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1. 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). 

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2. 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. 

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3. Addressing Monotone Likelihood in Duration Modelling of Political Events

   https://doi.org/10.1017/S0007123420000071  

   Anderson, Noel; Bagozzi, Benjamin E.; Koren, Ore (June 2020, British Journal of Political Science)

   This article provides an accessible introduction to the phenomenon of monotone likelihood in duration modeling of political events. Monotone likelihood arises when covariate values are monotonic when ordered according to failure time, causing parameter estimates to diverge toward infinity. Within political science duration model applications, this problem leads to misinterpretation, model misspecification and omitted variable biases, among other issues. Using a combination of mathematical exposition, Monte Carlo simulations and empirical applications, this article illustrates the advantages of Firth's penalized maximum-likelihood estimation in resolving the methodological complications underlying monotone likelihood. The results identify the conditions under which monotone likelihood is most acute and provide guidance for political scientists applying duration modeling techniques in their empirical research. 

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4. Sequential Domain Adaptation by Synthesizing Distributionally Robust Experts

   Taskesen, Bahar; Yue, Man-Chung; Blanchet, Jose; Kuhn, Daniel; Nguyen, Viet Anh (January 2021, Proceedings of the 38th International Conference on Machine Learning)

   Meila, Marina and (Ed.)

   Least squares estimators, when trained on a few target domain samples, may predict poorly. Supervised domain adaptation aims to improve the predictive accuracy by exploiting additional labeled training samples from a source distribution that is close to the target distribution. Given available data, we investigate novel strategies to synthesize a family of least squares estimator experts that are robust with regard to moment conditions. When these moment conditions are specified using Kullback-Leibler or Wasserstein-type divergences, we can find the robust estimators efficiently using convex optimization. We use the Bernstein online aggregation algorithm on the proposed family of robust experts to generate predictions for the sequential stream of target test samples. Numerical experiments on real data show that the robust strategies systematically outperform non-robust interpolations of the empirical least squares estimators. 

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5. The variational method of moments

   https://doi.org/10.1093/jrsssb/qkad025  

   Bennett, Andrew; Kallus, Nathan (April 2023, Journal of the Royal Statistical Society Series B: Statistical Methodology)

   Abstract The conditional moment problem is a powerful formulation for describing structural causal parameters in terms of observables, a prominent example being instrumental variable regression. We introduce a very general class of estimators called the variational method of moments (VMM), motivated by a variational minimax reformulation of optimally weighted generalized method of moments for finite sets of moments. VMM controls infinitely for many moments characterized by flexible function classes such as neural nets and kernel methods, while provably maintaining statistical efficiency unlike existing related minimax estimators. We also develop inference algorithms and demonstrate the empirical strengths of VMM estimation and inference in experiments. 

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