State Space Models
Friday, January 17, 2025
World-System (1872-1908) Expanded Outputs of the Classical Model for Germany
Saturday, January 11, 2025
World-System (1872-1908) A Classical Model of German Development
In a prior post (here), I discussed whether we should pay attention to the Classical Economists who wrote in the Nineteenth Century. They had brilliant insights but they lacked the statistical tools to test their ideas. Now that we have the tools and the historical data, there is no reason not to test and extend their ideas. One of the problems is figuring out what the Classics actually meant because their writing was verbose, obscure and difficult for modern readers to wade through.
Benjamin Higgins (1968) (here) has come to our rescue with a book (now out of print but still available used here) that develops a generalized mathematical model of economic development based on the classics (see Chapter 3). He presents eight structural equations (p. 63) and a time plot of the relationship between N (Population) and Q (GDP), above. His Figure 2-3 (above) looks very similar to the time series plot for the German 19th Century model (DEL19) at the beginning of this post which was based on an estimated dynamic state space model. The DEL19 model used the same variables identified by Higgins but did not arrive at the time plot using Higgins classical structural equations. Understanding how the DEL19 model was constructed will help me explain how to approach the Classics with modern tools.
Higgins identifies the following variables as central to the general Classical model: Production (Q), Labor (L), Capital (K), Wages (W), Profits (R), Investment (I) and Technology (T). Variables can be further grouped (using Systems Theory) as system output state O=(L,Q,T), Endogenous (W,R,I), Exogenous (N) and Output (K) yielding the directed graph above (Higgins actual structural equations are presented below in the Notes--the endogenous variables can be reduced out of the equation system).
To Neoclassical Economists, the directed graph will look strange. Technology is usually taken as exogenous and the Capital stock would be included in the system state. But the Classics believed that Technology had to be embedded within investments and the Capital stock. Also, I think some Outputs are missing from Higgin's model (what happened to Adam Smith's Free Market? What happened to Democracy?) but I'll pick up the issue in a future post on the way to dealing with Liberalism and Neoliberalism.
The Classics also struggled with definitional issues. Did Capital include land, machines, buildings, knowledge, etc.? Were wages driven to subsistence in order to increase profits (R = Q - wL) where w is the subsistence wage. How to define Technology (T)? So many questions, so much speculation, so little testing.
Systems Theory avoids these arguments by defining the System State, S = S(Q,L,K,W,R,I,T), as being a function of all the essential variables in a system. The problem then is to estimate a state variable index and other independent indexes that describe Error Correcting Controllers (ECCs) for the system, that is, describe growth and control as two separate issues that have to be estimated separately for the system--allowing that the system might not be under adequate control.
In terms of system behavior, the steady state depicted in the DEL19 Time plot was not the result of the DEL19 BAU model but required input from the World System (see the directed graph above). Understanding that every economy is embedded within the World-System had to wait for the development of World-Systems Theory at the end of the Twentieth Century and the development of Hierarchical Control Systems in the 21st Century.
Summary
- It is not easy to just speculate and try to understand Complex Systems. The systems are Black Boxes that only reveal their behavior by observing inputs and outputs.
- Higgins Classical model (see below) is static whereas writers such as William Baumol (1960) thought the primary attribute of Classical Models were their "Magnificent Dynamics" (download pdf here).
- The Classics were willing to go ahead and speculate without clearly defining their essential variables, for example, Capital and Technology.
- The policy recommendations derived from Classical Models (Population control, Free Markets, Free Trade, Steady States, etc.) were advanced from weak foundations.
- The Classics did not advance ideas about how the Economic System is controlled, aside from free markets. In Germany, the Classical Economy was mostly controlled by Investment relative to population and employment. These two Error Correcting Controllers might be implicit in Classical reasoning but had to wait until a reinterpretation by Systems Theory in the Twentieth Century.
- The concept of the Steady State was dropped in favor of unlimited growth by Neoclassical Economics, but has been revitalized by Ecological Economics. Unfortunately, it is a state that might only be observe in the Future, and the Future is unknowable.
- Linkage to the World System is an important part of German development in the Late Nineteenth Century. Had the link been pursued, rather than World Domination, Germany would have become a stable society in the 20th and 21at Centuries. It would not have pursued the World Wars and the Great Depression would probably not have happened. However, there was no role for the World System in either Classical Economics or Neoclassical economics. World-Systems Theory was based in Classical Marxian Economics but borrowed freely from Neoclassical Economics when needed. There is more work to do in expanding the economic underpinnings of World-Systems Theory and Classical Economics is a good place to start.
