st: Qustion about a state space model

[Masafumi Yabara <m.yabara@gmail.com>]

Dear Stata members,

I'm trying to run a state space model as below to see the trend of
stock market integration, following the literature on the subject
(e.g., I.-W. Yu et al./Journal of Banking & Finance 34 (2010) 2874-2885).

Signal equation: ln Rt - ln St = At + Bt (ln Rt - ln Gt) + error1(t)
State equation 1: At = A(t-1) + error2(t)
State equation 2: Bt = B(t-1) + error3(t)

where Rt: equity market index level of a dominant regional market (in
my case, Kenya) at time t
St: equity market index level of a country of interest (in my case,
Tanzania) at time t
Gt: equity market index level of a dominant external market (in my
case, US) at time t.

My question is, how I can construct the model in STATA, because my
model did not run.

Here are what I did.
I typed the following commands in STATA.
The variables "nsetse" and "nseiundu" correspond to "ln Rt - ln St" and
"ln Rt - ln Gt" in the signail equation above, respectively.

. constraint 1 [u1]L.u1 = 1
. constraint 2 [u1]e.u1 = 1
. constraint 3 [u2]L.u2 = 1
. constraint 4 [u2]e.u2 = 1
. constraint 5 [nsetse]u1 = 1
. constraint 6 [nsetse]u2 = nseindu
. constraint 7 [nsetse]e.nsetse = 1
.
. sspace (u1 L.u1 e.u1, state noconstant) ///
>           (u2 L.u2 e.u2, state noconstant) ///
>           (nsetse u1 u2 e.nsetse, noconstant), constraints(1/7)

Then I got the following error messages, and could not solve it
although I modified the scales of the variables and tried different
techniques (options) and a number of different settings.

(note: constraint number 6 caused error r(111))
searching for initial values .
(setting technique to bhhh)
Iteration 0:   log likelihood = -284.60372
......
(switching technique to nr)
Iteration 5:   log likelihood = -282.73863  (backed up)
optimization terminated because of numerical instability:
Hessian is not negative semidefinite r(430);

The tricky part of the model is, to me, that an unobserved state (Bt) is
multiplied by an independent variable (ln Rt - ln Gt) in the signal equation.
As a matter of fact, the result says the constraint No.6 is causing errors.
I guess my way of constructing the model is wrong, but I can't figure out
how I can resolve the problem.
Any advise and suggestion are very much appreciated.

Thank you so much in advance for your help.

Best regards,

Masafumi Yabara
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