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

• Applicant: Professor Dr. Alois Kneip
• Subject Area: Statistics and Econometrics
• Term: from 2017 to 2020
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 386140326

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.

• DFG Programme: Research Grants
• International Connection: France
• Cooperation Partner: Professor Dr. Valentin Patilea