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Inference on Sets in Finance

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  • Victor Chernozhukov
  • Emre Kocatulum
  • Konrad Menzel

Abstract

In 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.

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Paper provided by arXiv.org in its series Papers with number 1211.4282.

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Date of creation: Nov 2012
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Handle: RePEc:arx:papers:1211.4282

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  1. Arie Beresteanu & Francesca Molinari, 2006. "Asymptotic properties for a class of partially identified models," CeMMAP working papers, Centre for Microdata Methods and Practice, Institute for Fiscal Studies CWP10/06, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  2. Hansen, Lars Peter & Singleton, Kenneth J, 1982. "Generalized Instrumental Variables Estimation of Nonlinear Rational Expectations Models," Econometrica, Econometric Society, Econometric Society, vol. 50(5), pages 1269-86, September.
  3. Hansen, Lars Peter & Jagannathan, Ravi, 1991. "Implications of Security Market Data for Models of Dynamic Economies," Journal of Political Economy, University of Chicago Press, University of Chicago Press, vol. 99(2), pages 225-62, April.
  4. Raj Chetty, 2012. "Bounds on Elasticities With Optimization Frictions: A Synthesis of Micro and Macro Evidence on Labor Supply," Econometrica, Econometric Society, Econometric Society, vol. 80(3), pages 969-1018, 05.
  5. Hiroaki Kaido & Andres Santos, 2014. "Asymptotically Efficient Estimation of Models Defined by Convex Moment Inequalities," Econometrica, Econometric Society, Econometric Society, vol. 82(1), pages 387-413, 01.
  6. Critchley, Frank & Marriott, Paul & Salmon, Mark, 1996. "On the Differential Geometry of the Wald Test with Nonlinear Restrictions," Econometrica, Econometric Society, Econometric Society, vol. 64(5), pages 1213-22, September.
  7. Victor Chernozhukov & Han Hong & Elie Tamer, 2007. "Estimation and Confidence Regions for Parameter Sets in Econometric Models," Econometrica, Econometric Society, Econometric Society, vol. 75(5), pages 1243-1284, 09.
  8. repec:cup:cbooks:9780521496032 is not listed on IDEAS
  9. Harry Markowitz, 1952. "Portfolio Selection," Journal of Finance, American Finance Association, American Finance Association, vol. 7(1), pages 77-91, 03.
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