Let $e$ denote the base of the natural logarithm. The value of the real number $a$ for which the right hand limit
$$\lim _ { x \rightarrow 0 ^ { + } } \frac { ( 1 - x ) ^ { \frac { 1 } { x } } - e ^ { - 1 } } { x ^ { a } }$$
is equal to a nonzero real number, is $\_\_\_\_$