Some current topics in conditional moment equations models: generated regressors, unknown nuisance functions and panel data

经济学中的模型通常是由条件矩条件定义的。到目前为止，这类模型最常用的估计方法是GMM。在过去的几十年里，已经开发了几个新的估计程序，试图纳入更多的条件矩条件下的信息，以避免识别的损失，这是使用GMM时产生的一个主要风险。此外，一些新的模型在矩条件下引入了未知的干扰函数，这类模型需要特定的半参数估计方法。在条件矩模型中，大多数用于估计和推断的现代方法需要用户选择的调整参数，而这些参数对估计的影响仍未被广泛研究。由于预期的重要性和确定经济关系的不确定性的影响，在经济模型中使用生成的回归变量的情况有所增加。产生的回归变量的例子是个人对价格或通货膨胀形成的预期。如果在模型中使用这些变量，则需要在第一步估计这些量，因此它们是存在一定误差的随机变量。我们面临的挑战是在存在未知函数部分和生成的回归变量的情况下，研究由条件矩条件识别的模型中的所谓SmoothMD估计量。该估计器基于一个保证辨识的无条件矩方程。通过将SmoothMD与生成的回归变量和未知的函数形式相结合，我们还提出了更高程度的洞察用户选择的参数在这些模型中的影响。SmoothMD中最初使用的无条件矩方程包含一个需要估计的未知仪器函数。它可以通过使用可能的数据驱动用户选择的参数进行平滑来估计，或者通过对应于固定的用户选择的平滑参数的简单经验平均值来估计。因此，原则上，该方法允许控制估计仪器功能所需的用户选择的参数的影响。此外，我们希望将SmoothMD估计扩展到面板数据模型。到目前为止，SmoothMD不允许将面板数据集作为I.I.D.假设是强加的。由于面板数据的可获得性越来越强，并且可能包含比横截面或时间序列数据集更多的信息，我们认为将SmoothMD扩展到此类模型是有价值的。方法论的发展将以一个重要的应用为指导。我们计划研究当一些回归变量是内生的，并且内生回归变量与因变量之间的函数关系不完全已知时，回归变量对某些结果变量的影响。这是一种半参数工具变量方法。我们认为这很有趣，因为IV估计在计量经济学中经常被使用，而且非线性关系越来越多地被考虑。

Models in economics are frequently defined by conditional moment conditions. By far the most popular estimation method for this kind of models is GMM. Over the last decades several new estimation procedures have been developed that try to incorporate more of the information entailed in conditional moment conditions in order to avoid the loss of identification, a major risk incurred when using GMM. In addition, some of the new models introduce unknown nuisance functions in the moment conditions, and such models require specific semiparametric estimation methods. Most of the modern methods used for estimation and inference in conditional moment equations models require user-chosen tuning parameters whose influence on the estimates remains widely unexplored. Due to the importance of expectations and the impact of uncertainty in the determinationof economic relationships the use of generated regressors in economic models has increased. Examples of generated regressors are expectations formed by individuals for prices or inflation. If these variables are used in the model the quantities need to be estimated in a first step and are, thus, random variables available with some error.The challenge we face here is to study the so-called SmoothMD estimator in models identified by conditional moment conditions in the presence of unknown functional parts and generated regressors. This estimator is based on one unconditional moment equation that guarantees identification. By combining SmoothMD with generated regressors and unknown functional form, we also propose to get a higher degree of insight into the influence of user-chosen parameters in these models. The unconditional moment equation initially used in SmoothMD contains an unknown instrument function that has to be estimated. It could be estimated by smoothing with possibly a data driven user-chosen parameter, or by a simple empirical mean, which corresponds to a fixed user-chosen smoothing parameter. Hence, in principle the method allows to control for the influence of the user-chosen parameter required to estimate the instrument function. In addition, we want to extend SmoothMD estimation to panel data models.So far SmoothMD does not allow for panel data sets as an i.i.d. assumption is imposed. As panel data is more and more available and may contain more information then cross-sectional or time series data sets, we consider the extension of SmoothMD to such models as valuable. The methodological development well be guided by an important application. We plan to study the influence of regressors on some outcome variable when some regressors are endogenous and the functional relationship between the endogenous regressors and the dependent variable is not completely known. This is a semiparametric instrumental variable approach. We consider this as interesting as IV estimation is frequently employed in econometrics and nonlinear relationships are considered more and more often.