The (non) equivalence theorem when there are matching grants as well as lump sum grants

In developing their influential equivalence theorem Bradford and Oates (1971) implicitly assume that there is a lump sum grant only. This paper explores whether the equivalence result continues to hold when the lump sum grant is part of a program of grants-in-aid which includes a matching grant. It is shown that the equivalence results as stated by Bradford and Oates does not hold in these more general circumstances; however, a much weaker equivalence result does hold. This finding is important because there has been a tendency in the empirical literature to assume that the equivalence result holds under quite general circumstances. It is also shown here that the combined use of lump sum and matching grants can produce a reverse flypaper effect.