I am currently running a project using RDD in STATA where I am unable to use the handy "rdrobust" command, and hence have to use the conventional "regress" function instead, i.e., OLS. However, despite my best efforts, I have been unsuccessful to really find if I have understood the estimation of LATE correctly.
In this, I first run a restricted OLS on the values closest to the treatment point, $c_0$, i.e., $c_{-1}$, versus $c_{+1}$ as follows:
$Y_{it}$= $\alpha_0$ + $\beta_1$X + $D_1Treatment$+ $\varepsilon_{it}$
where $Treatment=1$ for $c_1$>$c$
First question: Am I correct to assume that this corresponds to LATE? Since the window is as small as possible, this should minimize the bias, right?
Second question: I also estimate local polynomials on the treatment with a slightly larger window, including the three closest values to $c_0$, i.e., $c_{-3}$, $c_{-2}$, $c_{-1}$, as well as $c_{+1}$, $c_{+2}$, $c_{+3}$ in the following two OLS regressions:
$Y_{it}$=$\alpha_0$ + $\beta_1X$+$(Untreated*C_{-3,-2,-1})$+$(Untreated*C_{-3,-2,-1}^2$) +$\varepsilon_{it}$
and, correspondingly
$Y_{it}$=$\alpha_0$ + $\beta_1X$+$(Treated*C_{1,2,3})$+$(Treated*C_{1,2,3}^2$) +$\varepsilon_{it}$
Where C contains the values of the running variable in the pre-, versus post-period.
I then estimate the LATE as: $\tau=E[Y|x,c>0]-E[Y|x,c<0]$
Is this correct? I am currently a bit stumped on documentation on how to do this "manually", and I am at my wits end trying to find answers through Google.
Any bit of help would be greatly appreciated.
Sincerely Johan