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.

Saturday, October 10, 2026

FRANCE (1980-2100): Debt Crisis Forecasts




In a prior post (French Debt, Collapse of the Government and COVID-19), I presented a single Business-As-Usual (BAU) forecast for French DEBT. In this post, I present some Geopolitical policy options (hypothetical forecasts)  for lowering DEBT. They are presented in the graphic above.

  • BAU Model (BAU) Debt keeps rising but eventually stabilizes after 2100 when France becomes a Steady-State Economy at a higher level of debt.
  • Random Walk Model (RW) In the random Walk (RW) policy makers try "one damned thing after another" trying to find a solution. Anything can happen, but the RW will create continuing street protests.
  • European Union (EU) Models Membership in the EU provides certain constraints on Debt. If France operates within these constraints, debt is forecast to return to pre-2000 levels (notice that policy actions after 2000 kept Debt from climbing).
  • US Geopolitical Leverage (Wall Street) If Wall street calls the shots, French debt is forecast to fall back to 1980 levels.
  • World Geopolitical Leverage (Global Debt Markets) If France aligns itself with Global Debt Markets, DEBT is forecast to fall to levels not seen in the Late 20th Century.
What the French Political System might do in the future is not clear, but see my best guesses below.


A Blog Roll of my current postings on France is available here.

You can run the FRL20 Model written in R-Code on my Google Site (here). The French Economy is stable and headed toward a Steady-State Economy around 2030.




Notes



Wikipedia Links


 FRL20 DEBT Measurement Model



The French Debt Controller is FR1 = (Q-DEBT). Typically, DEBT is measured as a percentage of GDP, however the comparison does not reveal whether DEBT in under control.


 FRL20 DEBT BAU Model




The FRL20 DEBT BAU model is stable and under control.


FRL20 DEBT AIC Statistics





The Akaike Information Criterion (AIC) statistics for the FRL20 DEBT Models are presented above. Using the AIC, the RW model is best. The other models have overlapping Confidence Intervals so it difficult to pick a second-place model. I imagine that, under uncertainty, policy makers choose BAU or RW but France also has to satisfy the EU.




Wednesday, September 30, 2026

JAPAN: JP1 Growth and Collapse Forecasts



This page is UNDER CONSTRUCTION.


There are two attractive modes for the Economy of Japan: (1) Growth as a regional player in Southeast Asia (AJ) or (2) Business-As-Usual (BAU, see the JP_LM BAU Model). Each of these "attractive" growth modes are compared to a Random Walk (RW or Muddling Through) in the graphic above.




There are also three Geopolitical Collapse Modes or Japan: (1) AXJ, alignment to the Asia Region without regard for the Japanese economy, (2) US, alignment with the United States and (3) W, alignment with the world-system (displayed above).


You can run the JP_LM BAU model using R-code on my Google site (here). Data is from the Maddison Project.



Notes


JP_LM Measurement Model



The JP_LM model has three component state variables that explain 100% of the variation in the indicators. JP1 = (Overall Growth), JP2 = (XREAL-HOURS) an Export-Employment controller and JP3 = (HOURS+XREAL - N) a Population-Export-Employment controller.




JP_LM AIC Statistics




All the Akaike Information Criterion (AIC) statistics have overlapping confidence intervals; models have to be chosen on other criteria.


JP_LM BAU Model



The JP_LM BAU model is unstable but easily stabilized by reduction growth rates (see the JP_LM Model in my Google site).


 

Sunday, September 27, 2026

USL20 Poverty-Hardship Forecast


In a prior post (here) I quoted President Trump saying that Poverty numbers were "Great" in the US and presented a forecast of the US Hardship Index (of which Poverty SI.POV.DDA is a component). This might confuse some readers who expected to see actual Poverty data, so I have presented that above with a Forecast and Prediction Intervals. It reaches the same conclusions.




Note


USL20 Poverty Model




USL20 Poverty Model AIC Statistics








 

Tuesday, September 8, 2026

Why is the US Labor Share in Income Declining and Will It Stop?



This page is UNDER CONSTRUCTION. Your comments and answers to questions would be appreciated. The topic is by no means simple and easy to analyze!

