By pointing out the spurious regression problem, Granger and Newbold (1974) have shown the importance of stochastic trends in time series data in the context of linear regression models. At the time, removing trends by differencing was already common practice in univariate time series modeling as part of the Box–Jenkins approach (Box and Jenkins, 1976). These new developments, however, emphasized the importance of autoregressive (AR) unit roots and motivated the development of statistical procedures for their detection. Dickey and Fuller (1979) and Fuller (1976) were pioneers in developing tests for unit roots that became widely used. The foundation of asymptotic theory for regressions involving stochastic trends was led by Phillips (1986, 1987) with the introduction of the functional limit theory, weak convergence methods, convergence to stochastic integrals, nonparametric unit root testing, and continuous record asymptotics. Phillips and Durlauf (1986) extended some of these results to the multivariate setting by presenting the multivariate invariance principles and the asymptotic theory of multivariate nonstationary and cointegrating regressions. These contributions provided the asymptotic tools that have served as the basis for most of the limit results derived in the context of unit root nonstationarity, and they have stimulated extensive subsequent research.We are grateful to Peter Phillips for proposing a special issue of Econometric Theory for papers from our conference Unit Root and Cointegration Testing. We thank all participants of the conference who contributed their papers to this special issue. We are also very grateful to those colleagues who agreed to serve as referees for the papers. They not only provided generous help through comments but also respected our rather tight deadlines. We are grateful to all those who helped us to complete the special issue unusually fast. To protect their identities, we do not list them here. They will be included in the general list of referees for Econometric Theory. Our conference would not have been possible without the generous financial support of a number of sponsors. We are grateful to the Bank of Portugal, to the Portuguese Science Foundation (FCT), to the Luso-American Foundation for Development (FLAD), and to the Journal of Applied Econometrics for their financial support.

The intercept of the binary response model is not regularly identified (i.e., $\sqrt n$ consistently estimable) when the support of both the special regressor V and the error term ε are the whole real line. The estimator of the intercept potentially has a slower than $\sqrt n$ convergence rate, which can result in a large estimation error in practice. This paper imposes additional tail restrictions which guarantee the regular identification of the intercept and thus the $\sqrt n$-consistency of its estimator. We then propose an estimator that achieves the $\sqrt n$ rate. Last, we extend our tail restrictions to a full-blown model with endogenous regressors.

I am delighted to announce the following Econometric Theory Awards for 2004.

We consider nonparametric identification and estimation of truncated regression models with unknown conditional heteroskedasticity. The existing methods (e.g., Chen (2010, Review of Economic Studies 77, 127–153)) that ignore heteroskedasticity often result in inconsistent estimators of regression functions. In this paper, we show that both the regression and heteroskedasticity functions are identified in a location-scale setting. Based on our constructive identification results, we propose kernel-based estimators of regression and heteroskedasticity functions and show that the estimators are asymptotically normally distributed. Our simulations demonstrate that our new method performs well in finite samples. In particular, we confirm that in the presence of heteroskedasticity, our new estimator of the regression function has a much smaller bias than Chen’s (2010, Review of Economic Studies 77, 127–153) estimator.

This interview with Michio Hatanaka is the first in this series given in the East, of which we are very proud. Hatanaka is a pioneer of econometrics in Japan. In the early 1950s he traveled to the United States to study as a graduate student at Vanderbilt University. That step was really unusual in the Japanese profession at that time. His stay in the States was extended to 1966, during which time he taught at Princeton and Rochester. His pathfinding behavior influenced and encouraged many Japanese scholars. Hatanaka started his academic career as a mathematical economist. This may partly explain why his research papers suggest deep economic thought as well as deep understanding of mathematics and statistics. His early contributions to econometrics are concerned with applying the spectral method to various economic problems. These contributions include the associate authorship of Spectral Analysis of Economic Time Series by C. W. J. Granger. His other contributions cover theoretical work on identification and estimation problems for dynamic econometric models, among which Hatanaka's efficient two-step estimator is well known. His research also includes empirical work on the Japanese economy and economic policy, which is relatively less known to people outside of Japan. His attitude toward research has set a standard for Japanese econometricians. His research papers are always a product of deep and full thought, and imbued with his own originality.

