R Programming/Method of Moments

First, it is possible to estimate a simple linear model or a simple linear model with instrumental variables using the gmm() function. The GMM method is often used to estimate heteroskedastic instrumental variable models.

• Package gmm implements the generalized method of moment and the generalized empirical likelihood.

> # Simple linear model
> N <- 1000
> u <- rnorm(N)
> x <- 1 + rnorm(N)
> y <- 1 + x + u
> res <- gmm(y ~ x, x)

> # Simple linear model with instrumental variables.
> library(gmm)
> N <- 1000
> u <- rnorm(N)
> z <- rnorm(N)
> x <- 1 + z + u + rnorm(N)
> y <- 1 + x + u
> res <- gmm(y ~ x, z)
> summary(res)