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CENTRAL LIMIT THEORY FOR COMBINED CROSS SECTION AND TIME SERIES WITH AN APPLICATION TO AGGREGATE PRODUCTIVITY SHOCKS

Published online by Cambridge University Press:  19 September 2022

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.
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Abstract

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Combining cross-sectional and time-series data is a long and well-established practice in empirical economics. We develop a central limit theory that explicitly accounts for possible dependence between the two datasets. We focus on common factors as the mechanism behind this dependence. Using our central limit theorem (CLT), we establish the asymptotic properties of parameter estimates of a general class of models based on a combination of cross-sectional and time-series data, recognizing the interdependence between the two data sources in the presence of aggregate shocks. Despite the complicated nature of the analysis required to formulate the joint CLT, it is straightforward to implement the resulting parameter limiting distributions due to a formal similarity of our approximations with Murphy and Topel’s (1985, Journal of Business and Economic Statistics 3, 370–379) formula.

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ARTICLES
Creative Commons
Creative Common License - CCCreative Common License - BY
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (https://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
Copyright
© The Author(s), 2022. Published by Cambridge University Press

Footnotes

We thank Peter Phillips and referees in previous rounds for many helpful suggestions.

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