Mildly Explosive Time Series and Economic Bubbles

Yale University, New Haven CT

Investigators

Abstract

The proposed research seeks to extend present econometric methodology of unit roots and cointegration to mildly integrated and mildly explosive data. Such time series were introduced in recent work by the PI and Tassos Magdalinos and have roots that belong to larger neighborhoods of unity than conventional local to unity roots. The new framework includes commonly occuring practical cases with roots such as rho = 0.95 and helps to bridge discontinuities in the asymptotic theory between stationary, local to unity and explosive models. The project will build on these ideas, develop a limit theory for multivariate regression with mildly integrated and mildly explosive regressors, and initiate a program of related empirical applications. In particular, the research will provide a framework for generalizing standard cointegrating regressions and for linking these regressions to simultaneous equations models with stationary regressors. Conventional approaches to estimating cointegrating regressions fail to produce even asymptotically valid inference procedures when the regressors are nearly integrated, and substantial size distortions can occur in econometric testing. The new framework will enable a general approach to inference that resolves this difficulty and permits mild integration in the regressors, making it suitable for general practical application. Mildly explosive regressions also offer intriguing new possibilities, including the use of central limit arguments. The project will explore multivariate systems and validate test procedures by invariance principles under a wide range of weakly dependent innovations, distributions, and initial conditions. These procedures will be useful in dealing with economic data that undergo periods of extreme behavior like financial bubbles, and cases where there are explosively cointegrated regressors embodying contamination effects across variables. Models of periodically collapsing bubbles will also be analyzed, some extensions to existing models that have more realistic sample path properties will be provided, and procedures for econometric testing and inference in the presence of bubbles will be developed. Broader Impact: Extreme movements in economic variables can have a wide socio-economic impact, producing swings in individual wealth and financial security, misallocating capital, and threatening the credibility of economic institutions. The methods will contribute to our understanding of these economic issues by developing new models of economic bubbles, new ways of detecting bubble activity, and new procedures for statistical inference in the presence of explosive behavior and for estimating contamination across variables. The project's intellectual merit is in its scientific contribution to the analysis of mildly integrated and mildly explosive data, its extension of cointegration methodology to cover such data, and its empirical contribution to the study of economic and financial bubbles. The investigator will assist the research training of graduate students of economics through joint and directed work on these topics.