# Peter C. B. PhillipsYale University | YU · Department of Economics

Peter C. B. Phillips

Ph.D London, 1974

## About

665

Publications

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Introduction

Peter C. B. Phillips is Sterling Professor Emeritus of Economics at Yale University, Distinguished Professor at the University of Auckland, and Distinguished Term Professor at Singapore Management University. Peter's research is in all areas of econometrics and many of its applications, including climate econometrics. His latest projects concerns the empirical assessment of global climate models and the use of machine learning methods in trend determination.

## Publications

Publications (665)

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 c...

Housing fever is a popular term to describe an overheated housing market or housing price bubble. Like other financial asset bubbles, housing fever can inflict harm on the real economy, as indeed the U.S. housing bubble did in the period following 2006 leading up to the general financial crisis and great recession. One contribution that econometric...

This paper develops an asymptotic theory for nonlinear cointegrating power function regression. The framework extends earlier work on the deterministic trend case and allows for both endogeneity and heteroskedasticity, which makes the models and inferential methods relevant to many empirical economic and financial applications, including predictive...

We study optimal bandwidth selection in nonparametric cointegrating regression where the regressor is a stochastic trend process driven by short or long memory innovations. Unlike stationary regression, the optimal bandwidth is found to be a random sequence which depends on the sojourn time of the process. All random sequences $h_{n}$ that lie with...

We propose a procedure of iterating the HP filter to produce a smarter smoothing device, called the boosted HP (bHP) filter, based on L2‐boosting in machine learning. Limit theory shows that the bHP filter asymptotically recovers trend mechanisms that involve integrated processes, deterministic drifts, and structural breaks, covering the most commo...

Commonly used tests to assess evidence for the absence of autocorrelation in a univariate time series or serial cross-correlation between time series rely on procedures whose validity holds for i.i.d. data. When the series are not i.i.d., the size of correlogram and cumulative Ljung-Box tests can be signiﬁcantly distorted. This paper adapts standar...

Commonly used tests to assess evidence for the absence of autocorrelation in a univariate time series or serial cross-correlation between time series rely on procedures whose validity holds for i.i.d. data. When the series are not i.i.d., the size of correlogram and cumulative Ljung–Box tests can be significantly distorted. This paper adapts standa...

This paper proposes a novel Lasso-based approach to handle unobserved parameter heterogeneity and cross-section dependence in nonstationary panel models. In particular, a penalized principal component (PPC) method is developed to estimate group-specific long-run relationships and unobserved common factors and jointly to identify the unknown group m...

Indices of financial returns typically display sample kurtosis that declines towards the Gaussian value 3 as the sampling interval increases. This paper uses stochastic unit root (STUR) and continuous time analysis to explain the phenomenon. Limit theory for the sample kurtosis reveals that STUR specifications provide two sources of excess kurtosis...

We discuss some conceptual and practical issues that arise from the presence of global energy balance effects on station level adjustment mechanisms in dynamic panel regressions with climate data. The paper provides asymptotic analyses, observational data computations, and Monte Carlo simulations to assess the use of various estimation methodologie...

In an early article on near-unit root autoregression, Ahtola and Tiao (1984) studied the behavior of the score function in a stationary first order autoregression driven by independent Gaussian innovations as the autoregressive coefficient approached unity from below. The present paper develops asymptotic theory for near-integrated random processes...

This article studies the asymptotic properties of empirical nonparametric regressions that partially misspecify the relationships between nonstationary variables. In particular, we analyze nonparametric kernel regressions in which a potential nonlinear cointegrating regression is misspecified through the use of a proxy regressor in place of the tru...

Limit theory for regressions involving local to unit roots (LURs) is now used extensively in time series econometric work, establishing power properties for unit root and cointegration tests, assisting the construction of uniform confidence intervals for autoregressive coefficients, and enabling the development of methods robust to departures from...

Housing fever is a popular term to describe an overheated housing market or housing price bubble. Like other financial asset bubbles, housing fever can inflict harm on the real economy, as indeed the US housing bubble did in the period following 2006 leading up to the general financial crisis and great recession. One contribution that econometricia...

This paper re-examines changes in the causal link between money and income in the United States over the past half century (1959–2014). Three methods for the data-driven discovery of change points in causal relationships are proposed, all of which can be implemented without prior detrending of the data. These methods are a forward recursive algorit...

This paper considers estimation and inference concerning the autoregressive coefficient ( ρ ) in a panel autoregression for which the degree of persistence in the time dimension is unknown. Our main objective is to construct confidence intervals for ρ that are asymptotically valid, having asymptotic coverage probability at least that of the nominal...

