Cross Section Dependence in Panel Data Models: Analysis of Short T Panels and Tests of Weak and Strong Cross Section Dependence

Lead Research Organisation: University of Cambridge
Department Name: Economics


The use of panels where the number of time periods and cross section units varies across applications creates a number of challenges for statisticians and econometricians, as well as for economic theory where network interactions are of interest. One very common form of interaction is spatial. Closeness or geographical contiguity is observable and there is a well developed field of spatial econometrics that deals with these issues. When the interaction is unobservable it may be that there is a common factor at work-global warming, for example, or a world financial crisis with pervasive effects globally. But there can also be more local forms of interaction which in addition to spatial patterns could take place in more abstract spaces such as social or economic networks.These abstract interactions can be both strong and weak.

Strong interactions do not die away as the number of agents increases or as we move away from a 'neighbourhood'. Weak interactions do.This project will address these issues by developing econometric techniques for taking account of these interactions in a wide range of applications in economics.

Description This project focused on the development of econometric techniques and applications for measuring and modelling cross-sectional dependence within panels of data with a temporal and cross sectional dimension.
The measurement of inter-connections is proposed in terms of a single parameter referred to as the exponent of cross-sectional dependence. A Monte Carlo study suggests that the estimated measure has desirable small sample properties. It is found that the proposed exponent can accommodate a wide spectrum of cross-sectional dependencies in macro and financial data sets.
For micro panels where the time dimension is short relative to the cross section dimension, often arising in microeconometric applications, the transformed maximum likelihood (ML) estimator is proposed. Specifically, short dynamic panel data models with interactive fixed effects are considered, allowing for a multifactor error structure. Small sample results obtained from Monte Carlo simulations show that the transformed ML estimator performs well in finite samples and outperforms the generalised method of moments (GMM) estimators proposed in the literature in almost all cases considered.
Large panel data sets, give rise to large covariance matrices in many fields such as finance, global macro-econometric modelling, bio-informatics, meteorology, signal processing and pattern recognition. When the cross-sectional dimension exceeds the time dimension the sample covariance matrix becomes ill-conditioned and is not a good estimator of the population covariance. A novel regularisation method for the estimation of large covariance matrices is proposed, which makes use of insights from the multiple testing literature. By using the inverse of the normal distribution at a predetermined significance level, it circumvents the challenge of evaluating the theoretical constant arising in the rate of convergence of existing thresholding estimators. Monte Carlo simulation results show that the proposed estimator performs well and tends to outperform existing estimators, particularly when the cross-sectional dimension is larger than the time series dimension.
A two stage procedure is proposed. First, the use of cross unit averages separates out the relationship between units that is due to common factors from that which is purely spatial. A multiple testing procedure is used to determine significant bilateral correlations between units. The proposed methods are applied to real house price changes at the level of Metropolitan Statistical Areas in the USA, and a heterogeneous spatiotemporal model for the de-factored real house price changes is estimated. Analysis of connections based on pair-wise correlations clearly points to negative as well as positive connections. This feature is absent if the spatial analysis is based exclusively on contiguity. Furthermore, results show that basing the spatial analysis without de-factoring ignores common national and regional factors and failing to condition on the common factors may bias the inferences that can be drawn.
Another contribution is the GVAR Toolbox 2.0, a user friendly tool for the modelling of global interactions. It represents a considerable advance over the earlier versions of this package offering a number of new options. This software is publicly available on the website ( and it includes a comprehensive user guide for global VAR (GVAR) models.
Exploitation Route The results of this project will be adopted by a number of users in central banks, international agencies, and government agencies. Specific groups include professional economists in government and commerce interested in global macroeconomic modelling, inter-connections of house prices, bank credit and the macro-economy, the analysis of economic growth across countries, and incomes dynamics across households. The methods provided are practical and straightforward to implement. Provision of data and computer codes is expected to contribute to increase usage of the proposed approaches by the non-academic community. They also have the advantage that they are widely applicable for investigating complex spatial-temporal interactions. The newly developed techniques will have an influence on regional modelling and analysis carried out by government departments since our work provides an integrated framework for the proper analysis of spatial relationships once spurious correlations among geographical units have been purged of common factors.
The release of the GVAR Toolbox 2.0 is expected to allow for a better understanding of the international propagation of various forms of shock in the world economy. An older version is regularly employed by the European Central Bank and the National Bank of Switzerland. It has also been used by the World Bank, IMF and the Inter American Development Bank. The new options provided will increase its popularity by not only international organisations and policy makers but also by private sector institutions. The annual course provided for GVAR modelling is also expected to further contribute to this. In fact, every year the diversity of the participants increases including people from a wider range of institutions as well as the private sector.
Sectors Other

Description .The wider impact of this kind of econometric research takes quite a long time in filtering through to best econometric practice in government, commerce and international organisations. One particular pathway is the incorporation of these new methods into commercial software such as Stata and Eviews which are very widely used outside of academia. Methods developed at Cambridge in the past under previous ESRC grants have been incorporated into Stata after 3 or 4 years. However, pooled mean group estimators for panel data that were first proposed by Pesaran, Shin and Smith in 1997 have only just been incorporated into the latest version of Eviews.
First Year Of Impact 2015
Sector Other
Impact Types Economic,Policy & public services