Abstract
This paper measures the efficiency and convergence of 37 stock exchanges in 35 countries over the period from 2006 to 2014, a period that encompasses a full business cycle of growth, recession and recovery. We combine a multi-stage data envelopment analysis with the window analysis approach to filter out the impact of economic environmental variables on stock exchange efficiency in the provision of trading services and track the efficiency changes over time. We show that economic growth, inflation and financial development are important drivers of efficiency. Lagging stock exchanges are catching up to the leading stock exchanges in terms of technical efficiency, pure technical efficiency and scale efficiency. Exchanges in developed countries converge faster than those in the emerging countries and the dispersion of the efficiency levels over the whole sample and the subsamples of developed vs emerging country stock exchanges diminished. Finally, stock exchanges in emerging countries are catching up to the stock exchanges in the developed countries and the dispersion of the efficiency levels between them also diminished. Overall, our findings indicate that integration has taken place in the stock exchange industry over the sample period.

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Notes
There is also some contradictory evidence, such as Serifsoy (2007), who finds that diversification and vertical integration contribute little or nothing to stock exchange efficiency.
Due to the fact that data for post-trading services and software sales of stock exchanges used by Serifsoy (2007) is no longer available for most of exchanges, we do not include them as output variables.
We acquired the PPP information from the World Development Indicators (WDI) provided by the World Bank.
In addition to these three environmental variables, as robustness tests we also included other variables in our analyses, such as the business freedom index and investment freedom index developed by the Heritage Foundation of the US as well as government effectiveness index, regulatory quality index and rule of law index developed by the World Bank etc. However, we find these environmental variables have no significant impact on the efficiency of stock exchanges.
In this step, so-called allowable input slacks due to the uncontrollable environment can be estimated. The allowable input slacks mean that a certain amount of input waste is acceptable because it is caused by an adverse external environment, not by managerial inefficiency. The remaining input slacks represent management’s excessive use of inputs (Huang and Eling, 2013).
The interpretation of the result in terms of β-convergence is not straightforward. That is to say, if exchanges with low initial level grow faster than those with high initial level, this can lead to a situation where the first ones overpass the latter ones, meaning the absence of convergence. Therefore, a σ-convergence test is needed.
Listed stock exchanges are those demutualized stock exchanges that have become publicly traded companies. Until the early 1990 s, most exchanges were non-profit, “mutual” organizations owned by their members with exclusive trading privileges. Starting with the demutualization of the Stockholm Stock Exchange in 1993, the number of stock exchanges that have adopted a for-profit, publicly listed organizational form has increased steadily.
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Acknowledgements
We are grateful to the editor and the anonymous referee for very helpful comments. Ephraim Clark gratefully acknowledges financial support from PHI and SARL. The corresponding author Zhuo Qiao gratefully acknowledges financial support from University of Macau (research grant no.: MYRG2015-00151-FBA) and thanks Jian Xu and Yunzhi Lin for research assistance.
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Clark, E., Qiao, Z. Stock exchange efficiency and convergence: international evidence. Ann Oper Res 313, 855–875 (2022). https://doi.org/10.1007/s10479-020-03869-1
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DOI: https://doi.org/10.1007/s10479-020-03869-1