Instrument validity
Hello.
I am currently working with Instrumental variable and two stage least square regression. I have a fundamental question. Let y be the outcome variable, x is an endogenous variable, z is the instrument for x.
As far as I know for z to be a valid instrument it must satisfy two conditions: instrumental relevance ( strong correlation between z) and instrumental exogeneity ( must be uncorrelated with the error term i.e. will have no direct impact on y unless through x).
For the first relevance condition, I ran a reduced from regression of x on z and looked at the p value, the correlation appears highly significant. I take it the first condition is satisfied.
The second condition cannot be tested explicitly. However, out of curiosity I ran a regression of y on z and found a significant correlation, does this imply anything? Is the instrument z not valid then?
Thanks in advance.
I am currently working with Instrumental variable and two stage least square regression. I have a fundamental question. Let y be the outcome variable, x is an endogenous variable, z is the instrument for x.
As far as I know for z to be a valid instrument it must satisfy two conditions: instrumental relevance ( strong correlation between z) and instrumental exogeneity ( must be uncorrelated with the error term i.e. will have no direct impact on y unless through x).
For the first relevance condition, I ran a reduced from regression of x on z and looked at the p value, the correlation appears highly significant. I take it the first condition is satisfied.
The second condition cannot be tested explicitly. However, out of curiosity I ran a regression of y on z and found a significant correlation, does this imply anything? Is the instrument z not valid then?
Thanks in advance.
