I'm a little confused as to why we need to go through an entire two-stage regression process to capture the effect of our instrumental variable on our independent variable, and then only use this variation on our dependent variable.
What is preventing us from using our instrumental variable directly as an explanatory variable in the regression, rather than our originally flawed dependent variable?
For example, suppose that we wanted to construct a regression to predict the what factors in a person's life lead to the average level of income they earned. We might choose to use 'years spent in education' as a regressor of interest. However, it's quite likely that this variable suffers from endogeneity. Thus, suppose we use 'parental education' as a predictor of 'years spent in education' that excludes endogeneity issues from self-selection, etc. (imagining it is a good predictor). Why go through the hassle of setting up parental education as an instrumental variable when you can just use it to replace 'years spent in education' as a better predictor?