In this paper, we derive the asymptotic properties of the density-weighted average derivative estimator when a regressor is contaminated with classical measurement error and the density of this error must be estimated. Average derivatives of conditional mean functions are used extensively in economics and statistics, most notably in semiparametric index models. As well as ordinary smooth measurement error, we provide results for supersmooth error distributions. This is a particularly important class of error distribution as it includes the Gaussian density. We show that under either type of measurement error, despite using nonparametric deconvolution techniques and an estimated error characteristic function, we are able to achieve a $\sqrt {n}$ -rate of convergence for the average derivative estimator. Interestingly, if the measurement error density is symmetric, the asymptotic variance of the average derivative estimator is the same irrespective of whether the error density is estimated or not. The promising finite sample performance of the estimator is shown through a Monte Carlo simulation.

For the problem of testing the hypothesis that all m coefficients of the right-hand-side endogenous variables in an instrumental variables (IV) regression are zero, the likelihood ratio (LR) test can, if the reduced form covariance matrix is known, be rendered similar by a conditioning argument. To exploit this fact requires knowledge of the relevant conditional cumulative distribution function (c.d.f.) of the LR statistic, but the statistic is a function of the smallest characteristic root of an (m + 1)-square matrix and is therefore analytically difficult to deal with when m > 1. We show in this paper that an iterative conditioning argument used by Hillier (2009) and Andrews, Moreira, and Stock (2007 Journal of Econometrics 139, 116–132) to evaluate the c.d.f. in the case m = 1 can be generalized to the case of arbitrary m. This means that we can completely bypass the difficulty of dealing with the smallest characteristic root. Analytic results are obtained for the case m = 2, and a simple and efficient simulation approach to evaluating the c.d.f. is suggested for larger values of m.

In time series regression models with “short-memory” residual processes, the Durbin–Watson statistic (DW) has been used for the problem of testing for independence of the residuals. In this paper we elucidate the asymptotics of DW for “long-memory” residual processes. A standardized Durbin–Watson statistic (SDW) is proposed. Then we derive the asymptotic distributions of SDW under both the null and local alternative hypotheses. Based on this result we evaluate the local power of SDW. Numerical studies for DW and SDW are given.

We develop a nonparametric Bayesian analysis of regression discontinuity (RD) designs, allowing for covariates, in which we model and estimate the unknown functions of the forcing variable by basis expansion methods. In a departure from current methods, we use the entire data on the forcing variable, but we emphasize the data near the threshold by placing some knots at and near the threshold, a technique we refer to as soft-windowing. To handle the nonequally spaced knots that emerge from soft-windowing, we construct a prior on the spline coefficients, from a second-order Ornstein–Uhlenbeck process, which is hyperparameter light, and satisfies the Kullback–Leibler support property. In the fuzzy RD design, we explain the divergence between the treatment implied by the forcing variable, and the actual intake, by a discrete confounder variable, taking three values, complier, never-taker, and always-taker, and a model with four potential outcomes. Choice of the soft-window, and the number of knots, is determined by marginal likelihoods, computed by the method of Chib [Journal of the American Statistical Association, 1995, 90, 1313–1321] as a by-product of the Markov chain Monte Carlo (MCMC)-based estimation. Importantly, in each case, we allow for covariates, incorporated nonparametrically by additive natural cubic splines. The potential outcome error distributions are modeled as student-t, with an extension to Dirichlet process mixtures. We derive the large sample posterior consistency, and posterior contraction rate, of the RD average treatment effect (ATE) (in the sharp case) and RD ATE for compliers (in the fuzzy case), as the number of basis parameters increases with sample size. The excellent performance of the methods is documented in simulation experiments, and in an application to educational attainment of women from Meyersson [Econometrica, 2014, 82, 229–269].

We derive asymptotic expansions of the distributions of test statistics for over-identifying restrictions in a system of simultaneous equations under the null and the non-null hypotheses. We investigate the effects of the normality assumption for disturbances on the test statistics based on their asymptotic expansions. We also study the power functions of test statistics based on their asymptotic expansions. After modifying their critical regions to the same significance level, the power function of Basmann's statistic is larger than that of the likelihood ratio test when the variance of disturbances is sufficiently small. However, the difference in powers of the two test statistics disappears as the sample size grows larger.

