@mrchae, I do not understand hat you are trying to do here. I do not know your model but if TFP is a state variable in your model you should write the equation as a_t = \rho a_{t-1} (note the difference in timing). Also the autoregressive parameters should be smaller that one in that case, otherwise the processes will be explosive…
What you are doing here, is that you consider TFP as a non predetermined variable. In this case it is correct to have an autoregressive parameter greater than one (see my recent post: The rank condition is verified. Eigenvalues are larger than 1). Setting A0t equal to 121.3 in the initval block you then ask Dynare (with the simul command) to compute a path for A0t such that the terminal condition is 121.3 (Dynare looks for an initial condition such that the iterations on the first equation is such that the terminal condition is equal to 121.3). I am not sure this what you… You probably need to read the manual (sections about deterministic simulations).
Best,
Stéphane.