Semiparametric efficiency in GMM models with auxiliary data

By Xiaohong Chen, Han Hong, Alessandro Tarozzi. 2007

240 citations recorded by the source corpus.

We study semiparametric efficiency bounds and efficient estimation of parameters defined through general moment restrictions with missing data. Identification relies on auxiliary data containing information about the distribution of the missing variables conditional on proxy variables that are observed in both the primary and the auxiliary database, when such distribution is common to the two data sets. The auxiliary sample can be independent of the primary sample, or can be a subset of it. For both cases, we derive bounds when the probability of missing data given the proxy variables is unknown, or known, or belongs to a correctly specified parametric family. We find that the conditional probability is not ancillary when the two samples are independent. For all cases, we discuss efficient semiparametric estimators. An estimator based on a conditional expectation projection is shown to require milder regularity conditions than one based on inverse probability weighting.

Subfields: Statistics and Probability

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Citations in the corpus

Deep Neural Networks for Estimation and Inference: Application to Causal Effects and Other Semiparametric Estimands (2018, background): “For causal inference, Chen, Hong, and Tarozzi (2008) and Athey, Imbens, and Wager (2018) obtain efﬁciency under weaker conditions than ours on p( x ) (the former under minimal smoothness on µ t ( x ) and the latter under a sparsity in a high-dimensional linear model).”
Approximate residual balancing: debiased inference of average treatment effects in high dimensions (2016, methodology): “This rate can be achieved by either non-parametric inverse propensity weighting or non-parametric regression adjustments on their own (Chen et al., 2008; Hirano et al., 2003); doubly robust methods can then be used to relax the regularity conditions that are needed for efficiency (Farrell, 2015;…”
Efficient Policy Learning (2017, methodology): “They show that this estimator is √ n-consistent and asymptotically unbiased Gaussian for θ, provided that the nuisance estimates ĝ(·) and m̂(·) converge sufficiently fast and that we use cross-fitting (Chernozhukov et al., 2018a; Schick, 1986). This estimator is also semiparametrically efficient und”
The Value of Knowing the Propensity Score for Estimating Average Treatment Effects (2016, background): “…estimators (sometimes also called imputation estimators) of the form τ̂reg = 1 n n ∑ i=1 (µ̂(1, Xi) − µ̂(0, Xi)) , with Imbens, Newey, and Ridder (2007) and Chen, Hong, and Tarozzi (2008) estimating µ(t, ·) directly through a nonparametric regression of Yi on Xi in the subgroup with Ti = t, and…”
Difference-in-Differences with multiple time periods (2018, background): “Interestingly, Wooldridge (2005), Chernozhukov et al. (2013), Borusyak and Jaravel (2017), Goodman-Bacon (2018), S loczyński (2018), de Chaisemartin and D’Haultfœuille (2018), Abraham and Sun (2018) and Athey and Imbens (2018) have shown that, in general, β does not represent an easy to interpret av”
Efficient Quantile Regression Analysis With Missing Observations (2015, methodology): “…article by the present authors that is pending publication, it is shown that under Xue’s (2009) setup, the empirical likelihood (EL) conditional mean estimator produced by the nonparametric AIPW method yields an EL estimator that attains the semiparametric efficiency bound of Chen et al. (2008).”
Semiparametric Estimation and Inference Using Doubly Robust Moment Conditions (2013, unknown): “They have thus clear advantages even relative to other efficient estimators that are commonly used in such settings, such as Inverse Probability Weighting (IPW) estimators in missing data and treatment effect models (e.g. Hirano, Imbens, and Ridder, 2003; Firpo, 2007; Chen, Hong, and Tarozzi, 2008).”
Estimating Treatment Effects using Multiple Surrogates: The Role of the Surrogate Score and the Surrogate Index (2016, methodology): “It is explicit in some studies on combining data sets, e.g., Ridder and Moffitt (2007) and Chen, Hong, and Tarozzi (2008).”
Using Census and Survey Data to Estimate Poverty and Inequality for Small Areas (2009, background): “Before proceeding further, it is useful to describe the kind of data on which estimation is based.”
Globally efficient non-parametric inference of average treatment effects by empirical balancing calibration weighting (2015, unknown): “A job training study We further demonstrate the performance of various weighting estimators by estimating the treatment impact of a labor training program data previously analyzed in Lalonde (1986) and Dehejia and Wahba (1999), among many others. The National Supported Work (NSW) Demonstration was a”
Estimation of Conditional Average Treatment Effects With High-Dimensional Data (2019, methodology): “Prior to this work, the use of doubly robust or locally robust methods for causal inference has been considered by an extensive body of literature including, but not limited to, Imbens (1992), Robins, Mark, and Newey (1992), Robins and Rotnitzky (1995), Hahn (1998), Van der Laan and Robins (2003), H”
Conformal inference of counterfactuals and individual treatment effects (2020, methodology): “Chen et al., 2008, Hirshberg and Wager, 2017, Ma and Wang, 2019, Hong et al., 2020]. We close this section with a last important bibliographical comment. As we were putting the finishing touch on this paper, we became aware of the independent work by Kivaranovic et al. [2020] applying unweighted sta”
Decomposing Wage Distributions using Recentered Influence Function Regressions (2018, background): “A proof of part (iii) (a) can be found in Chen et al. (2008).”
Estimating linear functionals in nonlinear regression with responses missing at random (2009, background): “Chen, Hong and Tarozzi (2008) consider parameter estimation as well.”