New Nonparametric Methods in Instrumental Variable Models

拟议研究项目的目标是为内生数据的非参数分析开发新的统计方法。非参数方法变得相当重要，因为由于技术进步，计量经济学中可获得的数据集越来越大。另一方面，人们往往希望以一种内生的方式对经济关系进行建模，以解释不可观察到的因果结构。研究项目分为以下几个部分：第一个目标是开发一个测试程序，在数据丢失的情况下检测内生选择。测试是基于与数据相关的工具，而不是与选择机制相关的工具。特别是，计划将该方法应用于调查数据集。第二个目标是发展新的内生回归模型的非参数检验和估计方法。在这里，我们寻求结构关系的部分信息的最优估计，如其平均值。此外，我们希望开发一个测试程序来证明模型简化是合理的，这完全是数据驱动的，不依赖于未知的总体参数。最后，我们着重于开发置信带，以图示估计的结构与其统计误差的关系。

The objective of the proposed research project is the development of new statistical methods for nonparametric analysis of endogenous data. Nonparametric methodology has gained considerable importance since, due to technical progress, increasingly larger data sets are available in econometrics. On the other hand, it is often desirable to model economic relationships in an endogenous way to account for unobservable causal structures. The research project is divided into the following parts: The first goal is to develop a testing procedure to the detect endogenous selection in case of missing data. The test is based on instruments which are correlated to the data but not to the selection mechanism. In particular, an application of this method to survey data sets is planned. The second aim is to develop new nonparametric test and estimation methods in endogenous regression models with instruments. Here, we pursue an optimal estimator for partial information of the structural relationship such as its average value. In addition, we want to develop a testing procedure to justify model simplification, which is completely data driven and does not rely on unknown population parameters. Finally, we focus on the development of confidence bands for the graphical illustration of the estimated structural relationship with its statistical error.