# “Economic” Variables in Short Rate Models

Hull (9 ed.) states on p 707,

"Equilibrium models usually start with assumptions about economic variables and derive a process for the short rate..."

He then states the usual short rate models such as Vasicek's, given by $$dr = a(b - r)dt + \sigma dW.$$ The "economic" variables to be calibrated are

1. $a$ = mean reversion speed
2. $b$ = long term mean
3. $\sigma$ = volatility.

What exactly is "economic" about these parameters? These seem like purely mechanical parameters, something to be tuned to the happenings of a time series. In fact, here's a time series of the 1-week LIBOR with daily observations - how is a diffusion model supposed to capture these stair step patterns, and then the puttering around zero for the last 6 years?

It seems dubious to attempt to calibrate a diffusion model in the hopes of capturing this observed behavior. Rather, I suppose a short rate modeler may decide on "regimes" in the data, and calibrate to only the data he feels best fits the current regime. But again - what "economic" assumptions am I making? Would a prudent modeler not calibrate to the data, and let that speak for itself? Is some senior manager with a PhD in economics supposed to have some insight into the values of the parameters and we use those instead?

$$dX_t = f(t,X_t)dt + \sigma(t,X_t)dW_t$$ where $$(X_t)_t$$ is some vector-valued stochastic process and each component of $$X$$ represents an economic variable such as inflation, GDP etc. You can then define your short rate to be $$r_t = h(t,X_t)$$ for some appropriate function $$h$$.