Sunday, March 6, 2016

Brian Romanchuk — Discrete Time Models And The Sampling Frequency

Economic data are available in discrete time; that is, they are time series that are available in the form of samples at a fixed frequency (for example, quarterly, monthly, daily). Similarly, most complex economic models are specified in terms of a discrete time specification. By contrast, models in physics, or things like analog circuits, are defined in continuous time: time series are defined at "all times" (the time axis is a subset of the real line). Building economic models using continuous time has been done, but doing so creates many problems. However, one of the issues with discrete time models is the choice of the sampling frequency: too low a frequency means that you might not be able to model some dynamics.…
Bond Economics
Discrete Time Models And The Sampling Frequency
Brian Romanchuk

Matt Franko said...

Aces from Brian here...

Brian I have been revisiting this control framework perhaps take a look:

https://en.wikipedia.org/wiki/PID_controller

It breaks down control into 3 mathematical terms

1. Proportional (might be a fixed/static tax policy)
2. Integral (might be leading govt spending deltaT)
3. Derivative (bank credit)

Or thereabouts... anyway might lead to other thoughts...

Matt Franko said...

PS also accommodates feedback...

Brian Romanchuk said...

PID controllers are the workhorse of control systems. The theory was developed in the 1950s, leaving academics to work on complicated stuff that is rarely used for the following decades.

Not sure about fiscal policy, but a Taylor Rule acts like the P term; the interest rate is set based on deviations from target. (I have my doubts about interest rate control of the economy, but I will assume that it works like the mainstream says so that I can explain the concept).

A "D" term would be to reduce control action if the economy was moving too fast in one direction. If we believe mainstream models, this would only happen if we are massively away from potential and it takes several years to get back to "equilibrium".

An "I" term integrates the tracking error. In a situation like secular stagnation, where we are persistently below target. You start increasing control action to crush out the deviation from target. This is the type of control law I actually spent years of my life analyzing; you need to be careful in a system with nonlinearities with this type of control.

The "automatic stabilizers" are similar to "P" control - the size of the stimulus is proportional to the number of people on Unemployment Insurance, and the reduction in income taxes.