Inference on sets in finance

Victor Chernozhukov, Emre Kocatulum and Konrad Menzel (km125@nyu.edu)
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Emre Kocatulum: Institute for Fiscal Studies
Konrad Menzel: Institute for Fiscal Studies

No CWP46/12, CeMMAP working papers from Centre for Microdata Methods and Practice, Institute for Fiscal Studies

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) variances for asset portfolio returns, and the set of structural elasticities in Chetty's (2012) analysis of demand with optimisation frictions. We show that the econometric structure of the problem allows us to construct convenient and powerful confidence regions based upon the weighted likelihood ration 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 analysing 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.

Keywords: Hansen-Jagannathan bound; Markowitz-Fama bounds; Chetty bounds; Mean-Variance sets; Optimisation Frictions; Inference; Confidence Set (search for similar items in EconPapers)
Date: 2012-12-27
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Citations: View citations in EconPapers (6)

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Related works:
Journal Article: Inference on sets in finance (2015)
Working Paper: Inference on Sets in Finance (2012)
Working Paper: Inference on sets in finance (2012)
Working Paper: Inference on sets in finance (2012)
Working Paper: Inference on sets in finance (2012)
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