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.
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.
Both DSGE and SFC models involve time steps, typically annual or quarterly. They are in no sense meant to be approximations of a continuous time model. His models are continuous time.
My reading is that his objection is that the DSGE and SFC approach is incorrect because they are fundamentally different than his preferred approach. Some solution properties do not transfer between the two types of models.
All the interesting parts of a macroeconomy are behavioural, the only “causal” parts are accounting identities and perhaps production functions. I see no evidence that continuous time has an advantage over discrete time, given the poor fit of most macro models to data. To the extent that we can say we have a good fit, that needs to be determined by comparing to actual data, which is typically monthly. Financial modelling might be continuous time, but there is going to be a tenuous relation to the macroeconomy.
Steve is free to follow his approach. One reason I do not follow it is that his models are not easily compared to observed data, and I doubt that I am the only one with that objection. There are continuous time DSGE models, but my reading is that they are generally not pursued since they are of limited use for econometric analysis.
I would concur for the most part, except to say that DSGE models are akin to Ptolemaic epicycles. I would never use them except as a punching bag to show how most econ institutions are doing things incorrectly, and lack parsimony in their models. The actual economy is best stochastically modelled in part, that's obviously true, but not by equilibrium analysis. I can see how single markets *might* have a valid equilibrium in a short run, but how short? Just asking over what time period a single commodity market could be in equilibrium leads one of reasonably sound mind to quickly conclude equilibrium models have almost no place at all in macroeconomics.
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?
As Neil noted (and in my text) there is a clock - banking transactions have a daily close. Accounting uses end of period values. You can get intraday data for some purposes, but accounting is end of period, and that is what economic data will be based on.
I am not debating conclusions, I instead argue that you can get pretty much the same conclusions using discrete time models. And those models can be a lot easier to work with than Keen’s approach.
Saying there is no such thing as “equilibrium” is a problem because the neoclassical treatment of it is pseudo-scientific piffle. But at a macro level, it is hard to get away from some notion of ‘market clearing” — even if the process is not as described by neoclassicals. Decision makers do react to events in the economy - people started hoarding toilet paper during the pandemic based on global news, not based on the need for toilet paper in their house.
A monetary economy does have a clock. The daily banking clearing cycle in that denomination.
What’s interesting is that with the internationalisation of the economy and the advent of faster payment systems that clock is increasingly being stretched.
However 10pm UTC is still the time by which you have to settle your FX trades. Until that point you are working “intraday”.
And it turns out that lots of the interesting stuff about the way a monetary economy co-ordinates itself happens intraday.
A fascinating reply, thanks. Based on your intraday comment I assume you’re in the Keen camp too?
My FE experience was a while ago and it was for fluid dynamics. It used a linear function across the element. I never explored the basics but the program was very robust. Finite difference approaches seemed far more prone to crashing and not converging.
I haven’t used Keen’s Minsky software but have the impression it’s quite robust. A colleague, Tyrone Keynes has assembled very large simulations that appear to be robust too.
I’d be interested in any comments you might have but the essential question is do you agree that ODE models based on continuous time are the way to go and using system-dynamics for economic policy is the way to go too, ie, the only way to capture feedback, time delays and, of course, interactions?
I'm more The Sims than SD - very much in the asynchronous agent based model camp. I'm not at all keen on system dynamics models. They tend to be too abstract and don't give an indication of how the people actually running the institutions in the model are behaving. That makes it difficult to check whether the modelled entities are behaving as they would in the real world, which tends to mean you end up curve fitting to a belief.
The most important problem with economic models is that they forget they have people in them, collected together into institutional frameworks. It's people doing things that run the system, not some pseudo-physics mathematical equation.
What i am not clear about from your post on discrete v differntial, is whether model proof is the priority or model fit is more important. Perhaps you can clarify that please.
I rather doubt there will be a predictive economic theorem proof, or a repeatable after the event (for all previous events) one, for either discrete of differential. I think the best we can hope for is getting closer to predicting downturns or inflation more often, or explaining better what just happened.
So is a differential or discrete approach better...
With respect there is a world of difference between clock ticks and the impact of most economic data, except say on October 1987. I thought Keen's argument is that if you use differential methods then you are on the same ground for anything that comes along, whereas with difference (discrete) methods you have problems with misalignment of events that don't match your time-keeping, eg a pandemic hitting, or October 1987 stock market crash, or 2000 NASDAQ. Having said that, if you are only arguing about simplicity of exposition, discrete is simpler, if you want to predict, you have to get below even quarterly data. Nowadays we have "indicators" that come out monthly.
If one-offs are the issue, then perhaps we need two models, one for fat-tail events and the other for what can be predicted most of the time.
If a higher frequency event - stock market crash - happens in the middle of your quarterly economic model, you need to ask: so what? You apply the crash to the quarterly stock market series.
Conversely, there is no plausible way of converting quarterly economic series to match the intraday ticks of the stock market that a continuous time model implies.
If you want to model financial markets, you can use continuous time. Most option pricing methodologies do (although numerical methods typically have a discrete time grid). The question is whether you can relate financial market dynamics to the real economy in a convincing fashion. Stock markets tear around at all times, even when economic growth is steady.
“ One may note that this is exactly the sort of behaviour post-Keynesians (including myself!)” is the only mention I see? (Don’t have a search option on my tablet to see whether I missed something else.)
Sorry about that -- was reading too quickly and missed it, possibly because the line break separated the hyphenated word such that "Keynesian" appears by itself at the start of the next line.
That's a relief, because nothing about what I have so far read of yours has been consistent with the Keynesians (a term that's terribly misleading to begin with, but I guess we're stuck with now).
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.