The Hodrick-Prescott (HP) filter is one of the most widely used econometric methods in applied macroeconomic research. The technique is nonparametric and seeks to decompose a time series into a trend and a cyclical component unaided by economic theory or prior trend specification. Like all nonparametric methods, the HP filter depends critically on...

This paper studies nonlinear cointegrating models with time-varying coefficients and multiple nonstationary regressors using classic kernel smoothing methods to estimate the coefficient functions. Extending earlier work on nonstationary kernel regression to take account of practical features of the data, we allow the regressors to be cointegrated a...

Two approaches have dominated formulations designed to capture small departures from unit root autoregressions. The first involves deterministic departures that include local-to-unity (LUR) and mildly (or moderately) integrated (MI) specifications where departures shrink to zero as the sample size n→∞. The second approach allows for stochastic depa...

This paper proposes a new model for capturing discontinuities in the underlying financial environment that can lead to abrupt falls, but not necessarily sustained monotonic falls, in asset prices. This notion of price dynamics is consistent with existing understanding of market crashes, which allows for a mix of market responses that are not univer...

Measurement of diminishing or divergent cross section dispersion in a panel plays an important role in the assessment of convergence or divergence over time in key economic indicators. Econometric methods, known as weak O-convergence tests, have recently been developed (Kong et al., 2019)) to evaluate such trends in dispersion in panel data using s...

This paper studies a continuous time dynamic system with a random persistence parameter. The exact discrete time representation is obtained and related to several discrete time random coefficient models currently in the literature. The model distinguishes various forms of unstable and explosive behavior according to specific regions of the paramete...

The concept of relative convergence, which requires the ratio of two time series to converge to unity in the long run, explains convergent behavior when series share commonly divergent stochastic or deterministic trend components. Relative convergence of this type does not necessarily hold when series share common time decay patterns measured by ev...

GMM methods for estimating dynamic panel regression models are heavily used in applied work in many areas of economics and more widely in the social and business sciences. Software packages in STATA and GAUSS are commonly used in these applications. We provide a new R program for difference GMM, system GMM, and within-group estimation for simulatio...

While each financial crisis has its own characteristics there is now widespread recognition that crises arising from sources such as financial speculation and excessive credit creation do inflict harm on the real economy. Detecting speculative market conditions and ballooning credit risk in real time is therefore of prime importance in the complex...

p>Behavior at the individual level in panels is often influenced by aspects of the system in aggregate. In particular, the interaction between individual-specific explanatory variables and an individual dependent variable may be affected by ‘global’ variables that are relevant in decision making and shared communally by all individuals in the sampl...

Price bubbles in multiple assets are sometimes nearly coincident in occurrence. Such near-coincidence is strongly suggestive of co-movement in the associated asset prices and likely driven by certain factors that are latent in the financial or economic system with common effects across several markets. Can we detect the presence of such common fact...

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, standard methods based on the (quasi-)likelihood function generally produce inconsistent estimates of both the spatial paramete...

This paper studies the relationship between the minimum wage and the employment rate in the US using the framework of a panel structure model. The approach allows the minimum wage, along with some other controls, to have heterogeneous e§ects on employment across states which are classiÖed into a group structure. The e§ects on employment are the sam...

Causal relationships in econometrics are typically based on the concept of predictability and are established by testing Granger causality. Such relationships are susceptible to change, especially during times of financial turbulence, making the real‐time detection of instability an important practical issue. This article develops a test for detect...

The asymptotic distribution of the least squares estimator in threshold regression is expressed in terms of a compound Poisson process when the threshold effect is fixed and as a functional of two-sided Brownian motion when the threshold effect shrinks to zero. This paper explains the relationship between this dual limit theory by showing how the a...

TJALLING C. KOOPMANS ECONOMETRIC THEORY PRIZE 2015–2017 - Volume 34 Issue 4 - Peter C.B. Phillips

This paper studies the estimation of a panel data model with latent structures where individuals can be classified into different groups with the slope parameters being homogeneous within the same group but heterogeneous across groups. To identify the unknown group structure of vector parameters, we design an algorithm called Panel‐CARDS. We show t...

Ergodic theorem shows that ergodic averages of the posterior draws converge in probability to the posterior mean under the stationarity assumption. The literature also shows that the posterior distribution is asymptotically normal when the sample size of the original data considered goes to infinity. To the best of our knowledge, there is little di...

This article studies functional local unit root models (FLURs) in which the autoregressive coefficient may vary with time in the vicinity of unity. We extend conventional local to unity (LUR) models by allowing the localizing coefficient to be a function which characterizes departures from unity that may occur within the sample in both stationary a...

