Results from the Defence and the Economy System Dynamics Model

In this post, I will summarize the approach used in the System Dynamics Model of Defence and the Canadian Economy.  Then I will provide some findings for Defence expenditure for three threat scenarios.  Finally, I will provide the results for all of the sectors in the economy.

The processes in the model of Defence and the economy can be summarized by the figure below.  The need for Defence is modified by shocking the system through changes to the Defence per capita normal.  The discrepancy between the current Defence per capita in the model and the Defence per capita normal creates a pressure on the need for Defence.

If the Defence per capita is less than the Defence per capita normal, such as after September 11th, 2001, then the need for Defence will increase.

If the need for Defence increases the desired expenditure on Defence increases and the "desired" expenditure on labour, capital and resources for Defence will increase.

This leads to actual increases in labour, capital and resources devoted to Defence and thereby allows the production of Defence to increase.

When Defence production increases, the Defence per capita increases and the discrepancy between the Defence per capita and Defence per capita normal decreases.  So the need for Defence will decrease.

Therefore, these are balancing or goal seeking loops in the language of System Dynamics.

Of course, if the Defence per capita is greater than the Defence per capita normal, such as at the end of the Cold War, then the relationships would work in the opposite direction and the desired expenditure on Defence and the Defence production would decrease.

The figure below shows the results from the model in terms of Defence expenditure for three scenarios.

  

The first scenario (the yellow curve) is the counter-factual situation in which there was no terrorist attack on September 11th, 2001.  We can see that the Defence budget is still assumed to increase because of an increase in the population of Canada.

The second scenario (the purple curve) mimics reality in which there was an increased need for Defence after September 11th, 2001 and that this period of increase need continued until the end of Canada's combat commitment in Afghanistan.  The the need for Defence returned to a lower lever after 2012.  We can see that the Defence expenditure gradually increases and then reaches a higher steady-state than the counter-factual.

The final scenario that was examined (the blue curve) was a continued state of higher tension that resulted in a higher need for Defence indefinitely.  In this case, Defence is believed to require continually increasing investment.

Preliminary findings for all of the sectors of the economy shown in the figure below suggest that the economy will be dominated by the private services sector which will continue to increase for the next 50 years.  The other sectors of the economy are predicted to reach a steady-state around 2060.

  

The results from the model suggest that increased Defence expenditure will have little or no impact on total gross domestic product of the nation in the short-term.  Continuing increases in Defence expenditure will have a positive effect on the gross domestic product of the nation in the long-term but the effect is believed to be relatively marginal.

The results from the model appear to show that increased Defence expenditure will not "crowd out" development in other sectors because there is inherent slack in the economy to draw additional resources for Defence.

These results seem realistic to me.  I believe that Defence is a small part of the Canadian economy and changes in Defence expenditure within the expected ranges will neither hurt nor aid the economy to a significant effect.  This is a somewhat negative result from the point of view of proponents for increased Defence expenditure.

One of the novel concepts provided by this model is Defence per capita as a measure of the appropriate expenditure on Defence.  The usual measure in Defence economics is Defence expenditure as a percent of GDP.

Defence as a percentage of GDP implies that richer countries will spend more to defend themselves than poorer countries. The threats faced by a country are not directly considered.  Instead, the idea might be that rich countries have more to lose from outside threats and therefore spend more on Defence to protect their assets.

As an alternative, in our model, the gap between Defence per capita and Normal Defence per capita suggests that the Defence expenditure would be based on the population's perception of the threats to their lives.  That is, citizens in countries with significant perceptions of threats to their lives would be willing to spend more per capita than countries with less of a perception of threat to their lives.  This might better explain why Canada spends relatively little on Defence; namely, because Canadians do not feel their lives are being threatened.

On this note, I retired from the Defence Research and Development Agency.

Nathan Forrester’s System Dynamics Model of the Canadian Economy

Nathan Forrester built his model of the Canadian economy in DYNAMO which was the original System Dynamics language developed in the early 1970’s but is no longer supported.  Therefore, the first thing we did was convert the model to the modern System Dynamics software environment, Vensim.  Fortunately, Nathan had used the same excellent documentation standards as his father, Jay Forrester, the inventor of System Dynamics.  So this conversion was not difficult. 

The model was initialized to the year 1900.  It was calibrated to provide representative results for 1972.  Then it ran to the year 2150.  Nathan provided both graphical results and tabular results for many intermediate variables.  We were able to replicate the results of Nathan’s original model to 7 decimal places.

Nathan also provided a number of diversions from the standard model that we were able to replicate.  These were useful because some of the diversions appeared to model the Canadian economy more realistically than the original model.

The model consisted of five sectors of the economy: agriculture, goods, services, capital and resources.  We used data from Statistics Canada on the production in these sectors of the economy to calibrate the model.  In the graph below, the smooth curves are taken from the model and the jagged curves are the Statistics Canada data.

The agriculture, goods and services sectors use labour, capital and resources which are allocated according to a competitive process.  Each of these economic sectors is derived from a common template.  So it was easy to build two new sectors for Defence expenditure and government expenditure excluding Defence.  I will postpone the discussion of these extensions to Nathan Forrester’s model until my next post.

System Dynamics Models of the Economy

I received funding to hire a contractor for two years to help me build a System Dynamics model to estimate the impact of Defence expenditure on the Canadian economy.  In the first year of the project, we examined the literature for existing System Dynamics models that could be used for macroeconomic modelling.

We found three.  The first was Threshold 21 built by the Millennium Institute.  The second one was a model developed by Nathan Forrester (Jay Forrester’s son) for the Natural Resources Canada in 1972.  The third was a model developed by Nathan Forrester for his PhD dissertation.

The Threshold 21 model had hundreds of equations and thousands of variables.  It had a sub-model for Defence spending and a timeline for GDP.  However, when we looked more closely, we found the model for Defence spending was simply a time series of Defence expenditure that was input to the model.  Therefore, there was no analysis being conducted by the model.  It was simply a situation where the Defence expenditure time series was input to the model and added to the GDP curve.  This was not satisfactory.

The Natural Resources Canada model developed by Nathan Forrester was an excellent example of how to build a System Dynamics model.  Nathan thanked his father Jay, the inventor of System Dynamics, for his help in building the model.  The model had five sectors of the economy but did not have sectors for Defence or government in general.

The third model was a classical macroeconomic model that might be useful to the Department of Finance.  It attempted to model monetary and fiscal policy to stabilize the economy but would not be useful to the Defence expenditure issue.

After the first year of study, we chose to continue the work by concentrating on the model of the Canadian economy built by Nathan Forrester for Natural Resources Canada.  We planned to add two new sectors to the model: for Government expenditure excluding Defence; and for Defence expenditure.