Nouveau Regression

Part 1 (Inside Time):

   The Goal: Predict the future quickly and accurately.

    The Insight: The random error in the Dependent Variable (Y) is the sum of the random error in the Independent Variables (Xs).
    The Intuition: A baker has three glasses.  The first contains eggs.  The second contains flour.  The third contains sugar.  The sum of the empty space in the glasses represents how many cakes that the baker cannot bake.  With his materials he bakes a box of cakes.  The empty space in the box represents how many cakes the baker cannot bake.  To find out how many eggs it takes to bake a cake, the baker takes the empty space in the first glass and divides it by the empty space in the box.  He now has his answer in terms of empty space and all he has to do is translate it into units he can understand.
    The Innovation: The Nouveau Regression instruments for the random error, or empty space, in the Independent Variable (X) of interest with a vector of random error that is orthogonal, but 100% correlated, to the Dependent Variable (Y).  Because the variation that the orthogonal instrument (Z) explains in X is uncorrelated with the random error in all other potential regressors, the Nouveau Regression is able to predict the relationship between Y and X with a simple bivariate regression.
    Translated R-Square: The instrumented regression produces negative R Square values.  The Nouveau Regression's interpretation of a negative R Square is that the regressor is predicting the variation in the random error of Y.  Because the Nouveau Regression's constructed instrument is fully correlated with Y, the amount of variation in random error that the regressor explains can be translated into the amount of variation the regressor explains in Y.  To translate the negative R Square values into a more conventional format, the Nouveau Regression inverts the traditional R Square formula to be Total Sum of Squares/Sum of Squared Errors.  As the Sum of Squared Errors heads towards 0 and approaches the Total Sum of Squares, the regressor explains more of the variation in Y, and the Translated R Square approaches 1. 
    Natural Regression: The Nouveau Regression is appropriate for all data that occurs naturally, i.e. it is not computer-simulated or transformed (e.g. logged).

    Inside Time:  The Nouveau Regression should control for longitudinal data.

Angrist and Pischke.  Mostly Harmless Econometrics.