Please use this identifier to cite or link to this item: https://hdl.handle.net/10419/79509 
Authors: 
Year of Publication: 
2013
Series/Report no.: 
cemmap working paper No. CWP37/13
Publisher: 
Centre for Microdata Methods and Practice (cemmap), London
Abstract: 
A parameter of an econometric model is identified if there is a one-to-one or many-to-one mapping from the population distribution of the available data to the parameter. Often, this mapping is obtained by inverting a mapping from the parameter to the population distribution. If the inverse mapping is discontinuous, then estimation of the parameter usually presents an ill-posed inverse problem. Such problems arise in many settings in economics and other fields where the parameter of interest is a function. This paper explains how ill-posedness arises and why it causes problems for estimation. The need to modify or regularize the identifying mapping is explained, and methods for regularization and estimation are discussed. Methods for forming confidence intervals and testing hypotheses are summarized. It is shown that a hypothesis test can be more precise in a certain sense than an estimator. An empirical example illustrates estimation in an ill-posed setting in economics.
Subjects: 
regularization
nonparametric estimation
density estimation
deconvolution
nonparametric instrumental variables
Fredholm equation
Persistent Identifier of the first edition: 
Document Type: 
Working Paper

Files in This Item:
File
Size
344.92 kB





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