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:
“When I speak of The Case for Equality I mean human equality; and that, of course, can only mean one thing: it means equality of income.”
—George Bernard Shaw (1856–1950)
“At first I intended to become a student of the Senate rules and I did learn much about them, but I soon found that the Senate had but one fixed rule, subject to exceptions of course, which was to the effect that the Senate would do anything it wanted to do whenever it wanted to do it.”
—Calvin Coolidge (1872–1933)
“If I had any doubts at all about the justice of my dislike for Shakespeare, that doubt vanished completely. What a crude, immoral, vulgar, and senseless work Hamlet is. The whole thing is based on pagan vengeance; the only aim is to gather together as many effects as possible; there is no rhyme or reason about it.”
—Leo Tolstoy (1828–1910)
“I don’t know what immutable differences exist between men and women apart from differences in their genitals; perhaps there are some other unchangeable differences; probably there are a number of irrelevant differences. But it is clear that until social expectations for men and women are equal, until we provide equal respect for both men and women, our answers to this question will simply reflect our prejudices.”
—Naomi Weisstein (b. 1939)