Peter C. B. Phillips

Overview

Peter C. B. Phillips is an econometrician at the Cowles Foundation, Yale University (at the time of the 1993 paper). One of the leading figures in the econometric theory of integrated and cointegrated processes, with foundational contributions to unit root asymptotics, regression with integrated regressors, and optimal inference in cointegrated systems.

Key Contributions / Features

• Phillips (1986) — "Understanding Spurious Regressions in Econometrics" (Journal of Econometrics 33: 311–340; received May 1985): rigorous asymptotic theory for the Granger-Newbold (1974) finding. Root cause identified as non-ergodicity of I(1) processes, not serial correlation. Theorem 1: $t_\beta \sim O_p(T^{1/2})$, $\mathrm{DW}\to_p 0$, $R^2$ has non-degenerate limit in $(0,1)$, $\hat\beta$ non-degenerate non-zero limit. Theorem 2: F-statistic diverges at $O(T)$ with $m$ I(1) regressors. Cointegration connection: DW→0 iff series not cointegrated → analytic basis for Engle-Granger test.
• Phillips and Durlauf (1986) — "Multiple Time Series Regression with Integrated Processes" (Review of Economic Studies 53): early characterization of the non-standard asymptotic theory for regressions involving $I(1)$ processes; showed Wald tests have nuisance-parameter-dependent limits.
• Park and Phillips (1988, 1989) — "Statistical Inference in Regressions with Integrated Processes: Parts I and II" (Econometric Theory): systematic treatment of large-sample theory for regressions with stochastic trends; foundational for the Toda-Phillips causality results.
• Phillips (1991) — "Optimal Inference in Cointegrated Systems" (Econometrica 59(2): 283–306): established the LAMN/LGF dichotomy as the theoretical basis for ML dominance over OLS in cointegrated systems. Triangular ECM → LAMN likelihood → mixed-normal MLE → $\chi^2$ tests and Cramér-Rao efficiency; unrestricted VAR in levels → LGF → nonstandard limits. OLS cointegrating vector estimates carry a $\Sigma_{12}$ simultaneous-equations bias; MLE is median unbiased and efficient. Single-equation ECM fails unless $\Sigma_{12}=0$. Transient dynamics need not be jointly estimated — only consistent $\hat\Omega$ required, justifying FM-OLS (Phillips-Hansen 1990).
• Toda and Phillips (1993) — "Vector Autoregressions and Causality" (Econometrica 61): complete asymptotic theory for Granger causality Wald tests under $I(1)$ and cointegration; rank conditions for $\chi^2$ validity.
• Phillips and Solo (1992) — "Asymptotics for Linear Processes" (Annals of Statistics 20): multivariate extension of the functional central limit theorem for linear processes; used in the proofs of the Toda-Phillips lemmas.

Related

• Hiro Y. Toda
• Granger Causality
• Cointegration
• Spurious Regression
• Vector Autoregression
• Phillips (1986) Understanding Spurious Regressions in Econometrics