semiparametric theory to causal inference has primarily focused on deriving estimators that exhibit statistical robustness under a prespecified causal model that permits identification of a desired causal parameter. However, a fundamental challenge is correct specification of such a model, which usually involves making untestable assumptions. Evidence factors is an approach to combining hypothesis tests of a common causal null hypothesis under two or more candidate causal models. Under certain conditions, this yields a test that is valid if at least one of the underlying models is correct, which is a form of causal robustness. We propose a method of combining semiparametric theory with evidence factors. We develop a causal null hypothesis test based on joint asymptotic normality of K asymptotically linear semiparametric estimators, where each estimator is based on a distinct identifying functional derived from each of K candidate causal models. We show that this test provides both statistical and causal robustness in the sense that it is valid if at least one of the K proposed causal models is correct, while also allowing for slower than parametric rates of convergence in estimating nuisance functions. We demonstrate the effectiveness of our method via simulations and applications to the Framingham Heart Study and Wisconsin Longitudinal Study. 

   more » « less
5. Locally Robust Semiparametric Estimation

   https://doi.org/10.3982/ECTA16294  

   Chernozhukov, V.; Escanciano, J.; Ichimura, N.; Newey, W.; Robins, J. (July 2022, Econometrica)

   Imbens, G. (Ed.)

   Many economic and causal parameters depend on nonparametric or high dimensional first steps. We give a general construction of locally robust/orthogonal moment functions for GMM, where first steps have no effect, locally, on average moment functions. Using these orthogonal moments reduces model selection and regularization bias, as is important in many applications, especially for machine learning first steps. Also, associated standard errors are robust to misspecification when there is the same number of moment functions as parameters of interest. We use these orthogonal moments and cross-fitting to construct debiased machine learning estimators of functions of high dimensional conditional quantiles and of dynamic discrete choice parameters with high dimensional state variables. We show that additional first steps needed for the orthogonal moment functions have no effect, globally, on average orthogonal moment functions. We give a general approach to estimating those additional first steps.We characterize double robustness and give a variety of new doubly robust moment functions.We give general and simple regularity conditions for asymptotic theory. 

   more » « less