Demand Analysis for Matching Markets

将学生分配到他们所在地区的不同学校对学生的成绩和学生福利有重要影响。经济学中有大量的理论著作研究匹配市场的设计。包括纽约、芝加哥、波士顿、剑桥、丹佛和新奥尔良在内的几个学区采用了学生对学校选择进行排名的机制，并通过计算机算法将学生与学校进行匹配。一个类似的机制被用来分配住院医师的住院医师培训职位。设计和他们的实施是基于理论的见解，阿尔文E。2012年，罗斯和罗伊德·沙普利被授予诺贝尔奖。然而，对这些市场的实证研究却相对滞后。取得进展的一个重要障碍是方法问题，因为目前仍在使用的大多数机制并不能使代理人安全地报告他们的真实偏好。这一事实可能对学生福利和公平有重要影响。该研究的主要目标是开发新的方法，利用匹配市场的数据估计偏好模型，并将其应用于分析迄今为止在理论和经验上难以解决的政策相关问题。拟议的研究将开发一种新的方法，用于估计离散选择模型，该模型使用来自参与者没有动机报告其偏好的分配机制的报告偏好说实话以往的研究估计偏好在很大程度上被限制在特定的机构/理论特征支持处理报告的偏好作为真实的或具体的机制细节提供部分信息的偏好设置。我们的基线方法分析的信息是通过假设观察到的报告是最佳的。然后，我们分析放松这种强形式的理性，研究什么可以学到较弱的假设下代理的复杂性。方法分析包括研究两步估计的大样本特性，从文献中的需求模型扩展技术来研究模型的非参数识别，并比较计算方法来实现估计。作为应用，拟议的研究将研究马萨诸塞州剑桥的小学招生系统，该系统使用（旧）波士顿机制的变体，该机制容易被操纵。随后，我们计划比较不同假设下的偏好估计，以评估其对经济假设的敏感性。

The assignment of students to various schools in their district can have important implications for student achievement and student welfare. A large body of theoretical work in Economics studies the design of matching markets. Several school districts including New York, Chicago, Boston, Cambridge, Denver and New Orleans employ mechanisms in which students rank schooling options and a computerized algorithm matches students to schools. A similar mechanism is used to assign medical residents to residency training positions. The design and their implementation is based on theoretical insights for which Alvin E. Roth and Loyd Shapley were awarded the Nobel Prize in 2012. However, the empirical study of these markets is lagging. An important barrier to progress is methodological since most mechanisms still in use today do not make it safe for agents to report their true preferences. This fact may have important implications on student welfare, and fairness. The primary goal of the proposed research is to develop new methods for estimating preference models using data from matching markets, and apply them to analyze policy relevant questions that have been thus far theoretically and empirically intractable.The proposed research will develop a new method for estimating a discrete choice model using reported preferences from an assignment mechanism where participants do not have the incentive to report their preferences truthfully. Previous research estimating preferences has largely been limited to settings where particular institutional/theoretical features support treating reported preferences as truthful or specific details of the mechanism provide partial information on preferences. Our baseline approach analyzes information that is revealed by assuming that the observed reports are optimal. We then analyze relaxations of this strong form of rationality to study what can be learned under weaker assumptions on agents' sophistication. The methodological analysis involves studying large sample properties of a two-step estimator, extending techniques from the literature on demand models to study non-parametric identification of the model, and comparing computational methods for implementing the estimator. As an application, the proposed research will study the elementary school admissions system in Cambridge, MA that uses a variant of the (old) Boston mechanism, which is susceptible to manipulation. Subsequently, we plan to compare preference estimates under varying assumptions on the sophistication to assess their sensitivity to economic assumptions.