We discuss the limiting behavior of the serial correlation coefficient in mildly explosive autoregression, where the error sequence is in the domain of attraction of an α-stable law, α ∈ (0,2]. Therein, the autoregressive coefficient ρ = ρn > 1 is assumed to satisfy the condition ρn → 1 such that n(ρn − 1) → ∞ as n → ∞. In contrast to the vast majority of existing literature in the area, no specific form of ρ is required. We show that the serial correlation coefficient converges in distribution to a ratio of two independent stable random variables.The authors thank P.C.B. Phillips and two anonymous referees for a very careful reading of the manuscript, pointing out several mistakes, and providing shorter and simpler proofs. This research was partially supported by NATO grant PST.EAP.CLG 980599 and NSF-OTKA grant INT-0223262. This work was done while the first author was at the University of Utah.

A new consistent test is proposed for the parametric specification of the diffusion function in a diffusion process without any restrictions on the functional form of the drift function. The data are assumed to be sampled discretely in a time interval that can be fixed or lengthened to infinity. The test statistic is shown to follow an asymptotic normal distribution under the null hypothesis that the parametric diffusion function is correctly specified. Monte Carlo simulations are conducted to examine the finite-sample performance of the test, revealing that the test has good size and power.The author is grateful to Yacine Aït-Sahalia, John Knight, Oliver Linton (the co-editor), Greg Tkacz, Jun Yang, and three anonymous referees for helpful comments and suggestions. He also thanks seminar participants at the Bank of Canada, the 2004 Semiparametrics Conference in Rio de Janeiro, and the 2005 Econometric Study Group in Bristol. The views expressed in this paper are those of the author. No responsibility for them should be attributed to the Bank of Canada.

We consider a model for a multivariate time series where the conditional covariance matrix is a function of a finite-dimensional parameter and the innovation distribution is nonparametric. The semiparametric lower bound for the estimation of the euclidean parameter is characterized, and it is shown that adaptive estimation without reparametrization is not possible. Based on a consistent first-stage estimator (such as quasi maximum likelihood), we propose a semiparametric estimator that estimates the efficient influence function using kernel estimators. We state conditions under which the estimator attains the semiparametric lower bound. For particular models such as the constant conditional correlation model, adaptive estimation of the dynamic part of the model is shown to be possible. To avoid the curse of dimensionality one can, e.g., restrict the multivariate density to the class of spherical distributions, for which we also derive the semiparametric efficiency bound and an estimator that attains this bound. A simulation experiment demonstrates the efficiency gain of the proposed estimator compared with quasi maximum likelihood estimation.Rombouts' work was supported by the Centre for Research on e-Finance, HEC Montreal. Hafner gratefully acknowledges financial support by the Fonds Spéciaux de Recherche (FSR 05) of the Université catholique de Louvain. The authors thank three anonymous referees for valuable comments and suggestions and Luc Bauwens, Geert Dhaene, Feico Drost, Wolfgang Härdle, Douglas Hodgson, Jens Peter Kreiss, Oliver Linton, and Bas Werker for helpful discussions. We also thank participants of the CORE econometrics seminar, the York annual meeting in econometrics, the annual econometric study group meeting 2002 in Bristol, the 2003 workshop “The Art of Semiparametrics” in Berlin, and the statistics seminar of the Stockholm School of Economics for valuable comments.

This paper develops a new semiparametric approach for the estimation of hazard functions in the presence of unobserved heterogeneity. The hazard function is specified parametrically, whereas the distribution of the unobserved heterogeneity is indirectly estimated using the method of kernels. The semiparametric efficiency bounds are derived. The estimator obtains these bounds in large samples.The authors thank Yongmiao Chen, James Heckman, Hidehiko Ichimura, Tony Lancaster, Qi Li, Adrian Pagan, Barry Smith, two anonymous referees, and the co-editor for helpful input. We particularly thank Steven Stern, who prompted us toward this line of research. Any errors are those of the authors. Research funding for Rilstone was provided by the Social Sciences and Humanities Research Council of Canada.

This paper provides a root-n consistent, asymptotically normal weighted least squares estimator of the coefficients in a truncated regression model. The distribution of the errors is unknown and permits general forms of unknown heteroskedasticity. Also provided is an instrumental variables based two-stage least squares estimator for this model, which can be used when some regressors are endogenous, mismeasured, or otherwise correlated with the errors. A simulation study indicates that the new estimators perform well in finite samples. Our limiting distribution theory includes a new asymptotic trimming result addressing the boundary bias in first-stage density estimation without knowledge of the support boundary.This research was supported in part by the National Science Foundation through grant SBR-9514977 to A. Lewbel. The authors thank Thierry Magnac, Dan McFadden, Jim Powell, Richard Blundell, Bo Honoré, Jim Heckman, Xiaohong Chen, and Songnian Chen for helpful comments. Any errors are our own.

Most nonparametric identification results for the mixed proportional hazards model for single spell duration data depend crucially on the proportional hazards assumption. Here, it is shown that variation in covariates over time, combined with variation across observations, is sufficient to ensure identification without the proportional hazards assumption. The required variation over time is minimal, and the mixed hazards model is identified without the proportional hazards assumption in the presence of standard time-varying covariates.Thanks to Kåre Bævre, Zhiyang Jia, Tore Schweder, Rolf Aaberge, and John K. Dagsvik for useful comments.

This note suggests a simple modification to the Kwiatkowski, Phillips, Schmidt, and Shin (1992, Journal of Econometrics, 54, 159–178) test (KPSS test) so that it is applicable to testing the null hypothesis of near integration against a unit root alternative. The modified KPSS test is shown not to suffer from the asymptotic size distortion problems of the original KPSS test that are described by Müller (2005, Journal of Econometrics 128, 195–213). The test also has good asymptotic and finite-sample properties relative to the point optimal tests of Müller (2005) and Elliott and Müller (2006, Journal of Econometrics 135, 285–310).

In a recent Econometric Theory problem, it was demonstrated that in a conditionally heteroskedastic time series regression with martingale difference errors the use of lagged values of regressors as instruments may not increase the efficiency of estimation relative to ordinary least squares. We provide an example of an analogous phenomenon in a model with serially correlated errors, where the optimal instrumental variables estimator is asymptotically as efficient as the instrumental variables estimator constructed as optimal when ignoring the presence of conditional heteroskedasticity.I thank a referee for providing useful comments that improved the presentation and the co-editor Paolo Paruolo for his patience.