I want to get the transition path for initial TFP process (exogenous variable) with 0<rho<1:
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z = rho*z(-1);
when the process changes permanently in period 2 (and this is known in period 1) to:
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z = rho*z(-1) + sigma;
What i did is the following:
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model block: z = rho*z(-1) + sigma + eps*sigma; (the NEW process)
initval: z = 0;
endval: z=(1-rho)*sigma;
shocks in eps:
periods 1 2:1000;
values -1 0; %the -1 is to keep z(1)=0;
When I get the results I see that z(2)=sigma/(1-rho); What did i do wrong? I thought it would calculate: z(2)=rho*z(-1) + sigma = sigma; but id doesnt. I havent used steady either.
(I know that I could get the correct result by setting the initval: z=0 and then add a shock eps=1 for period 2:1000, but i want to understand how to model it with initval and endval)
Thanks for your help!