Except for a peak in the year 2000 (graphic above), Labor's Share of national Income (Q/L) in the United States has been consistently declining. There are two outstanding questions: (1) Why? and (2) When will it stop or possibly reverse? This post tests seven State Space models of the US economy to decide which model best explains the decline and forecasts what might happen in the future under each of the different models. The "best" model explains the labor share time paths as a result of inputs from the World System in which the US Economy is embedded.

The competing explanations for the decline in Labor's share are:
  • Technological Change Technology can be embedded in the Capital Stock and cheaper Capital can be Substituted for Labor.
  • Dynamics of the US Economy Shocks to the economic system (for example, technological shocks) can lead, over time, to changes in Labor's Share.
  • Globalization and the World System Labor income can be driven down by cheap global competition and rewards for capital-labor substitution (using the KOF Index of Globalization).
In the graphic at the start of this post, six of the models are compared against a Random Walk, that is, no explanation.

In Neoclassical Economic Theory, Labor's Share of National Income and Capitals's share are constant parameters. At equilibrium, both are constant. Over time, differences can result from shocks and resulting system dynamics.

In Marxist Theory, Labor's share is driven to the subsistence level necessary to reproduce labor. Profit is whatever is left over after subsistence wages are paid.


ChatGPT summarizes it's findings as:




Here is a Causal Diagram of the ChatGPT explanation.



or a Simplified Model:



From the AIC Statistics below, the WL20-Input Model is best. However, the BAU model is a close second and the confidence intervals overlap.


Notes

Questions

  1. What policy measures (if any) would you recommend to address the decline in Labor's Share of National Income?
  2. Develop the Causal Diagram above in Neoclassical From (see see this post).
  3. Derive the Simplified model of Labor's share from the Causal Diagram above using Loop Reduction Rules.
  4. In the references below, do you find the World System mentioned directly or just indirectly? Do you think this is an important omission?
  5. Is it necessary to go on to test the structural models (Solow-Swan vs. Marx-Ricardo) to understand the decline in Labor'ss Share?

References

NY Times (Sep 7, 2026) Why is Labor's Share of National Income Declining Is Technology the most important factor?

BLS, Second Quarter 2026, Revised, Economic News Release Labor productivity by sector

IMF (2017) What Explains the Decline of the U.S. Labor Share of Income? An Analysis of State and Industry Level Data we find that in addition to changes in labor institutions, technological change and different forms of trade integration lowered the labor share. In particular, the fall was largest, on average, in industries that saw: a high initial intensity of “routinizable” occupations; steep declines in unionization; a high level of competition from imports; and a high intensity of foreign input usage.\

NBER (2018) Is Automation Labor-Displacing? Productivity Growth, Employment, and the Labor Share We find that automation displaces employment and reduces labor's share of value-added in the industries in which it originates (a direct effect).

BLS (2020) Assessing the Impact of New Technologies on the Labor Market: Key Constructs, Gaps, and Data Collection Strategies for the Bureau of Labor Statistics Private and public decisions related to labor markets and working conditions are increasingly being influenced by technological considerations. Spurred by a wave of technological developments related to digitization, artificial intelligence (AI), and automation, governments around the world have declared that the creation and deployment of these technologies present both important opportunities and challenges to their citizens.

AER (2022) The Decline of the Labor Share: New Empirical Evidence We use time series techniques to estimate the importance of four main explanations for the decline of the US labor income share: rising firm markups, falling bargaining power of workers, higher investment-specific technology growth, and more automated production processes ... Our results point to automation as the main driver of the labor share.
 

Wikipedia Links

Solow-Swan


In the Solow-Swan Neoclassical economic model, wages (W) and profits (R) have fixed parameters in the model, w and r respectively.



Marx-Ricardo



In the Marx-Ricardo model, the Iron Law of Wages determines that, in the long run, the wage parameter, (w), is fixed at the level of subsistence as a result of market pressure and capitalist exploitation.

AIC Statistics


In terms of the AIC Statistics (smaller is better), the best model takes the World System (WL20 model) as input.


TECHE Forecast: Union Membership


Union Membership is forecast to be zero around 2060 as a result of Technical Efficiency Changes (TECHE). However,


There is not a lot of separation between the model AIC Statistics (above) and their confidence intervals.


TECHE Forecast: KOF Globalization



The KOF Index of Globalization is forecast to continue growing beyond 2100.

USL201 Forecast: W Index




The WL20 Model is in growth-and-collapse mode and is forecast to peak after 2050.