  A locally compact groupoid is said to be exact if its associated reduced
crossed product functor is exact. In this paper, we establish some permanence
properties of exactness, including generalizations of some known results for
exact groups. Our primary goal is to show that exactness descends to certain
types of closed subgroupoids, which in turn gives conditions under which the
isotropy groups of an exact groupoid are guaranteed to be exact. As an initial
step toward these results, we establish the exactness of any transformation
groupoid associated to an action of an exact groupoid on a locally compact
Hausdorff space. We also obtain a partial converse to this result, which
generalizes a theorem of Kirchberg and Wassermann. We end with some comments on
the weak form of exactness known as inner exactness.
