EconPapers    
Economics at your fingertips  
 

Asymptotic properties for a class of partially identified models

Arie Beresteanu (arie@pitt.edu) and Francesca Molinari

No CWP10/06, CeMMAP working papers from Centre for Microdata Methods and Practice, Institute for Fiscal Studies

Abstract: We propose inference procedures for partially identified population features for which the population identification region can be written as a transformation of the Aumann expectation of a properly defined set valued random variable (SVRV). An SVRV is a mapping that associates a set (rather than a real number) with each element of the sample space. Examples of population features in this class include sample means and best linear predictors with interval outcome data, and parameters of semiparametric binary models with interval regressor data. We extend the analogy principle to SVRVs, and show that the sample analog estimator of the population identification region is given by a transformation of a Minkowski average of SVRVs. Using the results of the mathematics literature on SVRVs, we show that this estimator converges in probability to the identification region of the model with respect to the Hausdorff distance. We then show that the Hausdorff distance between the estimator and the population identification region, when properly normalized by vn, converges in distribution to the supremum of a Gaussian process whose covariance kernel depends on parameters of the population identification region. We provide consistent bootstrap procedures to approximate this limiting distribution. Using similar arguments as those applied for vector valued random variables, we develop a methodology to test assumptions about the true identification region and to calculate the power of the test. We show that these results can be used to construct a confidence collection, that is a collection of sets that, when specified as null hypothesis for the true value of the population identification region, cannot be rejected by our test.

Keywords: Partial Identification; Confidence Collections; Set-Valued Random Variables. (search for similar items in EconPapers)
JEL-codes: C14 (search for similar items in EconPapers)
Pages: 58 pp.
Date: 2006-06-09
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (40)

Downloads: (external link)
http://cemmap.ifs.org.uk/wps/cwp1006.pdf (application/pdf)
Our link check indicates that this URL is bad, the error code is: 500 Can't connect to cemmap.ifs.org.uk:80 (No such host is known. )

Related works:
Journal Article: Asymptotic Properties for a Class of Partially Identified Models (2008) Downloads
Working Paper: Asymptotic Properties for a Class of Partially Identified Models (2006) Downloads
Working Paper: Asymptotic Properties for a Class of Partially Identified Models (2006) Downloads
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:ifs:cemmap:10/06

Ordering information: This working paper can be ordered from
The Institute for Fiscal Studies 7 Ridgmount Street LONDON WC1E 7AE
mailbox@ifs.org.uk

Access Statistics for this paper

More papers in CeMMAP working papers from Centre for Microdata Methods and Practice, Institute for Fiscal Studies The Institute for Fiscal Studies 7 Ridgmount Street LONDON WC1E 7AE. Contact information at EDIRC.
Bibliographic data for series maintained by Emma Hyman (emma_h@ifs.org.uk).

 
Page updated 2024-12-23
Handle: RePEc:ifs:cemmap:10/06