Econometric Theory



Tjalling C. Koopmans, 1975

Ivana Komunjer “Global Identification in Nonlinear Models with Moment Restrictions,” Econometric Theory, Vol. 28, No. 4, August 2012, pages 719-729.

The paper derives sufficient conditions for global identifiability in nonlinear model classes. Themodels are characterized by a finite number of unconditional moment restrictions. A set of assumptions is given which guarantee that the moment conditions uniquely determine the underlying true parameter. The main findings are based on a homeomorphism result. The assumptions given in the paper provide an alternative to the sufficient conditions for global identifiability of nonlinear systems given by F.M. Fisher (1966) and T.J. Rothenberg (1971). Earlier, conditions for identifiability in systems which are linear in the variables, but where the parameters satisfy nonlinear restrictions, had been obtained by L. Wegge (1965).


Dimitris N. Politis, “Higher-Order Accurate, Positive Semi-Definite Estimation of Large-Sample Covariance and Spectral Density Matrices,” Econometric Theory, Vol. 27, No. 4, August 2011, pages 703-744.

A new class of HAC large-sample covariance and spectral density estimators is proposed based on the notion of flat-top kernels. These estimators are shown to be higher-order accurate when higher-order accuracy is possible. It is shown how a flat-top estimator can be modified to become positive semi-definite while retaining its higher-order accuracy. In addition, a consistent procedure for optimal bandwidth choice is described.


Wei Biao Wu and Xiaofeng Shao, "A Limit Theorem for Quadratic Forms and its Applications," Econometric Theory, Vol. 23, No. 5, October 2007, pages 930-951.

The paper derives a central limit theorem for quadratic forms of martingale differences. Particular emphasis is laid on the application of this result to estimation of the spectral density of a stationary process by the smoothed periodogram. For this case asymptotic normality is obtained from the result on general quadratic forms by approximating the Fourier transforms of the underlying stationary process by martingales. Such limiting results are important, for instance for hypothesis testing and construction of confidence intervals in frequency domain.

 For both, the general case and for the special case of estimation of spectra, there exists a substantial body of preceding literature. A special feature of this paper is that the results are derived under assumptions which are very general and easily verifiable. For spectral estimation the main assumptions are that the underlying stationary process is obtained from a – in general non-linear – causal transformation of an i.i.d. sequence and a very weak assumption of short range dependence. By the first assumption the stationary process can be interpreted as the output of a general, possibly nonlinear, system with iid inputs. The class of such processes is very large. The second assumption avoids the classical strong mixing conditions or summability conditions on the joint cumulants.


Yongmiao Hong and Tae-Hwy Lee, "Diagnostic Checking for the Adequacy of Nonlinear Time Series Models," Econometric Theory, Vol. 19, No. 6, December 2003, pages 1065–1121.

This paper proposes a diagnostic test for the adequacy of time series models, allowing for rather general model classes, involving possibly nonlinear parametric functions of past information that include both conditional heterogeneity and conditional duration specifications. The test is based on the estimated noise process, relying on the joint and marginal characteristic functions of pairs of noise variables at different time distances to test for pairwise independence. The test employs the (generalized) spectrum of these quantities and therefore does not require moment conditions, and applies under a suitable mixing condition. Under the null of correct specification the generalized spectrum is constant and the test measures departures from this null using a standardized L2 distance. Asymptotic properties of the test are derived, data driven choices of the bandwidth for estimation of the generalized spectrum and their asymptotic properties are discussed, Monte Carlo studies are presented and an empirical application to daily stock prices is given.


Stefan Sperlich, Dag Tjøstheim and Lijian Yang, "Nonparametric Estimation and Testing of Interaction in Additive Models," Econometric Theory, Vol. 18, No. 2, April 2002, pp 197–251.

The article was selected by the journal’s Advisory Board from papers published in Econometric Theory over the period 2000-2002 inclusive. The citation accompanying the award is as follows:

A large and useful class of nonlinear models, obtained by generalizing additive models through adding second order interaction terms, is analyzed using nonparametric techniques. This is a wide-open area for research and it is very useful to have available a firm foundation for empirical research in the area. The authors develop asymptotics for marginal integration and backfitting estimation techniques. They propose procedures for testing interaction effects and suggest bootstrap methods. Finally, they provide simulation evidence and give an empirical implementation to a livestock production function.


