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Dynastic cycle: A generic structure describing resource
allocation in political economies, markets and firms
January 9, 2006
Khalid Saeed and Oleg V. Pavlov
Abstract
A generic system embodies basic principles and insights that are common to a set of diverse cases and situations. For example, a generic system called “limits to growth” captures the constraints experienced by an organization due to the scarcity of an important resource. Its manifestations range from the tragedy of Easter Island to rise and decline of People Express Airline to the spotty performance of early peer-to-peer music networks. This paper presents a new generic system that we name the dynastic cycle system. It is based on a stylized model of events from the Chinese history. It describes resource allocation between social, asocial and control uses in a variety of institutions, including political economies, markets and firms that experience cyclical behavior and homeostasis symbolizing low levels of performance. Numerical simulations with the model are used to test several policy scenarios.
Keywords: system dynamics, political economy, dynastic cycle, systems, simulation
Introduction
Availability and use of resources affects institutional performance, whether the institution is a country, an economy, an organization or a firm. Because institutional decision makers act in the presence of externalities, feedbacks, constrained capacity and delays, resource misallocations and system instability are quite common. It is, therefore, desirable to identify the shared characteristics of resource allocation decisions and to describe generic policy frameworks for avoiding resource misallocation and instability in a variety of societal institutions.
Within the field of operations research, resource allocation problems are formalized as mathematical models, which are seen as “idealized representations” of reality (Hillier and Lieberman, 1972). Some well-known metaphorical models are: the diet problem, the shortest route problem (also known as the traveling salesman problem), the transportation problem, and the assignment problem (Hillier and Lieberman, 1972). Similar canonical models are found in other threads of modeling closely related to operations research. In system dynamics, for example, Morecroft et al. (Morecroft et al. , 1995) offer a model of two showers that share a water source. The model, which is a metaphor of competition for common resource, is used to explain difficulties experienced by a real-life international manufacturing firm.
As Krugman (Krugman, 1993) points out, socio-economic systems are also understood in terms of metaphorical models. Indeed, perfect market, competition, monopoly, equilibrium growth, etc., are all highly stylized abstract concepts that are often applied to more complex situation. Usher (Usher, 1989) presented a model of a dynastic cycle in ancient China. The model was later extended by Feichtinger and colleagues (Feichtinger and Novak, 1994; Feichtinger et al. , 1996). The distinctive feature of the dynastic cycle models is the presence of three resources framed as metaphorical populations of farmers, bandits and soldiers. Farmers are the only productive resource, while bandits plunder farmers and soldiers are hired to protect farmers. Such models produce cycles which are interpreted as oscillations between anarchy and tyranny.
While early models of the dynastic cycle captured the interdependence between populations, they did not include the capacity constraint, nor did they adequately address the dynamic patterns of behavior the system generates and their relevance to pervasive problems and policies. In this paper, we extend previous models in three ways. Firstly, we add the capacity constraint and explore its effect on the performance of the system. Secondly, we explore both the dynamic behavior and the homeostasis of the system under various policy regimes. Thirdly, we demonstrate that the underlying structure of the modified model is generic and contains elements that are common to political economies, markets and industries. Within system dynamics, sets of basic principles and insights common to diverse cases and situations are called generic structures (Lane, 1998). Hence, we suggest that the dynastic cycle model is an embodiment of a generic structure that describes a wide range of situations.
In the following section, we review early models of the dynastic cycle. We then present a formal computer model. A numerical implementation of the model is used for exploring the dysfunctions in political and economic institutions. We conclude that while a dynamic equilibrium can exist in a dynastic cycle system, the disturbance of this equilibrium will create oscillatory behavior. Finally, we recast the model as a generic structure before concluding in the last section.
Dynastic cycles
Over the four millennia of Chinese history, at least thirty three distinct political regimes, or dynasties, ruled the country (Rodzinski, 1984: 437). A regime succession was usually accompanied by a decline in economic well-being of the country and general lack of order. The succeeding dynasty would typically improve the economic situation and restore order but eventually follow its predecessor’s path of decline. Historians of China have dubbed the country’s fluctuations in political and economic conditions a dynastic cycle.
There have been several formal attempts to explain the dynastic cycle. Usher (Usher,
- introduced a three-class framework, which consisted of the interacting populations of rulers, farmers, and bandits. In his model, population of peasants grows according to the birth and mortality rates which are linked to the economic conditions and the casualties inflicted by bandits. This simple model oscillates between two states: anarchy
e is the economic well-being of a farmer. It is measured as the ratio of the perceived
disposable income per farmer, iF , to the normal farmer income, i % F^ :
F F
i e i
Some farmer produce is looted by bandits. Loot per bandit, l , deviates from some typical
level l %^ : l = l %^ ⋅ e. This formulation implies that the loot is greater when peasants are doing well, and the loot is smaller when the economic conditions of peasants are poor. The aggregate bandit appropriations are L = l B ⋅ , where B is the population of bandits.
