The article uses Godley tables in ways that I don't know how to implement in Minsky. In particular, the Godley tables include:
change variables; for example, to model a short-term equilibrium, the authors require that changes in loans to wage earners and capitalists must equal changes in loans given out by banks.
lagged variables; for example, to model disequilibrium growth, the authors follow "classical" economic practice by assuming wages are paid out at the start of a production period, so that demand at time t+1 depends on wages at time t.
Both aspects could be modeled if Minsky had a lag function, but I don't see one. This probably reflects my own inexperience with system simulation software like Minsky, but is there some other way to include changes and lags in Minsky?
The article raises a third question. Throughout Minsky's documentation and Steve's models, assets and liabilities are defined from the standpoint of a bank. Hence, loans are assets and deposits are liabilities. I realize this is standard practice in finance, but Dumenil and Levy define their Godley tables in terms of money flows so that, for example, loans given out by banks have negative values, while those wage earners & capitalists receive have positive values. Since all this is double-entry bookkeeping, intuitively I think it makes no difference which way we define such things so long as everything sums to zero. But I want to check this to make sure there's not some deep feature of Minsky that makes defining assets and liabilities from a bank's perspective much more desirable. So, does it matter?
Thanks very much for your help.
Last edit: marshf 2013-03-13
If you would like to refer to this comment somewhere else in this project, copy and paste the following link:
Minsky is about simulation of continuous time systems, not discrete time systems, as that paper is formulated. The paper you cite above, I find very confusing as a mathematician, but perhaps it makes more sense to an economist. I sat down and wrote out the equations without trying to assign meaning to the symbols.
The Godley table itself defines 4 equations (stock variables) with 10 flow variables. There are 6 conservation equations, leaving 4 undefined quantities needing constitutive relations to define. I found equations (5), (6) & (8), which serve this purpose - there must still be another equation lurking there in that paper, somewhere.
These equations are the lagged equations you were talking about. Since this discussion forum doesn't represent maths too well, I attach the rest of my response as a PDF.
Steve, does this sound right to you? As for your third question - hopefully Steve can answer. I would expect everything is fine, as long as you keep your signs correct.
I'm still a novice at Minsky, and I spent part of today searching for the answer to the unfinished section of the manual, "Why No Difference Equations?" I came across Steve's 2009 paper, which I had read some time ago, "The Dynamics of the Monetary Circuit." In it he argues that continuous-time models are superior to discrete-time models.
But then, in the cobwebs of my mind, I recalled having studied differential-difference equations when I was an engineering student majoring in operations research in the 1960s. A search for "differential difference equations" led to a paper by Bellman and Cooke which explains the need for combining differential and difference equations as follows (p. iii):
Detailed studies of the real world impel us, albeit reluctantly, to take account of the fact that the rate of change of physical [sic] systems depends not only on their present state, but also on their past history.
The paper then goes on to give the most simple, general form for a differential-difference equation.
So I need to spend some time studying the use of time constants in continuous models. Maybe it's because I haven't used this stuff in over forty years, or maybe I wasn't such a good student back then (or now), or maybe it just didn't stay in my mind (after all, it was the Sixties :), or maybe advances since then have made that whole course I took on stochastic (!) differential-difference equation models superfluous), but I'm still not entirely clear on how to map a discrete systems model into a continuous one.
In any case, my concern about this with regard to Minsky is twofold. (1) In many cases one will want to start with an existing model by someone else and then examine it. Not only Dumenil and Levy, but also Godley and Lavoie (2007) use the difference-equation form, and one would at least like to verify they've replicated an earlier model before pioneering a new direction based on such earlier work. (2) If Bellman and Cooke are still right, then a large class of problems cannot be modeled with purely continuous methods, and confining Minsky to purely continuous cases may be unnecessarily limiting.
This is not to say I'm complaining about Minsky. It's great. The question is just whether or not confining it to purely continuous models only is too crippling. And, so long as it's only for continuous modeling, how does one convert discrete models into continuous analogues that Minsky can handle? I'll start by reading more about time constants and your pdf. Thanks very much again for your help.
