[From Bill Williams UMKC 6 Feburary 2003 5:30 PM CST]

[From Bill Powers (2003.02.06.1556 MST)]

By the way, is there really any such thing as a "business cycle?"

My professor said the only _real_ business cycle started every weekday at 8:00AM. But, conventionally what should be captioned "Economic Fluctuations" is frequently titled, cateloged, and courses were once given as "Business Cycle Theory." I probably had one of, if not _the_ last courses offered in business cycle theory.

So, I guess the anwer should be no. But, you are being unnecesarily picky.

best

Bill Williams

[From Bill Williams UMKC 7 Feburary 2003 2:40 PM CST]

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-----Original Message-----

From: Bill Powers [mailto:powers_w@EARTHLINK.NET]

Sent: Fri 2/7/2003 9:49 AM

To: CSGNET@listserv.uiuc.edu

Cc:

Subject: Re: Where does leakage go?

[From Bill Powers (2003.02.07.0838 MST)]

Bill Williams UMKC 6 Feburary 2003 5:30 PM CST--

>>By the way, is there really any such thing as a "business cycle?"

> ...

>I guess the anwer should be no. But, you are being unnecesarily picky.

Well, I prefer picky over inconsistent.

So do I. Of course! I didn't think I needed to include the grin symbol.

People, even economists see even economists can learn and have for some time been aware that business fluctuations are not cycles in the sense of being regularly periodic. But, there's a widespread tendency to retain the original terminology while changing the meaning of the concepts. I don't think this is neccesarily a good practice, but then I don't have much if any control over it. To protest, as I do from time to time, just annoys people. Consider the following from Brurns and Mitchell who were leading economists of their day, late 1940's:.

"Business cycles are a type of fluctuation found in the aggregate acrivity of nations that organize their work mainly in business enterprizes; a cycle consists of expansions occurring at about the same time in many economic activities, followed by simiarly general recessions, contractions and revivals which merge into the next cycle; this sequence of changes is _recurrent but not periodic._ " ( 1946, p.3. Burns and Mitchell

in _Chaotic Dynamics: Theory and Applications to Economics_ Alfredo Medo 1992 Ca mbridge

The book is keyed to software package DMC which I hadn't heard of which takes care of the overhead of simulating simultaneous equations.

[From Bill Williams UMKC 7 Feburary 2003 4:10 PM CST]

[From Bill Powers (2003.02.07.0838 MST)]

Bill Williams UMKC 6 Feburary 2003 5:30 PM CST--

>>By the way, is there really any such thing as a "business cycle?"

> ...

>I guess the anwer should be no. But, you are being unnecesarily picky.

Well, I prefer picky over inconsistent. To me, a cycle is a temporal

pattern _that repeats_.

Either I don't have a future in stand-up, or you are taking this all too seriously. Do you still say sunrise?

consider a statement by Burns and Mitchel big names for their day-- the 1940's.

"Business cycles are a type of _fluctuation_ found in [aggregate economic activity in which the ] sequence of changes is recurrent but _not_ periodic. (1946, p. 3.) quoted in Alfredo Medio 1992 _Chaotic Dynamics: THeory and Applications to Economics_ Cambridge.

I compiled Econ004 last night, now I'm thinking about how go about verifying that its doing what we think it should be doing. It looks OK to me. You provided a lot of commentary documenting the code. My initial impression, and only very initial impression, is that a more extensive graphic routine will be needed in order to visualize what's happening. But, I haven't spent enough time looking at the code yet, to really have much to say.

best

Bill Williams

[From Wolfgang Zocher (2002.02.02.14.10 CET)]

[From Bill Powers (2003.02.01.2047 M<ST)]

Bill Williams UMKC 1 Feburary 2003 6:30 PM CST

>My idea is that if the most basic represesntation is a set of differential

>equations then changes can be introduced into the consideration in a way

>that doesn't violate the initial definitions. And, the digital simulation

>can be checked against the continous model so that there are only very

>trivial differences between the two.

You can trust that the digital model in Econ004 will perform exactly the

same, to a fraction of a percent, as the same model embodied in op-amps. Or

ask Wolfgang Zocher, who owns a real analog computer and checked out my

digital modeling method against its performance. There may be some small

differences, but they are not the kind on which a theory stands or falls,

and they can be made as small as you like by reducing the size of the

computing interval.

That's right! If you deal with _linear_ differential equations of first order

you can solve them analytically and you only have to compare your simulation

results for a given dt with the analytically function f(t) with the same

timesteps. The sesults of simulation are very stable, even with simple

integrators like euler...

For the case of stiff deq's (i.e. with parameters which differ very much in

quantity) you have to use more complex integrators (gear) and you are sure

to get stable results.

For the case that you have nonlinear deq's, i.e. the parameters of the deq are

itself functions of time, the result of your simulation strongly depends on the

smoothness of the parameter functions. There are lots of other things you must

be aware of when you analyze the result of simulations bases on nonlinear deq's.

Best,

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Wolfgang Zocher

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www: http://wzocher.bei.t-online.de/

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Wolfgang Zocher (2002.02.02.1853 CET

[From Bill Powers (2003.02.02.0929 MST)]

Wolfgang Zocher (2002.02.02.14.10 CET)--

>For the case that you have nonlinear deq's, i.e. the parameters of the

deq are

>itself functions of time, the result of your simulation strongly depends

>on the smoothness of the parameter functions.

Thanks for the verification of the basic method. I know that it's possible

to get into trouble when the equations behave badly. However, I don't think

we ever just take the behavior of a model without thinking about it, asking

if it makes sense in terms of other knowledge, and generally trying to

understand it. We have to start somewhere, and I think if we worry too much

about making a mistake, we'll never have any model at all.

Sure. My example of nonlinear deq's was only meant as a description of the

worst case where simulations on either analogs or digital computers can give

wrong results or at least results with large error-probability.

All the experiments with deq's I've done so far could be reduced to systems

of ordinary deq's. And that is a consequence of the thinking about the

experiments as you mentioned. And for those deq's we have all the math to

handle them correctly in simulation programs on digital computers.

Best,

Wolfgang

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Wolfgang Zocher

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