Monday, March 21, 2016

Jason Smith — An RLC circuit with R = S and L = F


SFC modeling.

Information Transfer Economics
An RLC circuit with R = S and L = F
Jason Smith

28 comments:

Bob said...

The economy is an oscillator?

Calgacus said...

Sigh. He's unfortunately obsessed with this. Should read Brian Romanchuk. Repeatedly. It's like he thinks - to the point that the alternative is inconceivable, ineffable - that we must always be approximating the continuous by the discrete, rather than the reverse. As in analytic number theory for instance.

So his arguments are like saying we can't know 3 to be prime because the prime number theorem is hard or because it takes infinitely many continuous functions to get an exact explicit formula for pi(x). Or something like that. In other words, complicated and defective arguments to show something obvious and true is false or unknowable. Pretty much standard for modern economics. :-)

P. S. : Ken Zimmerman has a great, apposite quote from Gabriel Tarde (meaning to read him for a while...) here. Archive.org has that book, I'll hunt for the page.

Brian Romanchuk said...

He is correct that if SFC models do not contain behavioural relationships, they are underdetermined (infinite solutions). But everyone knows that...

Neil Wilson said...

"He is correct that if SFC models do not contain behavioural relationships, they are underdetermined (infinite solutions). "

The problem with using mathematics and seeking 'solutions' via 'closure'.

Rather than admitting the truth - which is that we need a simulation of the real world with real world objects in it that domain specialists can recognise and then confirm are actually behaving in the model as they do in real life.

System Dynamics has moved things forward a little bit, but it is now bumping up against its limits. Which is that it struggles with entities that listen to the feedback, learn and then alter their behaviour. The metal in a bridge, or electrons in a circuit don't do that.

Bob said...

The metal in a bridge reacts to the stresses that are placed upon it. What electrons do in a circuit is determined by the components in that circuit and by the power source (its voltage, frequency and waveform).

The 'entities' in this example are resistance, capacitance and inductance. R is considered non-reactive, while C and L are reactive. All three components are passive, with linear responses.

The 'solutions' are voltage and frequency dependent, if those are the only variables. The R, L and C are generally fixed variables. The I (current) is a 'result'. The resonant frequency is a more interesting result - it is what gives this type of circuit utility.

How do these parameters compare with those used in SFC models?
How does the scope of an RLC circuit compare with the scope of an SFC model?
Are these entities comparable or merely analogous?

Brian Romanchuk said...

Bob - There is an analogy. You could think of Kirchoff's laws as the accounting identity, and Ohm's law (plus the relationships for capacitors and inductors) as the behavioural equations. If you do not specify R, you cannot calculate Ohm's law across that branch of the circuit, and so there would be no solution.

The same is true for SFC models. The accounting identities tell us how flows are connected, but we need the behavioural laws to tell us what determines the flows. Those behavioural laws are specified in the model; Jason Smith has this idea that they are not.

I discuss the solution technique on my blog - BondEconomics.com.

Matt Franko said...

Bob so you assert you are doing "modeling" in your comment there?

"What electrons do in a circuit is determined by the components in that circuit and by the power source "

Keyword here is "DETERMINED"...

Determination is NOT modeling....

Tom, there seems to be general confusion wrt Deterministic and Stochastic systems going on... cant be both...

When Bill says, "If you want to increase employment, then employ people..." this is a DETERMINISTIC statement, not a STOCHASTIC one....

Seems to me people are confused and perhaps somehow afraid to look at our economic systems as Deterministic...

Matt Franko said...

If we want to figure out what to do (Deterministic), then perhaps Electrical Theory could be a good place to start... because in Electrical Theory WE determine the system design/operation....

If we want to figure out what is going on NOW (ie morons in charge via Stochastics...) , then imo Biology Theory could be a good place to start... because in Biology Theory WE DO NOT determine the system design/operation....

Gotta choose one way or the other...

Bob said...

But R is known, and so is the impedance, Z. In an LC circuit, R can be assumed to be zero or negligible, and the circuit will still work.

It's not clear to me that electrical current is analogous to monetary flows. For example, what can the flow of electrons tell me about the flow of water? What doesn't it tell me?

Bob said...

Matt,

The electrons are not the 'entity' Neil mentioned. And no, it's theory that tells us this. The mathematical models describe it; measurements confirm it.

Matt Franko said...

Here (good):

http://www.slideshare.net/sohail40/deterministic-vs-stochastic


"A Deterministic model has no Stochastic elements..."

I think what I mean is that perhaps Electrical Theory uses Deterministic "modeling"... if you HAVE to use the word "model"...

So these economist people using their "DSGE models" are not using Deterministic "models"... while in Engineering, we use Deterministic "models"....

I dont think we are going to get anywhere with this whole "empiricism" shift without also recognizing the philosophical difference between Deterministic and Stochastic approaches...

