Publication Type

Journal Article

Version

publishedVersion

Publication Date

10-2023

Abstract

Functional coefficient (FC) regressions allow for systematic flexibility in the responsiveness of a dependent variable to movements in the regressors, making them attractive in applications where marginal effects may depend on covariates. Such models are commonly estimated by local kernel regression methods. This paper explores situations where responsiveness to covariates is locally flat or fixed. The paper develops new asymptotics that take account of shape characteristics of the function in the locality of the point of estimation. Both stationary and integrated regressor cases are examined. The limit theory of FC kernel regression is shown to depend intimately on functional shape in ways that affect rates of convergence, optimal bandwidth selection, estimation, and inference. In FC cointegrating regression, flat behavior materially changes the limit distribution by introducing the shape characteristics of the function into the limiting distribution through variance as well as centering. In the boundary case where the number of zero derivatives tends to infinity, near parametric rates of convergence apply in stationary and nonstationary cases. Implications for inference are discussed and a feasible pre-test inference procedure is proposed that takes unknown potential flatness into consideration and provides a practical approach to inference.

Discipline

Econometrics | Economic Theory

Research Areas

Econometrics

Publication

Econometric Theory

Volume

39

Issue

5

First Page

900

Last Page

949

ISSN

0266-4666

Identifier

10.1017/S0266466622000287

Publisher

Cambridge University Press

Copyright Owner and License

Authors CC-BY

Creative Commons License

Creative Commons Attribution 3.0 License
This work is licensed under a Creative Commons Attribution 3.0 License.

Additional URL

https://doi.org/10.1017/S0266466622000287

Download

Share

COinS