Butterfly Effect
5.1 in the 6th edition
Salkever’s Algebraic Trick
Salkever’s method of computing the forecasts and forecast variances
Multiple regression of
y 0
on
X X0
0 -I
produces the least squares coefficient vector followed
by the predictions. Residuals are 0 for the predictions, so s2( * )-1 gives the covariance matrix for the coefficient estimates and the variances for the forecasts. (Very clever, useful for understanding. Not actually used in modern software.)
Two groups (e.g., men=1, women=2)
Regression predictions:
垐y1 x1b1 , y 2 x 2b2 (e.g., wage equations) Explain 垐y1 - y 2. 垐y1 - y 2 x1 (b1 - b2 ) + (x1 - x 2 )b2
Multiple regression of y on X. We know that X'e = 0 where e = the column vector of residuals. That means d'e = 0, which says that ej = 0 for that particular residual.