(FD I am a Determinist...)

Bob said...

Electrical and mechanical systems operate within tolerance... thus predictable.

Matt Franko said...

"measurements confirm it."

That's where the ex post accounting comes in... but accounting is of no value when you are trying to determine something ex ante...

Brian Romanchuk said...

In an electrical circuit, the relationships amongst variables are deterministic; they are based on the laws of physics. If they did not hold, electrons would be created out of thin air, etc. (If you want, insert digression about quantum physics here...)

In order to make the system stochastic, you need to add random (stochastic) signals. If you are building a communications system, you design it so that it best rejects that random "noise". (That is what sounds like when you are talking on the phone...) Even though the noise is random (or effectively random), we know enough about its characteristics so that we can design the circuit to reject it. But that design is done using "deterministic" signal and system theory -- we shape the frequency response to best deal with the expected noise.

In other words, even in a random world, deterministic analysis is useful. Given the mathematical nightmare that is probability theory, probably more useful than stochastic analysis.

Matt Franko said...

Well if we think a human being can eat well on $138.50/mo. SNAP benefit, I predict they CANNOT...

Matt Franko said...

Well Brian it looks like the academe of economics is pretty much 100% stochastic based...

They approach it like "If a butterfly flaps its wings...."

Bob said...

$138.50 of beans, rice and lentils per month may be nutritionally sufficient.

Bob said...

An electrolytic capacitor is both deterministic and stochastic. They are manufactured with typically large tolerances, and the capacitance will vary with age.

Matt Franko said...

The tolerances are known hence not stochastic...

Brian Romanchuk said...

Matt - Yes the mainstream DSGE academics work from a stochastic starting point. And they have a complete inability to solve the initial system; they have to take a log-linear approximation *around a deterministic trivial trajectory*.

That complete inability to get anything done is highly predictable based on stochastic control systems; all they can do re-derive deterministic results.

For system estimation, you obviously want to use stochastic theory; deterministic makes limited sense. This is the area where the academic work might be doing something useful.

Brian Romanchuk said...

As for real-world capacitors, they can only be imperfectly modelled by capacitances in circuit theory. They have some resistance and inductive properties as well. In some cases, you try to reduce the model error, but you are never going to get a perfect fit, even without noise. For example, circuits have an embedded time delay that is not easily modelled.

Bob said...

At low frequencies, the non-ideal L and C properties can be ignored. If not, the approach is to calculate distributed L and C based on the circuit layout.

The tolerances are known hence not stochastic...

Is it chaotic?
https://en.wikipedia.org/wiki/Lorenz_system

From a technical standpoint, the Lorenz system is nonlinear, three-dimensional and deterministic.

Of course, the Lorenz example may not be applicable to the manufacture and internal operation of these capacitors.

Bob said...

https://en.wikipedia.org/wiki/Chaos_theory#Distinguishing_random_from_chaotic_data

Tom Hickey said...

@ Matt

Models can be either deterministic or stochastic. In physics, for example, classical physics is deterministic and QM is stochastic (pace Einstein).

Jason's post is that in science it's not just about models, but models that work. In philosophy, it's "let a hundred flowers bloom" because there are no agreed upon universal criteria for deciding non-empirical matters.

Theories are expressed as models and to be scientific, some argue that the model has to generate hypotheses that are testable empirically, that is, predictive as well as explanatory. Others hold that being explanatory is sufficient as long as the model fits into the general pattern of knowledge, is support by empirics and doesn't contradict empirics.

Some hold that theories are true or false, whereas other hold that only hypotheses are true or false and theories stand and fall based on usefulness and simplicity. QM doesn't falsify Newton in this view, and the heliocentric theory of planetary motion replaced the earth-centric because it was simpler. But both are potentially accurate ways of viewing the same events.

Some hold that genuine scientific models are causal explanations and causes must be demonstrated, e.g, through some mechanism. Others hold that high correlation is sufficient.

There are also some who hold that a satisfactory model has to be formalized to be truly scientific whereas other would be more relaxed about this.

So some would view the frontiers of physics as more philosophical whereas others would view it as the outset edge of science.

With biology, the frontier is closer to the center owing to the subject matter, especially evolutionary theory which is characterized by emergence, which by definition cannot be foreseen. The frontier of psychology, and social science including economic is even narrower owing to the subject matter, which is reflexive.

So physics can anticipate being "a theory of everything," but the other branches of science are more limited in generality.

Philosophy of science is a fairly contentious field, being philosophy after all. It is also grounded in different views of ontology, epistemology, ethics and aesthetics, and value theory and action theory. It also involves philosophy of language, philosophy of mathematics, and philosophical analysis.

