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.

We obtain an inequality for the sample variance of a vector Brownian motion on [0,1] and an associated Ornstein–Uhlenbeck process. The result is applied to a regression involving near-integrated regressors, and establishes that in the limit the dispersion of the least squares estimator is greater in the near-integrated than in the integrated case. Our proof uses a quite general integral inequality, which appears to be new.

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.

Asymptotically pivotal structural change tests are developed for simultaneous equations with weakly identified parameters, extending the boundedly pivotal tests of Caner (2007, Journal of Econometrics 137, 28–67) by means of a simple reparametrization of the model.

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.

A multivariate extension of the exponential continuous time GARCH (p, q) model (ECOGARCH) is introduced and studied. Stationarity and mixing properties of the new stochastic volatility model are investigated, and ways to model a component-wise leverage effect are presented.

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.

Effect of nonnormality on the asymptotic property of three estimators of a single structural equation with structural change is examined. The three estimators are the limited information maximum likelihood estimator, derived under normality and equality of structural variances in different samples, given by Hodoshima, a two-stage least squares type estimator due to Barten and Bronsard, and a minimum distance estimator presented here. Normality is relaxed but the equality assumption of structural variances is retained. Under nonnormality the limited information maximum likelihood estimator is consistent but may not be efficient relative to the Barten and Bronsard's estimator. A sufficient condition is given under which the limited information maximum likelihood estimator dominates the Barten and Bronsard's estimator in terms of the asymptotic covariance matrix. The minimum distance estimator dominates other estimators.

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