I am seeking to understand what it means for my IV model (2SLS, in Stata) if my controls are correlated with my instrument (e.g., such that when I add additional controls to my model that are positively correlated with Y, the coefficient on my instrument declines).
  • Is it correct to conclude that my instrument is "invalid"?
  • Or is my instrument still valid, and this is normal?
I am having difficulty locating an answer. The only paper that I could find that discusses IV controls in depth is Deuchert and Huber (2017), but I am having difficulty locating an answer to my question within it. Thank you!