We investigate the possible bimodality of the density of the two-stage least squares (TSLS) estimator in a just-identified/overidentified linear structural equation. By studying the interaction between weakness of instruments, degree of endogeneity, and degree of overidentification we are able to identify conditions for its existence.I thank Grant Hillier, Patrick Marsh, Don Poskitt, the editor Peter Phillips, and two anonymous referees for useful and encouraging comments.

This paper investigates a simple dynamic linear panel regression model with both fixed effects and time effects. Using “large n and large T” asymptotics, we approximate the distribution of the fixed effect estimator of the autoregressive parameter in the dynamic linear panel model and derive its asymptotic bias. We find that the same higher order bias correction approach proposed by Hahn and Kuersteiner (2002, Econometrica 70, 1639–1659) can be applied to the dynamic linear panel model even when time specific effects are present.We thank Peter Phillips and three anonymous referees for helpful comments. The first author gratefully acknowledges financial support from NSF grant SES-0313651. The second author appreciates the Faculty Development Awards of USC for research support.

The distributions of products and ratios of random variables are of interest in many areas of the sciences. In this note, the exact distributions of the product XY and the ratio X/Y are derived when X and Y are gamma and Weibull random variables distributed independently of each other.The authors thank the referee and the editor for carefully reading the paper and for their help in improving the paper.

In a simple model composed of a structural equation and identity, the finite-sample distribution of the instrumental variable/limited information maximum likelihood (IV/LIML) estimator is always bimodal, and this is most apparent when the concentration parameter is small. Weak instrumentation is the energy that feeds the secondary mode, and the coefficient in the structural identity provides a point of compression in the density that gives rise to it. The IV limit distribution can be normal, bimodal, or inverse normal depending on the behavior of the concentration parameter and the weakness of the instruments. The limit distribution of the ordinary least squares (OLS) estimator is normal in all cases and has a much faster rate of convergence under very weak instrumentation. The IV estimator is therefore more resistant to the attractive effect of the identity than OLS. Some of these limit results differ from conventional weak instrument asymptotics, including convergence to a constant in very weak instrument cases and limit distributions that are inverse normal.My thanks to Richard Smith and two referees for comments on an earlier version. Section 2 of the paper is based on lectures given to students over the 1970s and 1980s at Essex, Birmingham, and Yale. Partial support is acknowledged from a Kelly Fellowship at the University of Auckland School of Business and the NSF under Grant SES 04-142254.

This paper studies robust inference methods for nonlinear moment restriction models with weakly identified parameters in time series contexts. Our methods are based on generalized empirical likelihood with kernel smoothing. The proposed test statistics, which follow the standard χ2 limiting distributions, are robust to weak identification and dependent data.The author is deeply grateful to Bruce Hansen, John Kennan, and Gautam Tripathi for their guidance and time. Comments from a coeditor and two anonymous referees substantially helped this revision. The author also thanks Allan Gregory, Patrik Guggenberger, Philip Haile, Hiroyuki Kasahara, Matthew Kim, Yuichi Kitamura, and seminar participants at Queen's University, University of Wisconsin, and the 2003 North America Summer Meeting of the Econometric Society for helpful discussions and suggestions. Financial support from the Alice Gengler Wisconsin Distinguished Graduate Fellowship and Wisconsin Alumni Research Foundation Dissertation Fellowship is gratefully acknowledged.

This note analyzes the local asymptotic power properties of a test proposed by Breitung (2000, in B. Baltagi (ed.), Nonstationary Panels, Panel Cointegration, and Dynamic Panels). We demonstrate that the Breitung test, like many other tests (including point optimal tests) for panel unit roots in the presence of incidental trends, has nontrivial power in neighborhoods that shrink toward the null hypothesis at the rate of n−1/4T−1 where n and T are the cross-section and time-series dimensions, respectively. This rate is slower than the n−1/2T−1 rate claimed by Breitung. Simulation evidence documents the usefulness of the asymptotic approximations given here.The authors thank Paolo Paruolo and a referee for comments on an earlier version of the paper. Phillips acknowledges partial support from a Kelly Fellowship and the NSF under grant SES 04-142254. Perron acknowledges financial support from FQRSC, SSHRC, and MITACS.

In this note the nonparametric unit root test of Burridge and Guerre (1996, Econometric Theory, 12, 705–723), which is based on the standardized number of crossings of a level of a random walk, is extended in two ways, allowing for a deterministic trend in the process and more general innovations. The test has a well-known standard limit distribution. Monte Carlo experiments revealed the good finite-sample properties of the proposed test.The authors appreciate helpful comments from an anonymous referee. We gratefully acknowledge the financial support of the Ministerio de Ciencia y Tecnología and the Conselleria d'Economia, Hisenda i Innovació, grants BEC2002-03769 and PRIB-2004-10095, respectively.

We are pleased to announce two awards for the A.R. Bergstrom Prize in Econometrics for 2005.

I am delighted to announce the following Econometric Theory Awards for 2006.

