Local Average Treatment Effect Simulation

[Thanh Cong Gian]

Hi,

I would like to do the simulation for the Local Average Treatment Effect (LATE) using an instrumental variable (IV) as described in this lecture http://www.nber.org/WNE/lect_5_late_fig.pdf. For a simple setup of dummies W, Z and Y, It is quite straightforward to design a standard IV simulation. However, I'm trying to generate random sub-populations of never takers, the always takers and compliers and simulate the IV estimates from there. And after a quick search, I have never seen anyone do a simulation for a LATE estimate, especially in the case of heterogenous treatment effect model.

Any help is greatly appreciated

[Maarten Buis]

I am not sure what your question is, i.e. what you expect from us.

I can tell you that the process of creating such a simulation is very helpful in understanding the logic of these methods. That is for you probably the most useful part of the entire project. So, if you want to understand how these estimators work, what data generating process they assume, then that sounds like a reasonable and productive way to do it.

[wbuchanan]

Lee Adkins has some good examples available on different simulation studies that you may be able to use as a guide.

[Thanh Cong Gian]

Thank you for your posts. Perhaps I should be more specific. Below is the structural equation and the code I use for the simulation of IV

First stage eq.
di= dzi+v
outcome eq.
yi=beta0+ alphai*di+epsilon
set obs $numobs
global sigmaepsilon(100)
global sigmaz (100)
global sigmadistar (100)
global sigmaalphai(100)
global sigmav (100)
global beta0 100
global alpha0 100
global corzd (0.8)
global corze (0.0)
global corde (0.8)
gen nyui = rnormal(0,$sigmaalphai)
gen alphai = nyui+100
gen Vi = rnormal(0, $sigmav)

matrix corr = (1, $corde, $corze \ $corde, 1, $corzd \ $corze, $corzd, 1)
matrix sd = ($sigmaepsilon, $sigmadistar, $sigmaz)
drawnorm epsiloni distar Zi , n($numobs) sds(sd) corr(corr)
* BINARY Z
gen dZi = (Zi>0)
sum distar
gen di=(distar>0)
* Outcome eq.
gen yi= $beta0+ alphai*di + epsiloni

reg di dZi, robust
test dZi=0
scalar F = r(F)

ivregress 2sls yi (di=dZi), first robust
scalar ivorg = _b[di]
scalar ivseorg= _se[di]

* Always takers, never takers and compliers
reg distar dZi, robust
scalar fs = _b[dZi]
scalar coef= _b[dZi]
replace distar = coef*dZi+Vi
** Always takers
gen altak = 0
replace altak = 1 if Vi>=0
sum altak
scalar altak = r(mean)
** Never-takers
gen nevtak = 0
replace nevtak = 1 if Vi<-1*coef
sum nevtak
scalar nevtak = r(mean)
** Compliers
gen comp = 0
replace comp = 1 if Vi>=-1*coef & Vi<0
scalar comp= r(mean)

So I can have the compliers, never-takers and always-takers identified and the sizes of these groups depend on the instrument. so if I change z (or di) then the sizes will vary and I will get the IV estimates accordingly

However, I would like to create these subpopulations first. The intuition is that for a certain intervention/program and population, we sometimes are quite sure about whether a group of people will always take up the treatment, or never take up the treatment, both irrespective of the z. And also whether they comply with an inducement once there is a lottery, for instance. The bottom line is that I want to create these subpopulations first (maybe based on other information than z) and then vary the sizes of these subpopulations to get the IV estimates

Hope it makes sense. Appreciate any help