Notes
Higgins (1968: 57) defines his Classical Economic System using structural-functional notation. The final equation, W = wL, is the long run constraint that wages are driven to subsistence, w. Structural equations are very important to Academic Economists, but there is a problem. The Cybernetic Theory of Isomorphic Systems proves that structural equations are not unique if two systems have the same time path for the output variables. In other words, The graphics at the beginning of this post look alike but they were generated from two different systems. The first graphic is from a state space model (DEL19W model) and the second from Higgins Classical model.
Classic References
- Adam Smith Wealth of Nations
- Malthus An Essay on the Principal of Population
- Malthus Principles of Political Economy
- Ricardo Collected Works
- Marx Collected Works
- JS Mill Collected Works
- JM Keynes The Collected Writings
Wednesday, January 1, 2025
World-Systems Theory: The Malthusian Controller
A time plot of Malthus2 (above) shows that right after German Unification in 1872, there was a Malthusian Crisis (QA-N < 0) that ran from Unification until almost 1880. The dashed red line in the graphic above is the attractor path for the Malthusian model, an approximate straight line around (QA-N = 0).
But what about Malthus1 that explains 87% of the variation in Q and N? The graphic above indicates that the Malthusian growth component was underperforming below the attractor path for most of the late 19th Century in Germany. Germany's late and rapid growth and Modernization, thought to be a factor in World War I, was basically a return to the attractor path interrupted by German Unification.
Methodology
Wednesday, November 6, 2024
Wolf Hall and the Modern World-System (1450-1640)
Links
- Thomas Cromwell An English statesman and lawyer who served as chief minister to King Henry VIII from 1534 to 1540, when he was beheaded on orders of the king, who later blamed false charges for the execution.
- Catherine of Aragon The first wife of King Henry VIII from their marriage on 11 June 1509 until its annulment on 23 May 1533.
- King Henry VIII King of England from 22 April 1509 until his death in 1547.
- English Reformation Took place in 16th-century England when the Church of England was forced by its monarchs and elites to break away from the authority of the Pope and the Catholic Church.
- Anne Boleyn Queen of England from 1533 to 1536 and the second wife of King Henry VIII.
- Oliver Cromwell (25 April 1599 – 3 September 1658) was an English statesman, politician, and soldier, widely regarded as one of the most important figures in British history.
- Thomas Wolsey An English statesman and Catholic cardinal. When Henry VIII became King of England in 1509, Wolsey became the king's almoner.
- Elizabeth Wyckes The wife of Thomas Cromwell (1485 – 28 July 1540), died in 1529 and his daughters, Anne and Grace, are believed to have died not long after their mother.
- Hans Holbein the Younger A German-Swiss painter and printmaker who worked in a Northern Renaissance style, and is considered one of the greatest portraitists of the 16th century.
- Wolf Hall A 2009 historical novel by English author Hilary Mantel, published by Fourth Estate, named after the Seymour family's seat of Wolfhall, or Wulfhall, in Wiltshire. Set in the period from 1500 to 1535, Wolf Hall is a sympathetic fictionalised biography documenting the rapid rise to power of Thomas Cromwell in the court of Henry VIII through to the death of Sir Thomas More.
- World-Systems Theory A multidisciplinary approach to world history and social change which emphasizes the world-system (and not nation states) as the primary (but not exclusive) unit of social analysis.
- Sweating Sickness A mysterious and contagious disease that struck England and later continental Europe in a series of epidemics beginning in 1485.
- Holy Roman Empire A polity in Central and Western Europe, usually headed by the Holy Roman Emperor.[19] It developed in the Early Middle Ages and lasted for almost a thousand years until its dissolution in 1806 during the Napoleonic Wars.
- Timeline of British History 1500-1599
- Timelines of World History
- The Black Death The Black Death was a bubonic plague pandemic that occurred in Europe from 1346 to 1353. It was one of the most fatal pandemics in human history.
- English Civil War a series of civil wars and political machinations between Royalists and Parliamentarians in the Kingdom of England from 1642 to 1651.
- Holy Roman Empire a polity in Central and Western Europe, usually headed by the Holy Roman Emperor.
