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

  • Michael Beenstock
  • Daniel Felsenstein
Part of the Advances in Spatial Science book series (ADVSPATIAL)


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.


  1. Anselin L (1988) Spatial econometrics: methods and models. Kluwer Academic Publishers, DordrechtCrossRefGoogle Scholar
  2. Armstrong H, Taylor J (2000) Regional economics and policy, 3rd edn. Blackwell, OxfordGoogle Scholar
  3. Ascani A, Gagliardi L (2015) Inward FDI and local innovative performance. An empirical investigation on Italian provinces. Rev Reg Res 35(1):29–47Google Scholar
  4. Bai J, Ng S (2004) A PANIC attack on unit roots and cointegration. Econometrica 72:1127–1177CrossRefGoogle Scholar
  5. Bailey N, Holly S, Pesaran MH (2016) A two stage approach to spatiotemporal analysis with strong and weak cross-section dependence. J Appl Economet 31(1):249–280CrossRefGoogle Scholar
  6. Banerjee A, Carrion-I-Silvestre JL (2017) Testing for panel cointegration using common correlated effects estimators. J Time Ser Anal 38:610–636CrossRefGoogle Scholar
  7. Beenstock M (1986) The World Bank’s contribution to economic development. In: Recovery in the developing world. The World Bank, Washington, DC, pp 34–46Google Scholar
  8. Beenstock M (2017) How internally mobile is capital? Lett Spat Resour Sci 10(3):361–374CrossRefGoogle Scholar
  9. Beenstock M, Felsenstein D (2008) Regional heterogeneity, conditional convergence and regional inequality. Reg Stud 42(4):475–488CrossRefGoogle Scholar
  10. Beenstock M, Ben Zeev N, Felsenstein D (2011) Capital deepening and regional inequality: an empirical analysis. Ann Reg Sci 47:599–617CrossRefGoogle Scholar
  11. Beenstock M, Felsenstein D, Rubin Z (2017) Lett Spat Resour Sci 10(3):385–409CrossRefGoogle Scholar
  12. Blomstrom M, Kokko A (1998) Multinational corporations and spillovers. J Econ Surv 12:247–277CrossRefGoogle Scholar
  13. Bornschier V, Chase-Dunn C (1985) Transnational corporations and underdevelopment. Praeger, New YorkGoogle Scholar
  14. Breusch TS, Pagan AR (1979) A simple test for heteroscedasticity and random coefficient variation. Econometrica 47(5):1287–1294CrossRefGoogle Scholar
  15. Casi L, Resmini L (2010) Evidence on the determinants of foreign direct investment: the case of EU regions. East J Eur Stud 1(2):93–118Google Scholar
  16. Casi L, Resmini L (2014) Spatial complexity and interactions in the FDI attractiveness of regions. Pap Reg Sci 93:51–78CrossRefGoogle Scholar
  17. Dall’Erba S, de Gallo J (2007) The impact of EU regional support on growth and employment. Czech J Econ Financ 57(7–8):325–350Google Scholar
  18. Elhorst JP (2014) From spatial cross-section data to spatial panel data. Springer, BerlinGoogle Scholar
  19. EU (2011) Estimating the capital stock for the NUTS 2 regions of the EU-27. Working Papers no01/2011, DG Regional Policy, European Union, BrusselsGoogle Scholar
  20. Feenstra RC, Hanson GH (1997) Foreign direct investment and relative wages: evidence from Mexico’s maquiladoras. J Int Econ 42:371–393CrossRefGoogle Scholar
  21. Figinia P, Gorg H (2011) Does foreign direct investment affect wage inequality? An empirical investigation. World Econ 34(9):1455–1475CrossRefGoogle Scholar
  22. Fu X (2004) Limited linkages from growth engines and regional disparities in China. J Comp Econ 32:148–164CrossRefGoogle Scholar
  23. Halleck Vega S, Elhorst JP (2016) A regional employment model simultaneously accounting for serial dynamics, spatial dependence and common factors. Reg Sci Urban Econ 60:85–95CrossRefGoogle Scholar
