GMMmenetelmiä

GMMmenetelmiä refers to a set of statistical methods collectively known as Generalized Method of Moments (GMM). This econometric framework is widely used for estimating parameters in statistical models when the traditional assumption of independent and identically distributed (i.i.d.) errors is violated, or when the model is not fully specified. GMM is particularly useful in situations involving endogeneity, where independent variables are correlated with the error term.

The core idea behind GMM is to use a set of moment conditions. These are equations that express the expected value of certain functions of the data and model parameters as zero. In essence, GMM finds parameter values that make the sample averages of these functions as close to zero as possible. This is achieved by minimizing a quadratic form of the sample moment conditions, weighted by a chosen matrix. The optimal weighting matrix is one that minimizes the variance of the estimator.

GMM offers a flexible approach to estimation. It does not require the full specification of the data-generating process, only that the moment conditions are valid. This makes it robust to certain types of misspecification. Different choices of moment conditions lead to different GMM estimators, such as the basic GMM, efficient GMM, and continuous-updated GMM. The method is widely applied in various fields, including finance, economics, and econometrics, for estimating models of asset pricing, consumption behavior, and macroeconomic dynamics.