Following a broad interpretation, the bandit category also includes those extracting rent through bribes and levies and those engaged in forbidden production, such as gambling, gun running, prostitution and narcotic drugs. If AB is productivity of bandits engaged in
forbidden production, then the non-legitimate production of bandits is YB = AB ⋅ B.
The aggregate disposable income of bandits, therefore, is I (^) B = L + YB. The disposable
income per bandit is iB = IB B. Historic earnings create a perception of the income that a
bandit can earn. We model the perception formation as an exponential averaging process with a time constant of two years: the change in the perceived disposable income per bandit, iB , is
di B iB iB dt
Existence of bandits poses threat to society, which we measure with index γ :
B
b F S
where b γ is a marginal threat from a bandit, which we assume to be constant.
The threat to society dictates the desired size of the army. The desired number of soldiers,
S *, is also dependent on the financial resources available for their support T and the cost per soldier c :
S *^ T c
The actual number of soldiers, S , is adjusted according to the following equations:
S
dS r dt
in * out * rS = aS ⋅ F ⋅ S S − aS ⋅ S S S
where rS is the solder recruitment and attrition rate. The first element in rS is the inflow
of soldiers and the second element is the outflow of soldiers. Soldiers are hired from the population of farmers. When soldiers retire, they return to farming. Soldier inflow and
outflow include first order controls. Parameters aS in and aS out are required in order to
balance the inflow and outflow in a steady state.
Bandits come from the ranks of farmers. Some farmers are encouraged to turn to banditry when they perceive that banditry may provide them with better income than farming. This is measured by the farmer perceived relative income, which is a fraction of the perceived disposable income per farmer to the perceived disposable income per bandit: i = i F iB. Soldiers assure state control over the population. The extent of the control is
measured in the model as a fraction: ψ = b S ψ ( F + B ). Parameter b ψ is the marginal state
control achieved with each soldier.
We assume that there are some normal flows between the populations of farmers and bandits, that is, there are always some farmers turning to banditry and some bandits who return to farming. In a steady state the two flows are balanced. State control serves as a deterrent for the farmers to move to banditry, while it encourages the bandits to become farmers. A formulation that captures this recruitment and attrition dynamic is:
B
dB r dt
in out B B B
F
r a a B i i
The first element in rB is the flow from the stock of farmers to the stock of bandits and
the second element is the flow from the stock of bandits to the stock of farmers. Parameters aB in and a outB balance the flows in a steady state.
The farming population is governed by the equation:
S B
dF r r dt
where rS is the net flow into the population of soldiers and rB is the net flow into the
population of bandits.
The model was implemented in the simulation software ithink (available from ISEE Systems: http://www.hps-inc.com/). A graphical representation of the above-described model, as drawn by ithink , is shown in Figure 1. The diagram is a convenient visual way of representing equations, which adds to the transparency of the model. Following notation typical of system dynamics (Lane, 2000), stocks are shown as rectangles, flows are drawn as valve symbols, and parameters and intermediate computations are circles. Arrows indicate mathematical relationships between variables. To read more about the system dynamics methodology, one may start with Wolstenholme (Wolstenholme, 1982), which introduced system dynamics to the operations research audience of this journal. A comprehensive one-volume reference on system dynamics is Sterman (Sterman, 2000).
of the generic system provides insights into entry points for change. Each change is interpreted in terms of a related policy event. The model is simulated using the Runge- Kutta method. The results of our experiments are discussed below. Table 1: Equilibrium values Parameter Definition Value
F Farmers^100 S Soldiers^10 B Bandits^10 c (^) Cost per soldier 1. K Land^100
α Land elasticity 0.
A F Productivity of farmers^ 1. A B Productivity of bandits^ 0. i B Perceived disposable income per bandit^1 i F Perceived disposable income per farmer 1 i % F^ Normal farmer income^1 l %^ Typical loot per bandit^ 0. a φ Normalization constant 20/ a λ Normalization constant 10/ b γ Normalization constant 110/ b ψ Normalization constant 110/ in aB Normalization constant^ 0. out aB Normalization constant^ 0. in aS Normalization constant^ 0. out aS Normalization constant^ 0.
