Generalized method of moments with partially missing data

2025-11-26

AI Summary

This paper addresses identification and inference for target parameters in generalized method of moments (GMM) models when some data are missing in a nonrestrictive and potentially endogenous manner. We propose a support-function-based method to construct sharp identification sets, precisely characterizing the convex set of moment conditions compatible with the missing-data structure—applicable to both continuous and discrete variables. To handle endogenous missingness, we develop a novel hypothesis test statistic and adapt Fang & Santos’s (2019) directionally differentiable functional bootstrap by incorporating appropriate corrections to ensure valid inference. Monte Carlo simulations demonstrate that the proposed procedure delivers robust estimation and accurate confidence region coverage under moderate sample sizes and bounded data, substantially extending the applicability of GMM to settings with nonrandom missingness.

Technology Category

• Reasoning under Uncertainty: Graphical Models
• Machine Learning: Kernel Methods
• Search and Optimization: Non-convex Optimization

Application Category

• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Security and Privacy: Large-scale security measurements

Abstract

We consider a generalized method of moments framework in which a part of the data vector is missing for some units in a completely unrestricted, potentially endogenous way. In this setup, the parameters of interest are usually only partially identified. We characterize the identified set for such parameters using the support function of the convex set of moment predictions consistent with the data. This identified set is sharp, valid for both continuous and discrete data, and straightforward to estimate. We also propose a statistic for testing hypotheses and constructing confidence regions for the true parameter, show that standard nonparametric bootstrap may not be valid, and suggest a fix using the bootstrap for directionally differentiable functionals of Fang and Santos (2019). A set of Monte Carlo simulations demonstrates that both our estimator and the confidence region perform well when samples are moderately large and the data have bounded supports.

Problem

• Characterizes identified set for partially missing data using support function
• Proposes hypothesis testing and confidence region for true parameters
• Demonstrates estimator performance with Monte Carlo simulations

Innovation

• GMM with missing data using support function
• Sharp identified set for partially identified parameters
• Bootstrap fix for directional differentiability testing