Category Archives: Vensim

The dynamics of UFO sightings

The Economist reports on UFO sightings:

UFOdataThis deserves a model:

UFOs

UFOs.vpm (Vensim published model, requires Pro/DSS or the free Reader)

The model is a mixed discrete/continuous simulation of an individual sleeping, working and drinking. This started out as a multi-agent model, but I realized along the way that sleeping, working and drinking is a fairly ergodic process on long time scales (at least with respect to UFOs), so one individual with a distribution of behaviors over time or simulations is as good as a population of agents.

The model replicates the data somewhat faithfully:

UFOdistributionThe model shows a morning peak (people awake but out and about) and a workday dip (inside, lurking near the water cooler) but the data do not. This suggests to me that:

  • Alcohol is the dominant factor in sightings.
  • I don’t party nearly enough to see a UFO.

Actually, now that I’ve built this version, I think the interesting model would have a longer time horizon, to address the non-ergodic part: contagion of sightings across individuals.

h/t Andreas Größler.

Early economic dynamics: Samuelson’s multiplier-accelerator

Paul Samuelson’s 1939 analysis of the multiplier-accelerator is a neat piece of work. Too bad it’s wrong.

Interestingly, this work dates from a time in which the very idea of a mathematical model was still questioned:

Contrary to the impression commonly held, mathematical methods properly employed, far from making economic theory more abstract, actually serve as a powerful liberating device enabling the entertainment and analysis of ever more realistic and complicated hypotheses.

Samuelson should be hailed as one of the early explorers of a very big jungle.

The basic statement of the model is very simple:

NationalIncome

In quasi-System Dynamics notation, that looks like:

SamuelsonDiagramB

A caveat:

The limitations inherent in so simplified a picture as that presented here should not be overlooked. In particular, it assumes that the marginal propensity to consume and the relation are constants; actually these will change with the level of income, so that this representation is strictly a marginal analysis to be applied to the study of small oscillations. Nevertheless it is more general than the usual analysis.

Samuelson hand-simulated the model (it’s fun – once – but he runs four scenarios):Simulated Samuelson then solves the discrete time system, to identify four regions with different behavior: goal seeking (exponential decay to a steady state), damped oscillations, unstable (explosive) oscillations, and unstable exponential growth or decline. He nicely maps the parameter space:

parameterSpace

ParamRegionBehaviorSo where’s the problem?

The first is not so much of Samuelson’s making as it is a limitation of the pre-computer era. The essential simplification of the model for analytic solution is;

Simplified

This is fine, but it’s incredibly abstract. Presented with this equation out of context – as readers often are – it’s almost impossible to posit a sensible description of how the economy works that would enable one to critique the model. This kind of notation remains common in econometrics, to the detriment of understanding and progress.

At the first SD conference, Gil Low presented a critique and reconstruction of the MA model that addressed this problem. He reconstructed the model, providing an operational description of the economy that remains consistent with the multiplier-accelerator framework.

LowThe mere act of crafting a stock-flow description reveals problem #1: the basic multiplier-accelerator doesn’t conserve stuff.

inventory1 InventoryCapital2Non-conservation of stuff leads to problem #2. When you do implement inventories and capital stocks, the period of multiplier-accelerator oscillations moves to about 2 decades – far from the 3-7 year period of the business cycle that Samuelson originally sought to explain. This occurs in part because the capital stock, with a 15-year lifetime, introduces considerable momentum. You simply can’t discover this problem in the original multiplier-accelerator framework, because too many physical and behavioral time constants are buried in the assumptions associated with its 2 parameters.

Low goes on to introduce labor, finding that variations in capacity utilization do produce oscillations of the required time scale.

ShortTermI think there’s a third problem with the approach as well: discrete time. Discrete time notation is convenient for matching a model to data sampled at regular intervals. But the economy is not even remotely close to operating in discrete annual steps. Moreover a one-year step is dangerously close to the 3-year period of the business cycle phenomenon of interest. This means that it is a distinct possibility that some of the oscillatory tendency is an artifact of discrete time sampling. While improper oscillations can be detected analytically, with discrete time notation it’s not easy to apply the simple heuristic of halving the time step to test stability, because it merely compresses the time axis or causes problems with implicit time constants, depending on how the model is implemented. Halving the time step and switching to RK4 integration illustrates these issues:

RK4

It seems like a no-brainer, that economic dynamic models should start with operational descriptions, continuous time, and engineering state variable or stock flow notation. Abstraction and discrete time should emerge as simplifications, as needed for analysis or calibration. The fact that this has not become standard operating procedure suggests that the invisible hand is sometimes rather slow as it gropes for understanding.

