On the exhaustiveness of truncation and dropping strategies in many-to-many matching markets

We consider two–sided many–to–many matching markets in which each worker may work for multiple firms and each firm may hire multiple workers. We study individual and group manipulations in centralized markets that employ (pairwise) stable mechanisms and that require participants to submit rank order lists of agents on the other side of the market. We are interested in simple preference manipulations that have been reported and studied in empirical and theoretical work: truncation strategies, which are the lists obtained by removing a tail of least preferred partners from a preference list, and the more general dropping strategies, which are the lists obtained by only removing partners from a preference list (i.e., no reshuffling). We study when truncation / dropping strategies are exhaustive for a group of agents on the same side of the market, i.e., when each match resulting from preference manipulations can be replicated or improved upon by some truncation / dropping strategies. We prove that for each stable mechanism, truncation strategies are exhaustive for each agent with quota 1 (Theorem 1). We show that this result cannot be extended neither to group manipulations (even when all quotas equal 1 – Example 1), nor to individual manipulations when the agent’s quota is larger than 1 (even when all other agents’ quotas equal 1 – Example 2). Finally, we prove that for each stable mechanism, dropping strategies are exhaustive for each group of agents on the same side of the market (Theorem 2), i.e., independently of the quotas.

Small-area variation in health care affecting the choice of cesarean delivery: the case of a Colombian health insurer

In the midst of health care reform, Colombia has succeeded in increasing health insurance coverage and the quality of health care. In spite of this, efficiency continues to be a matter of concern, and small-area variations in health care are one of the plausible causes of such inefficiencies. In order to understand this issue, we use individual data of all births from a Contributory-Regimen insurer in Colombia. We perform two different specifications of a multilevel logistic regression model. Our results reveal that hospitals account for 20% of variation on the probability of performing cesarean sections. Geographic area only explains 1/3 of the variance attributable to the hospital. Furthermore, some variables from both demand and supply sides are found to be also relevant on the probability of undergoing cesarean sections. This paper contributes to previous research by using a hierarchical model and by defining hospitals as cluster. Moreover, we also include clinical and supply induced demand variables.