So it's unlikely that there is going to be universal agreement in the this debate anytime soon. What often happens in this case is that various schools form and try to dominate the debate politically. This is the case in econ now, for example, but it is also true in other fields. It was true in philosophy when Quine presided over the phil department at Harvard and Skinner over psych. Then philosophical logic and behavioral psych were dominant academically. In psychology the stimulus-response model was dominant. It's a simplistic model that can be compared to simplistic models in econ, for instance. Then psychology moved on to cognitive psych. So there is hope for econ, too.

Ignacio said...

The problem here Tom lies on to what point is the economy a true stochastic system.

There are elements of an economy which scape our control, those elements usually result either in scarcity or abundance of certain goods. The problem is when you are treating certain variables as uncontrollable, and modeling them as stochastic, but then they are not, because are subject to human decisions, usually at high levels of authority. this is where Matt is coming at, he is a "determinist and authoritarian".

The main problem with economics is that they read what Keynes wrote a long time ago and then proceeded to misunderstand what radical uncertainty means. So what we end up is with economists obsessing over non-stochastic issues and treating them as stochastic variables. Check: government debt, "money", asset prices, etc. Most of these are, most of the time, under control of humans and influenced by humans through decisions of policy design. Period.

Then they proceed to systematically ignore all the important, actual, stochastic variables: demographics (although there is certain elemnt of feedback between the state of the economy and demographics), climate, real resources, etc.

For them is all about talking about money, while pretending that money is neutral or doesn't matter, and central banks trying to apply some voodoo to shape an uncontrollable and unpredictable beast called the economy, the markets, etc.

Tom Hickey said...

The social science other than economics are either heavily conceptual or else rely chiefly on statistics. There aren't any laws of human action. No one is writing functions. It's sort of like logic a hundred or so years ago, when logic was conceived as the laws of thought. No one thinks that anymore.

Regularity is even decreasing now with the spread of technology and in the increase in feedback and learning. There's no predicting where influence is going to led and the big ? is who are tomorrow's influencers. It's an increasingly fast game as social change accelerates.

Where economics differs is in being based on both money and real stuff. They meet in the journal, where monetary transaction for exchange are recorded.'

SFC just says that books balance. But that has implications making certain things definite and other things ruled out. The space in the middle is that of possibility, which contingent on monetary decisions about both the financial and non-financial. SFC modeling enables exploration of contingencies.

The other matter is that monetary systems run on money which is created through credit and also on energy system to power technology as well as to produce caloric energy.

An electrical circuit is connected with a power source. Economies and their parts are connected to various types of credit creation and also depend on different types of physical energy.

So economics is unique in being a marriage between the financial and non-financial, and the record of that is in the accounting, which is ex post.

Tom Hickey said...

I would dispute that economic can be deterministic in the sense that this is usually meant, e.g., in physics. where initial conditions are determinative and time series are regular unless they become chaotic (go exponential).

The regularities in economics are based chiefly on institutional arrangements and policy that are stable over time. There are no initial conditions in economics and no functions that apply universally as it physics. Regularity is endogenously imposed by authority built into the system. Accounting is a system of rules. There is a certain generally in accounting owing to agreement but rules may be somewhat different in different jurisdiction and change within the same one.

The actual mean of determinists in science has nothing to do with authority but rather "nature" as the basis for regularity. There is no natural regularity in human action other than that which is biologically determined. Some say that is all determined biologically but at this point, that is an unsubstantiated assumption. Rather where large scale regularity is observed it is due to imposition of authority in the form of positive law.

Order is rule-based. The natural science have discovered some rules that order physical and biological systems. Such laws are largely unknown in psychology and social science, including economics. Most human behavior is socially determined and that is a result of nurture rather than nature. Culture, including custom and tradition, and instituitions are the source of most regularity and these shift over time an differ geographically.

The most that psychology and social science can discover is dispositions and tendencies. Of these "optimization" is only one. Culturally there might be evidence of a single representative agent with homogenous preferences as a sort of "average person." But that is statistical. The regularity can be accounted for through influence rather than "nature."

Of course, the out here is to say that everything is "natural" because everything is nature and nothing is supernatural. Then it is a distinction without a difference and it falls to Occam's razor.

Models have to be selected relative to the job they are suppose to do. Deterministic models are only suitable where initial conditions are determinaitve.

But statistical models are not the only alternative to deterministic ones. In econ, for example, SFC modeling can construct contingent models based on assuming different aggregates. That the government fiscal balance is always the inverse of the non-government balance so that they sum to zero is not a function representing causality. But this identity can illumine the probable consequences of different ways of satisfying that identity. This is prediction of a sort, in that if government doesn't provide a "full employment budget" (run a deficit that accommodates non-government saving desire) then the economy will evenually underperform and real resources will be idled.

Matthew Franko said...

"this is where Matt is coming at, he is a "determinist and authoritarian".

Yes... perhaps as opposed to "stochastic and libertarian..."

Two sides to the human coin....