Simulation-based multiple inference problems: theory and application

计量经济学家经常同时面临许多需要考虑的推理问题。虽然相关问题并没有被完全忽视，但最近的批评性评论表明，对这些问题的关注并不普遍，特别是在观察性研究中。这个程序考虑了基于模拟的测试和推理问题，重点是不等式分析。

Econometricians are often presented with many inference problems to consider at the same time. While related problems are not completely overlooked, recent critical reviews reveal that attention to these issues is not ubiquitous particularly in observational studies. This program considers combined simulation-based testing and inference problems, with focus on inequality analysis. Increasingly common statistical tools now involve simulation methods. With reference to the existing literature on the statistical validity of such methods, formal works on combined methods are relatively scarce. Methodologically, this proposal will also contribute to this literature. Research on inequality, including work by Nobel laureate Simon Kuznets, has a long history in the discipline. Timely questions popularized by e.g. Thomas Piketty have shaken the discipline worldwide. This proposal aims to develop and validate concrete statistical tools towards evidence-based inequality analysis, building on the fact that inequality measures are multi-dimensional, conceptually and definitionally. A wide range of such measures [e.g. the generalized entropy and Gini indexes, quantile ratios] involve nonlinear transformations of moments or quantiles. Whether estimated jointly or individually, parametrically or non-parametrically, with just one or using several variables, definitional non-linearities have non-trivial implications on the statistical properties of associated estimators and test statistics. Conflict among test criteria on inequality is also prevalent, and inference remains a challenging problem because underlying distributions have heavy tails. In this context, this research program aims to address the following questions. Is it legitimate from an error control perspective to apply existing and popular statistical methods for multi-criteria-based inference approach to inequality? Which error rate principles and combination methods will deliver reliable and policy relevant inference? Can existing validity conditions for simulation-based methods be verified or eventually extended for this purpose? I intend to propose and validate a concrete strategy for combined testing and simultaneous inference on a vector of measures, as well as a formal policy-relevant analysis on the concrete choice between combination and separation of the inference problems. Important features of the proposed methodology address nuisance parameters in locally identified and identification-robust contexts. In addition to testing, my research program will yield simultaneous confidence sets for objects of interest. Moments and quantile-based measures will differ importantly with respect to asymptotic and finite sample considerations. Distribution-free methods will be proposed for using quantiles, whereas parametric methods will embed distributional fit. As more and more measures may be combined, robustness to dimensionality will be considered.