Equality of Fixed Effects (FE) and First Differences (FD) Estimators When T=2
For the special two period case, the FE estimator and the FD estimator are numerically equivalent. To see this, establish that the fixed effects estimator is: ![{FE}_{T=2}= \left[ (x_{i1}-\bar x_{i}) (x_{i1}-\bar x_{i})' + (x_{i2}-\bar x_{i}) (x_{i2}-\bar x_{i})' \right]^{-1}\left[ (x_{i1}-\bar x_{i}) (y_{i1}-\bar y_{i}) + (x_{i2}-\bar x_{i}) (y_{i2}-\bar y_{i})\right]](http://upload.wikimedia.org/math/a/5/4/a54aad83c5652aef82b0f5265234e1d5.png)
Since each can be re-written as, we'll re-write the line as:
Read more about this topic: Fixed Effects Model
Famous quotes containing the words equality, fixed, effects and/or differences:
“It is a strange fact that freedom and equality, the two basic ideas of democracy, are to some extent contradictory. Logically considered, freedom and equality are mutually exclusive, just as society and the individual are mutually exclusive.”
—Thomas Mann (1875–1955)
“...a fixed aim furnishes us with a fixed measure, by which we can decide whether such or such an action proposed is worth trying for or not, and as aims must vary with the individual, the decisions of any two people as to the desirableness of an action may not be the same.”
—Anna C. Brackett (1836–1911)
“If one judges love according to the greatest part of the effects it produces, it would appear to resemble rather hatred than kindness.”
—François, Duc De La Rochefoucauld (1613–1680)
“The differences between revolution in art and revolution in politics are enormous.... Revolution in art lies not in the will to destroy but in the revelation of what has already been destroyed. Art kills only the dead.”
—Harold Rosenberg (1906–1978)