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.

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

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

World1 Measurement Model

Three components 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  

WL203 Model System Matrix

W1 Time Plot

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.