Bounds for Standard Errors in Combined Data

2026-06-23

AI Summary

This study addresses the critical challenge of reliably estimating sharp lower bounds for the standard errors of moment condition estimators when cross-sample correlation information is either absent or only partially available. By leveraging geometric inequalities, the authors derive explicit and tight lower bounds on standard errors and show that the general problem can be reformulated as a semidefinite programming (SDP) problem amenable to efficient computation. This approach yields the first sharp error bounds in settings with no knowledge of cross-sample correlations. Integrating insights from moment condition estimation and statistical inference theory, the method demonstrates both validity and practical utility across several applications, including menu cost models, heterogeneous-agent New Keynesian frameworks, and two-sample instrumental variable settings.

Abstract

We propose methods for constructing lower bounds on the standard errors of parameters estimated from moment conditions obtained across different samples. Sharp explicit bounds are derived by exploiting geometric inequalities when no information about correlations across samples is available. Furthermore, we develop computationally tractable sharp bounds for more general settings with no or partial correlation information, which can be obtained by solving a simple semidefinite program. Finally, we illustrate the practical usefulness of our method through three empirical cases: two macroeconomics examples involving menu cost and Heterogeneous Agent New-Keynesian models; and a two sample instrumental variable microeconomic study.

Problem

• standard errors
• moment conditions
• cross-sample correlation
• bounds
• semidefinite programming

Innovation

• standard error bounds
• moment conditions
• semidefinite programming
• cross-sample correlation
• combined data