# Generalized method of moments

GMM
In econometrics and statistics, the generalized method of moments (GMM) is a generic method for estimating parameters in statistical models.wikipedia
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### Econometrics

econometriceconometricianeconometric analysis
In econometrics and statistics, the generalized method of moments (GMM) is a generic method for estimating parameters in statistical models.
When these assumptions are violated or other statistical properties are desired, other estimation techniques such as maximum likelihood estimation, generalized method of moments, or generalized least squares are used.

### Lars Peter Hansen

Lars P. HansenHansenLars Hansen
GMM was developed by Lars Peter Hansen in 1982 as a generalization of the method of moments, introduced by Karl Pearson in 1894.
Hansen is best known for his work on the Generalized Method of Moments, he is also a distinguished macroeconomist, focusing on the linkages between the financial sector and the macroeconomy.

### Estimator

estimatorsestimateestimates
The GMM estimators are known to be consistent, asymptotically normal, and efficient in the class of all estimators that do not use any extra information aside from that contained in the moment conditions.

### Method of moments (statistics)

method of momentsmethod of matching momentsmethod of moment matching
GMM was developed by Lars Peter Hansen in 1982 as a generalization of the method of moments, introduced by Karl Pearson in 1894.

### Arellano–Bond estimator

In econometrics, the Arellano–Bond estimator is a generalized method of moments estimator used to estimate dynamic panel data models.

### Maximum likelihood estimation

maximum likelihoodmaximum likelihood estimatormaximum likelihood estimate
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.

### Statistics

statisticalstatistical analysisstatistician
In econometrics and statistics, the generalized method of moments (GMM) is a generic method for estimating parameters in statistical models.

### Statistical parameter

parametersparameterparametrization
In econometrics and statistics, the generalized method of moments (GMM) is a generic method for estimating parameters in statistical models.

### Statistical model

modelprobabilistic modelstatistical modeling
In econometrics and statistics, the generalized method of moments (GMM) is a generic method for estimating parameters in statistical models. We assume that the data come from a certain statistical model, defined up to an unknown parameter θ ∈ Θ.

### Semiparametric model

semiparametricsemi-parametricsemi-parametric model
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.

### Expected value

expectationexpectedmean
These moment conditions are functions of the model parameters and the data, such that their expectation is zero at the parameters' true values.

### Norm (mathematics)

normEuclidean normseminorm
The GMM method then minimizes a certain norm of the sample averages of the moment conditions.

### Consistent estimator

consistentconsistencyinconsistent
The GMM estimators are known to be consistent, asymptotically normal, and efficient in the class of all estimators that do not use any extra information aside from that contained in the moment conditions.

### Efficient estimator

efficientEfficiencyefficient estimators
The GMM estimators are known to be consistent, asymptotically normal, and efficient in the class of all estimators that do not use any extra information aside from that contained in the moment conditions.

### Karl Pearson

PearsonPearson, KarlCarl Pearson
GMM was developed by Lars Peter Hansen in 1982 as a generalization of the method of moments, introduced by Karl Pearson in 1894.

### Nobel Memorial Prize in Economic Sciences

Nobel Prize in EconomicsNobel PrizeEconomics
Hansen shared the 2013 Nobel Prize in Economics in part for this work.

### Multivariate random variable

random vectorvectormultivariate
Suppose the available data consists of T observations {Y t } t = 1,...,T, where each observation Y t is an n-dimensional multivariate random variable.

### Parameter

parametersparametricargument
We assume that the data come from a certain statistical model, defined up to an unknown parameter θ ∈ Θ.

### Stationary process

stationarynon-stationarystationarity
A general assumption of GMM is that the data Y t be generated by a weakly stationary ergodic stochastic process.

### Ergodic process

ergodicergodicitynon-ergodicity
A general assumption of GMM is that the data Y t be generated by a weakly stationary ergodic stochastic process.

### Stochastic process

stochastic processesstochasticrandom process
A general assumption of GMM is that the data Y t be generated by a weakly stationary ergodic stochastic process.

### Independent and identically distributed random variables

independent and identically distributedi.i.d.iid
(The case of independent and identically distributed (iid) variables Y t is a special case of this condition.)

### Vector-valued function

vector functionvector-valued functionsvector
In order to apply GMM, we need to have "moment conditions", that is, we need to know a vector-valued function g(Y,θ) such that

### Parameter identification problem

identificationidentification problemidentified
Moreover, the function m must differ from zero for θ ≠ θ 0, otherwise the parameter θ will not be point-identified.

### Law of large numbers

strong law of large numbersweak law of large numbersBernoulli's Golden Theorem
By the law of large numbers, for large values of T, and thus we expect that.