The model is in my library.

See Richardson’s Feedback Thought in Social Science and Systems Theory for more history.

Bulbs banned

The incandescent ban is underway.

Conservative think tanks still hate it:

Actually, I think it’s kind of a dumb idea too – but not as bad as you might think, and in the absence of real energy or climate policy, not as dumb as doing nothing. You’d have to be really dumb to believe this:

The ban was pushed by light bulb makers eager to up-sell customers on longer-lasting and much more expensive halogen, compact fluourescent, and LED lighting.

More expensive? Only in a universe where energy and labor costs don’t count (Texas?) and for a few applications (very low usage, or chicken warming).

bulb economicsOver the last couple years I’ve replaced almost all lighting in my house with LEDs. The light is better, the emissions are lower, and I have yet to see a failure (unlike cheap CFLs).

I built a little bulb calculator in Vensim, which shows huge advantages for LEDs in most situations, even with conservative assumptions (low social price of carbon, minimum wage) it’s hard to make incandescents look good. It’s also a nice example of using Vensim for spreadsheet replacement, on a problem that’s not very dynamic but has natural array structure.

bulbModelGet it: bulb.mdl or bulb.vpm (uses arrays, so you’ll need the free Model Reader)

What’s the empirical distribution of parameters?

Vensim‘s answer to exploring ill-behaved problem spaces is either to do hill-climbing with random restarts, or MCMC and simulated annealing. Either way, you need to start with some initial distribution of points to search.

It’s helpful if that distribution is somehow efficient at exploring the interesting parts of the space. I think this is closely related to the problem of selecting uninformative priors in Bayesian statistics. There’s lots of research about appropriate uninformative priors for various kinds of parameters. For example,

  • If a parameter represents a probability, one might choose the Jeffreys or Haldane prior.
  • Indifference to units, scale and inversion might suggest the use of a log uniform prior, where nothing else is known about a positive parameter

However, when a user specifies a parameter in Vensim, we don’t even know what it represents. So what’s the appropriate prior for a parameter that might be positive or negative, a probability, a time constant, a scale factor, an initial condition for a physical stock, etc.?

On the other hand, we aren’t quite as ignorant as the pure maximum entropy derivation usually assumes. For example,

  • All numbers have to lie between the largest and smallest float or double, i.e. +/- 3e38 or 2e308.
  • More practically, no one scales their models such that a parameter like 6.5e173 would ever be required. There’s a reason that metric prefixes range from yotta to yocto (10^24 to 10^-24). The only constant I can think of that approaches that range is Avogadro’s number (though there are probably others), and that’s not normally a changeable parameter.
  • For lots of things, one can impose more constraints, given a little more information,
    • A time constant or delay must lie on [TIME STEP,infinity], and the “infinity” of interest is practically limited by the simulation duration.
    • A fractional rate of change similarly must lie on [-1/TIME STEP,1/TIME STEP] for stability
    • Other parameters probably have limits for stability, though it may be hard to discover them except by experiment.
    • A parameter with units of year is probably modern, [1900-2100], unless you’re doing Mayan archaeology or paleoclimate.

At some point, the assumptions become too heroic, and we need to rely on users for some help. But it would still be really interesting to see the distribution of all parameters in real models. (See next …)

Timing Vensim models

Need to time model runs? One way to do it is with Vensim’s log commands, in a cmd script or Venapp:

LOG>CREATE|timing.txt
LOG>MESSAGE|timing.txt|"About to run."
LOG>TIMESTAMP|timing.txt
MENU>RUN|o
LOG>TIMESTAMP|timing.txt
LOG>MESSAGE|timing.txt|"Ran."

These commands were designed for logging user interaction, so they don’t offer millisecond resolution needed for small models. For that, another option is to use the .dll.

Generally, model execution time is close to proportional with equation count x time step count, with exceptions for iterative functions (FIND ZERO) and RK auto integration. You can use the .dll’s vensim_get_varattrib to count equations (expanding subscripts) if it’s helpful for planning to maximize simulation speed.

Vensim + data with ODBC

I haven’t had much time to write lately – too busy writing Vensim code, working on En-ROADS, and modeling the STEM workforce.

So, in the meantime, here’s a nice tutorial on the use of ODBC database links with Vensim DSS, from Mohammad Jalali:

This can be a powerful way to ingest a lot of data from diverse sources, and to share and archive simulations.

