Steve Keen recently wrote “I’m not Discreet, and Neither is Time” in which he discusses the alleged defects of discrete time models as opposed to continuous time ones. (In discrete time, the model state is defined on a time axis that can be labelled as integers: step 1, step 2, etc. In a continuous time, a model’s time axis is the real axis. A discrete time model can be thought of as being defined by difference equations, while continuous time is normally defined by differential equations.)
Isn't SK really talking about difference equations (discrete maps). I'd presume he knows all realistic nonlinear numerical methods for solving ODE/PDEs need discrete grids, so that can't be his beef.
Although the economics data arrives in discrete time, the underlying causal dynamics in a macroeconomy are fairly well modeled by analytic response functions, and that's a choice of convenience and compute efficiency - you might say best to not use transcendentals if you can avoid them, but with modern software this is hardly a big issue for run-time. It is much simpler to use analytic response functions. Let the numerical solver handle the discretization for you. Do not do it yourself using difference equations, since that is then a source of systematic model error.
This all begs the question: what is SK really objecting to? My thought (reading his opinions on difference equations a long time ago) is that it is the choice of model that he considers poor, not the method of solution. (He also mumbles about time constants, but that is a false objection, one can incorporate time constants in difference equations if one wants, maybe more awkwardly(?).) The other thing SK might mean is that difference equation models tend to bias modelling choices worse than choices based on piecewise analytic response functions. That is really the only objection worth having, the possible bias introduced.
I admire most of Keens work because it is well thought out and grounded on more reality than modest economists can fathom. But the dude has serious chip on his shoulder.
"nobody has the time (nor wants to take the academic political risks) of shredding existing papers that probably nobody will read anyway"
While I can't speak for Steve Keen, I imagine he would say that this quote covers most of neoliberal macroeconomics.
I really like this post, it's an important issue. And I didn't realize you were an electronic engineer, Brian. Good to know.
I am a physicist by training and barely competent in electronic engineering but I did FE analysis as an engineer so appreciate some of the issues of using discrete time - and space.
But what you have in common (I think) is a system-wide (systems dynamics) understanding. I think it's where Keen's modelling stands out, especially his demonstration of the Minsky Instability Hypothesis - credit money destabilizes and fiat money stabilizes. And there is no such thing as 'equilibrium', the economy is chaotic - as are most systems. It leads us into control methodologies and begs the question whether any economic 'control' levers can work in a predictive sense.
And, of course, while an electronic circuit has a single governing clock, the economy does not. Which leads me in the direction of Keen?
So, Neil, can you point me in the direction of something to read?
It seems there are three povs:
1) Keen’s - his Minsky SD model is his major achievement. It puts macro on a simple non-micro footing, readily predicts the Instability Hypothesis, seems robust for much larger simulations, and demonstrates chaotic behaviour, ie, like weather, the economy cannot be long-term predicted but simulations can give insight. It sounds about right to me.
2) Brian’s - not interested in predictions and discrete time methods can do just as well. So has a discrete time method ever predicted the Instability Hypothesis? And are we happy with managing the economy through interest rates? I’m not!
3) Neil’s - it’s not the system behaviour that matters it’s the agents in the system. For fiat money creation, I guess that means much more careful fiscal policy? I don’t disagree, it’s standard MMT. And how do you assess and re-vector? For credit money, does it mean much more careful bank regulation? For international trade, does it mean curtailing the FED? Unlikely! Or some new trading currency? And who would create it?
Isn't SK really talking about difference equations (discrete maps). I'd presume he knows all realistic nonlinear numerical methods for solving ODE/PDEs need discrete grids, so that can't be his beef.
Although the economics data arrives in discrete time, the underlying causal dynamics in a macroeconomy are fairly well modeled by analytic response functions, and that's a choice of convenience and compute efficiency - you might say best to not use transcendentals if you can avoid them, but with modern software this is hardly a big issue for run-time. It is much simpler to use analytic response functions. Let the numerical solver handle the discretization for you. Do not do it yourself using difference equations, since that is then a source of systematic model error.
This all begs the question: what is SK really objecting to? My thought (reading his opinions on difference equations a long time ago) is that it is the choice of model that he considers poor, not the method of solution. (He also mumbles about time constants, but that is a false objection, one can incorporate time constants in difference equations if one wants, maybe more awkwardly(?).) The other thing SK might mean is that difference equation models tend to bias modelling choices worse than choices based on piecewise analytic response functions. That is really the only objection worth having, the possible bias introduced.
I admire most of Keens work because it is well thought out and grounded on more reality than modest economists can fathom. But the dude has serious chip on his shoulder.
"nobody has the time (nor wants to take the academic political risks) of shredding existing papers that probably nobody will read anyway"
While I can't speak for Steve Keen, I imagine he would say that this quote covers most of neoliberal macroeconomics.
I really like this post, it's an important issue. And I didn't realize you were an electronic engineer, Brian. Good to know.
I am a physicist by training and barely competent in electronic engineering but I did FE analysis as an engineer so appreciate some of the issues of using discrete time - and space.
But what you have in common (I think) is a system-wide (systems dynamics) understanding. I think it's where Keen's modelling stands out, especially his demonstration of the Minsky Instability Hypothesis - credit money destabilizes and fiat money stabilizes. And there is no such thing as 'equilibrium', the economy is chaotic - as are most systems. It leads us into control methodologies and begs the question whether any economic 'control' levers can work in a predictive sense.
And, of course, while an electronic circuit has a single governing clock, the economy does not. Which leads me in the direction of Keen?
Brian, this may be hair-splitting, but you identify yourself as Keynesian in this post -- did you mean to write post-Keynesian?
Again, fascinating.
So, Neil, can you point me in the direction of something to read?
It seems there are three povs:
1) Keen’s - his Minsky SD model is his major achievement. It puts macro on a simple non-micro footing, readily predicts the Instability Hypothesis, seems robust for much larger simulations, and demonstrates chaotic behaviour, ie, like weather, the economy cannot be long-term predicted but simulations can give insight. It sounds about right to me.
2) Brian’s - not interested in predictions and discrete time methods can do just as well. So has a discrete time method ever predicted the Instability Hypothesis? And are we happy with managing the economy through interest rates? I’m not!
3) Neil’s - it’s not the system behaviour that matters it’s the agents in the system. For fiat money creation, I guess that means much more careful fiscal policy? I don’t disagree, it’s standard MMT. And how do you assess and re-vector? For credit money, does it mean much more careful bank regulation? For international trade, does it mean curtailing the FED? Unlikely! Or some new trading currency? And who would create it?
It’s a very interesting discussion.