Why not simply use your instrumental variable as your independent variable? 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?
 A: Indeed, one can use the instrument Z to predict the outcome variable Y. However, what you are then measuring is the effect of Z on Y (this is the so-called Reduced Form Effect). This could be interesting depending on the setting (and should always be reported anyway since its statistical significance tells us quite a lot).
However, often, we do not care about the effect of Z on Y, since Z is simply meaningless. Often, IV is done with observational data, but let's take an experiment for simplicity (potential outcome framework).
Say Z is the pure assignment to a treatment, D is indicating whether participants were actually treated or not, Y is the outcome. Take the classical case of unemployment and job training. Say Z is a binary variable that indicates assignment to a job training program or not. We do not care whether someone was merely assigned to the job training program or not, but we do care whether this someone actually took the training up and completed the training (the treatment). E.g., there could also be non-compliers (people that were assigned to the treatment, but did not take the treatment). In this case, the instrument Z is meaningless in estimating Y, we simply do not care whether someone found a job after the mere assignment to the treatment. We do care whether someone found a job after assignment to treatment AND after taking the treatment, so after being actually treated (attending job training).
Thus, we need the IV approach in order that we can estimate the effect of the treatment D on Y (LATE (local average treatment effect)).
Hope this helps.
