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 article investigates the instrumental variable quantile regression model (Chernozhukov and Hansen, 2005, Econometrica 73, 245–261; 2013, Annual Review of Economics, 5, 57–81) with a binary endogenous treatment. It offers two identification results when the treatment status is not directly observed. The first result is that, remarkably, the reduced-form quantile regression of the outcome variable on the instrumental variable provides a lower bound on the structural quantile treatment effect under the stochastic monotonicity condition. This result is relevant, not only when the treatment variable is subject to misclassification, but also when any measurement of the treatment variable is not available. The second result is for the structural quantile function when the treatment status is measured with error; the sharp identified set is characterized by a set of moment conditions under widely used assumptions on the measurement error. Furthermore, an inference method is provided in the presence of other covariates.

An unobserved components and a conventional first-order autoregressive (AR) model with constant are analyzed with the adjusted profile likelihood of Cox and Reid (1987, Journal of the Royal Statistical Society, Series B 49, 1–39; 1993, Journal of the Royal Statistical Society, Series B 55, 467–71). Both the unobserved components model and the Cox–Reid adjustment can provide more accurate estimates of an AR coefficient of unity. The unobserved components model yields more powerful unit-root tests. In general the most powerful test utilizes the adjustment. Under the unobserved components model the adjusted statistics follow the asymptotic distributions better than the unadjusted.The basis of this research is my D. Phil. thesis (1997) for the University of Oxford. I am grateful to David Hendry for supervision and to Pentti Saikkonen for most helpful advice. I appreciate also the CBRT Young Economist Award with which I was honored after presenting a previous version at the 1998 erc/METU International Conference on Economics. I remain responsible for any errors. Financial support by the Yrjö Jahnsson Foundation and Academy of Finland is gratefully acknowledged.

See solution below.

Least absolute deviations (LAD) estimation of linear time series models is considered under conditional heteroskedasticity and serial correlation. The limit theory of the LAD estimator is obtained without assuming the finite density condition for the errors that is required in standard LAD asymptotics. The results are particularly useful in application of LAD estimation to financial time series data.

Spatial units typically vary over many of their characteristics, introducing potential unobserved heterogeneity which invalidates commonly used homoskedasticity conditions. In the presence of unobserved heteroskedasticity, methods based on the quasi-likelihood function generally produce inconsistent estimates of both the spatial parameter and the coefficients of the exogenous regressors. A robust generalized method of moments estimator as well as a modified likelihood method have been proposed in the literature to address this issue. The present paper constructs an alternative indirect inference (II) approach which relies on a simple ordinary least squares procedure as its starting point. Heteroskedasticity is accommodated by utilizing a new version of continuous updating that is applied within the II procedure to take account of the parameterization of the variance–covariance matrix of the disturbances. Finite-sample performance of the new estimator is assessed in a Monte Carlo study. The approach is implemented in an empirical application to house price data in the Boston area, where it is found that spatial effects in house price determination are much more significant under robustification to heterogeneity in the equation errors.

Functional coefficient (FC) regressions allow for systematic flexibility in the responsiveness of a dependent variable to movements in the regressors, making them attractive in applications where marginal effects may depend on covariates. Such models are commonly estimated by local kernel regression methods. This paper explores situations where responsiveness to covariates is locally flat or fixed. The paper develops new asymptotics that take account of shape characteristics of the function in the locality of the point of estimation. Both stationary and integrated regressor cases are examined. The limit theory of FC kernel regression is shown to depend intimately on functional shape in ways that affect rates of convergence, optimal bandwidth selection, estimation, and inference. In FC cointegrating regression, flat behavior materially changes the limit distribution by introducing the shape characteristics of the function into the limiting distribution through variance as well as centering. In the boundary case where the number of zero derivatives tends to infinity, near parametric rates of convergence apply in stationary and nonstationary cases. Implications for inference are discussed and a feasible pre-test inference procedure is proposed that takes unknown potential flatness into consideration and provides a practical approach to inference.

