Dear Professor,

I have a simple AR type model were I introduce a contemporary and a lagged shock.

This is just one equation model: `0.9*a = 0.2*a(-1) + 0.1*a(+1) + 0.3*e - 0.4*e(-1)`

Dynare internally produces two equations where the second equation relates exogenous shocks with lags.

The equations matrix is:

```
jacobia =
0.4 -0.2 0 0.9 -0.1 -0.3
0 0 1 0 0 -1
```

I guess the unknowns are [e1, a(-1), . ,a ,a(+1), e2; 0, 0, e1(+1), 0, e2].

Here e1 = e(-1), e2 = e and jacobia is a Jacobian matrix passed to “dyn_first_order_solver.m” function.

Why an additional equation for shocks e1,e2 is introduced? Obviously, e1(+1) = e = e2.

Is this setting equivalent to a shock of 0.3 at period 1 and -0.4 at period 2?

When I run simulations without this additional equation by LBJ method (perfect foresight),

I am getting different results than when assuming this identity equation.

The lagged (A), contemporaneous(B) and lead (C) matrices are:

A =

0.4 -0.2

0 0

B =

0 0.9

1 0

C =

-0.1

0

The corresponding variables are: [e1,a(-1)]; [e2,a], and [e1(+1),a(+1)].

Should matrices B, C read?

B =

-0.3 0.9

1 0

C =

0 -0.1

-1 0

Thank you,

Alexei

```
var a;
varexo e;
model(linear);
0.9*a = 0.2*a(-1) + 0.1*a(+1) + 0.3*e - 0.4*e(-1);
end;
shocks;
var e;
stderr 1;
end;
stoch_simul(irf=7,graph);
```