What are Giffen Goods? What exactly are Giffen goods and are they of purely theoretical interest or has there been empirical evidence of their existence?
Consider the Slutsky equation,
$$
\frac{\partial x}{\partial p} = \frac{\partial x^c}{\partial p} -
\frac{\partial x}{\partial I} x.
$$

A giffen good is the case where the income effect $\frac{\partial x}{\partial I} x$ is negative and large (in magnitude) enough so
that $\frac{\partial x}{\partial p} &gt; 0$.

From Wikipedia:


  There are three necessary preconditions for this situation to arise:
  (1) the good in question must be an inferior good,
  (2) there must be a lack of close substitute goods, and
  (3) the good must constitute a substantial percentage of the buyer's income, but not such a substantial percentage of the buyer's income that none of the associated normal goods are consumed.


(Sufficient when (1) also adds that the good is so inferior that the income effect is greater than the substitution effect.)

A Giffen good does not generate utility directly through its price. Contrast this to a Veblen good where there the user actually derives utility directly from the price.

See this link for some info about empirical evidence.