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JOINT TIME-SERIES AND CROSS-SECTION LIMIT THEORY UNDER MIXINGALE ASSUMPTIONS

Published online by Cambridge University Press:  11 August 2020

Jinyong Hahn
Affiliation:
University of California, Los Angeles
Guido Kuersteiner*
Affiliation:
University of Maryland
Maurizio Mazzocco
Affiliation:
University of California, Los Angeles
*
Address correspondence to Guido Kuersteiner, Department of Economics, University of Maryland, Tydings Hall 3145, College Park, MD 20742, USA; e-mail: kuersteiner@econ.umd.edu.

Abstract

In this paper, we complement joint time-series and cross-section convergence results derived in a companion paper Hahn, Kuersteiner, and Mazzocco (2016, Central Limit Theory for Combined Cross-Section and Time Series) by allowing for serial correlation in the time-series sample. The implications of our analysis are limiting distributions that have a well-known form of long-run variances for the time-series limit. We obtain these results at the cost of imposing strict stationarity for the time-series model and conditional independence between the time-series and cross-section samples. Our results can be applied to estimators that combine time-series and cross-section data in the presence of aggregate uncertainty in models with rationally forward-looking agents.

Type
ARTICLES
Copyright
© The Author(s), 2020. Published by Cambridge University Press

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Footnotes

We thank Peter C.B. Phillips for his enormous contributions to the field of econometrics, both intellectually through his impressive research record and his time and effort with countless professional activities, not least starting this journal and running it as the lead editor for decades. Guido Kuersteiner is particularly grateful for Peter’s guidance and support as his Ph.D. advisor at Yale and ever since. We thank the Co-Editor Don Andrews and two anonymous referees for their careful reading of the manuscript and numerous helpful suggestions.

References

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