We examine the identifiability of a nonlinear state space system under general assumptions. The discrete time evolution of the state is generated by a recurrent Elman network. For a large set of Elman networks we determine the class of observationally equivalent minimal systems, i.e., minimal systems that exhibit the same input-output behavior.The authors are grateful for discussions with M. Deistler and D. Bauer. A.A. Al-Falou was funded by the ERNSI network within the European Union program Training and Mobility of Researchers (TMR). D. Trummer was funded by the FWF (Austrian Science Fund). We thank an anonymous referee for helpful comments and suggestions.

Two adaptive bandwidth selection methods for minimizing the mean squared error of nonparametric estimators in locally stationary processes are proposed. We investigate a cross-validation approach and a method based on contrast minimization and derive asymptotic properties of both methods. The results are applicable for different statistics under a general setting of local stationarity including nonlinear processes. At the same time, we deepen the general framework for local stationarity based on stationary approximations. For example, a general Bernstein inequality is derived for such processes. The properties of the bandwidth selection methods are also investigated in several simulation studies.

In many important textbooks the formal statement of the spectral representation theorem is followed by a process version, usually informal, stating that any stationary stochastic process {ξ(t), t ∈ T} is the limit in quadratic mean of a sequence of processes {S(n,t), t ∈ T}, each consisting of a finite sum of harmonic oscillations with stochastic weights. The natural issues, whether the approximation error ξ(t) − S(n,t) is stationary or whether at least it converges to zero uniformly in t, have not been explicitly addressed in the literature. The paper shows that in all relevant cases, for T unbounded the process convergence is not uniform in t (so that ξ(t) − S(n,t) is not stationary). Equivalently, when T is unbounded the number of harmonic oscillations necessary to approximate ξ(t) with a preassigned accuracy depends on t. The conclusion is that the process version of the spectral representation theorem should explicitly mention that in general the approximation of ξ(t) by a finite sum of harmonic oscillations, given the accuracy, is valid for t belonging to a bounded subset of the real axis (of the set of integers in the discrete-parameter case).The author is grateful for very useful suggestions to Francesco Battaglia, Gianluca Cubadda, Domenico Marinucci, Enzo Orsingher, Dag Tjøstheim, and Umberto Triacca and also to an anonymous referee and the Econometric Theory co-editor Benedikt M. Pötscher.

It is undoubtedly desirable that econometric models capture the dynamic behavior, like trends and cycles, observed in many economic processes. Building models with such capabilities has been an important objective in the continuous time econometrics literature, for instance, the cyclical growth models of Bergstrom (1966); the economy-wide macroeconometric models of, for example, Bergstrom and Wymer (1976); unobserved stochastic trends of Harvey and Stock (1988 and 1993) and Bergstrom (1997); and differential-difference equations of Chambers and McGarry (2002). This paper considers continuous time cyclical trends, which complement the trend-plus-cycle models in the unobserved components literature but could also be incorporated into Bergstrom type systems of differential equations, as were stochastic trends in Bergstrom (1997).

The Econometric Society Australasian Meeting in 1997 was hosted by the economics department at the University of Melbourne on July 2 to 4 with Peter Bardsley (economics) and Vance L. Martin (econometrics) as cochairpersons. Special features consisted of a star-studded lineup of invited speakers, the inaugural E.J. Hannan lecture, a range of special seminars in economic theory and econometric theory, and a number of nonacademic but spirited special events that took place both during and after the conference.

It is a challenging task to review the research carried out by Professor Sargan which has covered such a broad range of areas and which offers general and unifying approaches to tackling problems and to obtaining results.I can only apologize for my audacity in accepting to deliver this laudatio. In order to remedy the limitation of my resources, I have benefited from Manuel Arellano's help and I have used the papers by David Hendry and Ken Wallis (1984), Peter Phillips (1985), and Esfandiar Maasoumi (1988a, 1988b). These papers review and summarize the works of the common master, who is considered to be one of the major contributors to Econometrics; in the words of Professor T.W. Anderson: “one of the most distinguished econometricians of our generation.” I am grateful to Peter Phillips and Grayham Mizon for their comments in preparing the English version of this laudatio.

On the rank of a matrix useful in goodness-of-fit testing of structural equation models—solution.An excellent solution was independently proposed by A. Satorra and H. Neudecker, the posers of the problem.

This issue of Econometric Theory marks 20 full years of publication of the journal ET and the beginning of our third decade. To celebrate the occasion, I invited a group of econometricians, including all the present and past co-editors of ET, to reflect on the future of econometrics. To focus discussion, I selected a theme that relates to a recent trend in the practical use of econometric methodology, one that seems destined to play an increasing role in the future of the subject—automated modeling and inference. Accordingly, this issue contains contributions on various aspects of the theme of automation, introducing the notion of automated discovery, analyzing the validity of selection procedures, and discussing the practical utility of these automated methods in econometric modeling exercises.

In this paper, we develop methods for statistical inferences in a partially identified nonparametric panel data model with endogeneity and interactive fixed effects. Under some normalization rules, we can concentrate out the large-dimensional parameter vector of factor loadings and specify a set of conditional moment restrictions that are involved with only the finite-dimensional factor parameters along with the infinite-dimensional nonparametric component. For a conjectured restriction on the parameter, we consider testing the null hypothesis that the restriction is satisfied by at least one element in the identified set and propose a test statistic based on a novel martingale difference divergence measure for the distance between a conditional expectation object and zero. We derive a tight asymptotic distributional upper bound for the resultant test statistic under the null and show that it is divergent at rate-N under the global alternative. To obtain the critical values for our test, we propose a version of multiplier bootstrap and establish its asymptotic validity. Simulations demonstrate the finite sample properties of our inference procedure. We apply our method to study Engel curves for major nondurable expenditures in China by using a panel dataset from the China Family Panel Studies.

This paper proposes a nonparametric test to assess whether there exist heterogeneous quantile treatment effects (QTEs) of an intervention on the outcome of interest across different sub-populations defined by covariates of interest. Specifically, a consistent test statistic based on the Cramér–von Mises type criterion is developed to test if the treatment has a constant quantile effect for all sub-populations defined by covariates of interest. Under some regularity conditions, the asymptotic behaviors of the proposed test statistic are investigated under both the null and alternative hypotheses. Furthermore, a nonparametric Bootstrap procedure is suggested to approximate the finite-sample null distribution of the proposed test; then, the asymptotic validity of the proposed Bootstrap test is theoretically justified. Through Monte Carlo simulations, we demonstrate the power properties of the test in finite samples. Finally, the proposed testing approach is applied to investigate whether there exists heterogeneity for the QTE of maternal smoking during pregnancy on infant birth weight across different age groups of mothers.