Richard J. Smith, University of Cambridge
Jaap Abbring, Tilburg University
Massachusetts Institute of Technology
Michael Jansson, Berkeley
Andrew Patton, Duke University
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Special Issue 2014
This Special Issue of The Econometrics Journal celebrates the work and contributions of Joel L. Horowitz. Most of these papers were presented at a Conference in Honour of Joel's 70th birthday held in June 2011 at University College London. Joel has made influential contributions to many areas in econometrics and statistics. These include bootstrap methods, semi-parametric and non-parametric estimation, specification testing, non-parametric instrumental variables, estimation of high-dimensional models, and functional data analysis, among others. The six papers that appear in this Special Issue are related to the topics of Joel's past and present research interests.
Joel's work is often motivated by a desire to carry out econometric exercises under credible assumptions. In seminars, his typical question is to ask under what conditions the features of a model of interest are identified. In this regard, the paper authored by Andrew Chesher and Adam M. Rosen suits this Special Issue well. Their paper is concerned with a random coefficient model for a binary outcome. They consider endogeneity by letting explanatory variables be arbitrarily correlated with the random coefficients. Then they study partial identification when there exist instrumental variables that are independent of the random coefficients. In particular, they characterize the identified set for the distribution of random coefficients via a collection of conditional moment inequalities.
Semi-parametric and non-parametric estimation has been very popular in economics and statistics for several decades. Joel has contributed to this literature especially with his work on smoothed maximum score estimation, transformation models and additive models. The paper by Young K. Lee, Enno Mammen and Byeong U. Park belongs to this literature. They consider a couple of backfitting methods to estimate varying coefficient quantile regression models. They develop a general framework that includes the additive quantile regression model as a special case.
Joel has been at the research frontier in developing non-parametric tests in a variety of contexts. Two papers in this Special Issue are concerned with testing problems. Russell Davidson and James G. MacKinnon point out potential problems caused by inverting the Anderson–Rubin (AR) test. They argue that the confidence sets constructed by inverting the AR test may have undesirable properties when the test has more degrees of freedom than there are parameters of interest. Oliver Linton, Thierry Post and Yoon-Jae Whang consider testing the null hypothesis that a given portfolio is not dominated by any other feasible portfolio. They suggest using a modified version of the Kolmogorov–Smirnov test statistic proposed originally for testing stochastic dominance. In particular, they estimate a so-called “contact set” and compute the supremum of the test statistic only over the complement of a small enlargement of this set.
Joel's recent interest lies in estimation of high-dimensional models. Two papers in this Special Issue are related to this topic. In their paper, Alexandre Belloni and Victor Chernozhukov investigate the large sample properties of the posterior-based inference in the curved exponential family under increasing dimension. The curved structure can arise from, for example, imposing moment restrictions. They establish conditions under which the posterior distribution is approximately normal and emphasize the high-dimension set-up in which both the parameter dimension and the number of moments are increasing with the sample size. Song Song, Wolfgang K. Härdle and Ya'acov Ritov propose a generalized dynamic semi-parametric factor model for high-dimensional non-stationary time series. Their estimation procedure consists of two steps and is based on a sparse representation approach to regression.
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