I compiled a list of (mostly EA-related) writings on AI and economic growth in case it's of interest:

• Karnofsky: This Can't Go On, More on “multiple world-size economies per atom” and A note on historical economic growth
• Trammell and Korinek: Economic Growth under Transformative AI (pdf)
• Hanson: Limits to Growth
• Kokotajlo: Against GDP as a metric for timelines and takeoff speeds
• Wentworth: What Do GDP Growth Curves Really Mean?
• Bavarian, aogara: Argument against 20% GDP growth from AI within 10 years [Linkpost]
• Patel: This Can Go On - Pt 1: The Simmer Scenario and This Can Go On - Pt 2: Against intuitions about crazy growth
• Manheim & Sandberg: What is the upper limit of value? (pdf)
• Alexander: 1960: The Year The Singularity Was Cancelled
• Davidson: Report on Whether AI Could Drive Explosive Economic Growth
• Agrawal, Gans, Goldfarb: Artificial Intelligence
  and Economic Growth (pdf)

Note that I've only read a few of these, so no guarantees as to quality/relevance. Also note that these are generally (but not always) more on the qualitative/speculative side than quantitative/empirical.

Hi! If you're still interested, I think one of the most important questions in AI is how quickly it will transform the world. Effects on GDP are one way of measuring that impact, and growth theory is full of tools for forecasting growth. If this is interesting to you, here's one path you could work on:

• Tom Davidson's Full Takeoff Model is the best comprehensive economic model of AI timelines. Epoch is working on improving the model and making it more accessible to academics and policymakers. If you can identify substantive improvements to the model, plenty of folks are interested in doing so. 
• Dive into the theoretical this mathematical description of the model if you're already comfortable with growth theory, or read Davidson's and Trammell's literature reviews for a bit more background, or this Holden Karnofsky blog for the core intuitions. 
• Some good academic econ papers on the topic: Aghion Jones and Jones, Jones, and Nordhaus. 
• Think of an improvement to the model, and see if you can model it.  Theoretical demonstrations or code implementations both work.

Best of luck with this! If you have some good starting points, I'd be happy to chat, and the folks at Epoch likely would be too.