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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.
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]
Lars Peter Hansen re-worked through the derivations and showed that it can be extended to general non-linear GMM in a time series context. [3] The Sargan test is based on the assumption that model parameters are identified via a priori restrictions on the coefficients, and tests the validity of over-identifying restrictions.
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.
If higher taxes do not induce people to quit smoking (or not start smoking), then variation in tax rates tells us nothing about the effect of smoking on health. If taxes affect health through channels other than through their effect on smoking, then the instruments are invalid and the instrumental variables approach may yield misleading results.
In statistics, the Bayesian information criterion (BIC) or Schwarz information criterion (also SIC, SBC, SBIC) is a criterion for model selection among a finite set of models; models with lower BIC are generally preferred.
Huber-White standard errors improve the efficiency of Liang-Zeger GEE in the absence of serial autocorrelation but may remove the marginal interpretation. GEE estimates the average response over the population ("population-averaged" effects) with Liang-Zeger standard errors , and in individuals using Huber-White standard errors , also known as ...
In statistics, the Wald test (named after Abraham Wald) assesses constraints on statistical parameters based on the weighted distance between the unrestricted estimate and its hypothesized value under the null hypothesis, where the weight is the precision of the estimate.