"extra" inf eigenvalue

Perfect foresight simulations
1

I recently updated from dynare 4.5.7 to 5.4. In the simple Ramsey growth model I’m analyzing most things remain the same, but I’m puzzled by one difference. With 4.5.7 I got

EIGENVALUES:
         Modulus             Real        Imaginary

           0.949            0.949                0
           1.106            1.106                0

There are 1 eigenvalue(s) larger than 1 in modulus 
for 1 forward-looking variable(s)

while with 5.4 I get (for the same model specification)

EIGENVALUES:
         Modulus             Real        Imaginary

           0.949            0.949                0
           1.106            1.106                0
             Inf             -Inf                0

There are 2 eigenvalue(s) larger than 1 in modulus 
for 2 forward-looking variable(s)

It seems to me there’s only one “real” forward-looking variable, namely c, so I’m wondering where the extra infinite eigenvalue is coming from. The model spec is as follows

model;
// Resource constraint
y - A*x*k(-1)^alpha;
c + k - y - (1-delta)*k(-1);
s - (y-c)/y;
// Euler equation
c^(-sigma) - (1+theta)^(-1)*(A*alpha*x(+1)*k^(alpha-1) + 1 - delta)*c(+1)^(-sigma);
end;

Thanks for any enlightenment.

2

This must be about Dynare’s internal representation, which substitutes exogenous variables like x (I presume) with leads/lags in perfect foresight contexts, starting with Dynare 4.6. See Auxiliary variables · Wiki · Dynare / dynare · GitLab

Thus, x(+1) is internally another forward looking variable.

3

OK, thanks, that makes sense given the change in Dynare 4.6. x is indeed an exogenous variable.