Population infusion
In this experiment, 5 units were infused in one of the stocks of farmers, bandits and soldiers population. Five units represent an almost 4.2 percent increase in the total initial population. Farmer infusion would correspond to population growth with fixed resources in a political economy or use of overtime in a company with fixed capitalization. Soldier infusion would imply expansion of government role in a political economy or expansion of administration in an organization. Bandit infusion would imply an externally supported growth in insurgent activity or a growth of parasitic or asocial subeconomies (such as businesses receiving special concessions or privileges supported by public funds) in a political system or recruitment of people to cook books, and exploit customers, employees or shareholders in a company.
The consequent changes in the political and economic health of the organization are summarized in a phase diagram in Figure 2. Economic legitimacy index is plotted against
the horizontal axis and the freedom index is plotted against the vertical axis. The system is in the initial equilibrium in point (1,1).
economic legitimacy
initial equilibrium
new equilibrium
farmer infusion
soldier bandit infusion infusion
Figure 2: Dynamic behavior and homeostasis with infusion of 5 units in various population categories.
The end equilibrium for all cases is independent of the stock where the infusion was initially made and depends on the volume of the infusion, whereas, each infusion creates a unique path to the new equilibrium. We observe that the organization is worse off in the new equilibrium, since both freedoms and economic legitimacy are reduced. The change can be understood with the help of Figure 3, which gives major causal relationships of the model. Increase in the farmer population does not yield a proportionate increase in the produce due to land constraint and diminishing marginal productivity. The consequent decline in disposable income per farmer results in some defections into banditry, with concomitant hiring of additional soldiers – yielding lowering of legitimate produce, increase in bandit appropriations, increase in non-legitimate production and increase in taxes to support additional soldiers. With a higher proportion of population engaged in banditry and soldering than the initial proportions, freedoms in a political economy and worker autonomy and citizenship in a firm would suffer.
production starts diminishing, banditry becomes more attractive again and begins to draw defections, which also fuel soldier hiring, thus moving the system back towards its new equilibrium.
We find that with a resource constraint, increase in any population beyond equilibrium yields suboptimal conditions. Increase in control beyond an optimal level warranted by the resources may create economic growth in the short run, but this growth cannot be sustained. Likewise, an expansion in legitimate production portfolio may increase general welfare in the short run, but the economy would return to a suboptimal equilibrium. Last, an increase in non-legitimate activity may initially drastically reduce welfare, but this will be a temporary condition and the system will return to a suboptimal equilibrium. Thus another lesson to be learnt is that expansion beyond the state afforded by resources will always lead to a suboptimal condition, no matter what path of growth is adopted.
Sensitivity to policy-related parameters
We tested the sensitivity of the model to 20 percent increase in the following parameters:
- productivity of farmers, which simulated technological growth;
- land parameter, which corresponded to the discoveries of additional resources or their acquisition through colonization;
- typical loot per bandit, meant to emulate an extension of the scope of the parasitic/asocial subeconomy through collusion with the government, public acceptance or external assistance;
- productivity of bandits that imitated increased yields in the non-legitimate production process, possibly through collusion with government or external assistance, or through use of improved technology;
- cost per soldier, which mimicked an increase in compensation or other privileges of the ruling personnel or increased capital costs of control infrastructure.
Each simulation started in equilibrium with the default values of its parameters (Table 1). The consequent changes in the political and economic health of the organization are summarized in Figure 4.
economic legitimacy
initial equilibrium
typical bandit loot
cost per bandit soldier productivity
land
technical coefficient
Figure 4: Dynamic behavior and homeostasis with 20% increase in policy-related parameters
Increasing production possibilities, either through technological improvements or through acquisition of new resources will increase the size of the legitimate economy providing greater economic legitimacy. This also increases loot per bandit, which causes the economic legitimacy to retract some. Improved farmer income resulting from increase in legitimate production, however draws bandits into farming. A reduction in the number of bandits also decreases the need for the control instruments and some of the soldiers can be released into the farmer’s pool. Thus, the economy subsequently moves towards offering both greater freedoms, and more economic legitimacy. The crowding of the farmers sector, however, reduces income in it making banditry attractive again. As farmers move back into banditry, more soldiers need to be hired, which takes away more of the production. The system comes to a new balance at a higher level of legitimacy and freedoms than the initial level. The new homeostasis depends, of course, on the degree of technological growth achieved or the volume of additional resources acquired.
The effects of an increase in bandit productivity and loot per bandit almost coincide since both make banditry more attractive while also increasing the relative size of the non-legitimate economy. Defections into banditry require subsequent hiring of soldiers to maintain control, which further reduces farmer income because of the hike in taxation. Subsequently, economic legitimacy and freedoms are reduced. Crowding of the bandits sector and a reduction in bandit appropriations due to diminishing produce turn things around – moving the economy to a new equilibrium at a lower level of welfare in terms of freedoms and economic legitimacy.
distribution. A model of urban development (Forrester, 1969) was offered as a basic methodology for social analysis. The “World Model” (Forrester, 1971) was a general theory of the resource use on the planet.
