Dynamic Component Models (DCMs)

 

The Dynamic Components Model (DCM) is a form of State Space Model where the approximate state variables are first computed using Principal Components Analysis (PCA). The difference between a standard State Space Model and the DCM are (1) how the Measurement Matrix (see graphic above) is computed (with PCA) and (2) how the state variables are analyzed directly. The advantage of the DCM is that it separates the growth and control state variables so that growth and control can be analyzed independently (the PCs are statistically independent). In the Cannonical DCM, there are only three state variables (one for growth and one for control) that explain at least 80% of the variation in the Output Variables. The control components are typical made up of Error Correcting Controllers (ECCs). In SocioEconomic systems the ECCs are typically associated with a theoretical tradition. For example, the Malthusian Controller is presented here and generalized here. ECCs are key elements of Cybernetics and the dominant growth component is a key element of Systems Theory and Economic Growth Theory.

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).

Forecasting and Scenario Construction

 

Of course, we cannot know The Future. Think about trying to predict the Future in 1900: World War I, The Great Depression, World War II, the Cold War, etc. Even after the fact, we have trouble explaining what happened in the InterWar Period. Yet, we persist. We try to predict the effects of Climate Change. We try to predict the path of Hurricanes. We try to predict next Quarter's Economic performance. 

Our vision for all this effort is (1) Science Fiction Psycho-Historian Harry Seldon created a hand-held device called the Prime Gradient that predicts the collapse of the Galactic Empire in the Foundation Trilogy and (2) Limits to Growth Engineer J. Wright Forrester created a computer program, World1, that predicted the collapse of the World System in 2050 as a result of resource shortage. These aren't the work of cranks. Issac Asimov was a scientist. J. Wright Forrester taught at MIT.

It is a mistake to think anyone knows the future. It is unknowable. What I think we can do is Explore the Future with state space models, systems analysis, multi-model inference and scenario construction. Some scenarios constructed in this manner are too awful to contemplate and must be avoided at all costs. An entire group of middle-range scenarios will seem likely but the best model cannot be chosen in advance. Systems are too complex and there is significant random error. An example of my approach is Five Futures for Russia in which I use five models of the Russian SocioEconomic system to construct statistical scenarios for the future (one is a statistical surprise). You can actually run the Business as Usual Model (BAU) on line here.

Computer simulation of statistically estimated systems models is essential. We have to get beyond the stage of arm-chair speculation which still seems to be the privileged mode of academic discourse based on The Classics. When faced with having to make predictions about the future of Climate Change, the science-based IPCC made the right choice: simulation and scenario construction. The Social Sciences have supplied few useful models for the IPCC project. Neoclassical Economics has provided the DICE Integrated Assessment Model but it is based on flawed neoclassical assumptions and is not statistically estimated or tested.

Here is some more detail on my approach. The methodology is all readily available and it remains for the Social Sciences to make a serious effort to apply it.

Atlanta Fed Economy Now

My approach to forecasting is similar to the EconomyNow model used by the Atlanta Federal Reserve. Since the new Republican Administration is signaling that they would like to eliminate the Federal Reserve, the app might well not be available in the future.

One important comment about the Atlanta Fed GDP Now App. The underlying forecasting model is based on the work of Stock and Watson (2012) on Diffusion Indexes. In Systems Theory, the diffusion index should be interpreted as a set of approximate state variables (essential variables) for a State Space model. The actual state of the system is then computed using the Kalman Filter and estimated using the dse package (see below).

Hurricane Forecasting

My vision for SocioEconomic system forecasting is to follow the US National Oceanic and Atmospheric Administration's (NOAA) approach to hurricane (Economic Crisis?) forecasting using Spaghetti Models.

Currently, Economic forecasting does not use Multimodel Inference but it is getting there! Model selection is based on the AIC Criterion.

Climate Change

My approach takes the IPCC Emission Scenarios and generalizes them to include many other variables, not just CO2 emissions and Global temperature. These scenarios are for the World System. Needless to say, the new Right-Wing Republican administration plans on withdrawing the US from all attempts to study or ameliorate Climate Change.

Compare the graphic above to my Alternate Futures for the US.

Data Sources and Estimation

There is a wealth of historical data sources that remain to be exploited for statistical analysis. My primary sources for the Late Twentieth Century are the World Development Indicators which contains a treasure trove of historical data on every country in the modern World-System. For longer-term historical analysis I use the Historical Statistics for the World Economy and the Maddison Historical Statistics Project. For detailed models of individual economies I use each country's historical statistics (for example, the Historical Statistics of the US or the European Historical Statistics). To deal with missing data I use the E-M (Estimation-Maximization) Algorithm and Nonlinear Spline Soothing. For model estimation I use the dse package in the R programming language. You can run R-code on line using the Snippets web-based service. My main purpose in using historical data is to develop models, not to understand the true course of World History.