Forward looking & predetermined variables

Stochastic simulations
1

Dear all,

I’m very new to both Dynare and econometrics, but have some experience in
computer science and dynamic programming.
Regarding the use of Dynare, I have two very simple questions:
(I read the recommended topics of “martom - Feb 1, 2006, and bigbigben - Sept 28, 2006”
but didn’t get a clear answer)

  1. I am very confusing about “forward-looking variables” vs. “predetermined variables”.
    It seems to me that the statement,

x(t+1) = Ax(t) + b, (x is forward-looking)

is exactly the same as

x(t) = Ax(t-1) + b. (x is predetermined)

Then, in Dynare how can I know that my variables are forward looking or predetermined?
Unfortunately, I couldn’t find clear definitions about these types of variables.

  1. This is related to the first question. I want to model the simplest demand-supply equations.
    Here, I have 3 endogenous variables: Price, Qdemand & Qsupply and 2 exogenous variables, shock1 & shock2;

Qdemand = Qsupply;
Qdemand = 200 - 5Price + shock1;
Qsupply = 25 + 12.5Price + shock2;

Now, Dynare requires me to specify at least 1 forward-looking variable & 1 pre-determined variable; what is the proper way to
specify the time indices in this simplest model? In order to make it work, I specify the time indices as follows:

Qdemand = Qsupply;
Qdemand = 200 - 5Price(-1) + shock1;
Qsupply(+1) = 25 + 12.5Price + shock2;

This works fine, but it seems to me quite ad-hoc since Qdemand and Qsupply now are of different types.
Does anyone have any suggestions? I’m very new to this.

Thanks and Kind Regards,
Ratthachat Chatpatanasiri

2

  1. The difference between “forward-looking variables” vs. “predetermined variables” has to do with conditional expectations. In your example, Dynare treats the statement
    x(t+1) = Ax(t) + b, (x is forward-looking) as E_t x(t+1) = Ax(t) + b.
    In contrast, in x(t) = Ax(t-1) + b. (x is predetermined), you could also add an conditional expectation at time t, but it would be redundant. Due to this conditional expectations operator, both statements are not (!) the same.

  2. I am not sure if Dynare is the right application to solve static problems like the one you mention. I guess your code should look like this:

var Qdemand Qsupply Price;
varexo shock1 shock2;

model;
Qdemand = Qsupply;
Qdemand = 200 - 5*Price + shock1;
Qsupply = 25 + 12.5*Price + shock2;
end;

shocks;
var shock1; stderr 0.01;
var shock2; stderr 0.01;
end;

stoch_simul(order=1);

Of course, you get an error message, when autocovariances are computed, which is natural as there is no intertemporal link in your model.

3

Dear jpfeifer,
Thank you very much for your kind answers. Those did help. :smiley:
Ratthachat