Please use this identifier to cite or link to this item: https://hdl.handle.net/10419/217162 
Year of Publication: 
2019
Citation: 
[Journal:] Quantitative Economics [ISSN:] 1759-7331 [Volume:] 10 [Issue:] 3 [Publisher:] The Econometric Society [Place:] New Haven, CT [Year:] 2019 [Pages:] 1019-1068
Publisher: 
The Econometric Society, New Haven, CT
Abstract: 
This paper develops extremum estimation and inference results for nonlinear models with very general forms of potential identification failure when the source of this identification failure is known. We examine models that may have a general deficient rank Jacobian in certain parts of the parameter space. When identification fails in one of these models, it becomes underidentified and the identification status of individual parameters is not generally straightforward to characterize. We provide a systematic reparameterization procedure that leads to a reparametrized model with straightforward identification status. Using this reparameterization, we determine the asymptotic behavior of standard extremum estimators and Wald statistics under a comprehensive class of parameter sequences characterizing the strength of identification of the model parameters, ranging from nonidentification to strong identification. Using the asymptotic results, we propose hypothesis testing methods that make use of a standard Wald statistic and data-dependent critical values, leading to tests with correct asymptotic size regardless of identification strength and good power properties. Importantly, this allows one to directly conduct uniform inference on low-dimensional functions of the model parameters, including one-dimensional subvectors. The paper illustrates these results in three examples: a sample selection model, a triangular threshold crossing model, and a collective model for household expenditures.
Subjects: 
Reparameterization
deficient rank Jacobian
asymptotic size
uniform inference
subvector inference
extremum estimators
identification
nonlinear models
Wald test
weak identification
underidentification
JEL: 
C12
C15
Persistent Identifier of the first edition: 
Creative Commons License: 
cc-by-nc Logo
Document Type: 
Article

Files in This Item:
File
Size
361.31 kB





Items in EconStor are protected by copyright, with all rights reserved, unless otherwise indicated.