I've got a bunch of questions about <xtabond>. I apologize for the long
email, but if you are v. familiar with <xtabond> and have a few extra
minutes, I'd really appreciate any input.
Consider a simple model where x(t) is endog:
y(t) - y(t-1) = a[y(t-1) - y(t-2)] + b[x(t-1) - x(t-2)] + u(t) - u(t-1)
(Notice that unlike the example in the manual, I use lagged diff's of
the x's.)
I start out with 4 obs per person. So I am left w/ 2 obs for each person
once I've taken lagged differences.
1) I thought that <xtabond> would run the following 4 regressions in the
first stage:
y2-y1 = a * y1 + b * x1 --> predict y2-y1
x2-x1 = a * y1 + b * x1 --> predict x2-x1
y3 - y2 = a * y1 + b * y2 + c * x1 + d * x2 --> predict y3 - y2
x3 - x2 = a * y1 + b * y2 + c * x1 + d * x2 --> predict x3 - x2
Then I thought it would use those predictions in the second stage to
estimate the first eqn above. When carry out these steps manually,
however, I don't get the same results as when I just use <xtabond>. The
code for using <xtabond> would look like this:
ge x_lag = L.x
xtabond y, pre(x_lag, endog)
Which part of what <xtabond> am I misunderstanding?
2) If x(t) is predetermined instead of endog in my model, there is no
need to instrument for x(t-1) - x(t-2). Will Stata know this?
3) It seems reasonable to me that if I have only 1 obs per person, then
<xtabond> is equivalent to using <ivreg>. I tested this by dropping my
y4 observations. The only equation I have to estimate then is:
y3-y2 = a(y2-y1) + b(x2-x1) + (u3-u2)
I was able to run <ivreg> just fine, but <xtabond> dropped my x variable
from the estimation. I think this has to do with the fact that the
Sargan DF = -1, but I don't know why this matters.
e(df_m) = 3
e(zcols) = 2
e(sar_df) = -1
As I understand it, e(zcols) is the total # of vars used to instrument
for y2-y1 & x2-x1 and e(df_m) is the total # of parameters (y2-y1,
x2-x1, & _cons).
If you've read this far and have any input, thanks v. much for taking
the time.
