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由条件矩条件定义。迄今为止，这类模型的最流行的估计方法是GMM。在过去的几十年中，一些新的估计程序已被开发，试图纳入更多的信息，在条件矩条件，以避免损失的识别，使用GMM时产生的主要风险。此外，一些新的模型在矩条件下引入了未知的滋扰函数，这类模型需要特定的半参数估计方法。大多数用于条件矩方程模型中的估计和推断的现代方法需要用户选择的调谐参数，其对估计的影响仍然广泛未被探索。由于预期的重要性和不确定性的影响，在determinationof经济关系的使用生成的回归模型已经增加.生成的回归量的例子是个人对价格或通货膨胀的预期。如果这些变量在模型中使用的数量需要估计在第一步，因此，随机变量与一些error.The挑战，我们在这里面临的是研究所谓的SmoothMD估计在模型中确定的条件矩条件下存在未知的功能部件和生成的回归。这个估计是基于一个无条件的时刻方程，保证识别。通过将SmoothMD与生成的回归量和未知函数形式相结合，我们还建议更深入地了解这些模型中用户选择的参数的影响。SmoothMD中最初使用的无条件矩方程包含一个未知的工具函数，必须进行估计。它可以通过可能使用数据驱动的用户选择的参数进行平滑来估计，或者通过简单的经验平均值来估计，该平均值对应于固定的用户选择的平滑参数。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参数的影响。另外，我们希望将SmoothMD估计扩展到面板数据模型，目前SmoothMD还不允许将面板数据集作为独立同分布。假设是强加的。随着面板数据越来越可用，并且可能包含更多的信息，然后横截面或时间序列数据集，我们认为SmoothMD扩展到这些模型是有价值的。该方法的发展很好地由一个重要的应用程序来指导。我们计划研究的回归变量对一些结果变量的影响时，一些回归变量是内生的，内生回归变量和因变量之间的函数关系是不完全已知的。这是一种半参数工具变量方法。我们认为这是有趣的，因为IV估计在计量经济学中经常使用，并且越来越多地考虑非线性关系。

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.