In an early article on near-unit root autoregression, Ahtola and Tiao (1984) studied the behavior of the score function in a stationary first order autoregression driven by indepen- dent Gaussian innovations as the autoregressive coefficient approached unity from below. The present paper develops asymptotic theory for near-integrated random process...

This paper re-examines changes in the causal link between money and income in the United States over the past half century (1959 - 2014). Three methods for the data-driven discovery of change points in causal relationships are proposed, all of which can be implemented without prior detrending of the data. These methods are a forward recursive algor...

Indices of nancial returns typically display sample kurtosis that declines towards the Gaussian value 3 as the sampling interval increases. This paper uses stochastic unit root (STUR) and continuous time analysis to explain the phenomenon. Limit theory for the sample kurtosis reveals that STUR specications provide two sources of excess kurtosis, bo...

During his period at LSE from the early 1960s to the mid-1980s, John Denis Sargan rose to international prominence and LSE emerged as the world’s leading centre for econometrics. Within this context, we examine the life of Denis Sargan, describe his major research accomplishments, recount the work of his many doctoral students and track this remark...

This paper studies estimation in threshold regression with endogeneity in the regressors and thresholding variable. Three key results differ from those in regular models. First, both the threshold point and the threshold effect parameters are shown to be identified without the need for instrumentation. Second, in partially linear threshold models,...

Phoebus J. Dhrymes (1932–2016) - Volume 33 Issue 5 - Aris Spanos, Peter C.B. Phillips

We provide a new test for equality of two symmetric positive-definite matrices that leads to a convenient mechanism for testing specification using the information matrix equality or the sandwich asymptotic covariance matrix of the GMM estimator. The test relies on a new characterization of equality between two k dimensional symmetric positive-defi...

This paper proposes a new model for capturing discontinuities in the underlying financial environment that can lead to abrupt falls, but not necessarily sustained monotonic falls, in asset prices. This notion of price dynamics is consistent with existing understanding of market crashes, which allows for a mix of market responses that are not univer...

This paper studies nonlinear cointegrating models with time-varying coecients and multiple nonsta-tionary regressors using classic kernel smoothing methods to estimate the coecient functions. Extending earlier work on nonstationary kernel regression to take account of practical features of the data, we allow the regressors to be cointegrated and to...

This paper studies nonlinear cointegrating models with time-varying coefficients and multiple nonsta-tionary regressors using classic kernel smoothing methods to estimate the coefficient functions. Extending earlier work on nonstationary kernel regression to take account of practical features of the data, we allow the regressors to be cointegrated...

Lieberman and Phillips (2017; LP) introduced a multivariate stochastic unit root (STUR) model, which allows for random, time varying local departures from a unit root (UR) model, where nonlinear least squares (NLLS) may be used for estimation and inference on the STUR coefficient. In a structural version of this model where the driver variables of...

We provide a methodology for testing a polynomial model hypothesis by generalizing the approach and results of Baek, Cho, and Phillips (Journal of Econometrics, 2015, 187, 376–384; BCP), which test for neglected nonlinearity using power transforms of regressors against arbitrary nonlinearity. We use the BCP quasi-likelihood ratio test and deal with...

New limit theory is developed for co-moving systems with explosive processes, connecting continuous and discrete time formulations. The theory uses double asymptotics with infill (as the sampling interval tends to zero) and large time span asymptotics. The limit theory explicitly involves initial conditions, allows for drift in the system, is provi...

Expansion and collapse are two key features of a financial asset bubble. Bubble expansion may be modeled using a mildly explosive process. Bubble implosion may take several different forms depending on the nature of the collapse and therefore requires some flexibility in modeling. This paper first strengthens the theoretical foundation of the real...

This paper develops exact finite sample and asymptotic distributions for structural equation tests based on partially restricted reduced form estimates. Particular attention is given to models with large numbers of instruments, wherein the use of partially restricted reduced form estimates is shown to be especially advantageous in statistical testi...

This paper develops exact finite sample and asymptotic distributions for a class of reduced form estimators and predictors, allowing for the presence of unidentified or weakly identified structural equations. Weak instrument asymptotic theory is developed directly from finite sample results, unifying earlier findings and showing the usefulness of s...

This paper studies nonlinear cointegration models in which the structural coefficients may evolve smoothly over time. These time-varying coefficient functions are well-suited to many practical applications and can be estimated conveniently by nonparametric kernel methods. It is shown that the usual asymptotic methods of kernel estimation completely...

The concept of relative convergence, which requires the ratio of two time series to converge to unity in the long run, explains convergent behavior when series share commonly divergent stochastic or deterministic trend components. Relative convergence of this type does not necessarily hold when series share common time decay patterns measured by ev...

