A Bayesian panel data framework for examining the economic growth convergence hypothesis: do the G7 countries converge?

Abstract

In this paper, we suggest a Bayesian panel (longitudinal) data approach to test for the economic growth convergence hypothesis. This approach can control for possible effects of initial income conditions, observed covariates and cross-sectional correlation of unobserved common error terms on inference procedures about the unit root hypothesis based on panel data dynamic models. Ignoring these effects can lead to spurious evidence supporting economic growth divergence. The application of our suggested approach to real gross domestic product panel data of the G7 countries indicates that the economic growth convergence hypothesis is supported by the data. Our empirical analysis shows that evidence of economic growth divergence for the G7 countries can be attributed to not accounting for the presence of exogenous covariates in the model.

Keywords:

• Bayesian inference
• cross-sectional dependence
• economic growth convergence
• exogenous covariates
• panel data
• unit root testing

JEL Classifications :

• C11
• C22
• G10

Acknowledgements

The authors thank the associate editor and two anonymous referees for their comments and suggestions. We would also like to thank Dimitris Christopoulos and Kaddour Hadri, as well as participants of the MMF10 conference, held in Cyprus, year 2010, for useful comments on the paper.

Notes

See, for example, 3 5 15 or 12 for a recent survey.

To capture these unobservable effects, Barro and Sala-i-Martin 2 suggested testing the β-convergence hypothesis based on a system of seemingly unrelated regressions (SUR) of growth equations across different countries. However, consistent estimation of this system requires a substantial number of time-series observations.

See 16 27 for single time-series analysis.

Note that these assumptions about the error term u _it are quite general. They can capture common factors of u _it like , where v _t is a common, t-time innovation term, for all i, and e _it is a white noise process 17. For f _i =1, the above factor model reduces to the standard error component model: , which is frequently used in the empirical literature 1.

PPP conversion is based on current prices. The G7 countries include Canada, France, Germany, Italy, Japan, UK and USA. The data were collected from the Penn World table of Alan Heston, Robert Summers and Bettina Aten, Center for International Comparisons of Production, Income and Prices at the University of Pennsylvania.

Note that these tests are suitable for panel data sets whose time dimension T is large, while their cross-sectional dimension N is small relative to T, like the panel data set considered by our study.

To see if classical panel unit root tests can reject the unit root hypothesis if covariate information is taken into account, we have used the following approach to calculate the Levin et al. 20 and Im et al. 14 tests, denoted by t _LLC and W _IPS, respectively. In conducting the above tests, we have considered individual effects and linear trends after adjusting the panel data series for the covariate effects. The above tests are suitable for panel data sets whose time dimension T is large, while their cross-sectional dimension N is small relative to T, like the panel data set considered by our study. The values of the test statistics, t _LLC and W _IPS, were found to be −2.23 and −3.47, respectively. These test statistics assume asymptotic normality, and their values clearly reject the null hypothesis of a unit root, and thus confirm our results that the stationary model m ₄ is appropriate to describe the data.