- Peasant's Revolt a major uprising across large parts of England in 1381.
- Feudalism a combination of legal, economic, military, cultural, and political customs that flourished in medieval Europe from the 9th to 15th centuries.
- The 15th Century the century which spans the Julian calendar dates from 1 January 1401 (represented by the Roman numerals MCDI) to 31 December 1500 (MD).
Saturday, May 31, 2014
A Systems Perspective on World-Systems Theory
My major preoccupation in this blog is how the quantitate concepts of General Systems Theory (GST) can be applied to qualitative World Systems Theory (WST) in order to generate testable conjectures and hypotheses. In a prior post (here), I discussed the world-system as a unit of analysis. Since then, I have been looking for a reference that might summarize the relationship between GST and WST. A 1997 article in the Journal of Geography by Debra Straussfogel (referenced below) is excellent. In this post, I'll summarize the article and suggest a direction for future posts (for more detail, please reference the article).
WST is an interdisciplinary perspective meant to refocus artificial academic disciplines (arts and sciences) on a unified study of macro-societal systems. The Straussfogel article is written from the perspective of Human Geography rather than from the discipline of Sociology where WST was developed. In Human Geography, GST (General Systems Theory as developed by von Bertalanffy, 1971) was considered a mechanistic way "...of portraying humans as deterministic entities behaving in predictable ways, like so many molecules and chemical reactions" (p. 119). The more qualitative, humanist WST approach provided a path to Complex Systems Theory (CST) "the study of complex, hierarchically structured, nonequilibrium, and dynamic systems" (p. 119).
In the late 1970's, Wallerstein developed WST without reference to GST. He was dissatisfied with Marxist theories of development (historical materialism) and Western theories of Modernization. Wallerstein saw classes and nations as part of a larger social system. That larger system, the world-system, should be the unit of analysis for societal development as discussed in the last post.
The logic of the world-system is defined by its economic mode of production, diagrammed above from Wikispaces (here). Three modes of production are described and interrelated: (1) Core production processes involve the most advanced levels of technology that take cheaply produced raw materials and turn them into high-value consumer goods. (2) Peripheral production processes use cheap labor to extract raw materials used in core production processes. (3) Semi-peripheral production and consumption processes contain some advanced technology and also provide markets for high-profit consumer goods.
A1: The world-system is structured hierarchically into core, semi-perpheral and peripheral states.
H1: Production processes and technological processes are different in core, semi-peripheral and peripheral states. The higher in the world-system hierarchy, the more advanced the technology.
Different modes of production within the assumed (A1) world-system hierarchy (core-, semi-peripheral and peripheral) suggest a testable hypothesis (H1). Unlike neoclassical economic models which assume the same Cobb-Douglas production process throughout the world system (see my discussion here), WST predicts different production processes. The theoretical problem will be to come up with a model (other than the Cobb-Douglas model) that provides a more general description of economic modes of production that can be estimated across the world-system (one candidate model I have discussed in other posts, here, is the I=PAT model).
A2: The modern world-system is globalized and devoted the ceaseless accumulation of capital.
The modern world-system is the first truly global system dedicated to the "ceaseless accumulation of capital". Earlier "world empires" (single states) and "mini-systems" were not based on advanced technology. I have left "capital accumulation" as an assumption because, as I will discuss later, "capital" is a poorly defined term with questionable operational definitions and poor measurement.
H2: Economic production advantages lead to commercial, financial and political-military advantages.
C2: The nation with the strongest economic production advantages becomes the hegemonic leader of the world-system and uses it's cultural values to reinforce it's dominance.
Wallerstein borrowed economic determinism from Marxist theory and used it to derive hypotheses about production advantages (H2) and corollaries (C2) about hegemonic leadership within the world-system. At base, these hypotheses require a good definition of technology and economic production to be testable.
WST views economic production in terms of "commodity chains" that lead from the sites of agricultural production or natural resource extraction to consumption. Processes that can be monopolized and made more capital intensive become core processes. With global commodity chains and the world-wide division of labor, wages are lowest in the peripheral and highest in the core states, perpetuating inequality. Core-peripheral relations are thus based on "unequal exchange" and exploitation for profit of the periphery by the core.
H2a: Peripheral nation states are disadvantaged by unequal exchange with the core and semi-peripheral nation states.
