On the evening of March 7, 2008, the New Zealand Econometric Study Group Meeting held its Conference Dinner. The venue was the Owen Glenn Building, the spectacular new home of the Auckland Business School and the Department of Economics at the University of Auckland. The meeting was organized by my colleagues, co-authors, and close companions Donggyu Sul and Chirok Han. Chirok did double duty by videotaping the evening, Donggyu coordinated festivities with consummate skill, and we settled in to a memorable evening.

Econometricians, old friends, former students, two of my former teachers, faculty, and senior administrators were gathered together to celebrate my 60th birthday. Many had traveled long distances from overseas and navigated busy schedules to come to this event. It was a singular honor. My wife and daughter were with me. Opening speeches from Bas Sharp and John McDermott broke the ice with endearing tales from the past and jokes about some mysterious hole in my vita. I stood at the front table, looked out, and felt a glow of fellowship envelop me. I was fortunate indeed. Life had bestowed many gifts. The warmth of family, friends, and collegiality were at the top of the list. My education and early training in New Zealand were a clear second.

What follows is a graduate student story. It draws on the first part of the speech I gave that evening at the NZESG conference dinner. It mixes personal reflections with recollections of the extraordinary New Zealanders who shaped my thinking as a graduate student and beginning researcher—people who have had an enduring impact on my work and career as an econometrician. The story traces out these human initial conditions and unit roots that figure in my early life of teaching and research.

Econometric analysis of continuous time models has drawn the attention of Peter Phillips for 40 years, resulting in many important publications by him. In these publications he has dealt with a wide range of continuous time models and the associated econometric problems. He has investigated problems from univariate equations to systems of equations, from asymptotic theory to finite sample issues, from parametric models to nonparametric models, from identification problems to estimation and inference problems, and from stationary models to nonstationary and nearly nonstationary models. This paper provides an overview of Peter Phillips’ contributions in the continuous time econometrics literature. We review the problems that have been tackled by him, outline the main techniques suggested by him, and discuss the main results obtained by him. Based on his early work, we compare the performance of three asymptotic distributions in a simple setup. Results indicate that the in-fill asymptotics significantly outperforms the long-span asymptotics and the double asymptotics.

Peter C. B. Phillips has made fundamental contributions to unit root econometrics. This paper provides a selective review of Peter’s contribution to unit roots, with a focus on unit root asymptotics, unit root tests, and testing for stationarity against the unit root alternative. The discussion puts a relatively heavier weight on Peter’s most recent work.

The work of Professor P.C.B. Phillips, even if it is focused on the area of linear nonstationary models, is enormous. So it is hard for me to explore the whole of his work in this paper. Therefore, I have decided to take up only a few results of his work. The topics chosen here are applications of the martingale approximation and the problem of choosing between stochastic and deterministic trends, which I discuss and, hopefully, extend.

This paper considers estimating a panel data simultaneous equations model under both coefficient and covariance matrix restrictions in a scenario where one or the other set of identifying restrictions may be invalid or may hold only weakly. We study the limiting properties of various estimators in an asymptotic framework, which takes both the cross-sectional dimension N and the time dimension T to infinity. In this setting as in the pure cross-sectional setup, the performance of the 2SLS estimator depends on the strength of the identifying conditions imposed on the coefficients of the model, and it fails to be consistent once these conditions break down sufficiently resulting in instruments that are too weakly correlated with the endogenous regressors. On the other hand, the between-group (BG) estimator is consistent and asymptotically normal even when coefficient restrictions fail, but it has the shortcoming that its precision depends only on variations in the cross-sectional dimension; and, hence, it is less efficient and has slower rate of convergence than alternatives, which make better use of the large time dimension. A GMM estimator, which combines the moment conditions of the BG estimator with that of the within-group IV estimator, is more robust to instrument weakness than 2SLS and is more efficient than the BG estimator, but it has a second-order bias even under strong instruments if the assumed covariance restrictions do not hold. To remedy the deficiency of the aforementioned estimators, we propose in this paper two new model averaging estimators, which are weighted averages of the GMM estimator and a bias-corrected GMM estimator. The two proposed estimators have weighting functions that depend on alternative transformations of the Bayesian Information Criterion (BIC), which is employed here to assess the validity of the covariance restrictions. We show that these new estimators have some nice robustness properties against possible failure of either the coefficient restrictions or the covariance restrictions.

This paper discusses Peter Phillips’s contributions to panel data methods. These include contributions in the areas of seemingly unrelated regressions, nonstationary panel data, dynamic panels, and the development of multiple index asymptotic theory. We also discuss his empirical contributions in the area of economic growth and convergence that use macro panel data.

In this paper, we provide a survey of Peter Phillips’s works on the econometrics for models with nonstationary nonlinearity, and some of the extensions that were made possible due to his original contributions. Parametric and nonparametric models are considered in both discrete time and continuous time setups. Although some of the asymptotics in the paper are applicable more generally for a wide variety of nonstationary models, we mainly analyze models with nonstationary processes that allow for the functional limit theory with limit processes having well defined local times.