Asymptotic normality is established for a class of statistics which includes as special cases weighted sum of independent and identically distributed (i.i.d.) random variables, unsigned linear rank statistics, signed rank statistics, linear combination of functions of order statistics, and linear function of concomitants of order statistics. The results obtained unify as well as extend a number of known results.

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 presents conditions under which a quadratic form based on a g-inverted weighting matrix converges to a chi-square distribution as the sample size goes to infinity. Subject to fairly weak underlying conditions, a necessary and sufficient condition is given for this result. The result is of interest because it is needed to establish asymptotic significance levels and local power properties of generalized Wald tests (i.e., Wald tests with singular limiting covariance matrices). Included in this class of tests are Hausman specification tests and various goodness-of-fit tests, among others. The necessary and sufficient condition is relevant to procedures currently in the econometrics literature because it illustrates that some results stated in the literature only hold under more restrictive assumptions than those given.

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].

We provide rankings of academic institutions according to the publication record of their faculty members in the specialization of econometrics. The rankings are based on standardized page counts of articles published by faculty members in 14 journals over the period 1980 to 1985. Separate rankings of the 200 leading institutions are provided for their theoretical contributions, as well as their contributions in theory and applied work. The rankings are compared with a ranking in the general field of economics.

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.

The invariant polynomials (Davis [8] and Chikuse [2] with r(r ≥ 2) symmetric matrix arguments have been defined, extending the zonal polynomials, and applied in multivariate distribution theory. The usefulness of the polynomials has attracted the attention of econometricians, and some recent papers have applied the methods to distribution theory in econometrics (e.g., Hillier [14] and Phillips [22]).

The ‘top order’ invariant polynomials , in which each of the partitions of ki 1 = 1,…,r, and has only one part, occur frequently in multivariate distribution theory (e.g., Hillier and Satchell [17] and Phillips [27]). In this paper we give three methods of constructing these polynomials, extending those of Ruben [28] for the top order zonal polynomials. The first two methods yield explicit formulae for the polynomials and then we give a recurrence procedure. It is shown that some of the expansions presented in Chikuse and Davis [4] are simplified for the top order invariant polynomials. A brief discussion is given on the ‘lowest order’ invariant polynomials.

We compare the distributional properties of the four predictors commonly used in practice. They are based on the maximum likelihood, two types of the least squared, and the Yule-Walker estimators. The asymptotic expansions of the distribution, bias, and mean-squared error for the four predictors are derived up to O(T−1), where T is the sample size. Examining the formulas of the asymptotic expansions, we find that except for the Yule-Walker type predictor, the other three predictors have the same distributional properties up to O(T−1).

We give an expression to order O(T-1), where T is the sample size, for bias to the estimated coefficient on a lagged dependent variable when all other regressors are exogenous. The general expression is a nonlinear function of the coefficient on the lagged dependent variable, the autoregressive structure of the exogenous variables, and the coefficients on the exogenous variables. The maximum bias that can arise is a linear function of the number of exogenous regressors in the estimating equation.

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.

Many observed macrovariables are simple aggregates over a large number of microunits. It is pointed out that the generating process of the macrovariables is largely determined by the common factors in the generating mechanisms of the microvariables, even though these factors may be very unimportant at the microlevel. It follows that macrorelationships are simpler than the complete microrelationships, but that empirical investigations of microrelationships may not catch those components, containing common factors, which will determine the macrorelationship. It is also shown that an aggregate expectation or forecast is simply the common factor component of the individual agents expectations.

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.

The distributions of the test statistics are investigated in the context of an AR(1) model where the root is unity or near unity and where the exogenous process is a stable process, a random walk or a time trend. The finite sample distributions are estimated by Monte Carlo methods assuming normal disturbances. The sensitivity of the distributions to both the values of the parameters of the AR(1) model and the process generating the exogenous time series is examined. The Monte Carlo results motivate several theorems which describe the exact sampling behavior of the test statistics. The analytical and empirical results present a mixed picture with respect to the accuracy of the relevant asymptotic approximations.

In this paper we develop full information methods for estimating the parameters of a system of simultaneous equations with error component structure and establish relationships between the various structural estimators.

A Taylor series approach is used to derive approximations to the approximate slope of LR, W, and LM test statistics. These can be useful when the approximate slopes themselves are complicated. The results are applied to the test of linear coefficient restrictions in the linear model with a nonscalar covariance matrix. They can be used to find cases where the Wald test may badly over-reject in this model. The results shed some new light on the over-rejection that has been noted in the special cases of AR(1) disturbances and the SURE model.

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.

Econometrics owes its essence and much of its ongoing vitality to the infusion of ideas from economic theory, the development of appropriate statistical methods, and the quantitative recording of economic phenomena. Each of these elements is an important source of energy for further scientific change. As professionals, we contribute to this evolution through research and teaching, most commonly in individual specialisms and all too frequently with little concern for holistic issues. Few economists indeed have the knowledge, the scientific expertise, and the professional experience to speak out with authority on the subject in its entirety and its scientific achievements. Even fewer command the respect of colleagues and authorities in neighboring disciplines, like mathematical statistics. For some time now, Edmond Malinvaud has stood out from the rest of our profession as a scholar who is uniquely qualified in this regard. His writings influence every field of economics. His advanced textbooks are cornerstones of graduate teaching programs. The scientific standards of his work set an example to the entire profession. And his recent evaluations of scientific accomplishments in quantitative economics have brought unity and direction to what was earlier just uncoordinated, individual research.