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 nuisanceparameters for which boundedly complete sufficientstatistics exist under the null hypothesis, theclass of all similar regions for the problem ischaracterized by the conditional distribution of thedata given these sufficient statistics. If thereexists a one-to-one transformationy → (t, u) ofthe data, y, to the sufficientstatistic, t, and a second vectorof statistics, u, that isindependent of t under the nullhypothesis, then the statistic uitself characterizes the class of similar regions.This paper applies this idea to five testingproblems of interest in econometrics. In each casewe obtain the density of the relevant statisticunder the null hypothesis, when it is free ofnuisance parameters, and under the alternative.Using the density under the alternative, we discussthe power properties of the class of similar testsfor each problem. Other applications are alsosuggested.

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.

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 studies the statistical properties of vectorautoregressions (VAR's) for quite general multipletime series which are integrated processes of orderone. Functional central limit theorems are given formultivariate partial sums of weakly dependentinnovations and these are applied to yieldfirst-order asymptotics in nonstationary VAR's.Characteristic and cumulant functionals forgeneralized random processes are introduced as ameans of developing a refinement of central limittheory on function spaces. The theory is used tofind asymptotic expansions of the regressioncoefficients in nonstationary VAR's under verygeneral conditions. The results are specialized tothe scalar case and are related to other recent workby the author [21].

This paper addresses two related issues in theliterature of non-nested hypotheses testing.Firstly, by means of a measure of “closeness” ofprobability density functions, it shows howany two hypotheses can be placedinto the nested and the non-nested categories withthe 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 papershows that only in the case of partially non-nestedhypotheses is it possible to specify localalternatives. In this case the paper derives theasymptotic distribution of the Cox test statisticunder local alternatives and shows that it isdistributed as a normal variate with a mean which isdirectly related to the measure of “closeness” ofthe alternative to the null hypothesis.

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).

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 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 squaresestimators in (i) a multiple regression model withintegrated regressors and explosive, non-mixingerrors, and (ii) a dynamic linear regression modelwith regressors and errors that may have infinitevariances. In the former context, the asymptoticdistribution of the least squares estimator also isobtained, 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 ofeconometrics, publishing in the field from 1927until the early 1950s. This was the frontier age ofeconometrics when the distinction betweenmathematical economics and econometrics, let alonebetween theoretical and applied econometrics, didnot yet exist. Tinbergen's approach to economics hasalways been a practical one. This was highlyappropriate for the new field of econometrics, andenabled him to make important contributions toconceptual and theoretical issues, but always in thecontext of a relevant economic problem. Thedevelopment of the first macroeconometric models,the solution of the identification problem, and theunderstanding of dynamic models are perhaps histhree most important legacies to econometrics.Tinbergen was awarded the first Nobel Memorial Prizein economics in 1969 (jointly with Ragnar Frisch)for his contributions to econometrics.

Tinbergen's desire to communicate his ideas to othersis matched by a talent for clear and direct writing.This gives his econometric work great appeal and anapparent simplicity which should not beunderestimated. This talent was also fruitfullyapplied to the development of pedagogical tools forteaching econometrics to his students.

Since the early 1950s Tinbergen's interests have movedon and he has made notable contributions to suchdiverse fields as the theory of economic policy,development planning, and income distribution.Tinbergen's political and pacifist views have alwaysbeen an important element in his economics, andeven, as this interview shows, his econometrics. Hisoverriding aim has been to improve the welfare ofthe less fortunate in this world.

It is now 60 years since Tinbergen's first article ineconomics appeared, yet he shows no signs ofretiring. We met him on May 27, 1986, in the studyof his house in The Hague, where he has lived formost of his working life and which bears thehallmarks of continued study and writing. Most ofthe discussion during the afternoon concerned hiseconometric work published in the 1930s and 1940s.He gave us his views of those earlydevelopments—both what he thought then and how hesees them now. What follows is an edited transcriptof the conversation. We hope that this interviewwill bring alive to the readers of the 1980s theissues and difficulties faced by econometricians inthe 1930s, as well as Tinbergen's characteristicresponse to those problems. One of Tinbergen'sattributes is a considerable modesty about his ownachievements; the reader should bear this in mindwhen 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 exactdiscrete model that corresponds to a closed linearfirst-order continuous-time system with mixed stockand flow data. This exact discrete model is (underappropriate additional conditions) a stationaryautoregressive moving average time series model andmay allow one to obtain asymptotically efficientestimators of the parameters describing thecontinuous-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.