There are few researches may help you in conducting your project. Please see the following:
Zakat as a Benchmark to Evaluate Economic Growth: An Alternative Approach by Adel M. Sarea
http://tinyurl.com/y25u6bkn
http://tinyurl.com/y6mydt2o
http://tinyurl.com/yxc5xeek
Muhammad Azam & Nasir Iqbal & Muhammad Tayyab, 2014. "Zakat and Economic Development: Micro and Macro Level Evidence from Pakistan," Bulletin of Business and Economics (BBE), Research Foundation for Humanity (RFH), vol. 3(2), pages 85-95, June.
The Influence of Zakat on Economic Growth and Welfare Society in Indonesia
My scientific understanding supports the positive stimuli of Zakat on economic growth; country and community specific effects (on best practice) have still to be studied empirically.
Its interesting to see how a person like Bill Gates clearly suggests that simple "income tax" is not enough to ensure equality, but rather a tax on stored wealth is a better idea (the same idea of Zakat).
See his interview here. Part on taxing wealth starts around 2:30
I think that zakat increases money, develops it and disinfects it, and makes the distribution of money between the poor and the rich just and thus increases the movement of money and its cycle .
Since Zakat is a compulsory gift from wealth or excessive income (once a year) to poor people (as opposed to sadaka who is voluntary) by increasing their basket as a consumer, increasing their well-being by influencing their productivity growth in society and in a longer period of time reflects also on economic growth.
If zakat is well collected,and spent in a normal way.either from private or government. It can boost economy and brings about economic growth. And also in the long run, it will enhance economic development.
That needs to be measured where Zakat is collected. For now, Zakat has indirect effect on growth that is not officially identified in many places, countries etc.
Dr. Najeeb Zada from INCEIF has written about Zakat Re-Investment Trusts and its impacts. You can google him. His work is available on Springer too. Moreover, the Malaysians have written plenty on Zakat and its impacts. Likewise, some studies are available on Durham Online Thesis Repository.
Here an example of studies regarding your concern:
Daly, S., & Frikha, M. (2015). Islamic finance, a support to development and economi c growth: the principle of Zakat as an Example. Journal of Behavioural Economics, Finance, Entrepreneurship, Accounting and Transport, 3(1).