| 讲座简介： | This lecture deals with recent methodological developments in microeconometric analysis that treats unobserved heterogeneity in flexible ways. It emphasizes the direct use of preference orderings (e.g. revealed preference), which are potentially powerful in terms of dealing with unobserved heterogeneity in high-dimensions (Kitmaura and Stoye, 2013). We explore the approach based on preference orderings in details, though we also contrast it with other recently proposed nonparametric methods which often rely on smoothing techniques. The nonparametric methods discussed in the course require computation in high dimensions, and therefore we investigate their algorithmic aspects as well. As recognized in the recent literature, accounting for unobserved heterogeneity is tremendously important for applied microeconometric analysis (Compiani and Kitamura, 2015). In particular, it is highly desirable and often crucial to incorporate infinite dimensional heterogeneity in empirical research. This makes some of conventional nonparametric methods, which often demand monotonicity type restrictions and smoothness assumptions, difficult to apply. We pursue an alternative framework based on preference orderings. It enables us to avoid reliance of smoothness assumptions and other ad hoc restrictions on functional properties: it instead utilizes geometric properties (see, for example, Ziegler, 1995, Gruber, 2007 and Grunbaum, 2003 for geometric background) provided by economic theory. Another benefit is that implementing this approach typically requires only linear/quadratic programming, which can be carried out even in extremely high dimensions, and recent progress in computational methods can be used to execute them. Our approach is quite general and avoids arbitrary restrictions, and consequently we typically need to deal with partially identified objects. To that end, we briefly review basics of modern methods in partially identified models and moment inequalities. |
