centre for microdata methods and practice

ESRC centre

cemmap is an ESRC research centre


Keep in touch

Subscribe to cemmap news

Inference on sets in finance

Authors: Victor Chernozhukov , Emre Kocatulum and Konrad Menzel
Date: 27 December 2012
Type: cemmap Working Paper, CWP46/12
DOI: 10.1920/wp.cem.2012.4612


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.

Download full version
Now published:
Victor Chernozhukov, Emre Kocatulum and Konrad Menzel July 2015, Inference on sets in finance, Journal article, Wiley Online Library
Previous version:
Victor Chernozhukov, Emre Kocatulum and Konrad Menzel February 2012, Inference on sets in finance, cemmap Working Paper

Search cemmap

Search by title, topic or name.

Contact cemmap

Centre for Microdata Methods and Practice

How to find us

Tel: +44 (0)20 7291 4800

E-mail us