State Space Models

All state space models are written and estimated in the R programming language. The models are available here with instructions and R procedures for manipulating the models here here.
Showing posts with label Canada. Show all posts
Showing posts with label Canada. Show all posts

Thursday, August 21, 2025

World-System (1960-2100) Geopolitical Linkages: Canada, Mexico and the US

 



A recent article in the New York Times (here) suggests that Trump II Administration bullying (Trade Threats to both Canada and Mexico) might bring the two countries (CA and MX) closer together. It's hard to imagine Geopolitical Linkages between Canada and Mexico without the US. Mexico has strong cultural and economic relations with the Southwestern US and Canada has solid culture and economic relationships with the entire Northern US. There are strong inertial forces that will keep the Free Trade Agreements between the three countries moving forward well beyond the limited and inconsistent influence of the Trump II Administration.

The results presented below also suggest (not unexpectedly) that President Trump is tinkering with a system that he does not understand.

In this post, I will put the Growth Components (CA1, MX1, and US1, presented in the Notes below) of the three countries (CA, MX, US) together in a systems model and see what shape the future dynamics might take.** The first question would be which model would be best (from an AIC perspective), the two country model (CA1, MX1) or the three country model (CA1, MX1, US1)? The AICs  for the models are presented in the Notes below. From the AIC perspective, the three-country World-System linkage model is best.

But, let me clarify these results. I assume that politicians follow a BAU strategy: "our country is able to make it's own decisions without regard for other countries or the World System". The reality is, however, that each country is part of the World-System, whether they like it or not and whether they do or do not take into account World-System forces. The BAU results in the Notes suggest that CA and MX might reasonably consider going it alone together. The history of US, Canada and Mexico Free Trade Agreements also suggests that the countries understand the importance of the US as Hegemonic Leader of the World-System. Strong inertial forces will keep the three countries trading with each other long past the Trump II Administration. Inertia does not mean that there are not tensions and contradictions in the system!

The problem with forecasts from the WS-linkage model (above) is that each country will face a possible growth-and-collapse, Limits-to-Growth future. The US will peak a little later (2050) than CA or MX (2025). So, right out of the gate, World System linkage will seem like a bad idea to growth-obsessed politicians. From the standpoint of Environmental Damage from growth, Degrowth would be a positive outcome. So my assumption is that growth-obsessed politicians will turn away from a Limits-to-Growth future and focus on a BAU strategy such as NAFTA or the USMCA (the Trump I version of  NAFTA).

If each country (MX, CA, US) focuses on business-as-usual and their existing linkages (which  is very likely after the Trump II Administration), each country could experience unlimited exponential growth well after 2150 driven by the US, which is the unstable part of the system (you can experiment with the MX_CA_US model using the code provided here). At least unstable, unlimited growth was the vision prior to the Trump II Administration



I have suggested here that the Trump II Administration  is essentially taking the US on a Random Walk. If Trump is successful, the result (graphic above) could be a steady state (well after 2150) for all three countries if the US Random Walk persists (you can experiment with setting the US to an RW here; try to determine when the steady state will occur--it's way off in the future)




In the short-run (year-to-year), the Mexican Economy is also a Random Walk (here). Additionally, setting the Mexican Economy to a Random Walk (graphic above) destabilizes the system and pushes the US into collapse mode. President Trump has to be careful with his RW-policy-approach because it can also destabilize the system.


All of the above is a round-about but necessary way of getting to the question of what effect will Trump Shocks have on the USMCA system? The graphic above shows how a negative shock to the US will affect each country, to include the US. Both MX and CA will be affected negatively to about the same extent and take over twenty years to reach equilibrium again. The US will respond positively in the first years (a prediction of the Shock Doctrine) but will eventually have to deal with the negative consequences for about the same twenty years. In other words, 

the Trade War works in the short run but in the long run helps none of the parties.

You can experiment with the MX_CA_US Model here and the MX_CA_US_W Input Model here. You can experiment with the MXL20 model here, the USL20 model here, the CA_LM model here and the WL20 model here.

