The Tjalling C. Koopmans Econometric Theory Prize is named in honor of Tjalling C. Koopmans, the 1975 Nobel Laureate in economic science, whose contributions to the development of econometrics are of fundamental and lasting importance to the subject. The prize is awarded once every three years for the best article reporting original research published in the Journal Econometric Theory over that period. The selection of the winning article is made by the Advisory Board of the Journal and the criteria for selection is based on Tjalling Koopmans’ own research which is universally admired for its rigor, clarity and originality. All articles published in Econometric Theory are candidates for the prize except those that are authored or co-authored by the Editor and members of the Advisory Board.

The prize is accompanied by a financial award of $1,000, that was originally supported by the publishers, Cambridge University Press, and the estate of Tjalling C. Koopmans. The prizes are now supported by the Cowles Foundation for Research in Economics, Yale University.

Cambridge Press and the Advisory Editors of Econometric Theory join me in congratulating the authors on their success in receiving these awards.

2021-2023

Pötscher, B.M. and D. Preinerstorfer (2023) “How Reliable are Bootstrap-Based Heteroskedasticity Robust Tests?”, Econometric Theory, Volume 39, Issue 04, pp. 789-847.

Bootstrap-based heteroskedasticity robust tests have been suggested for linear regression models in the literature to ameliorate overrejection problems often arising with heteroskedasticity robust tests, based on standard critical values derived from asymptotic theory. While there is Monte Carlo evidence suggesting that the bootstrap can attenuate this overrejection problem, the question arises whether this observation generalizes beyond the specific Monte Carlo settings considered. In their paper, the authors establish sufficient conditions under which bootstrap-based tests can be shown to “break down” in the sense that the size equals one. This theoretical insight can be used to check whether a given bootstrap-based test procedure should not be used in a given problem. Furthermore, the results allow the authors to conduct a numerical “stress test” on a wide variety of existing bootstrap-based test procedures, leading to the conclusion that none of these tests is immune to considerable overrejection. Thus any such bootstrap-based test is no reliable panacea for heteroskedasticity robust testing. In the paper theoretical finite-sample results concerning the size of wild bootstrap-based heteroskedasticity robust tests in linear regression models have been derived. In particular, these results provide an efficient diagnostic check, which can be used to weed out tests that are unreliable for a given testing problem in the sense that they overreject substantially. This allows the authors to assess the reliability of a large variety of wild bootstrap-based tests in an extensive numerical study.

Debaly, Z.M. and L. Truquet (2021) “Iterations of Dependent Random Maps and Exogeneity in Nonlinear Dynamics”, Econometric Theory, Volume 37, Issue 06, pp. 1135-1172.

The authors discuss the existence and uniqueness of stationary and ergodic nonlinear autoregressive processes, when exogenous regressors are incorporated into the dynamic. To this end, they consider the convergence of the backward iterations of dependent random maps. In particular, the authors derive a new result when the classical condition of contraction on average is replaced by a contraction in conditional expectation. Under some conditions, they also discuss the dependence properties of these processes using the functional dependence measure of Wu (2005, Proceedings of the National Academy of Sciences 102, 14150–14154) that delivers a central limit theorem giving a wide range of applications. The results obtained are illustrated by conditional heteroscedastic autoregressive nonlinear models, Generalized Autoregressive Conditional Heteroskedasticity (GARCH) processes, count time series, binary choice models and categorical time series, for which they provide many extensions of existing results.

2018-2020

Beare, B.K. and W.-K. Seo (2020): “Representation of I(1) and I(2) Autoregressive Hilbertian Processes", Econometric Theory, Volume 36, Issue 05, October 2020, 773-802.

Franchi, M. and P. Paruolo (2020): “Cointegration in Functional Autoregressive Processes”, Econometric Theory, Volume 36, Issue 05, October 2020, 803-839.

These articles provide a representation theory for autoregressive models of functional time series, with an emphasis on integration and cointegration. To model functional time series, random variables take values in a complex separable Hilbert space H (thus admitting certain classes of functions, rather than conventional n-dimensional vectors) with linear operators from H to H as autoregressive coefficients. Correspondingly, the autoregressive polynomial A(z) is an operator-valued function of the complex variable z. Analogous to the “classical” case in integration, A(z) is assumed invertible in the closed unit disc except at z=1. The integration and cointegration properties of the corresponding process are based on an analysis of A(z) at z=1. The results obtained show that, under the assumption that 1 is an eigenvalue of finite type of A(z), the integration and cointegration properties of (generally infinite-dimensional) H-valued processes are the same as for the classical finite-dimensional VAR case - except for the number of cointegrating relations being infinite. 

2015-2017

Javier Hidalgo and Myung Hwan Seo “Specification Tests for Lattice Processes,” Econometric Theory, April 2015, volume 31(2), pages 294-336.

The article explores the properties of weakly stationary (scalar) random sequences x(t) in which the parameter (t) may be d dimensional on a lattice. Important examples are, for d=1, non-causal linear dynamical systems and, for d>1, spatial and spatio-temporal systems, which play a major role in many scientific areas. Many relevant examples of such processes arise in environmental and development economics. Within this wide context, x(t) is assumed to be a generalized “spatial” linear process, with unobserved “spatial” i.i.d. inputs. This formulation leads to a transfer function in d variables and a spectral density in d variables. The article contributes by developing statistical tests for correct specification of the dynamics of x(t), or more precisely, tests of the hypothesis that the covariogram of x(t) follows a specific parametric model. The (tapered) periodogram may be used for a Whittle-type estimator leading to a corresponding test. Such a test-statistic, however, is not pivotal. To address this difficulty, the authors introduce a transformation that leads to an asymptotic distribution, which is free of nuisance parameters. As a second result, the authors propose a bootstrap analogue of the transformation and confirm its validity. Thirdly the authors analyze linear parametric regression models, where x(t) is the (unobserved) additive noise component. These contributions provide a foundation for further study of such multidimensional spatio-temporal processes and a mechanism for their use in econometric work in many different applied fields.   

 2012-2014

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).

 2009-2011

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.

2006-2008

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.

2002–2005

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.

2000–2002

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.

1997–1999

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

Stephane 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.

1994–1996

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.

1991–1993

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.

and

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.

1988–1990

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.

1985–1987

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.