What kind of market research does your startup do by itself and what kind do you outsource?

No outsourcing, only a thorough market research in house

I agree with Andrija below, outsourcing does have its benefits, but the agency you use won't know your product as well as you do. So they might not ask the right questions and (by extension) you won't get the right data. Doing it yourself can be a little daunting, but there are a lot of automated and AI-powered tools that make it much easier than it used to be. I would suggest checking out platforms like SightX.io they make the market research process very user-friendly and intuitive. But the techniques and analysis are top notch!