In an hypothesis testing problem involving nuisance parameters for which boundedly complete sufficient statistics exist under the null hypothesis, the class of all similar regions for the problem is characterized by the conditional distribution of the data given these sufficient statistics. If there exists a one-to-one transformation y → (t, u) of the data, y, to the sufficient statistic, t, and a second vector of statistics, u, that is independent of t under the null hypothesis, then the statistic u itself characterizes the class of similar regions. This paper applies this idea to five testing problems of interest in econometrics. In each case we obtain the density of the relevant statistic under the null hypothesis, when it is free of nuisance parameters, and under the alternative. Using the density under the alternative, we discuss the power properties of the class of similar tests for each problem. Other applications are also suggested.

This paper studies the statistical properties of vector autoregressions (VAR's) for quite general multiple time series which are integrated processes of order one. Functional central limit theorems are given for multivariate partial sums of weakly dependent innovations and these are applied to yield first-order asymptotics in nonstationary VAR's. Characteristic and cumulant functionals for generalized random processes are introduced as a means of developing a refinement of central limit theory on function spaces. The theory is used to find asymptotic expansions of the regression coefficients in nonstationary VAR's under very general conditions. The results are specialized to the scalar case and are related to other recent work by the author [21].

This paper addresses two related issues in the literature of non-nested hypotheses testing. Firstly, by means of a measure of “closeness” of probability density functions, it shows how any two hypotheses can be placed into the nested and the non-nested categories with the latter category being subdivided further into “globally” and “partially” non-nested hypotheses. Secondly, by emphasizing the distinction between a “local null” and a “local alternative,” the paper shows that only in the case of partially non-nested hypotheses is it possible to specify local alternatives. In this case the paper derives the asymptotic distribution of the Cox test statistic under local alternatives and shows that it is distributed as a normal variate with a mean which is directly related to the measure of “closeness” of the alternative to the null hypothesis.

This paper establishes consistency of least squares estimators in (i) a multiple regression model with integrated regressors and explosive, non-mixing errors, and (ii) a dynamic linear regression model with regressors and errors that may have infinite variances. In the former context, the asymptotic distribution of the least squares estimator also is obtained, in certain cases.

Jan Tinbergen is one of the founding fathers of econometrics, publishing in the field from 1927 until the early 1950s. This was the frontier age of econometrics when the distinction between mathematical economics and econometrics, let alone between theoretical and applied econometrics, did not yet exist. Tinbergen's approach to economics has always been a practical one. This was highly appropriate for the new field of econometrics, and enabled him to make important contributions to conceptual and theoretical issues, but always in the context of a relevant economic problem. The development of the first macroeconometric models, the solution of the identification problem, and the understanding of dynamic models are perhaps his three most important legacies to econometrics. Tinbergen was awarded the first Nobel Memorial Prize in economics in 1969 (jointly with Ragnar Frisch) for his contributions to econometrics.

Tinbergen's desire to communicate his ideas to others is matched by a talent for clear and direct writing. This gives his econometric work great appeal and an apparent simplicity which should not be underestimated. This talent was also fruitfully applied to the development of pedagogical tools for teaching econometrics to his students.

Since the early 1950s Tinbergen's interests have moved on and he has made notable contributions to such diverse fields as the theory of economic policy, development planning, and income distribution. Tinbergen's political and pacifist views have always been an important element in his economics, and even, as this interview shows, his econometrics. His overriding aim has been to improve the welfare of the less fortunate in this world.

It is now 60 years since Tinbergen's first article in economics appeared, yet he shows no signs of retiring. We met him on May 27, 1986, in the study of his house in The Hague, where he has lived for most of his working life and which bears the hallmarks of continued study and writing. Most of the discussion during the afternoon concerned his econometric work published in the 1930s and 1940s. He gave us his views of those early developments—both what he thought then and how he sees them now. What follows is an edited transcript of the conversation. We hope that this interview will bring alive to the readers of the 1980s the issues and difficulties faced by econometricians in the 1930s, as well as Tinbergen's characteristic response to those problems. One of Tinbergen's attributes is a considerable modesty about his own achievements; the reader should bear this in mind when reading his remarks.

This article deals with the derivation of the exact discrete model that corresponds to a closed linear first-order continuous-time system with mixed stock and flow data. This exact discrete model is (under appropriate additional conditions) a stationary autoregressive moving average time series model and may allow one to obtain asymptotically efficient estimators of the parameters describing the continuous-time system.

Forecasts based on two information sets, one of which includes the other plus additional causal variables are considered. Given a general cost function of forecast errors, it is shown that the expected cost is smaller for the information set that includes the causal variables.