# Non-convex technology

Hello,

Is taking technology to be a random walk process a good approximation to taking technology as non-convex?

I want to take technology as non-convex in a dsge-model setting. Please suggest!

What do you mean with

?
The random walk is about time-series properties.

I mean the time series evolution of technology when taken as a random walk with its non-mean reverting and other properties, can it represent the evolution of technology as a non-convex process? For example, take technology as a convex set in Euclidean space R^n and then convexify it in a convex hull upto R^{n+1}, there is no ‘jump’ or deviation from convexity here, let’s say it’s a normal mean-reverting autoregressive technology process. But what if it’s not, can random walk account for the said deviations from the smoothness of convex technology assumption?

Additionally, can a random walk technology process in a dsge model be assumped or expected to create unexpected income shocks, idiosyncratic income shocks?

Thank you

I am still not sure I fully understand your question. Even for a mean-reverting autoregressive process with normally distributed shocks, there is an \varepsilon>0 probability of a sufficiently big shock happening that kicks you out of a convex set defined by convexifying the previous realizations from -\infty to time t (I guess that is what you meant with n)

Yes, quite close. So this kind of ar process with that probability, is it the best way available in the toolkit here to characterize technology process as non-convex? I mean, if there is a standard way to take technology as non-convex in dsge models, that is what I’m after.

You are too much focused on technicalities. What exactly is the research question you are after? Then one can try to find a suitable model and solve it.

I’m afraid it is a necessary technicality. My hypothesis is that the non-convexity of technology can explain idiosyncratic risk and income shocks to portfolio returns and consumption shocks.

Shocks are something exogenous, while non-convexity refers to properties of the production set. Where is the link? Also, how is the time series of aggregate productivity related idiosyncratic risk, which is about the cross-section?

That risk is cross-sectional but its income and consumption implications move across time and that cross-sectional risk comes from the gaps (non-convexity) in the production technology set: is my hypothesis which I intend to test.

But TFP is just a number. How do you get from that number that evolves over time to characteristics about the choice set for production.

That’s why technology should be taken as a process with an appropriate innovation term (with ar or rw) such that it approximates an explicit assumption of non-convexity. Can the non-mean reversion account for such a notion?!

But what is your explicit assumption about convexity? Convexity is about the relation between inputs and outputs. How do you relate that to a technology measure?