There are lots of papers explaining this relationship. It also depends on how you want to measure competitiveness. Please, find some examples here:
Vilanova, M., Lozano, J. M., & Arenas, D. (2009). Exploring the nature of the relationship between CSR and competitiveness. Journal of business Ethics, 87(1), 57-69.
Marín, L., Rubio, A., & de Maya, S. R. (2012). Competitiveness as a strategic outcome of corporate social responsibility. Corporate social responsibility and environmental management, 19(6), 364-376.
Marin, L., Martín, P. J., & Rubio, A. (2017). Doing good and different! The mediation effect of innovation and investment on the influence of CSR on competitiveness. Corporate social responsibility and environmental management, 24(2), 159-171.
Saeidi, S. P., Sofian, S., Saeidi, P., Saeidi, S. P., & Saaeidi, S. A. (2015). How does corporate social responsibility contribute to firm financial performance? The mediating role of competitive advantage, reputation, and customer satisfaction. Journal of business research, 68(2), 341-350.
There are also lots of papers studying the mediating and moderating effects between CSR and firm's competitiveness.
Prof. Pavlo Brin , there is already a rich literature available answering your concern, that 'increased recourse to CSR leads to increasing competitiveness of a company', which motivates the companies to earmark funds for social spending. It's already an established point of enquiry. Please state more details of your purpose of enquiry on the topic. Is it part of an ongoing research?
There are two approaches towards creating a competitive advantage:
1. competitor centric
2. customer centric
The first one is conventional approach. But very successful companies like Amazon and many major Japanese companies take the second approach and have created vast blue oceans, i.e. they were able to create a competitive advantage that is not easily assailable. The second strategy or vision carries a deep understanding and inclusion of CSR. That shows CSR based strategies can be highly successful.
The practical measure will be to understand how the CSR competitive edge not only create harmony and boost smooth operations, also it get the buy-ins from major stakeholders i.e. government, which to my knowledge every shareholder or investor will consider when engaging with a company of the 21st Century.
Marc Vilanova, Josep Maria Lozano and Daniel Arena (2009) Exploring the Nature of the Relationship Between CSR and Competitiveness, Journal of Business Ethics, 87:57–69.