ECONOMETRIC ANALYSIS OF NONSTATIONARY DATA

October 1998

These lectures describe some of the author’s recent research in areas that have potential for empirical applications. The lectures emphasize the motivating ideas, provide a conceptual development of the econometric methods and discuss and illustrate some practical implementations. Technical details will be covered at a level that should be accessible to persons with a graduate economics background. The theme of the lectures is econometric methodology for describing and analyzing nonstationary economic data and the course has several distinct but related components.

The first part of the course discusses some new methods of econometric model determination and shows how they can be used to construct vector time series models in an automated way, to generate economic forecasts and to perform policy analysis. The judgmental elements in using these methods for forecasting are minimal and are confined to the choice of variables, the selection of the model classes to be used, and the setting of certain maximal parameters like the maximal lag order in a vector autoregression. The methods provide a simple procedure for finding consistent estimates of cointegrating rank in vector autoregressions and can be used to determine jointly the cointegrating rank and the lag order, thereby facilitating the use of reduced rank regression methods in practice without the use of complicated testing procedures. Some experience that the author has had in using the techniques in practical ex ante macroeconometric forecasting over the last four years for a group of Asia-Pacific countries are reported.

The second component of the course discusses some new methods of description that can be applied to both stationary and nonstationary data. These descriptive tools help to characterize the properties of observed series and to assist in a novel way in making agnostic assessments of such matters as level shifts and trend breaks. The methods also provide a new way of measuring quantities of empirical interest like inflation hazards. Some empirical illustrations to interest rates and inflation are provided. The third part of the course addresses the longstanding issue of trends and spurious regressions from a new perspective. It is argued that, in spite of serious statistical analysis in recent years, the phenomenon is still imperfectly understood. While the commonality of trending mechanisms in economic data is well known to make econometric regressions vulnerable to spurious empirical relationships, such relationships will be shown to frequently have their own mathematical justification. In consequence, some new interpretations of the phenomena are put forward and the implications for empirical research are discussed.

The final component of the course is concerned with the econometric analysis of panel data where the time series have nonstationary characteristics, as in most multi-country macroeconomic panels. Some new methods are described that should be useful in various empirical applications like testing growth convergence theories in macroeconomics, estimating long-run relations between international financial series such as relative prices and exchange rates, and testing hypotheses about international capital mobility.

Reference and Reading1

Econometric Model Determination: Automated Time Series Modeling and Forecasting

Phillips, Peter C.B. (1995). "Bayesian Model Selection and Prediction with Empirical Applications," Journal of Econometrics, 69, 289-332.

Phillips, Peter C.B. (1995). "Automated forecasts of Asia-Pacific Economic Activity," Asia Pacific Economic Review, 1, 92-102.

Phillips, Peter C.B. (1996). "Econometric Model Determination," Econometrica, 64, 763-812.

Phillips, P.C.B. (1998). "Impulse Response and Forecast Error Variance Asymptotics in Nonstationary VAR's," Journal of Econometrics, 83, 21-56.

Ploberger, W. and P.C.B. Phillips (1999). "Rissanen's Theorem and Econometric Time Series" in Hugo A. Keuzenkamp, Michael McAleer and Arnold Zeller Simplicity, Inference and Econometric Modelling, Cambridge: Cambridge University Press, (forthcoming).

Spatial Analysis for Nonstationary Time Series Data: Densities and Hazard Functions

Phillips, P.C.B. (1998). ""Econometric Analysis of Fisher's Equation," mimeographed, Yale University.

Phillips, P.C.B. and J.Y. Park (1998). "Nonstationary Density Estimation and Kernel Autoregression," mimeographed, Yale University.

Park, J.Y. and P.C.B. Phillips (1999). "Asymptotics for Nonlinear Transformations of Integrated Time Series," Econometric Theory (forthcoming).

Trends, Trend Elimination and Spurious Regressions

Phillips, P.C.B. (1986). "Understanding Spurious Regressions in Econometrics," Journal of Econometrics, 33, 311-340.

Durlauf, S.N. and P. C. P. Phillips (1988). "Trends versus Random Walks in Time Series Analysis," Econometrica, 56, 1333-1354.

Phillips, P.C.B. (1995). "Nonstationarity and Cointegration: Recent Books and Themes for the Future," Journal of Applied Econometrics, 10, 87-94.

Phillips, P.C.B. (1998). "New Tools for Understanding Spurious Regression," Econometrica (forthcoming)

Phillips, P.C.B. (1998). "New Unit Root Asymptotics in the Presence of Deterministic Trends," mimeographed, Yale University.

Nonstationary Panel Data and Cointegration

Phillips, P.C.B. and H.R. Moon (1998) "Nonstationary Panel Data Analysis: An Overview of Some Recent Developments" mimeographed, Yale University.

Phillips, P.C.B. and H.R. Moon (1999) "Linear Regression Limit Theory for Nonstationary Panel Data", Econometrica (forthcoming)

Moon, H.R. and P.C.B. Phillips (1998) "A Reinterpretation of the Feldstein-Horioka Regressions from a Nonstationary Panel Viewpoint," mimeographed, Yale University.

1 Copies of forthcoming/unpublished papers can be downloaded from the author's web site.