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My question is in what ways the predicted values of a dependent variable are more accurate than the actual values. The issue is that I want to investigate the effect of X on Y.

In addition to X the right hand side contains other factors Z that influence both Y and X. I was recommended to use the predicted values of X based on a model where Zs are in the right hand side. Later, I use the predicted values of X to investigate its effect on Y.

Why this is a better way than using the actual values of X in an econometric wordings.

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The predicted values of X may be better approximation to the true values if the measurement errors in X are large but the measurement errors for the predictors are small or zero.

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