In a future post, I will explore finding a steady state for the World System and what it's effect on the MX_CA_US_W Model could be.




 Notes

** More information about how the dynamic component state space models can be found in the Boiler Plate.

AICs

The AICs are: (CA1MX1 = [104 > AIC=121.6, 137.5]) and (CA1MX1US1 [112.5 > AIC=138.5 > 163]) for the Business-as-Usual Models (BAU) and (CA1MX1 = [58.03  > AIC=101.6 > 134.2]) and (CA1MX1US1 = [ 51.14 < AIC=94.59 < 132.4]) for the World System (WS) input model (smaller is better for the AIC).

MX Components


CA Components


US Components


World Components











Thursday, February 6, 2025

World-System (1980-2100) Eight Futures for Canada


The Trump II administration has threatened a Trade War with Canada and the imposition of tariffs has been delayed while negotiations proceed (here). Canada, Mexico, China and the EU are the US's largest trading partners. I have presented the MXL20 (Mexico Late 20th Century) model here with eight future growth forecasts. In this post, I will do the same for Canada.

The Canadian forecasts are a little different in that they group clearly into two classes: Growth and Steady State (presented above) or Collapse (presented below) when compared against a the Random Walk (RW)--I give more detail about the classes of models with the MXL20 model here--the best two forecasts are the TECHE (Technical Efficiency) forecast and the Business as Usual (BAU) forecast. The forecasts do not predict growth forever (the Techno-Optimist forecast) but rather a steady-state after 2100 (the type of forecast one would get with a Classical Economic model).

The forecast for Geopolitical Alignment with the United States is very interesting and, I would argue, speaks directly to the threatened Trade War. The forecast with the USL20 model driving inputs to the CAL20 model suggests a Growth-and-Collapse scenario with a peak around 2025 at the start of the Trump II administration. In other words, the benefits of Canada's alignment with US have reached their peak and are not forecast to continue into the future--and my forecasts start in 2010!

Both the IMF (here) and the OECD (here) argue (as of 2024) that Canada needs to focus on internal structural issues and Technology, the BAU and the TECHE (Technical Efficiency) forecasts above. Reorienting the Canadian Economy will be difficult during a Trade War with the US, to say the least.


It would be reasonable to argue that some other Geopolitical Alignment might serve Canada better than alignment with the US, which appears to be ending.  I have estimated three other alignment models: World System (W), North America (NA) and China (CN). All of these models (presented above) predict collapse, some collapses being severe (NA and CN, respectively). Even focusing on Technical Productivity (TECHP) is worse than a Random Walk (RW, tomorrow being like today except for random shocks).

In summary, the CAL20 model suggests that Canada should concentrate on getting it's structural house in order and implementing efficiency-producing technologies, two steps that the IMF and the OCED have been emphasizing for the last twenty years. Let the Trade War with the US play it's way out. Geopolitical Alignment with the US has run it's course.

The IMF (here) and the OECD (here) economic reports about Canada bring up many other macro-economic issues. I'll look at those issues in the future. Setting the big picture for the Canadian Economy will help put detailed policy issues in a better perspective. I want to emphasize again that the future is unknowable. All I am doing is creating scenarios based on state space models. We will have to wait for the future to understand how useful such models might be.

NOTES

The Measurement Matrix for the CAL20 model is:


The first six indicators in standard scores are taken from the World Development Indicators (WDI). KOF = KOF Index of Globalization, EF = Ecological Footprint, HDI = Human Development Index. The second two components: CA2=(0.721 LU - 0.675 EF) and CA3 = (0.586 LU + 0.680 EF - 0.249 CO2 - 0.263 Q - 0.2076 N) describe Environmental and Unemployment Error Correction Controllers (ECCs). I will present the behavior of the Canadian ECCs in a future post.

You can run the CAL20 model here. The Bootstrap confidence intervals for the coefficients are:


You can convert the model into a Techno-Optimist model by setting F[1,1] = 1.0 in the System Matrix, but that would be an improbable value although it is close to the Upper Confidence Interval (UCI) of 0.990595.