Peter C. B. Phillips

Yale University | YU · Department of Economics

Spatial autoregressive (SAR) and related models offer flexible yet parsimonious ways to model spatial and network interactions. SAR specifications typically rely on a particular parametric functional form and an exogenous choice of the so-called spatial weight matrix with only limited guidance from theory in making these specifications. Also, the c...

Australian housing markets experienced widespread and, in some cases, extraordinary growth in prices between 2020 and 2023. Using recently developed methodology that accounts for fundamental economic drivers, we assess the existence and degree of speculative behaviour, as well as the timing of exuberance and downturns in these markets. Our findings...

This paper considers a linear panel model with interactive fixed effects and unobserved individual and time heterogeneities that are captured by some latent group structures and an unknown structural break, respectively. To enhance realism the model may have different numbers of groups and/or different group memberships before and after the break....

This study provides new mechanisms for identifying and estimating explosive bubbles in mixed‐root panel autoregressions with a latent group structure. A postclustering approach is employed that combines k ‐means clustering with right‐tailed panel‐data testing. Uniform consistency of the k ‐means algorithm is established. Pivotal null limit distribu...

May 17, 2008 A model of financial asset price determination is proposed that incorporates flat trading features into an efficient price process. The model involves the superposition of a Brownian semimartingale process for the effcient price and a Bernoulli process that determines the extent of price trading. The approach is related to sticky price...

Datasets from field experiments with covariate-adaptive randomizations (CARs) usually contain extra covariates in addition to the strata indicators. We propose to incorporate these additional covariates via auxiliary regressions in the estimation and inference of unconditional quantile treatment effects (QTEs) under CARs. We establish the consisten...

The global financial crisis and Covid recession have renewed discussion concerning trend-cycle discovery in macroeconomic data, and boosting has recently upgraded the popular HP filter to a modern machine learning device suited to data-rich and rapid computational environments. This paper sheds light on its versatility in trend-cycle determination,...

New methods are developed for identifying, estimating, and performing inference with nonstationary time series that have autoregressive roots near unity. The approach subsumes unit-root (UR), local unit-root (LUR), mildly integrated (MI), and mildly explosive (ME) specifications in the new model formulation. It is shown how a new parameterization i...

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 res...

This paper explores predictive regression models with stochastic unit root (STUR) components and robust inference procedures that encompass a wide class of persistent and time-varying stochastically nonstationary regressors. The paper extends the mechanism of endogenously generated instrumentation known as IVX, showing that these methods remain val...

This paper studies high-dimensional vector autoregressions (VARs) augmented with common factors that allow for strong cross-sectional dependence. Models of this type provide a convenient mechanism for accommodating the interconnectedness and temporal co-variability that are often present in large dimensional systems. We propose an ℓ1-nuclear-norm r...

We propose a framework for estimation of the conditional mean function in a parametric model with function space covariates. The approach employs a functional mean squared error objective criterion. Under regularity conditions, consistency and asymptotic normality are established. The analysis extends to situations where the asymptotic properties a...

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 is 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 f...

Limit distribution theory in the econometric literature for functional coefficient cointegrating regression is incorrect in important ways, influencing rates of convergence, distributional properties, and practical work. The correct limit theory reveals that components from both bias and variance terms contribute to variability in the asymptotics....

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...

The discrete Fourier transform (dft) of a fractional process is studied. An exact representation of the dft is given in terms of the component data, leading to the frequency domain form of the model for a fractional process. This representation is particularly useful in analyzing the asymptotic behavior of the dft and periodogram in the nonstationa...

This paper examines methods of inference concerning quantile treatment effects (QTEs) in randomized experiments with matched-pairs designs (MPDs). Standard multiplier bootstrap inference fails to capture the negative dependence of observations within each pair and is therefore conservative. Analytical inference involves estimating multiple function...

Multicointegration is traditionally defined as a particular long run relationship among variables in a parametric vector autoregressive model that introduces additional cointegrating links between these variables and partial sums of the equilibrium errors. This paper departs from the parametric model, using a semiparametric formulation that reveals...

Multicointegration is traditionally defined as a particular long run relationship among variables in a parametric vector autoregressive model that introduces additional cointegrating links between these variables and partial sums of the equilibrium errors. This paper departs from the parametric model, using a semiparametric formulation that reveals...

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 examines regression-adjusted estimation and inference of unconditional quantile treatment effects (QTEs) under covariate-adaptive randomizations (CARs). Datasets from field experiments usually contain extra baseline covariates in addition to the strata indicators. We propose to incorporate these extra covariates via auxiliary regressions...

This paper examines methods of inference concerning quantile treatment effects (QTEs) in randomized experiments with matched-pairs designs (MPDs). The standard multiplier bootstrap inference fails to capture the negative dependence of observations within each pair, and thus, is conservative. The analytical inference involves estimating multiple fun...

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 sample....

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...

Trend elimination and business cycle estimation are analyzed by finite sample and asymptotic methods. An overview history is provided, operator theory is developed, limit theory as the sample size n → ∞ is derived, and filtered series properties are studied relative to smoothing parameter (λ) behavior. Simulations reveal that limit theory with λ =O...

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...

This paper examines inference for quantile treatment effects (QTEs) in randomized experiments with matched-pairs designs (MPDs). We derive the limiting distribution of the QTE estimator under MPDs and highlight the difficulty of analytical inference due to parameter tuning. We show that a naive weighted bootstrap fails to approximate the limiting d...

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...

THE ECONOMETRIC THEORY AWARDS 2020 - Volume 36 Issue 2 - Peter C. B. Phillips

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...

The usual t test, the t test based on heteroskedasticity and autocorrelation consistent (HAC) covariance matrix estimators, and the heteroskedasticity and autocorrelation robust (HAR) test are three statistics that are widely used in applied econometric work. The use of these significance tests in trend regression is of particular interest given th...

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...

How sensitive is Earth’s climate to a given increase in atmospheric greenhouse gas (GHG) concentrations? This long-standing question in climate science was recently analyzed by dynamic panel data methods using extensive spatio-temporal data of global surface temperatures, solar radiation, and GHG concentrations over the last half century to 2010 (S...

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...

The global temperature trend observed over the last century is largely the result of two opposing effects—cooling from aerosol particles and greenhouse gas warming. While the effect of increasing greenhouse gas concentrations on Earth's radiation budget is well constrained, that due to anthropogenic aerosols is not, partly due to a lack of observat...

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...