Can commutes be used to test the spatial mismatch hypothesis?

This paper uses a simple spatial model of urban employment to demonstrate that the relationship between spatial mismatch and commuting times is indeterminate if employment probabilities decline as the distance from job site to residence increases. Specifically, if employment probabilities decline faster (slower) than a threshold rate, then spatial mismatch will decrease (increase) the commuting times of central-city minorities. Thus, commuting-based tests of the spatial mismatch hypothesis are not just biased but mis-specified because spatial mismatch is theoretically consistent with both the null and alternative hypotheses. Evidence that this concern is empirically important is taken from the 'contradictory' findings of recent studies that use commutes to test the spatial mismatch hypothesis.