Hello,

I have a simple question:

Assume I have an AR(1) process *b = rho_b*b(-1) + e_b* and another process which depends on this process, *a = rho_a*a(-1) + psi_b*b + e_a*. Now assume I can observe *b* and estimate *rho_b* and the variance of the shock *e_b*. Then, I observe additionally the variable *a* and estimate both processes at the same time in one mod-file. That is, I estimate the parameters *rho_a, rho_b* and *psi_b* and the variances of the shocks *e_a* and *e_b*. It turns out, that the estimate for *rho_b* is slightly different for both cases, 0.4398 in the first case and 0.4423 in the second one (I have attached the mod-file and data file).

Just to be sure, this is a numerical problem? Theoretically, we should get exactly the same estimate for the AR(1) process of *b*, right? I am asking because in a bigger model, the difference is much higher (*0.5* vs. *0.8*) for *rho_b*. What would be the best way to estimate both processes? First estimate the AR(1) process of *b* only, then calibrate *rho_b* and the variance of *e_b* to the estimated values and then estimate the process for *a* (with *b* being still an observable)?

I am thankful for any help or comment,

all the best,

Niklas

data_AR_1.xls (20.5 KB)

AR_1.mod (681 Bytes)