Last edit: marshf 2013-03-14
If you would like to refer to this comment somewhere else in this project, copy and paste the following link:
There may well be a case for adding support for difference equations in Minsky, and even possibly a "wizard" of some kind to transform difference equations to differential, and vice-versa. May as well think big.
Not sure when we'll have the resources to implement that, though :).
If you would like to refer to this comment somewhere else in this project, copy and paste the following link:
Hi,
I am trying to simulate some of the models described in this article:
Duménil, Gérard, and Dominique Lévy. 2012. “MODELING MONETARY MACROECONOMICS: KALECKI RECONSIDERED.” Metroeconomica 63 (1): 170–199. doi:10.1111/j.1467-999X.2011.04134.x.
The article uses Godley tables in ways that I don't know how to implement in Minsky. In particular, the Godley tables include:
change variables; for example, to model a short-term equilibrium, the authors require that changes in loans to wage earners and capitalists must equal changes in loans given out by banks.
lagged variables; for example, to model disequilibrium growth, the authors follow "classical" economic practice by assuming wages are paid out at the start of a production period, so that demand at time t+1 depends on wages at time t.
Both aspects could be modeled if Minsky had a lag function, but I don't see one. This probably reflects my own inexperience with system simulation software like Minsky, but is there some other way to include changes and lags in Minsky?
Thanks very much for your help.
Last edit: marshf 2013-03-13
Minsky is about simulation of continuous time systems, not discrete time systems, as that paper is formulated. The paper you cite above, I find very confusing as a mathematician, but perhaps it makes more sense to an economist. I sat down and wrote out the equations without trying to assign meaning to the symbols.
The Godley table itself defines 4 equations (stock variables) with 10 flow variables. There are 6 conservation equations, leaving 4 undefined quantities needing constitutive relations to define. I found equations (5), (6) & (8), which serve this purpose - there must still be another equation lurking there in that paper, somewhere.
These equations are the lagged equations you were talking about. Since this discussion forum doesn't represent maths too well, I attach the rest of my response as a PDF.
Steve, does this sound right to you? As for your third question - hopefully Steve can answer. I would expect everything is fine, as long as you keep your signs correct.
Thanks for this answer.
I'm still a novice at Minsky, and I spent part of today searching for the answer to the unfinished section of the manual, "Why No Difference Equations?" I came across Steve's 2009 paper, which I had read some time ago, "The Dynamics of the Monetary Circuit." In it he argues that continuous-time models are superior to discrete-time models.
But then, in the cobwebs of my mind, I recalled having studied differential-difference equations when I was an engineering student majoring in operations research in the 1960s. A search for "differential difference equations" led to a paper by Bellman and Cooke which explains the need for combining differential and difference equations as follows (p. iii):
The paper then goes on to give the most simple, general form for a differential-difference equation.
So I need to spend some time studying the use of time constants in continuous models. Maybe it's because I haven't used this stuff in over forty years, or maybe I wasn't such a good student back then (or now), or maybe it just didn't stay in my mind (after all, it was the Sixties :), or maybe advances since then have made that whole course I took on stochastic (!) differential-difference equation models superfluous), but I'm still not entirely clear on how to map a discrete systems model into a continuous one.
In any case, my concern about this with regard to Minsky is twofold. (1) In many cases one will want to start with an existing model by someone else and then examine it. Not only Dumenil and Levy, but also Godley and Lavoie (2007) use the difference-equation form, and one would at least like to verify they've replicated an earlier model before pioneering a new direction based on such earlier work. (2) If Bellman and Cooke are still right, then a large class of problems cannot be modeled with purely continuous methods, and confining Minsky to purely continuous cases may be unnecessarily limiting.
This is not to say I'm complaining about Minsky. It's great. The question is just whether or not confining it to purely continuous models only is too crippling. And, so long as it's only for continuous modeling, how does one convert discrete models into continuous analogues that Minsky can handle? I'll start by reading more about time constants and your pdf. Thanks very much again for your help.
Last edit: marshf 2013-03-14
There may well be a case for adding support for difference equations in Minsky, and even possibly a "wizard" of some kind to transform difference equations to differential, and vice-versa. May as well think big.
Not sure when we'll have the resources to implement that, though :).