This study examines identification and estimation in a correlated random coefficients (CRC) model with an unknown transformation of the dependent variable, namely $\lambda \left (Y^{*}\right)=B_{0}+X^{\prime }B$, where the latent outcome $Y^{*}$ may be subject to a certain kind of censoring mechanism, $\lambda (\cdot)$ is an unknown, one-to-one monotone function, and the random coefficients $\left (B_{0},B\right)$ are allowed to be correlated with one or several components of X. Under a conditional median independence plus a conditional median zero restriction, the mean of B is shown to be identified up to scale. Moreover, we show the derivative of the median structural function (MSF) is point identified. This derivative of MSF resembles the marginal treatment effect introduced by Heckman and Vytlacil (2005, Econometrica 73, 669–738).

It generalizes the usual average treatment effect in a linear CRC model and coincides with $E(B)$ when $\lambda $ is equal to the identity function; it is invariant to both location and scale normalization on the coefficients. We develop estimators for the identified parameters and derive asymptotic properties for the derivative of MSF. An empirical example using the U.K. Family Expenditure Survey is provided.

The left-tailed unit-root tests of the panel analysis of nonstationarity in idiosyncratic and common components (PANIC) proposed by Bai and Ng (2004, Econometrica 72, 1127–1177) have standard local asymptotic power. We assess the size and power properties of the right-tailed version of the PANIC tests when the common and/or the idiosyncratic components are moderately explosive. We find that, when an idiosyncratic component is moderately explosive, the tests for the common components may have considerable size distortions, and those for an idiosyncratic component may suffer from the nonmonotonic power problem. We provide an analytic explanation under the moderately local to unity framework developed by Phillips and Magdalinos (2007, Journal of Econometrics 136, 115–130). We then propose a new cross-sectional (CS) approach to disentangle the common and idiosyncratic components in a relatively short explosive window. Our Monte Carlo simulations show that the CS approach is robust to the nonmonotonic power problem.

This paper derives the joint moment generating function of quadratic forms occurring in seasonal autoregressive models under stationary, unit root, and explosive specifications. The results are then used to investigate the impact of the seasonal periodicity parameter on various distributional results for both the normalized ordinary least squares coefficient and t-ratio and its effects on the asymptotic bias of parameter estimates.

We study identification in nonparametric regression models with a misclassified and endogenous binary regressor when an instrument is correlated with misclassification error. We show that the regression function is nonparametrically identified if one binary instrument variable and one binary covariate satisfy the following conditions. The instrumental variable corrects endogeneity; the instrumental variable must be correlated with the unobserved true underlying binary variable, must be uncorrelated with the error term in the outcome equation, but is allowed to be correlated with the misclassification error. The covariate corrects misclassification; this variable can be one of the regressors in the outcome equation, must be correlated with the unobserved true underlying binary variable, and must be uncorrelated with the misclassification error. We also propose a mixture-based framework for modeling unobserved heterogeneous treatment effects with a misclassified and endogenous binary regressor and show that treatment effects can be identified if the true treatment effect is related to an observed regressor and another observable variable.

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.

In the AR(2) model, with a double root at unity, we consider the asymptotic distribution of the likelihood ratio with respect to a nearly nonstationary alternative. It is shown how the distribution can be represented as a Radon-Nikodym derivative of an Ito process with respect to Brownian motion. Using this result, we point out how standard contiguity arguments can be applied to obtain a representation of the asymptotic power function in nearly nonstationary alternatives.

We consider nonparametric identification and estimation of pricing kernels, or equivalently of marginal utility functions up to scale, in consumption-based asset pricing Euler equations. Ours is the first paper to prove nonparametric identification of Euler equations under low level conditions (without imposing functional restrictions or just assuming completeness). We also propose a novel nonparametric estimator based on our identification analysis, which combines standard kernel estimation with the computation of a matrix eigenvector problem. Our estimator avoids the ill-posed inverse issues associated with nonparametric instrumental variables estimators. We derive limiting distributions for our estimator and for relevant associated functionals. A Monte Carlo experiment shows a satisfactory finite sample performance for our estimators.