Publication Type

Journal Article

Version

submittedVersion

Publication Date

1-2012

Abstract

The delta method and continuous mapping theorem are among the most extensively used tools in asymptotic derivations in econometrics. Extensions of these methods are provided for sequences of functions that are commonly encountered in applications and where the usual methods sometimes fail. Important examples of failure arise in the use of simulation-based estimation methods such as indirect inference. The paper explores the application of these methods to the indirect inference estimator (IIE) in first order autoregressive estimation. The IIE uses a binding function that is sample size dependent. Its limit theory relies on a sequence-based delta method in the stationary case and a sequence-based implicit continuous mapping theorem in unit root and local to unity cases. The new limit theory shows that the IIE achieves much more than (partial) bias correction. It changes the limit theory of the maximum likelihood estimator (MLE) when the autoregressive coefficient is in the locality of unity, reducing the bias and the variance of the MLE without affecting the limit theory of the MLE in the stationary case. Thus, in spite of the fact that the IIE is a continuously differentiable function of the MLE, the limit distribution of the IIE is not simply a scale multiple of the MLE, but depends implicitly on the full binding function mapping. The unit root case therefore represents an important example of the failure of the delta method and shows the need for an implicit mapping extension of the continuous mapping theorem.

Keywords

Binding function, Delta method, Exact bias, Implicit continuous maps, Indirect inference, Maximum likelihood

Discipline

Econometrics

Research Areas

Econometrics

Publication

Econometrica

Volume

80

Issue

1

First Page

425

Last Page

454

ISSN

0012-9682

Identifier

10.3982/ECTA9350

Publisher

Econometric Society

Copyright Owner and License

Authors

Additional URL

https://doi.org/10.3982/ECTA9350

Download

Included in

Econometrics Commons

Share

COinS