What does it mean for a technology to have a $|\rho|<1$? Nowadays, when trying to model (log)technology $a_t$, I've seen many times the following: $a_t = \rho a_{t-1}+\epsilon$, where epsilon is given a certain probability distribution. What does it mean for $|\rho|&lt;1$? I know that in this way, the time series is stationary. My question is related towards more the interpretation. With such a $rho$ does this mean that our technological discoveries are being lost in time? We're forgetting our past? or That the discoveries give a surge of increase in 'productivity', but then the 'productivity' decreases...

Any help would be appreciated.
New technology makes past technology obsolete. How many people know these days how to light a fire by rubbing wood together? How many people know the nuts and bolts of tending to the engine of a train powered by coal? Heck, how many coal-trains are still operational?

So yes, we do forget our past discoveries and technologies, as they are replaced by new ones. But the technology as inserted in the production function, operates as a production shifter, a "mark-up", it does not represent the composition of technology, but rather its final effect on the production inputs.

Modeling the technological production shifter as a stationary auto-regressive scheme (without drift), we essentially assume that, random shocks aside, we are set today to produce less efficiently than yesterday.

Does this accord with observed reality? Do we depend on positive random discoveries to produce more efficiently? My impression is that, on the contrary, humans very purposefully try to make their production processes more efficient.

Now, if you were to add a drift (a constant term) in the log-technology process,

$$a_t = \delta + \rho a_{t-1}+\epsilon_t$$

you would capture, the rising trend in efficiency we have observed historically, and also implicitly, the fact that we discard old technologies.
This also has the benefit that it envisions rising efficiency while also, an eventual level-off (which seems wise to me).