In establishing the Problems and Solutions (P&S) series of Econometric Theory, the primary objective was pedagogical—to provide an intellectual resource for students, instructors, and researchers through the publication of student exercises and research-level problems in econometrics. Over the past 20 years, the P&S series has successfully served this goal. Large numbers of worked exercises and problems have now been published, and the series has promoted interaction between problem solvers, problem posers, and the ET readership, thereby helping to bring the wider econometric community together in a common purpose.

In this paper we derive representations for the limiting distributions of the regression-based seasonal unit root test statistics of Hylleberg, Engle, Granger, and Yoo (1990, Journal of Econometrics 44, 215–238) and Beaulieu and Miron (1993, Journal of Econometrics 55, 305–328), inter alia, when the underlying process displays near seasonal integration. Our results generalize those presented in previous studies by allowing for an arbitrary seasonal periodicity (including the nonseasonal case), a wide range of possible assumptions on the initial conditions, a range of (seasonal) deterministic mean effects, and finite autoregressive behavior in the driving shocks. We use these representations to simulate the asymptotic local power functions of the seasonal unit root tests, demonstrating a significant dependence on serial correlation nuisance parameters in the case of the pairs of t-statistics, but not the associated F-statistic, for unit roots at the seasonal harmonic frequencies. Monte Carlo simulation results are presented that suggest that the local limiting distribution theory provides a good approximation to the finite-sample behavior of the statistics. Our results lend further weight to the advice of previous authors that inference on the unit root hypothesis at the seasonal harmonic frequencies should be based on the F-statistic, rather than on the associated pairs of t-ratios.We are grateful to Bruce Hansen and two anonymous referees for their helpful comments and suggestions on earlier versions of this paper.

This paper considers testing for normality for correlated data. The proposed test procedure employs the skewness-kurtosis test statistic, but studentized by standard error estimators that are consistent under serial dependence of the observations. The standard error estimators are sample versions of the asymptotic quantities that do not incorporate any downweighting, and, hence, no smoothing parameter is needed. Therefore, the main feature of our proposed test is its simplicity, because it does not require the selection of any user-chosen parameter such as a smoothing number or the order of an approximating model.We are very grateful to Don Andrews and two referees for useful comments and suggestions. We are especially thankful to a referee who provided a FORTRAN code. Lobato acknowledges financial support from Asociación Mexicana de Cultura and from Consejo Nacional de Ciencia y Tecnologìa (CONACYT) under project grant 41893-S. Velasco acknowledges financial support from Spanish Dirección General de Enseñanza Superior, BEC 2001-1270.

In this paper we derive the necessary and sufficient conditions for the t-ratio to be Student's t distributed. In particular, it is demonstrated for a special case that under conditions of nonnormality characterized by elliptical symmetry, the t-ratio remains Student's t distributed provided that the random vector forming the t-ratio has a diagonal covariance structure. Our results also show that the findings of Magnus (2002, in A. Ullah, A.T.K. Wan, & A. Chaturvedi (eds.), Handbook of Applied Econometrics and Statistical Inference, 277–285) on the sensitivity of the t-ratio remain invariant in the elliptically symmetric distribution setting. Extension to the linear model is considered. Exact results giving finite sample justification for the t-statistic under nonnormal error terms are derived. Furthermore, the distribution of the F-ratio assuming elliptical errors is examined. Our results reject the argument by Zaman (1996, Statistical Foundations for Econometric Techniques) that nonnormality of disturbances has in general no effect on the F-statistic.The authors thank Anurag Banerjee, Judith Clarke, Kazuhiro Ohtani, and Guohua Zou for their helpful suggestions and advice during the course of this work. In particular, we are very grateful to Judith Clarke for bringing to our attention the unpublished work of D.H. Thomas and to Guohua Zou for his careful reading of an earlier version of this paper. Thanks also go to the co-editor Benedikt Pötscher and two anonymous referees for their valuable comments. The second author gratefully acknowledges financial support from the Hong Kong Research Grant Council.

Existing simulation-based estimation methods are either general purpose but asymptotically inefficient or asymptotically efficient but only suitable for restricted classes of models. This paper studies a simulated maximum likelihood method that rests on estimating the likelihood nonparametrically on a simulated sample. We prove that this method, which can be used on very general models, is consistent and asymptotically efficient for static models. We then propose an extension to dynamic models and give some Monte-Carlo simulation results on a dynamic Tobit model.We thank Jean-Pierre Florens, Arnoldo Frigessi, Christian Gouriéroux, Jim Heckman, Guy Laroque, Oliver Linton, Nour Meddahi, Alain Monfort, Eric Renault, Christian Robert, Neil Shephard, and two referees for their comments. Remaining errors and imperfections are ours. Parts of this paper were written while Bernard Salanié was visiting the University of Chicago, which he thanks for its hospitality.

We derive the asymptotic distribution of the estimate of the cointegration rank of a multivariate model when Akaike's information criterion is used. It is shown that the use of this criterion is ill-advised given that the estimate is severely upward biased even asymptotically.I thank the editor, Professor Peter Phillips, and three anonymous referees for comments and suggestions that improved this paper significantly. All remaining errors are my own.

Professor David F. Hendry is interviewed by Neil R. Ericsson.

Solution to Normal's deconvolution and the independence of sample mean and variance problem.

Solution to the asymptotic distribution of the Dickey–Fuller statistic under nonnegativity constraint problem.

In Econometric Theory, vol. 20, no. 2 (April 2004), on page 428 the number of the Solution should be changed to Solution 03.2.1.