World1 Model: The Limits to Growth

 

The graphic above displays data from the World1 Limits to Growth Model (Forrester, 1974). Historically, the 1972 Limits to Growth Report was important because it was the first modern challenge to the Unlimited Infinite Exponential Growth orthodoxy of Neoclassical Economics. The computer simulation model showed that, as a result of some reasonable assumptions about Natural Resource Exhaustion (e.g., Oil and Minerals), the World system was on a growth-and-collapse path.

To avoid Growth-and-Collapse, growth rates must be limited.

In another post (here), Gaya Harrington analyze the model in more detail and compares it to available historical data. In this post, I convert the World1 model into a State Space Dynamic Components (DCM) model to allow comparison with other World System models I have constructed and other analyses available in Systems Theory.

You can run you World1 Model using R-code here. The system is stable, nonlinear and cyclical. You can compare the World1 Model to the WL203 World Model** which is stable, linear and cyclical. Instructions are available in the R-code for conducting Counterfactual Analysis.

Notes

** The World1 Model and the WL203 World Model differ in the number of data points used to calibrate or estimate the models. The World1 Model uses six data points plus initial conditions (6 x 6 =12) while the WL203 World Model uses complete historical series (14 x 50 = 700) as data points.

Forrest (1973) World Dynamics: Second Edition (pdf).

World1 Measurement Model

Three Principal Components were extracted from the World1 data explain 100% of the variation in the variables (NR= Natural Resources, K=Capital Stock, POL=Pollution, QL=Quality of Life). The components are: W1=(0.440 N + 0.464 K + 0.4619 POL - 0.46659 NR), W2=(Overall Growth - 0.00684 NR) and W3 = (0.6143 POL + 0.354 QL - 0.596 N - 0.3616 NR).

World1 System Matrix

The World1 System is nonlinear, unstable and cyclical.

World1 W1 Time Plot

WL203 Model Measurement Matrix  

Three Principal Components were extracted from the World data explaining 97.3% of the variation in the variables: (N = Population, OIL = Oil Production, QA = Agricultural Output, GWP = Gross World Product, P.Wheat. = World Price of Wheat, P.Oil. = World Price of Oil, TEMP = Global Temperature, CO2 = Carbon Dioxide Emissions, Carbon = All Carbon Emissions, TotalFootprint = Ecological Footprint, Earths = Number of Earths needed to maintain production, WorldGlobal = Globalization, LivingPlanet = Living Planet Index, URBAN = World Urbanization.

WL203 Model System Matrix

W1 Time Plot

W1 Steady State

A Steady-State Economy in the WL203 World Model can be created with the following command:

f[2,3] <- f[3,2] <- 0

Which eliminates the feedback effects from W2=(LP + P.Wheat. + OIL - TEMP) and W3=(P.Oil. + P.Wheat.- OIL - EF), in words,  the feedback effects from the World-Market-Global-Temperature controller and the World-Market-Ecological-Footprint Controller.

Eliminating the Historical Feedback controllers is not a reasonable policy recommendation. However, reducing growth rates:

f[1,1] <- f[2,2] <- f[2,3] <- .9

Will produce a very rapid steady state in the graphic above. The same aergument made by the 1972 Limits to Growth Report. From Google AI:

Two different Systems Models reaching the same conclusion: 

To avoid Growth-and-Collapse, growth rates must be limited.

I should also point out that Systems Models include Historical Feedback Controllers that are absent from conventional Economic theory (for example, see the DICE Model).

Perspectives on the Limits to Growth

Data Mining

Technology Long Waves

  

The Kondratiev Wave is an important element of World-Systems Theory. The graphic above is taken from Andreas Goldschmidt and gives historical specifics for technological cycles. Goldschmidt's formulation allows for the idea to be tested (one of the models I always test), is partially consistent with economic Growth theory (particularly if we do not assume a functional form for exogenous disembodied technological change in the Solow-Swan Model) and I can present some examples.

• The Iranian Economy prior to 1979 and associated Tech Bubble.

Again: Why Macroeconomic Models have Failed!

Almost two decades after the Financial Crisis of 2008, economists are still puzzling over why they failed to predict the Financial Crisis and what the failure of predictions has to do with the underlying economic models. The answer is simple but the solution, needless to say, isn't.

Economic Models are unable to predict systemic crises because they do not look at the Economy as a system but rather as a collection of individuals.

The System, as opposed to the individual participants, has its own rules and the rules have very little, if anything, to do with the rational economic behavior of individuals, even if all participants in the system behave rationally, which they certainly don't! The System can still produce optimum solutions, but that is also basically hypothetical.

All of this has been argued before (see the references in the Notes below), but we aren't making progress because we don't have examples of economic system models that can be estimated from historical data. I will provide examples in this post.

Researchers in Biology, Earth Sciences, and Engineering have basically solved the "Systems Problem," but the Social Sciences are still struggling with qualitative mental models that, even in mathematical versions, cannot be tested and refuted. There are great examples in Sociology (Parsonian Systems Theory), Political Science (Easton's Political Systems Model) and Economics (Classical Economic Models). 

Notes

 

How Does Systems Theory Differ from Economics?

 

 

The DCM is implemented in the public domain R Programming language as an extension to the dse (Dynamic System Estimation) package. The dse package can be downloaded on all Computer platforms and can be run on line with a web browser (here). The DCM extensions with documentation are available here.

In the dse package, a state space model can be created using the SS command in R:

The State Space model has two forms: non-innovations and innovations:

The matrices are (double click to enlarge):

An example of the USL20 model can be found here. Other examples of the models with written analysis can be found on my blog at Blogger.com (here). For more information on Dynamic Component Models see Pasdirtz, 2007.

Controlling Dynamic Components Models

 

For more information on Dynamic Component Models see Pasdirtz, 2007.