I must say this is a very relevant and interesting topic. Celebrity endorsement, especially in the days of social media will continue to play a huge role in business management and marketing communications.
From a research perspective, you might want to understand
1. The type of brands that are more likely to use celebrity endorsement - banks, telecom or gambling company?
2. What type of advertising appeal are being adopted? Are they emotional appeal or rational appeal?
3. What type of celebrity do we have endorsing products? This can be cross tabulated with point 1.
4. What are consumers attitude towards celebrity endorsement? Is it a norm or people are tired of it?
5. Speaking with Brand Managers, what are their challenges in selecting and working with celebrity influencers?