Space and Time are Inextricably Interwoven

Michael Beenstock*, Daniel Felsenstein

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review


Panel data may be stationary or nonstationary and independent or dependent. Dependence may be strong (induced by common factors) or weak (induced by spatial dependence). The econometric analysis of nonstationary, independent panel data developed during 1999–2003. The econometric analysis of stationary, strongly dependent panel data developed during the mid 2000s, and was extended to nonstationary panel data during 2011–2014. Development of the econometric analysis of stationary, weakly (spatially) dependent panel data began in 2003. We identify a lacuna in the literature for the case in which the panel data are nonstationary and the panel units are weakly dependent. Our book is mainly concerned with completing this lacuna. The asymptotic theory of panel data econometrics assumes that the number of panel units (N) and the number of time periods (T) tend to infinity. Since space is inherently finite whereas time is not, our asymptotic analysis is carried out with N fixed while T tends to infinity. Strong dependence induces correlated effects in which the panel units are not causally related. By contrast, weak or spatial dependence induces endogenous effects in which the panel units are causally related. Weak dependence induces contagion, but strong dependence does not.

Original languageAmerican English
Title of host publicationAdvances in Spatial Science
PublisherSpringer International Publishing
Number of pages20
StatePublished - 2019

Publication series

NameAdvances in Spatial Science
ISSN (Print)1430-9602
ISSN (Electronic)2197-9375

Bibliographical note

Publisher Copyright:
© 2019, Springer Nature Switzerland AG.


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