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Keynes Fund

Summary of Project Results

The project has been primarily concerned with the provision of robust and efficient methods of estimation and powerful tools for the detection of the presence of unobserved agent heterogeneity. The two main themes of the project comprised (a) the use of auxiliary, semiparametric information to guarantee efficiency gains for the estimation of parameters of interest and (b) concentration inequalities for the detection of neglected heterogeneity in moment condition models.

Research Output

Conditional Empirical Likelihood with Auxiliary Moment Restrictions

Conditional Empirical Likelihood with Auxiliary Moment Restrictions. Ashish Patel and Richard J. Smith, (Preliminary)


The paper consider models where the parameter of interest is described by one set of conditional moment restrictions and there exists another set of conditional moment restrictions with unknown nuisance parameters. A leading example is the study of conditional treatment effects; one set of moment restrictions describe a treatment effects model and another set describes the propensity score. This paper introduces two-step conditional empirical likelihood-weighted estimation of the parameter of interest. The estimator gives guaranteed efficiency gains over just using the identifying moment restrictions. To achieve this, moment restrictions may need to be adjusted to account for first-stage nuisance estimation of plug-in components (Chernozhukov, V., J.C. Escanciano, H. Ichimura and W.K. Newey (2016): “Locally Robust Semiparametric Estimation”, Cemmap working paper CWP31/16). When auxiliary restrictions require no nuisance estimation, the estimator is asymptotically efficient. This generalises existing the approach of F. Bravo (2010) “Efficient M-Estimators with Auxiliary Information”, Journal of Statistical Planning and Inference, to the conditional moments setting.

IVC Approach to Non-Asymptotic Inference in Moment Condition Models

IVC Approach to Non-Asymptotic Inference in Moment Condition Models. Ashish Patel and Richard J. Smith (In Preparation)


This paper develops concentration inequalities that can be used for finite-sample inference of moment condition models. The statistics are similar in spirit to Kolmogorov-Smirnov tests; analysing regional differences between the empirical distribution function (EDF) and the distribution function implied by the moment conditions. Implied probabilities present an information-theoretic tool to estimate such a distribution function. Model misspecification due to parameter instability yields systematic differences in the behaviour of generalised empirical Likelihood (GEL) implied probabilities relative to the EDF weights. Parameter heterogeneity may therefore be identified by the contrast of GEL implied probabilities and the EDF over regions of the sample space partitioned by characteristics suspected to be driving the heterogeneity. Data-driven methods can carefully select partitions that pick out points that are inconsistent with the moment restrictions. Using VC theory, tail bounds are provided for maximum deviations of the sum of GEL implied probabilities from their empirical average.

Project Information

Project Code: JHOK
Project Investigators
  • Dr Ashish Patel
  • Professor Richard J. Smith
Research Round
Ninth Round (September 2016)

Project Investigators

Prof. Richard J. Smith is Emeritus Professor of Econometric Theory and Economic Statistics at the Faculty of Economics, University of Cambridge. His research interests are in Econometric Theory, Estimation and Inference, Hypothesis Testing, Model Selection.Prof. Richard J. Smith

Dr Ashish Patel is a Posdoc at MRC Biostatistics Unit, University of Cambridge. The current focus of his work is on Developing Methodology for Mendelian Randomization Analysis with a High-dimensional set of Genetic Instruments.