Microstructures are representative computer models that also incorporate the stock and flow structure, but are smaller than canonical models. Each microstructure explains some specific mode of behavior: exponential growth, overshoot and collapse, exploding oscillations, damped oscillations, etc. Abstracted microstructures are the building blocks of larger models including the canonical models (Lane and Smart, 1996). Andersen and Richardson (Richardson and Andersen, 1980: 99) offered a catalogue of abstracted microstructures (they referred to them as elementary structures). Eberlein and Hines (Eberlein and Hines, 1996) offered a set of abstracted microstructures; they refer to the microstructures as molecules.
System archetypes do not include stocks and flows. They are feedback maps representing mental models (Senge, 1990). They can assist in understanding the behavior of complex systems and in devising solutions to problems that arise in such systems. An archetype can also facilitate the communication of simulation results, especially to a policy oriented non-technical audience (Lane, 1998). To aid in the selection of an appropriate archetype for a given situation, the archetype family tree can be used (Senge et al. , 1994). For example, the limits to growth archetype can be adapted to explain the Easter Island tragedy (Mahon, 1997) and the spotty performance of early peer-to-peer music networks (Pavlov and Saeed, 2004).
Table 3: Examples of generic structures Generic structures Canonical situation models Abstracted microstructures (Richardson and Andersen, 1980: 100)
System archetypes (Senge, 1990)
- Product launch (Forrester,
- Urban development (Forrester, 1969)
- Commodity production cycles (Meadows 1970)
- Ambitious product development (Graham, 1988)
- Economic growth and income distributions in a developing country (Saeed, 1994) - A first order positive loop - First-order negative loop - Overshoot and oscillation - Pure exploding oscillation - Pure damped oscillation - Limits to growth (also known as Limits to Success) - Shifting the Burden - Eroding Goals - Escalation - Success to the Successful - Tragedy of the Commons - Fixes that Fail (also known as Fixes that Backfire) - Growth and Underinvestment - Accidental Adversaries - Attractiveness Principle
Following Lane’s terminology, our dynastic cycle model can be classified as a canonical situation model. When stripped of case-specific details, it is reduced to the level of abstract microstructure, as shown in Figure 5. Table 4 matches the generic resource allocation structure to some cases, which are explained below.
At the macro level, Saeed (Saeed 1988, 1994) suggested that resource distribution between production and renting institutions of an economy underlie income distribution patterns. Resource allocation between economic and control resources in an authoritarian political system can also be described by the structure (Saeed, 1986; Saeed, 1990). Under such conditions, the political economy vacillates between despotic rule and anarchy. The
anarchy state begets a habitat for terrorism. Pavlov, Radzicki and Saeed (Pavlov et al. ,
- explain the influence a superpower may have on a developing country using a similar generic structure.
There are several examples at the organizational level. Andersen and Sturis (Andersen and Sturis, 1988) describe the generic structure for the case of a manufacturing firm. In their model, a fixed number of employees are transferred between production and sales. A university may need to decide on the allocation of financial resources between administration and faculty (Saeed 1996). Professional and administrative groups compete for resources in an innovation organization (Saeed 1998). The production of an organization depends on the stock and productivity of its professional resource (for example, research stuff, professors, or consultants). However, there is also clearly a need for supporting administrative staff. An organization continuously balances the allocation of resources between these two uses in attempts of achieving organizational objectives, but may suffer an imbalance over the course of change.
Table 4: Selected cases subsuming the dynastic cycle structure Case description Social use Control use Asocial use Dynastic cycle model Farmers Soldiers Bandits
A university or an innovation organization (Saeed 1996, 1998)
Faculty Administration Bureaucracy
A manufacturing firm (Andersen and Sturis
Manufacturing Sales
New realities in Central Asia (Saeed, 2003) Legitimate economy
Authoritarian institutions, military, civil administration
Non-legitimate economy, terrorists, dissidents
Developing country political economies (Saeed 1986, 1990)
Economic resources Control resources Dissidence
Global political economy (Pavlov et al. ,
Economic assistance Military and security operations
Global terrorists
Peer-to-peer file sharing networks (Pavlov and Saeed,
Subscribers Free riders
A dual economic system (Saeed, 1988; Saeed, 1994)
Economic production Rent appropriation
Long term economic growth (Day, 2001)
Economic production Infrastructure
population growth and the resource constraints on it, nor does it subsume reformist movements that would often precede exacerbation of resource misallocation in a political economy. Finally, it excludes learning processes that may change decision rules governing the resource allocation process. These limiting assumptions should be relaxed to develop specialized models related to specific issues to which our proposed archetype is applied.
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