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st: VAR with Granger causal ordering


From   Karlygash Kuralbayeva <kkuralb@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   st: VAR with Granger causal ordering
Date   Fri, 4 May 2012 21:10:34 +0100

Dear all:

I need to estimate a VAR with strict exogeneity assumption (or Granger
causal ordering), where the first variable is strictly exogenous:
x(t) = x(t-1) + x(t-2) + error
y(t) = x(t) + x(t-1) + x(t-2) + y(t-1) + y(t-2) + z(t-1) + z(t-2) + error
z(t) = x(t) + x(t-1) + x(t-2) + y(t-1) + y(t-2) + z(t-1) + z(t-2) + error
Note that in 2nd and 3rd equations allows for contemporaneous effect
of x(t) on endogenous variables.
I use –svar- with constraints. Why do I get the error message that I
need more identification constraints? And why do years appear in the
error message against each constraint?
Many thanks for your help.

Here is the Stata code:
gen date=yq(year, q)
format date %tq
sort date
tsset date
constraint 1 [x]L.y = 0
constraint 2 [x]L2.y = 0
constraint 3 [x]L.y = 0
constraint 4 [x]L2.y = 0
matrix A = (1,0,0\.,1,0\.,0,1)
matrix B = (1,0,0\.,.,.\.,.,.)
svar x y z, aeq(A) beq(B) lags(1/2)

Error message:
With the current starting values, the constraints are not sufficient
for identification
The constraints placed on A and B are
 1992:  [a_1_1]_cons = 1
 1991:  [a_1_2]_cons = 0
 1990:  [a_1_3]_cons = 0
 1989:  [a_2_2]_cons = 1
 1988:  [a_2_3]_cons = 0
 1987:  [a_3_2]_cons = 0
 1986:  [a_3_3]_cons = 1
 1985:  [b_1_1]_cons = 1
 1984:  [b_1_2]_cons = 0
 1983:  [b_1_3]_cons = 0
These constraints place 10 independent constraints on A and B
The order condition requires at least 12 constraints.
Identification requires a rank of 18, but the identification matrix
only has rank 15
r(498);

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