Big data is always a double-edged sword in consulting projects. Without it, you don’t know much. But with it, your time is consumed with discovering all the flaws of the data, which remain because most likely no one else ever looked at it seriously from a strategic/dynamic perspective before. It’s typically transactionally correct, because people verify that they get their orders and paychecks. But at an aggregate level it’s often rife with categorization mismatches across organizational boundaries and other pathologies.

Setting up Vensim compiled simulation on Windows

If you don’t use Vensim DSS, you’ll find this post rather boring and useless. If you do, prepare for heart-pounding acceleration of your big model runs:

  • Get Vensim DSS.
  • Get a C compiler. Most flavors of Microsoft compilers are compatible; MS Visual C++ 2010 Express is a good choice (and free). You could probably use gcc, but I’ve never set it up. I’ve heard reports of issues with 2005 and 2008 versions, so it may be worth your while to upgrade.
  • Install Vensim, if you haven’t already, being sure to check the Install external function and compiled simulation support box.
  • Launch the program and go to Tools>Options…>Startup and set the Compiled simulation path to C:\Documents and Settings\All Users\Vensim\comp32 (WinXP) or C:\Users\Public\Vensim\comp32 (Vista/7).
    • Check your mdl.bat in the location above to be sure that it points to the right compiler. This is a simple matter of checking to be sure that all options are commented out with “REM ” statements, except the one you’re using, for example:
  • Move to the Advanced tab and set the compilation options to Query or Compile (you may want to skip this for normal Simulation, and just do it for Optimization and Sensitivity, where speed really counts).

This is well worth the hassle if you’re working with a large model in SyntheSim or doing a lot of simulations for sensitivity analysis and optimization. The speedup is typically 4-5x.

Elk, wolves and dynamic system visualization

Bret Victor’s video of a slick iPad app for interactive visualization of the Lotka-Voltera equations has been making the rounds:

Coincidentally, this came to my notice around the same time that I got interested in the debate over wolf reintroduction here in Montana. Even simple models say interesting things about wolf-elk dynamics, which I’ll write about some other time (I need to get vaccinated for rabies first).

To ponder the implications of the video and predator-prey dynamics, I built a version of the Lotka-Voltera model in Vensim.

After a second look at the video, I still think it’s excellent. Victor’s two design principles, ubiquitous visualization and in-context manipulation, are powerful for communicating a model. Some aspects of what’s shown have been in Vensim since the introduction of SyntheSim a few years ago, though with less Tufte/iPad sexiness. But other features, like Causal Tracing, are not so easily discovered – they’re effective for pros, but not new users. The way controls appear at one’s fingertips in the iPad app is very elegant. The “sweep” mode is also clever, so I implemented a similar approach (randomized initial conditions across an array dimension) in my version of the model. My favorite trick, though, is the 2D control of initial conditions via the phase diagram, which makes discovery of the system’s equilibrium easy.

The slickness of the video has led some to wonder whether existing SD tools are dinosaurs. From a design standpoint, I’d agree in some respects, but I think SD has also developed many practices – only partially embodied in tools – that address learning gaps that aren’t directly tackled by the app in the video: Continue reading

Vensim Compiled Simulation on the Mac

Speed freaks on Windows have long had access to 2 to 5x speed improvements from compiled simulations. Now that’s available on the Mac in the latest Vensim release.

Here’s how to do it, in three easy steps:

  • Get a Mac.
  • Get the gcc compiler. The only way I know to get this is to sign up as an Apple Developer (free) and download Xcode (I grabbed 3.2.2, which is much smaller than the 3.2.6+iOS SDK, but version shouldn’t matter much). There may be other ways, but this was easy.
  • Get Vensim DSS. After you install (checking the Install external function and compiled simulation support to: box), launch the program and go to Vensim DSS>Preferences…>Startup and set the Compiled simulation path to /Users/Shared/Vensim/comp. Now move to the advanced tab and set the compilation options to Query or Compile (you may want to skip this for normal Simulation, and just do it for Optimization and Sensitivity, where speed really counts).

OK, so I cheated a little on the step count, but it really is pretty easy. It’s worth it, too: I can run World3 1000 times in about 8 seconds interpreted; compiled gets that down to about 2.

Update: It turns out that an installer bug prevents 5.10d on the Mac from installing a needed file; you can get it here.

Monday tidbits- tools, courses

I neglected to cross-post an interesting new Vensim model documentation tool that’s in my model library.

Shameless commerce dept.: I’m teaching Vensim courses in Palo Alto in April and Bozeman in June. Following the June offering, Ventana’s Bill Arthur will be teaching “SMLOD” – Small Models with Lots of Data – a deep technical dive into the extraction of insight from large datasets.