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

这项研究项目包括五个不同的主题。第一个研究为具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独立于潜在结果的二元辅助变量(IV)的模型的平均治疗效果(ATE)开发了新的治疗效果界限。由于治疗效果的异质性，ATE尚未确定。该研究通过首先考虑治疗效果分布为二元分布的情况，发展了利用独立性条件和IV限制的ATE的界限。对于任意的治疗效果分布，这个界限是成立的。这些界明确地依赖于IV估计量的概率极限，并且具有简单的形式，有利于推断。强加的假设既不比目前文献中考虑的更强，也不比目前认为的更弱。第二部分建立了确定性时变自回归(AR)模型，该模型可能表现出(局部)非平稳性或平稳性以及两者之间的平稳过渡。PI考虑了在时间域中通过非参数平滑来估计参数。在(局部)非平稳的情况下，减小由于时变参数引起的偏差的标准方法不起作用。因此，需要引入新的减少偏差的方法。另一个需要解决的重要问题是局部平滑估计器初始条件的内生性，它由AR系数和的时变路径决定。PI分析评估、测试、CS构建和预测的方法。他还开发了时变参数存在的测试。这项研究将提供一种考虑时变非平稳性/平稳性的有用的新的时间序列模型。第三，他发展了对矩条件模型中的弱辨识和辨识失败具有鲁棒性的推理方法。一些现有的方法使用了条件似然比(CLR)检验和CS检验，这些检验推广了Moreira(2003)对于线性IV回归模型的CLR检验。已有的方法(I)当参数的维度大于或等于2时不一定具有正确的渐近大小，(Ii)在线性IV模型中不退化为已知具有最优功率特性的Moreira？S CLR检验。PI引入了新的CLR型程序，但没有这些缺陷。最后两个研究领域是部分辨识模型的推理，这些模型是由无穷多个条件矩的非线性函数的不等式限制和弱辨识或缺乏辨识下的拉格朗日乘子检验定义的。这项研究为社会科学数据的统计分析开辟了新的方法。该项目将使社会受益，因为它将提高用于各种重要问题的数据分析的质量。这些方法将对经济政策分析有用，但也将被分析具有类似统计特征的数据的医学和工程研究人员使用。

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.