Both DSGE and SFC models involve time steps, typically annual or quarterly. They are in no sense meant to be approximations of a continuous time model. His models are continuous time.
My reading is that his objection is that the DSGE and SFC approach is incorrect because they are fundamentally different than his preferred approach. Some solution properties do not transfer between the two types of models.
All the interesting parts of a macroeconomy are behavioural, the only “causal” parts are accounting identities and perhaps production functions. I see no evidence that continuous time has an advantage over discrete time, given the poor fit of most macro models to data. To the extent that we can say we have a good fit, that needs to be determined by comparing to actual data, which is typically monthly. Financial modelling might be continuous time, but there is going to be a tenuous relation to the macroeconomy.
Steve is free to follow his approach. One reason I do not follow it is that his models are not easily compared to observed data, and I doubt that I am the only one with that objection. There are continuous time DSGE models, but my reading is that they are generally not pursued since they are of limited use for econometric analysis.
I would concur for the most part, except to say that DSGE models are akin to Ptolemaic epicycles. I would never use them except as a punching bag to show how most econ institutions are doing things incorrectly, and lack parsimony in their models. The actual economy is best stochastically modelled in part, that's obviously true, but not by equilibrium analysis. I can see how single markets *might* have a valid equilibrium in a short run, but how short? Just asking over what time period a single commodity market could be in equilibrium leads one of reasonably sound mind to quickly conclude equilibrium models have almost no place at all in macroeconomics.
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?
As Neil noted (and in my text) there is a clock - banking transactions have a daily close. Accounting uses end of period values. You can get intraday data for some purposes, but accounting is end of period, and that is what economic data will be based on.
I am not debating conclusions, I instead argue that you can get pretty much the same conclusions using discrete time models. And those models can be a lot easier to work with than Keen’s approach.
Saying there is no such thing as “equilibrium” is a problem because the neoclassical treatment of it is pseudo-scientific piffle. But at a macro level, it is hard to get away from some notion of ‘market clearing” — even if the process is not as described by neoclassicals. Decision makers do react to events in the economy - people started hoarding toilet paper during the pandemic based on global news, not based on the need for toilet paper in their house.
A monetary economy does have a clock. The daily banking clearing cycle in that denomination.
What’s interesting is that with the internationalisation of the economy and the advent of faster payment systems that clock is increasingly being stretched.
However 10pm UTC is still the time by which you have to settle your FX trades. Until that point you are working “intraday”.
And it turns out that lots of the interesting stuff about the way a monetary economy co-ordinates itself happens intraday.
A fascinating reply, thanks. Based on your intraday comment I assume you’re in the Keen camp too?
My FE experience was a while ago and it was for fluid dynamics. It used a linear function across the element. I never explored the basics but the program was very robust. Finite difference approaches seemed far more prone to crashing and not converging.
I haven’t used Keen’s Minsky software but have the impression it’s quite robust. A colleague, Tyrone Keynes has assembled very large simulations that appear to be robust too.
I’d be interested in any comments you might have but the essential question is do you agree that ODE models based on continuous time are the way to go and using system-dynamics for economic policy is the way to go too, ie, the only way to capture feedback, time delays and, of course, interactions?
I'm more The Sims than SD - very much in the asynchronous agent based model camp. I'm not at all keen on system dynamics models. They tend to be too abstract and don't give an indication of how the people actually running the institutions in the model are behaving. That makes it difficult to check whether the modelled entities are behaving as they would in the real world, which tends to mean you end up curve fitting to a belief.
The most important problem with economic models is that they forget they have people in them, collected together into institutional frameworks. It's people doing things that run the system, not some pseudo-physics mathematical equation.
What i am not clear about from your post on discrete v differntial, is whether model proof is the priority or model fit is more important. Perhaps you can clarify that please.
I rather doubt there will be a predictive economic theorem proof, or a repeatable after the event (for all previous events) one, for either discrete of differential. I think the best we can hope for is getting closer to predicting downturns or inflation more often, or explaining better what just happened.
So is a differential or discrete approach better...
With respect there is a world of difference between clock ticks and the impact of most economic data, except say on October 1987. I thought Keen's argument is that if you use differential methods then you are on the same ground for anything that comes along, whereas with difference (discrete) methods you have problems with misalignment of events that don't match your time-keeping, eg a pandemic hitting, or October 1987 stock market crash, or 2000 NASDAQ. Having said that, if you are only arguing about simplicity of exposition, discrete is simpler, if you want to predict, you have to get below even quarterly data. Nowadays we have "indicators" that come out monthly.
If one-offs are the issue, then perhaps we need two models, one for fat-tail events and the other for what can be predicted most of the time.
If a higher frequency event - stock market crash - happens in the middle of your quarterly economic model, you need to ask: so what? You apply the crash to the quarterly stock market series.
Conversely, there is no plausible way of converting quarterly economic series to match the intraday ticks of the stock market that a continuous time model implies.
If you want to model financial markets, you can use continuous time. Most option pricing methodologies do (although numerical methods typically have a discrete time grid). The question is whether you can relate financial market dynamics to the real economy in a convincing fashion. Stock markets tear around at all times, even when economic growth is steady.
Brian, this may be hair-splitting, but you identify yourself as Keynesian in this post -- did you mean to write post-Keynesian?
“ One may note that this is exactly the sort of behaviour post-Keynesians (including myself!)” is the only mention I see? (Don’t have a search option on my tablet to see whether I missed something else.)
Sorry about that -- was reading too quickly and missed it, possibly because the line break separated the hyphenated word such that "Keynesian" appears by itself at the start of the next line.
That's a relief, because nothing about what I have so far read of yours has been consistent with the Keynesians (a term that's terribly misleading to begin with, but I guess we're stuck with now).
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.