Suppose I am interested in studying the effect of schooling on earnings. I have two valid IVs for schooling namely:
- distance of residence from school, and
- quarter of birth.
I use each instrument separately and obtain two different IV estimates of the effect of schooling on earnings - b using (1) and c using (2). And it's found that b is not equal to c. Why do I get two different estimates of the effect of schooling on earnings despite both IVs being valid?