This paper considers estimation and inference concerning the autoregressive coefficient (?) in a panel autoregression for which the degree of persistence in the time dimension is unknown. The main objective is to construct confidence intervals for ? that are asymptotically valid, having asymptotic coverage probability at least that of the nominal l...

“Malinvaud is one of the enduring figures of 20th century economics. In the world of econometrics he reinstated the rigor of the Cowles Commission researchers of the 1940s and delivered a unified thematic for the field that echoed the genius of Ragnar Frisch. His advanced textbook ‘Méthodes Statistiques de l'Économétrie’ stood without peer as a com...

This paper studies nonlinear cointegrating models with time-varying coefficients and multiple nonstationary regressors using classic kernel smoothing methods to estimate the coefficient functions. Extending earlier work on nonstationary kernel regression to take account of practical features of the data, we allow the regressors to be cointegrated a...

Limit theory for regressions involving local to unit roots (LURs) is now used extensively in time series econometric work, establishing power properties for unit root and cointegration tests, assisting the construction of uniform confidence intervals for autoregressive coefficients, and enabling the development of methods robust to departures from...

p>This article studies functional local unit root models (FLURs) in which the autoregressive coefficient may vary with time in the vicinity of unity. We extend conventional local to unity (LUR) models by allowing the localizing coefficient to be a function which characterizes departures from unity that may occur within the sample in both stationary...

Two approaches have dominated formulations designed to capture small departures from unit root autoregressions. The first involves deterministic departures that include local-to-unity (LUR) and mildly (or moderately) integrated (MI) specifications where departures shrink to zero as the sample size n --- oo. The second approach allows for stochastic...

This paper provides a novel mechanism for identifying and estimating latent group structures in panel data using penalized techniques. We consider both linear and nonlinear models where the regression coefficients are heterogeneous across groups but homogeneous within a group and the group membership is unknown. Two approaches are considered—penali...

This paper extends recent findings of Lieberman and Phillips (2014) on stochastic unit root (STUR) models to a multivariate case including asymptotic theory for estimation of the model's parameters. The extensions are useful for applications of STUR modeling and because they lead to a generalization of the Black–Scholes formula for derivative prici...

This paper studies nonlinear cointegration models in which the structural coefficients may evolve smoothly over time, and considers time-varying coefficient functions estimated by nonparametric kernel methods. It is shown that the usual asymptotic methods of kernel estimation completely break down in this setting when the functional coefficients ar...

This paper reexamines changes in the causal link between money and income in the United States for over the past half century (1959-2014). Three methods for the data-driven discovery of change points in causal relationships are proposed, all of which can be implemented without prior detrending of the data. These methods are a forward recursive algo...

Causal relationships in econometrics are typically based on the concept of predictability and are established in terms of tests for Granger causality. These causal relationships are susceptible to change, especially during times of financial turbulence, making the real-time detection of instability an important practical issue. This paper develops...

This paper considers stationary regression models with near-collinear regressors. Limit theory is developed for regression estimates and test statistics in cases where the signal matrix is nearly singular in finite samples and is asymptotically degenerate. Examples include models that involve evaporating trends in the regressors that arise in condi...

We study Kolmogorov–Smirnov goodness-of-fit tests for evaluating distributional hypotheses where unknown parameters need to be fitted. Following the work of Pollard (1980), our approach uses a Cramér–von Mises minimum distance estimator for parameter estimation. The asymptotic null distribution of the resulting test statistic is represented by inva...

Earth's climate sensitivity has long been subject to heated debate and has spurred renewed interest after the latest IPCC assessment report suggested a downward adjustment of its most likely range. Recent observational studies have produced estimates of transient climate sensitivity, that is, the global mean surface temperature increase at the time...

This paper explores in several prototypical models a convenient inference procedure for nonstationary variable regression that enables robust chi-square testing for a wide class of persistent and endogenous regressors. The approach uses the mechanism of self-generated instruments called IVX instrumentation developed by Magdalinos and Phillips (2009...

We construct a model of asset market exuberance, collapse and recovery using subjective investor-based rational expectations about the impact of fundamentals on the market price. Investors are assumed to have heterogeneous market sentiments, allowing them to be exuberant, cautious, or fundamentalist via boundary conditions that describe their respe...

Denis Sargan was the leading British econometrician of his generation, playing a central role in establishing the technical basis for modern time-series econometric analysis. In a distinguished 40-year career as teacher, researcher, and practitioner Sargan transformed the role of econometrics in the analysis of macroeconomic time series and the tea...

Model selection by BIC is well known to be inconsistent in the presence of incidental parameters. This paper shows that, somewhat surprisingly, even without fixed effects in dynamic panels BIC is inconsistent and overestimates the true lag length with considerable probability. The reason for the inconsistency is explained and the probability of ove...