TL;DR
This paper establishes conditions under which delta-method-based asymptotic approximations are uniformly valid, providing a unified framework to identify when pointwise approximations may fail across different econometric contexts.
Contribution
It offers easily verifiable sufficient and necessary conditions for the uniform negligibility of delta-method remainders, enhancing understanding of asymptotic approximation validity.
Findings
Provides a set of sufficient conditions for uniform validity.
Identifies parameter regions where pointwise approximations are inadequate.
Framework applicable across various econometric sub-fields.
Abstract
When are asymptotic approximations using the delta-method uniformly valid? We provide sufficient conditions as well as closely related necessary conditions for uniform negligibility of the remainder of such approximations. These conditions are easily verified and permit to identify settings and parameter regions where pointwise asymptotic approximations perform poorly. Our framework allows for a unified and transparent discussion of uniformity issues in various sub-fields of econometrics. Our conditions involve uniform bounds on the remainder of a first-order approximation for the function of interest.
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Taxonomy
TopicsMonetary Policy and Economic Impact · Statistical Methods and Inference · Advanced Statistical Methods and Models