His achievements in administration are also impressive. During 1969–1971 and 1979–1980, he was director of the Institute of Social and Economic Research of Osaka University. And during 1983–1985 he was the dean of the faculty of economics at the same university. In addition, he served on the boards of several committees for the Japanese government and the Council of Science of Japan. Among his achievements in administration is the reform of the university entrance examination system, which was notoriously competitive and selective. This was really pathbreaking and led other universities to reform their systems.

This interview, which was given in Japanese, took place on November 20, 1989 in the Economics Department of Osaka University. What follows is a translated version of an edited transcript of that interview. We hope that the readers will share with us the privilege of hearing about the evolution of econometrics as encountered by him since just after the second world war.

We propose a nonparametric test of significant variables in the partial derivative of a regression mean function. The derivative is estimated by local polynomial estimation and the test statistic is constructed through a variation-based measure of the derivative in the direction of variables of interest. We establish the asymptotic null distribution of the test statistic and demonstrate that it is consistent. Motivated by the null distribution, we propose a wild bootstrap test, and show that it exhibits the same null distribution, whether the null is valid or not. We perform a Monte Carlo study to demonstrate its encouraging finite sample performance. An empirical application is conducted showing how the test can be applied to infer certain aspects of regression structures in a hedonic price model.

This paper analyzes the higher-order approximation of instrumental variable (IV) estimators in a linear homoskedastic IV regression model when a large set of instruments with potential invalidity is present. We establish theoretical results on the higher-order mean-squared error (MSE) approximation of the two-stage least-squares (2SLS), the limited information maximum likelihood (LIML), the Fuller (FULL), the bias-adjusted 2SLS, and jackknife version of the LIML and FULL estimators by allowing for local violations of the instrument exogeneity conditions. Based on the approximation to the higher-order MSE, we consider the instrument selection criteria that can be used to choose among the set of available instruments. We demonstrate the asymptotic optimality of the instrument selection procedure proposed by Donald and Newey (2001, Econometrica 69, 1161–1191) in the presence of locally (faster than $N^{-1/2}$) invalid instruments in the sense that the dominant term in the MSE with the chosen instrument is asymptotically equivalent to the infeasible optimum. Furthermore, we propose instrument selection procedures to choose instruments among the sets of conservative (known) valid instruments and potentially locally ($N^{-1/2}$) invalid instruments based on the higher-order MSE of the IV estimators by considering the bias-variance trade-off.

Inoue and Solon (2006, Econometric Theory 22, 835–851) presented a test against serial correlation of arbitrary form in fixed-effect models for short panel data. Implementing the test requires choosing a regularization parameter that may severely affect power and for which no optimal selection rule is available. We present a modified version of their test that does not require any regularization parameter. Asymptotic power calculations illustrate the improvement of our procedure. An extension of the approach that accommodates dynamic models is also provided.

This problem discusses an I(2) model in the VAR(1) case. The I(2) representation theorem of Johansen (1992) (JRT) holds also for VAR(1) processes. The I(2) model for VAR(k) processes has been discussed for k ≥ 2 in Johansen (1996, Ch. 9; 1997). We here discuss a parametrization for the I(2) case of VAR(1) that differs from the VAR(k) model.

Cost-effective survey methods such as multi(R)-phase sampling typically generate samples that are collections of monotonic subsamples, i.e., the variables observed for the units in subsample r are also observed for the units in subsample r + 1 for r = 1,…,R – 1. These subsamples represent subpopulations that can be systematically different if the selection of a unit in each phase of sampling depends on the observed variables for that unit from past phases. Our article is about optimally combining all the subsamples for the efficient estimation of a finite dimensional parameter defined by moment restrictions on a generic target population that is an arbitrary union of these subpopulations. Only the R-th subsample is assumed to contain all the variables that are arguments of the moment function. Semiparametric efficiency bounds for estimation are obtained under a unified framework, allowing for full generality of the selection on observables in the sampling design. Contribution of each subsample toward efficient estimation is analyzed; and this turns out to differ fundamentally from that in setups where the same collection of subsamples is instead generated unplanned by unknown sampling. Uniquely, our setup enables all the subsamples to contribute to the efficient estimation for all the target populations, which we show is not possible in other setups. Efficient estimation is standard. Simulation evidence of substantive efficiency gains from using all the subsamples is provided for all the targets.