Dear All,
I am estimating a multilevel (hierarchical) linear model using PROC MIXED. In simplified form (omitting subscripts and most independent variables), the model is
Y = b0 + b1 X1 + b2 X2 + u + e
where u denotes random effects and e error terms.
The SAS code is as follows:
proc mixed data=mydata;
class i j k m;
model Y = X1 X2 m/ ddfm=bw ;
random intercept /subject=j type=vc;
random intercept /subject=k type=vc;
random intercept /subject=j*k type=vc;
random intercept /subject=i(j*k) type=vc;
run;
I suspect that Y and X1 are endogenous because they are simultaneously determined. However, X2 is exogenous. My questions are:
1. How do I test if Y and X1 are endogenous? I know that there are endogeneity tests in PROC QLIM and other procedures, however, I am not sure how to add random effects in these procedures. Could I use these endogeneity tests without random effects?
2. Should I test for correlation between X1 and e only? Or should I also test for correlation between X1 and u (random effects)?
3. If I were to estimate the following system of equations using 2SLS in PROC SYSLIN, would I have to still worry about endogeneity?
Eq.1 Y = b0 + b1 X1 + b2 X2 + u + e1
Eq.2 X1 = c0 + c2 X2 + c3 Z + v + e2
where Z is an instrumental variable, u and v are random effects and e1 and e2 are errors terms.
4. If yes, how do I include random effects in PROC SYSLIN?
Any and all responses will be greatly appreciated. Many thanks in advance!
Sincerely,
Cuneyt
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