Inference on Sets in Finance
AbstractIn this paper we consider the problem of inference on a class of sets describing a collection of admissible models as solutions to a single smooth inequality. Classical and recent examples include, among others, the Hansen-Jagannathan (HJ) sets of admissible stochastic discount factors, Markowitz-Fama (MF) sets of mean-variances for asset portfolio returns, and the set of structural elasticities in Chetty (2012)'s analysis of demand with optimization frictions. We show that the econometric structure of the problem allows us to construct convenient and powerful confidence regions based upon the weighted likelihood ratio and weighted Wald (directed weighted Hausdorff) statistics. The statistics we formulate differ (in part) from existing statistics in that they enforce either exact or first order equivariance to transformations of parameters, making them especially appealing in the target applications. Moreover, the resulting inference procedures are also more powerful than the structured projection methods, which rely upon building confidence sets for the frontier-determining sufficient parameters (e.g. frontier-spanning portfolios), and then projecting them to obtain confidence sets for HJ sets or MF sets. Lastly, the framework we put forward is also useful for analyzing intersection bounds, namely sets defined as solutions to multiple smooth inequalities, since multiple inequalities can be conservatively approximated by a single smooth inequality. We present two empirical examples that show how the new econometric methods are able to generate sharp economic conclusions.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
Bibliographic InfoPaper provided by arXiv.org in its series Papers with number 1211.4282.
Date of creation: Nov 2012
Date of revision:
Contact details of provider:
Web page: http://arxiv.org/
Other versions of this item:
- Victor Chernozhukov & Emre Kocatulum & Konrad Menzel, 2012. "Inference on sets in finance," CeMMAP working papers CWP04/12, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
- Victor Chernozhukov & Emre Kocatulum & Konrad Menzel, 2012. "Inference on sets in finance," CeMMAP working papers CWP46/12, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
- NEP-ALL-2012-12-06 (All new papers)
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Critchley, Frank & Marriott, Paul & Salmon, Mark, 1996. "On the Differential Geometry of the Wald Test with Nonlinear Restrictions," Econometrica, Econometric Society, vol. 64(5), pages 1213-22, September.
- Raj Chetty, 2009.
"Bounds on Elasticities with Optimization Frictions: A Synthesis of Micro and Macro Evidence on Labor Supply,"
NBER Working Papers
15616, National Bureau of Economic Research, Inc.
- Raj Chetty, 2012. "Bounds on Elasticities With Optimization Frictions: A Synthesis of Micro and Macro Evidence on Labor Supply," Econometrica, Econometric Society, vol. 80(3), pages 969-1018, 05.
- Lars Peter Hansen & Ravi Jagannathan, 1990.
"Implications of security market data for models of dynamic economies,"
Discussion Paper / Institute for Empirical Macroeconomics
29, Federal Reserve Bank of Minneapolis.
- Hansen, Lars Peter & Jagannathan, Ravi, 1991. "Implications of Security Market Data for Models of Dynamic Economies," Journal of Political Economy, University of Chicago Press, vol. 99(2), pages 225-62, April.
- Lars Peter Hansen & Ravi Jagannathan, 1990. "Implications of Security Market Data for Models of Dynamic Economies," NBER Technical Working Papers 0089, National Bureau of Economic Research, Inc.
- Hansen, Lars Peter & Singleton, Kenneth J, 1982. "Generalized Instrumental Variables Estimation of Nonlinear Rational Expectations Models," Econometrica, Econometric Society, vol. 50(5), pages 1269-86, September.
- Arie Beresteanu & Francesca Molinari, 2008.
"Asymptotic Properties for a Class of Partially Identified Models,"
Econometric Society, vol. 76(4), pages 763-814, 07.
- Arie Beresteanu & Francesca Molinari, 2006. "Asymptotic properties for a class of partially identified models," CeMMAP working papers CWP10/06, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
- Beresteanu, Arie & Molinari, Francesca, 2006. "Asymptotic Properties for a Class of Partially Identified Models," Working Papers 06-04, Duke University, Department of Economics.
- Beresteanu, Arie & Molinari, Francesca, 2006. "Asymptotic Properties for a Class of Partially Identified Models," Working Papers 06-07, Cornell University, Center for Analytic Economics.
- Harry Markowitz, 1952. "Portfolio Selection," Journal of Finance, American Finance Association, vol. 7(1), pages 77-91, 03.
- Victor Chernozhukov & Han Hong & Elie Tamer, 2007. "Estimation and Confidence Regions for Parameter Sets in Econometric Models," Econometrica, Econometric Society, vol. 75(5), pages 1243-1284, 09.
- repec:cup:cbooks:9780521496032 is not listed on IDEAS
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (arXiv administrators).
If references are entirely missing, you can add them using this form.