Measure Frictional Sorting

This paper constructs an index to measure sorting in a two-sided market with matching friction. The index uses the cumulative distribution function (cdf) of the matching partners for each individual and incorporates matching failures as a mass point at the lowest type of the partners. The area between this cdf and the cdf in the efficient allocation without friction represents the reduction in sorting. The sorting index is equal to one minus the aggregate reduction in sorting normalized by the amount under uniform matching. In contrast to most measures of sorting in the literature, the sorting index captures the effect of matching failures and compares the matching partner's type with the ideal type instead of the individual's own type. Relative to this sorting index, the correlation coefficient of matched types tends to over-estimate sorting when sorting is positive. The over-estimation increases sharply when matching failures increase or when the market becomes more imbalanced.