Generalized Method of Moments
Introduction
The Generalized Method of Moments (GMM) is a statistical method used in econometrics, the branch of economics that applies statistical methods to economic data. GMM was developed by Lars Peter Hansen in 1982 and is used for estimating parameters of a statistical model. It is a flexible method that can be applied to a wide range of economic models.
Theoretical Background
The Generalized Method of Moments is based on the principle of Method of Moments, which involves equating sample moments to their theoretical counterparts. The GMM extends this principle by allowing the use of more moment conditions than the number of parameters to be estimated. This makes GMM particularly useful in situations where there are more moment conditions than parameters, also known as over-identified models.
Methodology
The GMM methodology involves three main steps:
1. Specification of the moment conditions: This involves identifying the moment conditions that the parameters of the model should satisfy. These conditions are derived from the assumptions of the model.
2. Formulation of the GMM estimator: This involves formulating an estimator that minimizes the distance between the sample moments and their theoretical counterparts. This is done by solving a minimization problem.
3. Evaluation of the GMM estimator: This involves evaluating the properties of the GMM estimator, such as its consistency and asymptotic normality. This is done using statistical theory.
Application
The Generalized Method of Moments has wide applications in econometrics. It is used in the estimation of dynamic models, panel data models, and models with instrumental variables, among others. It is also used in the testing of model specifications and the evaluation of model fit.
Advantages and Disadvantages
The main advantage of the GMM is its flexibility. It can be applied to a wide range of models and allows the use of more moment conditions than parameters. This makes it particularly useful in situations where there are more moment conditions than parameters.
The main disadvantage of the GMM is its complexity. The formulation and evaluation of the GMM estimator involve complex mathematical and statistical concepts. This makes the GMM difficult to understand and apply for those without a strong background in mathematics and statistics.