A google scholar search turns up numerous papers on testability, including models for computing testability, recommendations for how ones code can be more testable, etc.

They all come with the assertion that more testable code is more stable, but I can't find any studies which actually demonstrate this.

Can someone link me to a study evaluating the effect of testable code vs. quality? The closest I can find is Improving the Testability of Object Oriented Systems, which discusses the relationship between design flaws and testability.