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.

Tuesday, September 8, 2026

Why is the US Labor Share in Income Decline 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 test 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
  • Dynamics of the US Economy
  • Globalization and the World System
In the graphic above, six of the models are compared against a Random Walk, that is, no explanation.

In Neoclassical Economic Theory

In Marxist Theory


ChatGPT summarizes it's findings as:




Here is a Causal Diagram of the ChatGPT explanation.













Notes

Questions

  1. What policy measures (if any) would you recommend to address the decline in Labor's Share of National Income?

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-Rocardo 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




USL201 Forecast: W Index





















 

Thursday, September 3, 2026

USL20 Health Care Forecasts


Recently, the PBS News Hour interviewed a Primary Care Physician (here) to discuss problems in the US Healthcare System.


The summary of problems (from Google AI, above) suggests the following solutions  (also Google AI) to get control of the system:


To help understand the problems and difficulties, I ran four forecasts with the USL20HC Model (presented in the graph above). Both the Business-As-Usual (BAU) model and the USL203 Model as input** are unstable. Stabilizing (controlling) the BAUC model produces more moderate growth until after 2100.

Controlling specific parts of the system (Prices and Hospital Investment) without affecting Quality of Service will not be easy. Attempts to control Prices have failed (see Pasdirtz, 2007) largely for political reasons. ChatGPT notes:



A reduction in demand for Healthcare when the Baby Boomer Generation has aged out of the system might help. Until then, I do not see the political will necessary to change the system. However, Healthcare costs are directly related to the US Affordability Crisis (Google AI):



If dealing with the US Affordability Crisis becomes one of the outputs of the US Political System, then Healthcare expenditure has to be considered. If the US Healthcare System becomes more fully integrated with the US Political System, the relationships between HC1 = (Growth - Hospitals) might become more closely related to Austerity, Hardship and Debt management--and be affected by Growth or Collapse in the US Political System.

Right now, problems in the US Healthcare System are more a function of what the US Political System thinks it is supposed to be doing for the American people. In the Trump II Administration, it is not entire clear what the US Political System thinks it is supposed to be doing for the American people.


Notes


** The idea behind using the USL203 Model as input is to keep growth of the US Healthcare system in line with growth of the US Economy (see Pasdirtz, 2007). See also, US Healthcare, Austerity and Debt.


For more of my posts about the US Healthcare system, see Blog Roll: Healthcare. For more information about how the State Space models were constructed and the data sources, see the Boiler Plate. You can run the USL20HC Model model yourself using the R-code on my Google Site.



USL20HC Measurement Model




The indicators above implement the basic Kaya Identity: N -> L -> Q -> K -> GDP.




Expanding the Kaya Identity to fit the US Healthcare system, we get the Directed Graph above.




Three components in the USL20HC State Space (computed using Principal Components Analysis, PCA) explain 99.80% of the variation in the indicators. HC1 is the Hospital-Growth Controller. HC2 is Output Controller and HC3 is the investment controller.

Using the Expanded Kaya Identity (above) chatGPT suggests controlling the US Healthcare system by direct interventional in the following indicators: Capping Prices, Controlling Investment and limiting Hospital Consolidation. Healthcare labor and insured population would depend on the growth limits imposed. Direct intervention would allow direct control of growth rates.


USL20HC BAU Model System Matrix



The USL20HC Model has two unstable components, HC1= (Hospital-Growth Controller) and HC3 = (Investment Controller).



USL20HC BAUC Model System Matrix




Notice that stabilizing the USL20HC Model model turns the HC1 = (Hospital-Growth Controller) into a Random Walk while HC3 = (Investment Controller) requires a reduced growth rate.





 

Sunday, July 26, 2026

INDIA: The New Axis of Evil and Hardship

 




In a prior posts (here and here), I looked at the Geopolitical Effects on Hardship as a result of India's "Cockroach" Protests and the possibility of a New Axis of Evil forming involving Russia, China and India. In this post, I'll explore the effects of potential alliances between China, Russia and India on Hardship in India.






Notes


HARD1 CN-RU-BAU-RW AIC STATISTICS

The best short-term model, using the AIC Statistics, is the Random Walk (RW). 

IN CN-INPUT HARD1 MODEL






Saturday, July 25, 2026

Hardship and Protest in India


India has had two decades of mass protest culminating in the 2026 Delhi Jantar Mantar protests or "Cockroach Protests". My questions are  (1) how much of the protests are a result of material conditions (Hardship) and (2) What possible response might the government consider in the face of discontent?

My Hardship Index (HARD1) for India has been increasing since the 1960s (see the graphic above). The Business-as-Usual forecast (BAU) suggests that, even though the model is stable (see below), Hardship will increase linearly until well after 2100--not a desirable outcome.

Linking India Geopolitically with the United States would result in a Hardship peak around 2040 and decline after that. Future increases in Hardship before the decline might or might not be sustainable politically.

Linking India Geopolitically to the World System keeps Hardship steady until after 2040 when it starts decreasing. This would be the best outcome but the most difficult to achieve politically (I will explore the difficulty of linking to the World System more fully in future posts).

Of course, India can keep muddling through, randomly responding to Protests (a Random Walk, RW) and hope that  protesters will retreat from the streets, pushing problems off into the future at the current level of Hardship. 

For more of my posts on India see Blog Roll: IndiaThe WL20 India Model in R-Code is available on my Google site. INL20 BAU is an example of a moving equilibrium model that can both easily be stabilized or destabilized. Also, see the About page and the Boiler Plate.



 Notes


INL20 Hardship Measurement Model





HARD1 =  (Growth - mortality and longterm unemployment ),  HARD2: Unemployment and poverty, HARD3 = Business cycle, Unemployment and reduction in CPI.  From the World Development Indicators.




INL20 HARD1 AIC STATISTICS


Best model is W-input.


INL20 HARD1 W-INPUT MODEL




The model is stable. Commodity Markets have the biggest negative impact on Hardship.

WL20 MEASUREMENT MODEL



W1 = (Growth-LP), W2 = (LP+P.Wheat-TEMP), W3 = (Commodity Markets).