This book, Topics in Advanced Econometrics, is written primarily as a textbook for an advanced graduate econometrics course. The topics covered include consistent model specification testing, unit roots and cointegration, and nonparametric regression estimation; they are mainly the topics in which Professor Bierens has made significant contributions to the literature over the last 15 years. This book is unusual as a textbook in the sense that it treats both cross-sectional and time series (i.e., both subscript i and t) issues in econometrics at an advanced level. Most of the results given, other than those available in standard econometrics or statistics textbooks, are drawn from the published work of the author. The book is very useful because it puts together a number of important current issues that have been treated separately in the literature and presents them systematically using a well-organized set of statistical tools. Another advantage of this book is that the materials given are almost self-contained, making this book suitable for self-tuition. This book thus ideally suits students who need tools for independent research especially in the area of nonlinear and nonparametric models and time series analysis. It will also be useful to more advanced researchers who are interested in a thorough understanding of some of the author's original and influential work in these areas.

This paper studies the uniform convergence rates of Li and Vuong’s (1998, Journal of Multivariate Analysis 65, 139–165; hereafter LV) nonparametric deconvolution estimator and its regularized version by Comte and Kappus (2015, Journal of Multivariate Analysis 140, 31–46) for the classical measurement error model, where repeated noisy measurements on the error-free variable of interest are available. In contrast to LV, our assumptions allow unbounded supports for the error-free variable and measurement errors. Compared to Bonhomme and Robin (2010, Review of Economic Studies 77, 491–533) specialized to the measurement error model, our assumptions do not require existence of the moment generating functions of the square and product of repeated measurements. Furthermore, by utilizing a maximal inequality for the multivariate normalized empirical characteristic function process, we derive uniform convergence rates that are faster than the ones derived in these papers under such weaker conditions.

It is shown that in a first-order mixed autoregressive moving average model, a Lagrange multiplier test for the autoregressive unit-root hypothesis can be inconsistent against stationary alternatives.

In this comment we identify a lacuna in a proof in the paper by M. Caner published in 1997 in Econometric Theory concerning the weak limit behavior of various expressions involving heavy-tailed multivariate vectors and the convergence of stochastic integrals. In a later paper (Caner, 1998) the results for these limit relations are used to formulate tests for cointegration with infinite variance errors.

Phoebus J. Dhrymes is one of the best known econometricians of the last 40 years. He has made substantial contributions to econometric theory through articles in leading journals and by way of a series of outstanding texts on the foundations and methods of econometrics. His early research began with an applied econometric focus on problems of production and investment. His later contributions concentrated on the foundations of econometric methodology, including systems of simultaneous equations. Throughout the econometrics community, Dhrymes is well known for his influential textbooks, some of which have been translated into several languages. His 1970 book Econometrics: Statistical Foundations and Applications provided an accessible and rigorous foundation for both students and teachers of econometrics. His subsequent books have continued to treat foundational issues and have tracked new areas of econometric interest through to his 1998 book Time Series, Unit Roots, and Cointegration. Reading his books reveals Dhrymes as a teacher, synthesizer, and master expositor. As he says in the interview that follows, “my books are not typical textbooks. I perceive them more as books that bridge the gap between ordinary textbooks and journal articles and as filters that distill and synthesize the wisdom of many contributors to the subject. On this score I was influenced in my writing by the way I learn when studying by myself.”

This paper investigates Granger noncausality and the cointegrating relation between two time series in the Hilbert space framework. This framework allows us to analyze the relationship between cointegration and distance between two information sets. In particular, we prove that if two variables, X and Y, are cointegrated, then the distance between two information sets, concerning the differenced series ΔX and ΔY, must be less than the standard deviation of ΔX.

We propose a series-based nonparametric specification test for a regression function when data are spatially dependent, the “space” being of a general economic or social nature. Dependence can be parametric, parametric with increasing dimension, semiparametric or any combination thereof, thus covering a vast variety of settings. These include spatial error models of varying types and levels of complexity. Under a new smooth spatial dependence condition, our test statistic is asymptotically standard normal. To prove the latter property, we establish a central limit theorem for quadratic forms in linear processes in an increasing dimension setting. Finite sample performance is investigated in a simulation study, with a bootstrap method also justified and illustrated. Empirical examples illustrate the test with real-world data.

This paper develops a test for homogeneity of the threshold parameter in threshold regression models. The test has a natural interpretation from time series perspectives and can also be applied to test for additional change points in the structural break models. The limiting distribution of the test statistic is derived, and the finite sample properties are studied in Monte Carlo simulations. We apply the new test to the tipping point problem studied by Card, Mas, and Rothstein (2008, Quarterly Journal of Economics 123, 177–218) and statistically justify that the location of the tipping point varies across tracts.