Market efficiency and the pricing kernel are closely related. A non-monotonic decreasing pricing kernel implies the existence of a trading strategy in contingent claims that stochastically dominates a direct investment in the market. Moreover, a market is assumed to be efficient only if no dominating strategies exist. Empirically, many studies of the pricing kernel find non-monotonicity, apparently ruling out market efficiency. However, these results are often unreliable, because the pricing measures of the pricing kernel are estimated using differing filtration sets. We show this effect both theoretically and empirically, and we discuss recent approaches in the literature for achieving more reliable estimates of the pricing kernel, potentially leading to better tests of market efficiency.