# 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.