  24. Haskell JE, Pereira SC, Slaughter MJ (2007) Does inward foreign direct investment boost the productivity of domestic firms? Rev Econ Stat 87(3):482–496CrossRefGoogle Scholar
  25. Im K, Pesaran MH, Shin Y (2003) Testing for unit roots in heterogeneous panels. J Econ 115:53–74CrossRefGoogle Scholar
  26. Kapitanios G, Pesaran MH, Yamagata T (2011) Panels with nonstationary multifactor error structures. J Econ 160:326–348CrossRefGoogle Scholar
  27. Manski CF (1993) Identification of endogenous social effects: the reflection problem. Rev Econ Stud 60(3):531–542CrossRefGoogle Scholar
  28. Markusen JR, Venables AJ (1998) Multinational firms and the new trade theory. J Int Econ 46:183–203CrossRefGoogle Scholar
  29. Midelfart-Knarvik KH, Overman H (2002) Delocation and European integration: is structural spending justified? Econ Policy 17:323–359CrossRefGoogle Scholar
  30. Navon G, Frisch R (2009) The effect of Israel’s encouragement of capital investments in industry law on product, employment, and investment: an empirical analysis of micro data. Discussion Paper Series, 2009.12, Research Department, Bank of Israel, Jerusalem (Hebrew)Google Scholar
  31. Pedroni P (1999) Critical values for cointegration tests in heterogeneous panels with multiple regressors. Oxf Bull Econ Stat 61:653–670CrossRefGoogle Scholar
  32. Pellegrini G, Terribile F, Tarola O, Muccigrsso T, Busillo F (2013) Measuring the effects of European regional policy on economic growth: a discontinuity approach. Pap Reg Sci 92(1):217–233CrossRefGoogle Scholar
  33. Pesaran MH (2006) Estimation and inference in large heterogeneous panels with a multifactor error structure. Econometrica 74:967–1012CrossRefGoogle Scholar
  34. Pesaran MH (2007) A simple panel unit root test in the presence of cross section dependence. J Appl Economet 22(2):265–310CrossRefGoogle Scholar
  35. Pesaran MH (2015) Time series and panel data econometrics. Oxford University Press, OxfordCrossRefGoogle Scholar
  36. Regelink M, Elhorst JP (2015) The spatial econometrics of FDI and third country Effects. Lett Spat Resour Sci 8:1–13CrossRefGoogle Scholar
  37. Schwartz D, Keren M (2006) Location incentives and the unintentional generation of employment instability: some evidence from Israel. Ann Reg Sci 40:449–460CrossRefGoogle Scholar
  38. Sjöholm F (1999) Productivity in Indonesia: the role of regional characteristics and direct foreign investment. Econ Dev Cult Chang 47:559–584CrossRefGoogle Scholar
  39. Wei K, Yao S, Liu A (2009) Foreign direct investment and regional inequality in China. Rev Dev Econ 13(4):778–791CrossRefGoogle Scholar
  40. Westerlund J (2007) Testing for error correction in panel based data. Oxf Bull Econ Stat 69(6):709–748CrossRefGoogle Scholar
  41. Wren C (2005) Regional grants: are they worth it? Fisc Stud 26(2):245–275CrossRefGoogle Scholar
  42. Wren C, Jones J (2011) Assessing the regional impact of grants on FDI location: evidence from UK regional policy 1985–2005. J Reg Sci 51(3):497–517CrossRefGoogle Scholar
  43. Zhang X, Zhang KH (2003) How does globalization affect regional inequality within a developing country? Evidence from China. J Dev Stud 39:47–67CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Michael Beenstock
    • 1
  • Daniel Felsenstein
    • 2
  1. 1.Department of EconomicsHebrew University of JerusalemJerusalemIsrael
  2. 2.Department of GeographyHebrew University of JerusalemJerusalemIsrael

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