Hypothesis H2a seems at first to involve a value judgement and is directly contradicted by the neoclassical economic theory of comparative advantage. However, H2a is essentially a counterfactual: what would development have been like for a peripheral country without links to core and semi-peripheral nation states? In order to test the counterfactual, we need a model that can be "experimentally" manipulated, that is, simulated under different exogenous conditions. For a number of reasons (the most important being lack of internal dynamics that I will discuss in future posts), neoclassical economic models are not particularly useful for counterfactual analysis while state-space systems models are.
Although the hierarchical structure of the world-system might seem static, there are business cycles and trends (long waves or Kondratiev cycles) as well as cycles of hegemonic succession, war, trade and control. None of these cycles can be captured by neoclassical economic models that assume continuous exponential growth. There is also, over time, "broadening and depending" of the world-system as more states become incorporated into the division of labor and more land, labor and capital are commodified and mechanized. Cycles and trends in the world-system are driven by the open nature of the system.
A3: Each state in the world-system is an open system.
H3: State variables are open to influences internal to each nation state, from other nation states in the world system and from random forces.
C3: Weak peripheral states have weak internal state dynamics and are more subject to external forces than strong core states.
Here is the point where CST enters WST. Typically, economic models (such as William Nordhaus' DICE and RICE models) are only open to trade. Each nation has the same state variables with different parameters. The models are not open to random influences, technology transfer or information transfer. The models have no internal or external cyclical dynamics. The entire neoclassical world economic system is deterministic.
CST argues that economies are dissipative systems, that is, they grow by exchanging energy and matter with their environment (not by disembodied technological progress as is assumed in neoclassical economic theory). As each economic system grows, it depletes it's environment. Changes in the environment force changes and adaptions within the system. The history of dissipative systems is not repeatable because the environment surrounding the systems has changed over time.
The implications of these assumptions, hypotheses and corollaries are many. In future posts I will look in more detail at WST, GST and CST trying to derive more testable hypotheses from the qualitative writings. In another blog (here) I will be looking at existing causal macro systems and evaluating them in terms of systems theory. In other blogs, I am statistically estimating and simulating open state-space systems models of the stock market (here) and nation states within the world system (here and here). Hopefully, in the future, this work will come together in some coherent, punishable form.
REFERENCES
Straussfogel, D. (1997) A Systems Perspective on World-Systems Theory, Journal of Geography, Volume 96, Issue 2, ops 119-126.
von Bertalanffy, L. (1971) General Systems Theory. Harmondsowrth, UK: The Penguin Press.
Thursday, December 13, 2012
The Modern World-System as a Unit of Analysis
There are a number of variants of world-systems analysis, however Immanuel Wallerstein has arguably developed the best known version. In the video above, Wallerstein talks about why he gravitated toward the world-system as a unit of analysis. He also talks about some of the epistemological problems he encountered when he pursued world-system analysis. The video is poor, but it is the only one I can find which discussed the unit of analysis and provides a useful starting point for this blog.
To him, the state as a unit of analysis didn't make sense, it's not where social action occurred. He saw the states organized within a hierarchical system. The Modern world system evolved in the 15th century and was a significant break, a capitalist world economy.
The epistemological problems hinted at involved the artificial academic disciplines between history, sociology, economics and history. From the standpoint of systems theory, the world system could only be studied from the system perspective, not from the perspectives of narrow academic disciplines.
The epistemological problems were clear to me when I was working on my dissertation in the late 1970's and early 1980's. The University of Wisconsin formally allowed interdisciplinary degrees but the academic disciplines I was interested in bringing together (sociology, history and economics) did not look very favorably on the project. Interestingly, the problems really had to do with the systems models I was using. Economists were not entirely comfortable they way concepts were being operationalized and the strong emphasis on empirical-statistical rather than theoretical model building (Kalman's data -> model approach that I'll discuss later), the sociologists were not yet comfortable with macro analysis and the historians were having trouble with quantitative history.
Wallerstein took, instead, a qualitative approach and was in the end more successful. I still think a quantitative approach to world-systems analysis using systems models is possible, especially since Wallerstein has paved the way with excellent qualitative analysis.
One other important epistemological point is that Wallerstein rejects the idea that he is developing world-system "theory". Rather, he looks at his project as world-systems "analysis". His perspective highlights the problem of theory construction in this area and is a topic I am pursuing in the Causal Macrosystems blog.