Mundlak (1978, Econometrica 46, 69–85) showed that the fixed effects estimator can be obtained as generalized least squares (GLS) for a panel regression model where the individual effects are random but are all hopelessly correlated with the regressors. This result was obtained by partitioned inversion after substituting the reduced form expression for the individual effects as a function of the means of all the regressors. This note shows that Mundlak's result can be obtained using system estimation without using partitioned inversion. System estimation has proved useful for deriving two-stage least squares (2SLS) and three-stage least squares (3SLS) counterparts for the random effects panel models by Baltagi (1981, Journal of Econometrics 17, 189–200). It also has been used for obtaining an alternative derivation of the Hausman tests that is robust to heteroskedasticity of unknown form (see Arellano, 1993, Journal of Econometrics 59, 87–97) and more recently, for obtaining generalized method of moments (GMM) estimators for dynamic panel models (see Arellano and Bover, 1995, Journal of Econometrics 68, 29–51; and Blundell and Bond, 1998, Journal of Econometrics 87, 115–143, to mention a few). We also show that a necessary and sufficient condition for ordinary least squares (OLS) to be equivalent to GLS is satisfied for this model.

Vector time series analysis has become a standard tool in macroeconometrics and in empirical finance since the early 1980s. Over the last two decades, Helmut Lütkepohl has published extensively on virtually all topics covered in this book, which puts him in an excellent position for writing an authoritative textbook on this subject.

Necessary and sufficient conditions are established for the second subsample to be partially redundant given the first subsample for the best linear unbiased estimator of a subset of the coefficient vector of a general linear regression model.We thank the Co-editor for his very helpful comments on an earlier draft.

Econometric Theory acknowledges the services of the following persons who acted as referees for the Journal during 2004–2005. The quality of the final research product that appears in each issue of the Journal owes much to the specialist knowledge and the painstaking, silent contributions of our referees. The Editor, Co-Editors, and Cambridge University Press thank all our referees for their services and apologize if the following list is in any way incomplete.

Econometric Theory is proud to announce the winning article for The Tjalling C. Koopmans Econometric Theory Prize for the period 2003–2005 inclusive.

In most cases where estimation with averaged data is performed, interest lies on the parameters of a model at the individual level, but grouped data are used because disaggregate data are not observed. In this note we study the conditions under which it is possible to consistently estimate the parameters of the individual data model using averaged data, giving particular attention to the case of endogenous selection into groups.We are grateful to an anonymous referee for helpful comments and suggestions. We also thank Pedro Duarte Neves, Les Godfrey, Paulo Parente, Maximiano Pinheiro, and Pedro Portugal for helpful discussions. The usual disclaimer applies. Machado is consultant for the Research Department of Banco de Portugal. Santos Silva is grateful for the hospitality, working conditions, and financial support provided by Banco de Portugal, which made this work possible. The authors also gratefully acknowledge partial financial support from Fundação para a Ciência e Tecnologia, program POCTI, partially funded by FEDER.

Applications are now being sought for the eighth A.R. Bergstrom Prize in Econometrics.

This book, Matrix Algebra, is the first volume of the Econometric Exercises series. Other volumes of the series (Statistics [vol. 2], Econometric Theory I [vol. 3], and Empirical Applications [vol. 4]) are to appear in the near future. A variety of planned titles will also follow (e.g., Time Series, Microeconometrics, and Financial Econometrics). Although there have been a few worked-exercise books in econometrics (e.g., Phillips and Wickens, 1978), this series is the first comprehensive exercise series in modern econometrics that covers the materials for advanced undergraduate and graduate econometrics courses. According to the preface, each volume follows the same format. Chapters start with a brief overview, and then exercises and solutions follow. Solutions are provided immediately after the exercise is posed. There is a variety of exercises from proofs and applications of theorems to numerical examples. In this review I discuss only the first volume in the Econometric Exercises series and find it very useful and successful. I expect succeeding volumes in the series to be of similar quality and usefulness, given the overall objectives of the series.

This note considers a panel data regression model with spatial autoregressive disturbances and random effects where the weight matrix is normalized and has equal elements. This is motivated by Kelejian, Prucha, and Yuzefovich (2005, Journal of Regional Science, forthcoming), who argue that such a weighting matrix, having blocks of equal elements, might be considered when units are equally distant within certain neighborhoods but unrelated between neighborhoods. We derive a simple weighted least squares transformation that obtains generalized least squares (GLS) on this model as a simple ordinary least squares (OLS). For the special case of a spatial panel model with no random effects, we obtain two sufficient conditions where GLS on this model is equivalent to OLS. Finally, we show that these results, for the equal weight matrix, hold whether we use the spatial autoregressive specification, the spatial moving average specification, the spatial error components specification, or the Kapoor, Kelejian, and Prucha (2005, Journal of Econometrics, forthcoming) alternative to modeling panel data with spatially correlated error components.I thank Paolo Paruolo and an anonymous referee for helpful comments and suggestions.

We consider a family of GARCH(1,1) processes introduced in He and Teräsvirta (1999a, Journal of Econometrics 92, 173–192). This family contains various popular generalized autoregressive conditional heteroskedasticity (GARCH) models as special cases. A necessary and sufficient condition for the existence of a strictly stationary solution is given.This research was financially supported by the Jan Wallander's and Tom Hedelius' Foundation, Grant J03–41. The author thanks the editor, an anonymous referee, Pentti Saikkonen, and Timo Teräsvirta for useful comments.