An asymptotic optimality theory for the estimation of cointegration regressions is developed in this paper. The theory applies to a reasonably wide class of estimators without making any specific assumptions about the probability distribution or short-run dynamics of the data-generating process. Due to the nonstandard nature of the estimation problem, the conventional minimum variance criterion does not provide a convenient measure of asymptotic efficiency. An alternative criterion, based on the concentration or peakedness of the limiting distribution of an estimator, is therefore adopted. The limiting distribution of estimators with maximum asymptotic efficiency is characterized in the paper and used to discuss the optimality of some known estimators. A new asymptotically efficient estimator is also introduced. This estimator is obtained from the ordinary least-squares estimator by a time domain correction which is nonparametric in the sense that no assumption of a finite parameter model is required. The estimator can be computed with least squares without any initial estimations.

This paper deals with the problem of estimating the covariance matrix of the least-squares regression coefficients under heteroskedasticity and/or autocorrelation of unknown form. We consider an estimator proposed by White [17] and give a relatively simple proof of its consistency. Our proof is based on more easily verifiable conditions than those of White. An alternative estimator with improved small sample properties is also presented.

We consider least absolute error estimation in a dynamic nonlinear model with neither independent nor identically distributed errors. The estimator is shown to be consistent and asymptotically normal, with asymptotic covariance matrix depending on the errors through the heights of their density functions at their medians (zero). A consistent estimator of the asymptotic covariance matrix of the estimator is given, and the Wald, Lagrange multiplier, and likelihood ratio tests for linear restrictions on the parameters are discussed. A Lagrange multiplier test for heteroscedasticity based upon the absolute residuals is analyzed. This will be useful whenever the heights of the density functions are related to the dispersions.

This paper investigates the local robustness properties of a general class of multidimensional tests based on M-estimators. These tests are shown to inherit the efficiency and robustness properties of the estimators on which they are based. In particular, it is shown that small perturbations of the distribution of the observations can have arbitrarily large effects on the asymptotic level and power of tests based on estimators that do not possess a bounded influence function. An asymptotic ‘admissibility’ result is also presented, which provides a justification for tests based on optimal bounded-influence estimators.

Sir Richard Stone, knighted in 1978 and Nobel Laureate in Economics in 1984, is one of the pioneering architects of national income and social accounts, and is one of the few economists of his generation to have faced the challenge of economics as a science by combining theory and measurement within a cohesive framework. He was awarded the Nobel Prize in Economics for his “fundamental contributions to the development of national accounts,” but he has made equally significant contributions to the empirical analysis of consumer behavior. His work on the “Growth Project” has also been instrumental in the development of appropriate econometric methodology for the construction and the analysis of large disaggregated macroeconometric models.

Throughout his long and productive career, stretching over more than half a century, Stone has been an inspiration to applied econometricians all over the world. His influence goes well beyond his written work. He has made a lasting impact on the large number of (now prominent) economists and statisticians who visited the Department of Applied Economics when he was its Director. He is a scientist, a scholar, and above all, a gentleman. He gives generously of himself and is always willing to help the cause of applied econometrics. He has been a Fellow of King's College, Cambridge since 1945 and has served as the President of the Econometric Society (in 1955) and the President of the Royal Economic Society (during 1978–1980). In the interview that follows, Richard Stone gives us a delightful account of his time as a student at Westminster School, his early introduction to economics at Cambridge University, and he shares with us his memories and thoughts on a long and productive career. The interview was conducted in Stones' magnificent private library in Cambridge, and I hope that readers enjoy reading the interview as much as I enjoyed recording it.

Further details of Richard Stone's biography and research activities can be found in:

Deaton, A. Stone, John Richard Nicholas. In J. Eatwell, M. Milgate and P. Newman (eds.), The New Palgrave: A Dictionary of Economics, Vol. 4, pp. 509–512. London: Macmillan, 1987.

Stone, J.R.N. An autobiographical sketch. In Les Prix Nobel 1984. Stockholm: Almquist and Wicksell International, 1985.