Factor Models in Panels with Cross-sectional Dependence: An Application to the Extended SIPRI Military Expenditure Data

Abstract

Strategic interactions between countries, such as arms races, alliances and wider economic and political shocks, can induce strong cross-sectional dependence in panel data models of military expenditure. If the assumption of cross-sectional independence fails, standard panel estimators such as fixed or random effects can lead to misleading inference. This paper shows how to improve estimation of dynamic, heterogenous, panel models of the demand for military expenditure allowing for cross-sectional dependence in errors using two approaches: Principal Components and Common Correlated Effect estimators. Our results show that it is crucial to allow for cross-sectional dependence, that the bulk of the effect is regional and there are large gains in fit by allowing for both dynamics and between country heterogeneity in models of the demand for military expenditures.

Keywords:

• Military expenditures
• panel data
• factor models

AMS Subject Classifications:

• C33
• C82
• H56

Acknowledgements

This paper is part of a larger SIPRI project supported by Sweden’s Riksbankens Jubileumsfond. The authors would like to thank participants at the SIPRI Expert Workshop on Military Expenditure Data (Stockholm) and the Econometrics workshop on Cross-sectional, Spatial Dependence and Heterogeneity in Panel Data Models (Queen Mary, University of London) for stimulating discussions. We are grateful to Hashem Pesaran, Sam Perlo-Freeman, Paul Dunne, Christos Kollias and an anonymous referee for comments. The responsibility for any errors or omissions is our own.

Notes

No potential conflict of interest was reported by the authors.

1 The countries are Algeria, Argentina, Australia, Austria, Belgium, Benin, Bolivia, Brazil, Burkino Faso, Burundi, Canada, Chile, Colombia, Denmark, Dominican Republic, Ecuador, Egypt, El Salvador, Ethiopia, Finalnd, France, Germany, Ghana, Greece, Guatamala, Honduras, India, Iraq, Ireland, Israel, Italy, Japan, Jordan, Kenya, Korea South, Liberia, Libya, Luxemburg, Madagascar, Malawi, Malaysia, Mali, Mauritius, Mexico, Morocco, Myamar, Netherlands, New Zealand, Nigeria, Norway Pakistan Paraguay Peru Phillipines Portugal, Saudi Arabia, Sierra Leone, South Africa, Spain Sri Lanka, Sweden Switzerland, Thailand, Tunisia, Turkey, Uganda, UK, USA Venuezela Zimbabwe.

2 If the dependence was on own and others lagged military expenditure, (1(1) ) would correspond to the infinite VAR discussed by Chudik and Pesaran (2011).

3 The BIC seems more appropriate than the AIC because it is more parsimonious and with large data-sets, it is easy for parameters to proliferate.

4 Breitung and Pesaran (2008) discuss unit roots and cointegration in panels. Kapetanios, Pesaran, and Yamagata (2011) discuss panels with non-stationary multifactor error structures.

5 The other seven were Portugal–Burkina Faso; Burkina Faso–Austria; Pakistan–Japan; Belgium–Austria; Colombia–Mali; Colombia–Paraguay; Libya–Malaysia; all with correlations between 0.5 and 0.45.

Additional information

Funding

This work was supported by the Sweden’s Riksbanken Jubileumsfond.