I review recent work in the statistics literature on instrumental variables methods from an econometrics perspective. I discuss some of the older, economic, applications including supply and demand models and relate them to the recent applications in settings of randomized experiments with noncompliance. I discuss the assumptions underlying instrumental variables methods and in what settings these may be plausible. By providing context to the current applications, a better understanding of the applicability of these methods may arise.

The modern formulation of the instrumental variable methods initiated the valuable interactions between economics and statistics literatures of causal inference and fueled new innovations of the idea. It helped resolving the long-standing confusion that the statisticians used to have on the method, and encouraged the economists to rethink how to make use of instrumental variables in policy analysis.

In the presence of a missing response, reweighting the complete case subsample by the inverse of nonmissing probability is both intuitive and easy to implement. When the population totals of some auxiliary variables are known and when the inclusion probabilities are known by design, survey statisticians have developed calibration methods for improving efficiencies of the inverse probability weighting estimators and the methods can be applied to missing data analysis. Model-based calibration has been proposed in the survey sampling literature, where multidimensional auxiliary variables are first summarized into a predictor function from a working regression model. Usually, one working model is being proposed for each parameter of interest and results in different sets of calibration weights for estimating different parameters. This paper considers calibration using multiple working regression models for estimating a single or multiple parameters. Contrary to a common belief that overfitting hurts efficiency, we present three rather unexpected results. First, when the missing probability is correctly specified and multiple working regression models for the conditional mean are posited, calibration enjoys an oracle property: the same semiparametric efficiency bound is attained as if the true outcome model is known in advance. Second, when the missing data mechanism is misspecified, calibration can still be a consistent estimator when any one of the outcome regression models is correctly specified. Third, a common set of calibration weights can be used to improve efficiency in estimating multiple parameters of interest and can simultaneously attain semiparametric efficiency bounds for all parameters of interest. We provide connections of a wide class of calibration estimators, constructed based on generalized empirical likelihood, to many existing estimators in biostatistics, econometrics and survey sampling and perform simulation studies to show that the finite sample properties of calibration estimators conform well with the theoretical results being studied.

We investigate the utility to computational Bayesian analyses of a particular family of recursive marginal likelihood estimators characterized by the (equivalent) algorithms known as “biased sampling” or “reverse logistic regression” in the statistics literature and “the density of states” in physics. Through a pair of numerical examples (including mixture modeling of the well-known galaxy data set) we highlight the remarkable diversity of sampling schemes amenable to such recursive normalization, as well as the notable efficiency of the resulting pseudo-mixture distributions for gauging prior sensitivity in the Bayesian model selection context. Our key theoretical contributions are to introduce a novel heuristic (“thermodynamic integration via importance sampling”) for qualifying the role of the bridging sequence in this procedure and to reveal various connections between these recursive estimators and the nested sampling technique.

This note reexamines the data from a weight-judging competition described in an article by Francis Galton published in 1907. Following the correction of some errors, it is shown that this forecasting competition is an interesting precursor of two more recent developments in the statistical forecasting literature. One is forecast combination, with the mean forecast here exactly coinciding with the outcome, and the second is the use of two-piece frequency and probability distributions to describe asymmetry.

Howell Tong has been an Emeritus Professor of Statistics at the London School of Economics since October 1, 2009. He was appointed to a lectureship at the University of Manchester Institute of Science and Technology shortly after he started his Master program in 1968. He received his Ph.D. in 1972 under the supervision of Maurice Priestley, thus making him an academic grandson of Maurice Bartlett. He stayed at UMIST until 1982, when he took up the Founding Chair of Statistics at the Chinese University of Hong Kong. In 1986, he returned to the UK, as the first Chinese to hold a Chair of Statistics in the history of the UK, by accepting the Chair at the University of Kent at Canterbury. He stayed there until 1997, when he went to the University of Hong Kong, first as a Distinguished Visiting Professor, and then as the Chair Professor of Statistics. At the University of Hong Kong, he served as a Pro-Vice-Chancellor and was the Founding Dean of the Graduate School. He was appointed to his Chair at the London School of Economics in 1999. He is a pioneer in the field of nonlinear time series analysis and has been a scientific leader both in Hong Kong and in the UK. His work on threshold models has had lasting influence both on theory and applications. He has drawn important connections between time series and deterministic dynamical systems, linking statistics with chaos theory, and the models he has developed have found significant applications in fields as diverse as economics, epidemiology and ecology. He has made novel contributions to nonparametric and semi-parametric statistics, especially in model selection and dimension reduction for time series data. He has written four books (one with Kung-Sik Chan and another with Bing Cheng) and over 162 papers (sometimes with collaborators) in Statistics, Ecology, Actuarial Science, Control Engineering, Reliability, Meteorology, Water Engineering, Engineering Mathematics and Mathematical Education. His 1990 monograph Non-linear Time Series Analysis—A Dynamical System Approach is a classic. He is a Foreign Member of the Norwegian Academy of Science and Letters, an elected member of the ISI, a Fellow of IMS and an Honorary Fellow of the Institute of Actuaries (UK). He won a Chinese National Natural Science Prize (Class II) in 2000 and the Royal Statistical Society awarded him the Guy Medal in Silver in 2007.

The following conversation is partly based on an interview that took place in the Hong Kong University of Science and Technology in July 2013.

Donald Bruce Rubin is John L. Loeb Professor of Statistics at Harvard University. He has made fundamental contributions to statistical methods for missing data, causal inference, survey sampling, Bayesian inference, computing and applications to a wide range of disciplines, including psychology, education, policy, law, economics, epidemiology, public health and other social and biomedical sciences.