Strong and Weak Cross-Section Dependence in Non-Stationary Spatial Panel Data

Michael Beenstock*, Daniel Felsenstein

*Corresponding author for this work

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


We begin by recalling that dependence in nonstationary panel data may by weak or strong, and statistical tests to distinguish between weak and strong dependence are presented. In Chaps. 7, 8, and 9 dependence is assumed to be weak or spatial. This chapter is concerned with deciding whether dependence is weak, strong or both. We describe the econometric theory of common factor models, which induce strong dependence in stationary and nonstationary spatial panel data. We report critical values for panel cointegration tests from the literature in the presence of common factors when the data are nonstationary. In the first empirical illustration time series data for the stock of foreign direct investment is hypothesized as a common factor in the determination of capital deepening, measured by regional capital-labor ratios in Israel. Another common factor is time series for national capital-labor ratios. Common factor models in which panel dependence is assumed to be strong are compared with spatial models in which panel dependence is assumed to be weak. In a second empirical illustration the residuals for the spatial general equilibrium model in Chap. 8 and the SpVECM in Chap. 9 are tested for weak versus strong panel dependence. The residuals from Chap. 8 are not weakly dependent, but the residuals from Chap. 9 are weakly dependent. The former suggests that common factors should be specified in Chap. 8. However, strong cross-section dependence still remains indicating a need for ‘mixed dependence’ models incorporating both spatial and common factors.

Original languageAmerican English
Title of host publicationAdvances in Spatial Science
PublisherSpringer International Publishing
Number of pages25
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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