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Register a new userDouble robust inference for continuous updating GMM
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We propose the double robust Lagrange multiplier (DRLM) statistic for testing hypotheses specified on the pseudo-true value of the structural parameters in the generalized method of moments. The pseudo-true value is defined as the minimizer of the population continuous updating objective function and equals the true value of the structural parameter in the absence of misspecification. ocite{hhy96} The (bounding) chi-squared limiting distribution of the DRLM statistic is robust to both misspecification and weak identification of the structural parameters, hence its name. To emphasize its importance for applied work, we use the DRLM test to analyze the return on education, which is often perceived to be weakly identified, using data from Card (1995) where misspecification occurs in case of treatment heterogeneity; and to analyze the risk premia associated with risk factors proposed in Adrian et al. (2014) and He et al. (2017), where both misspecification and weak identification need to be addressed.
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This paper proposes a criterion for simultaneous GMM model and moment selection: the generalized focused information criterion (GFIC). Rather than attempting to identify the true specification, the GFIC chooses from a set of potentially mis-specified moment conditions and parameter restrictions to minimize the mean-squared error (MSE) of a user-specified target parameter. The intent of the GFIC is to formalize a situation common in applied practice. An applied researcher begins with a set of fairly weak baseline assumptions, assumed to be correct, and must decide whether to impose any of a number of stronger, more controversial suspect assumptions that yield parameter restrictions, additional moment conditions, or both. Provided that the baseline assumptions identify the model, we show how to construct an asymptotically unbiased estimator of the asymptotic MSE to select over these suspect assumptions: the GFIC. We go on to provide results for post-selection inference and model averaging that can be applied both to the GFIC and various alternative selection criteria. To illustrate how our criterion can be used in practice, we specialize the GFIC to the problem of selecting over exogeneity assumptions and lag lengths in a dynamic panel model, and show that it performs well in simulations. We conclude by applying the GFIC to a dynamic panel data model for the price elasticity of cigarette demand.
We study identification and estimation of causal effects in settings with panel data. Traditionally researchers follow model-based identification strategies relying on assumptions governing the relation between the potential outcomes and the unobserved confounders. We focus on a novel, complementary, approach to identification where assumptions are made about the relation between the treatment assignment and the unobserved confounders. We introduce different sets of assumptions that follow the two paths to identification, and develop a double robust approach. We propose estimation methods that build on these identification strategies.
Inverse Probability Weighting (IPW) is widely used in empirical work in economics and other disciplines. As Gaussian approximations perform poorly in the presence of small denominators, trimming is routinely employed as a regularization strategy. However, ad hoc trimming of the observations renders usual inference procedures invalid for the target estimand, even in large samples. In this paper, we first show that the IPW estimator can have different (Gaussian or non-Gaussian) asymptotic distributions, depending on how close to zero the probability weights are and on how large the trimming threshold is. As a remedy, we propose an inference procedure that is robust not only to small probability weights entering the IPW estimator but also to a wide range of trimming threshold choices, by adapting to these different asymptotic distributions. This robustness is achieved by employing resampling techniques and by correcting a non-negligible trimming bias. We also propose an easy-to-implement method for choosing the trimming threshold by minimizing an empirical analogue of the asymptotic mean squared error. In addition, we show that our inference procedure remains valid with the use of a data-driven trimming threshold. We illustrate our method by revisiting a dataset from the National Supported Work program.
We propose a new estimator for the average causal effects of a binary treatment with panel data in settings with general treatment patterns. Our approach augments the two-way-fixed-effects specification with the unit-specific weights that arise from a model for the assignment mechanism. We show how to construct these weights in various settings, including situations where units opt into the treatment sequentially. The resulting estimator converges to an average (over units and time) treatment effect under the correct specification of the assignment model. We show that our estimator is more robust than the conventional two-way estimator: it remains consistent if either the assignment mechanism or the two-way regression model is correctly specified and performs better than the two-way-fixed-effect estimator if both are locally misspecified. This strong double robustness property quantifies the benefits from modeling the assignment process and motivates using our estimator in practice.
We use identification robust tests to show that difference, level and non-linear moment conditions, as proposed by Arellano and Bond (1991), Arellano and Bover (1995), Blundell and Bond (1998) and Ahn and Schmidt (1995) for the linear dynamic panel data model, do not separately identify the autoregressive parameter when its true value is close to one and the variance of the initial observations is large. We prove that combinations of these moment conditions, however, do so when there are more than three time series observations. This identification then solely results from a set of, so-called, robust moment conditions. These robust moments are spanned by the combined difference, level and non-linear moment conditions and only depend on differenced data. We show that, when only the robust moments contain identifying information on the autoregressive parameter, the discriminatory power of the Kleibergen (2005) LM test using the combined moments is identical to the largest rejection frequencies that can be obtained from solely using the robust moments. This shows that the KLM test implicitly uses the robust moments when only they contain information on the autoregressive parameter.
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