## Sunday, August 12, 2012

### Mata: program your own IV Estimator

* Mata: program your own IV Estimator

* First let see how we could program an IV estimator without matrices.
version 11

clear
set obs 1000

gen z = rnormal()

gen u= rnormal()

gen x = u + z + rnormal()

gen y = 2 + 2*x + 15*u

reg y x

foreach v in x y z {
foreach vv in x y z {

gen `v'`vv' = `v'*`vv'
qui sum
local `v'`vv' = r(mean)*r(N)
}
}

di "IVhat = " (`xz'*(`zz')^-1*`zx')^-1 * (`xz'*(`zz')^-1*`zy')

ivreg y (x=z)
* Looks pretty close.  However, there is some divergence due to the above estimator not allowing for a constant.

ivreg y (x=z), nocon

* Now let's see how to do it in Mata.

mata

x = st_data(.,("x"))
z = st_data(.,("z"))
y = st_data(.,("y"))

IVhat1 = invsym((x'*z)*invsym(z'*z)*(z'*x))*(x'*z)*invsym(z'*z)*(z'*y)

"IV estimate without constant"
IVhat1

"Create a constant vector of length x"
cons = J(rows(x), 1, 1)

X = (x, cons)
Z = (z, cons)

IVhat2 = invsym((X'*Z)*invsym(Z'*Z)*(Z'*X))*(X'*Z)*invsym(Z'*Z)*(Z'*y)

"IV estimate with constant"
IVhat2

end
* End is necessary with mata do files to indicate when the mata subsystem is completed.