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In econometrics and statistics, the generalized method of moments (GMM) is a generic method for estimating parameters in statistical models.Usually it is applied in the context of semiparametric models, where the parameter of interest is finite-dimensional, whereas the full shape of the data's distribution function may not be known, and therefore maximum likelihood estimation is not applicable.
The EM algorithm consists of two steps: the E-step and the M-step. Firstly, the model parameters and the () can be randomly initialized. In the E-step, the algorithm tries to guess the value of () based on the parameters, while in the M-step, the algorithm updates the value of the model parameters based on the guess of () of the E-step.
In econometrics, the Arellano–Bond estimator is a generalized method of moments estimator used to estimate dynamic models of panel data.It was proposed in 1991 by Manuel Arellano and Stephen Bond, [1] based on the earlier work by Alok Bhargava and John Denis Sargan in 1983, for addressing certain endogeneity problems. [2]
The estimator can be derived in terms of the generalized method of moments (GMM). Also often discussed in the literature (including White's paper) is the covariance matrix Ω ^ n {\displaystyle {\widehat {\mathbf {\Omega } }}_{n}} of the n {\displaystyle {\sqrt {n}}} -consistent limiting distribution:
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The identification conditions require that the system of linear equations be solvable for the unknown parameters.. More specifically, the order condition, a necessary condition for identification, is that for each equation k i + n i ≤ k, which can be phrased as “the number of excluded exogenous variables is greater or equal to the number of included endogenous variables”.