Advances in Econometrics for Treatment Effect Bounds, Time-Varying-Parameter Nonstationary/Stationary Autoregressive Models, and Identification-Robust Inference

该研究项目包括五个不同的主题。 第一个开发新的治疗效果边界的平均治疗效果（ATE）的模型中有两个连续或离散的潜在结果变量，一个二元治疗变量，和一个二元工具变量（IV）是独立的潜在结果。由于治疗效应异质性，未确定ATE。该研究开发的ATE，利用独立条件和IV限制的范围，首先考虑的情况下，治疗效果分布是二进制的。 该界限适用于任意的治疗效果分布。 该界显式地依赖于IV估计的概率极限，并且具有简单的形式，这有利于推断。所施加的假设既不强也不弱于目前在文献中考虑的。 结果适用于经济学中的治疗效果分析和不完全compliance. Second部分的医疗随机试验的分析开发确定性时变自回归（AR）模型，可以表现出（局部）非平稳性或平稳性和两者之间的平滑过渡。PI考虑通过时域中的非参数平滑来估计参数。标准的方法，减少偏差，由于随时间变化的参数失败的（局部）非平稳的情况下。因此，将需要引入新的偏差减少方法。另一个需要解决的重要问题是局部平滑估计的初始条件的内生特性，这是由AR系数之和的时变路径确定的。PI分析用于估计、测试、CS构建和预测的方法。他还开发了测试随时间变化的参数的存在。这项研究将提供一个有用的新的时间序列模型，允许随时间变化的非平稳性/stationarity.Third，他开发的推理方法，是强大的弱识别和识别故障的时刻条件模型。几种现有的方法采用条件似然比型（CSTR）检验和CS，将Moreira（2003）的CSTR检验推广到线性IV回归模型。现有的程序（i）不一定有正确的渐近尺寸时，尺寸的参数是两个或更多，（ii）不减少莫雷拉？s检验的线性IV模型，这是已知的具有最佳的功率特性。PI引入了新的CLR类型的程序，没有这些缺陷。最后两个领域的研究是在部分识别模型的推理，定义的非线性函数的无限多个条件矩和拉格朗日乘子测试下的弱识别或缺乏识别的不等式限制。本研究为社会科学数据的统计分析开拓了新的方法。 该项目将造福社会，因为它将提高用于各种重要问题的数据分析的质量。 这些方法将有助于经济政策分析，但也将用于医学和工程研究人员分析具有类似统计特征的数据。

This research project includes five different topics. The first develops new treatment effect bounds for the average treatment effect (ATE) in models with two continuous or discrete potential outcome variables, a binary treatment variable, and a binary instrumental variable (IV) that is independent of the potential outcomes. The ATE is not identified due to treatment effect heterogeneity. The research develops bounds on ATE that exploit the independence condition and an IV restriction by first considering the case where the treatment effect distribution is binary. The bounds hold for arbitrary treatment effect distributions. The bounds depend explicitly on the probability limit of the IV estimator and are of a simple form, which is conducive to inference. The assumptions imposed are neither stronger nor weaker than those currently considered in the literature. The results are applicable to treatment effect analysis in economics and to the analysis of medical randomized trials with incomplete compliance.The second portion develops deterministically time-varying autoregressive (AR) models that may exhibit (local) nonstationarity or stationarity and smooth transitions between the two. The PI considers estimation of the parameters by nonparametric smoothing in the time domain. Standard methods of reducing bias due to the time-varying parameters fail in the (locally) nonstationary case. Hence, new bias reduction methods will need to be introduced. Another important issue to be addressed is the endogenous character of the initial conditions for the local smoothing estimator, which are determined by the time-varying path of the sum of the AR coefficients. The PI analyzes methods for estimation, testing, CS construction, and forecasting. He also develops tests for the presence of time-varying parameters. This research will provide a useful new time series model that allows for time-varying nonstationarity/stationarity.Third, he develops inference methods that are robust to weak identification and identification failure in moment condition models. Several existing methods employ conditional likelihood ratio-type (CLR) tests and CS's that generalize the CLR test of Moreira (2003) for the linear IV regression model. Existing procedures (i) do not necessarily have correct asymptotic size when the dimension of the parameter is two or greater and (ii) do not reduce to Moreira?s CLR test in the linear IV model, which is known to have optimal power properties. The PI introduces new CLR-type procedures that do not have these deficiencies.The last two areas of research are on inference in partially-identified models that are defined by inequality restrictions on nonlinear functions of infinitely-many conditional moments and Lagrange multiplier tests under weak identification or lack of identification. This research develops new methods for the statistical analysis of social science data. The project will benefit society because it will improve the quality of data analysis used for a variety of important questions. These methods will be useful for economic policy analysis but will also be used by medical and engineering researchers who analyze data with similar statistical features.