Stéphane Gregoir, "Multivariate Time Series with Various Hidden Unit Roots, Part I: Integral Operator Algebra and Representation," Econometric Theory, Vol. 15, 1999, pp. 435–468.

Stéphane Gregoir is awarded the Tjalling Koopmans Econometric Theory Prize for a pair of related high quality papers. The first considers a vector of time series, each of which may contain several unit roots of various frequencies. There may also exist several linear combinations, or generalized cointegrations, which produce series with less unit roots. A general representation theorem is stated, with an associated vector error correction model. The theory includes as special cases the standard cointegration model with I(1) series, multi-cointegration with I(2) series and seasonal unit root cointegration. This representation theorem is a substantial and useful addition to the available theory.

The second paper develops estimation and test strategies for models with possible multiple unit roots at the zero and seasonal frequencies, together with polynomial (in lags) error-correction terms, possibly with deterministic terms. Although the situation considered is rather complicated the empirical techniques use simple procedures such as principal components.


Richard A. Davis and William T.M. Dunsmuir, "Maximum Likelihood Estimation for MA(1) Processes With A Root on or Near the Unit Circle," Econometric Theory, Vol. 12, 1996, pp. 1–29.

The paper solves one of the last open questions in the asymptotic theory of likelihood estimation for ARMA models, concerning the properties of estimates of parameter estimates for MA(1) models on and near the unit circle. The results are both of theoretical and of practical interest, as it is found, for example, that estimates are surprisingly accurate even for small sample sizes.

Because of the quality of the theoretical analysis, of the importance of the question considered, and of the practical relevance of the results, it is thought that this paper deserves the Koopmans Prize.


Pentti Saikkonen, "Estimation of Cointegration Vectors with Linear Restrictions," Econometric Theory, Vol. 9, 1993, pp 19–35.

This paper develops a general method of estimating and testing cointegration vectors with linear restrictions. In the case of zero restrictions the cointegration relations are formally similar to the structural equations of a traditional simultaneous equations model, and the paper provides an important link between the literature on statistical inference in simultaneous equations models and the more recent literature on cointegration analysis. The asymptotic distribution of the estimators are shown to be mixed normal, so that Wald tests with asymptotic chi-square distributions under the null hypothesis are obtained in the usual way. Convenient test procedures for checking the validity of overidentifying restrictions are also provided.


Katsuto Tanaka, "An Alternative Approach to the Asymptotic Theory of Spurious Regression, Cointegration, and Near Cointegration," Econometric Theory, Vol. 9, 1993, pp 36–61.

This paper uses the Fredholm approach in order to derive new expressions for the asymptotic sampling distributions of estimators and test statistics in cointegration models. It is shown that, in some cases, these expressions provide a basis for the accurate computation of the limiting distributions. The paper also introduces a definition of near cointegration, for which asymptotic properties are studied. It then devises tests which take cointegration as the null hypothesis and discusses the limiting local power of these tests under the alternative of near cointegration.


Yuzo Hosoya, Yoshihiko Tsukuda and Nobuhiko Terui, "Ancillarity and the Limited Information Maximum-Likelihood Estimation of a Structural Equation in a Simultaneous Equation System," Econometric Theory, Vol. 5, 1989, pp 385–404.

In this paper three concepts in current research are focused on the now classical econometric methodology of limited information maximum likelihood estimation in simultaneous equation models. The model under the assumption of normality constitutes a curved exponential family of distributions. The effect of conditioning on the ancillary statistic of the smallest root of the usual determinantal equation is analyzed by means of second-order asymptotics. This study gives new insight into a familiar subject and suggests promising approaches to other econometric problems.


Christian Gourieroux, Alan Monfort and Alain Trognon, "A General Approach to Serial Correlation," Econometric Theory, Vol. 1, 1985, pp 315–340.

This paper is a fundamental contribution to econometric theory. It provides a general framework for analyzing systematically a variety of autoregressive models with latent variables, including nonlinear simultaneous equation models, qualitative response models, and disequilibrium models. The authors show how diverse testing and estimation problems can be handled by this approach. It can be expected that this paper, which organizes the statistical analysis of data with time dependence, will also stimulate the development of new methodology.