The behavior of exact tests for homogeneity (F and Hotelling T-2) is c
ompared with size-adjusted LR tests in the linearized AIDS model with
different approximating price indexes (Stone, Paasche, Laspeyres). The
Monte Carlo evidence shows that test size distortions are sensitive t
o the correlation structure of prices, the time-series properties of t
he data, and the choice of price index. None of the results explains t
he persistent over-rejection of homogeneity in applied work.