Generalized Method of Moments :
Generalized Method of Moments (GMM) is a statistical estimation technique that uses a set of sample moments to estimate the parameters of a model. Unlike other methods such as the least squares method, GMM does not require the assumption of a specific functional form for the model. This makes it a flexible and powerful tool for analyzing a wide range of data.
One of the key advantages of GMM is that it can incorporate a variety of moment conditions, which allows for a more flexible and efficient estimation of the model parameters. In particular, GMM allows for the incorporation of both unconditional and conditional moments, as well as cross-sectional and time-series moments. This makes it possible to estimate a model that is more closely aligned with the underlying data.
For example, suppose we are interested in estimating the relationship between income and education. Using GMM, we could incorporate a variety of moment conditions that capture the different aspects of this relationship. This could include unconditional moments that capture the overall relationship between income and education, as well as conditional moments that capture the relationship between these two variables within different subgroups of the population.
Another advantage of GMM is that it allows for the incorporation of additional information, such as exogenous variables, into the estimation of the model parameters. For example, suppose we are interested in estimating the relationship between income and education, but we also want to control for the effects of other factors such as age and gender. Using GMM, we could incorporate these additional variables into the moment conditions, which would allow us to more accurately estimate the relationship between income and education.
Overall, GMM is a powerful and flexible tool for estimating the parameters of a statistical model. Its ability to incorporate a variety of moment conditions and additional information makes it well-suited for a wide range of applications.