Improved methods for moment restriction models with data combination and an application to two-sample instrumental variable estimation

Heng Shu, Zhiqiang Tan

Research output: Contribution to journalArticlepeer-review

Abstract

Combining-100 information from multiple samples is often needed in biomedical and economic studies, but differences between these samples must be appropriately taken into account in the analysis of the combined data. We study the estimation for moment restriction models with data combined from two samples under an ignorability-type assumption while allowing for different marginal distributions of variables common to both samples. Suppose that an outcome regression (OR) model and a propensity score (PS) model are specified. By leveraging semi-parametric efficiency theory, we derive an augmented inverse probability-weighted (AIPW) estimator that is locally efficient and doubly robust with respect to these models. Furthermore, we develop calibrated regression and likelihood estimators that are not only locally efficient and doubly robust but also intrinsically efficient in achieving smaller variances than the AIPW estimator when the PS model is correctly specified but the OR model may be mispecified. As an important application, we study the two-sample instrumental variable problem and derive the corresponding estimators while allowing for incompatible distributions of variables common to the two samples. Finally, we provide a simulation study and an econometric application on public housing projects to demonstrate the superior performance of our improved estimators. The Canadian Journal of Statistics 48: 259–284; 2020

Original languageEnglish (US)
Pages (from-to)259-284
Number of pages26
JournalCanadian Journal of Statistics
Volume48
Issue number2
DOIs
StatePublished - Jun 1 2020

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

Keywords

  • Data combination
  • double robustness
  • intrinsic efficiency
  • inverse probability weighting
  • local efficiency
  • moment restriction models
  • two-sample instrument variable estimation

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