# Asset pricing - Technology

I am working a bit on this paper, which is about Long-run risk through Consumption Smoothing.

In equation (8) and (9) the authors define the stochastic process for the technology as:

$$Z_t = \exp(\mu t + z_t)$$

$$z_t = \varphi z_{t-1}+\epsilon_t$$

My question is straightforward, why do they specify these two equations? Wouldn't it be exactly the same to specify: $z_t = \mu_t + \varphi z_{t-1}+\epsilon_t$

Also, with their specification, if you take logs of the first equation, the $z_t$ cancel out, right?

I am assuming that $z_t = \ln(Z_t)$ which I believe is correct.

• For the user who voted it down, it would be helpful to have some constructive comment... – phdstudent Jul 26 '15 at 10:54
• I guess the problem is that you didn't link or name the paper. It would certainly help! – Bob Jansen Jul 26 '15 at 16:38
• Why do you assume $z_t = \ln(Z_t)$, it should be $z_t = \ln(Z_t) - \mu t$... and how does that help? $Z$ and $z$ are different here, but I think the notation is pretty bad. Basically this "is" a geometric brownian motion with autoregressive local volatility. – SRKX Oct 26 '15 at 7:14