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The Growth Of Hierarchy With Economic Development

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Posted on 11 May 2021 Written by Blair Fix Economic Development and the Death of the Free Market - Part 2 The major transitions in evolution suggest that hierarchy is an important tool for organizing complex living systems. Might the same principle be true in human societies? If so, then as societies become more complex, they should also become more hierarchical. Please share this article - Go to very top of page, right hand side, for social media buttons. (2.2) A clash of theories: To suppress or stoke self-interest Returning to economics, this evolutionary prediction puts free-market theory on its head. That's because according to the neoclassical theory of free markets, hierarchy is unnecessary for group organization. Instead, neoclassical theory argues that humans can

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posted on 11 May 2021

Written by Blair Fix

Economic Development and the Death of the Free Market - Part 2

The major transitions in evolution suggest that hierarchy is an important tool for organizing complex living systems. Might the same principle be true in human societies? If so, then as societies become more complex, they should also become more hierarchical.

The Growth Of Hierarchy With Economic Development


Please share this article - Go to very top of page, right hand side, for social media buttons.


(2.2) A clash of theories: To suppress or stoke self-interest

Returning to economics, this evolutionary prediction puts free-market theory on its head. That's because according to the neoclassical theory of free markets, hierarchy is unnecessary for group organization. Instead, neoclassical theory argues that humans can organize effectively without any form of centralized control. All that is needed is a competitive market.

To arrive at this conclusion, neoclassical theory argues that groups can organize by stoking self-interest. If each person acts selfishly, they will be led 'as if by an invisible hand' to benefit the whole society. First proposed by Adam Smith (1776), this idea is now a central tenet of mainstream economics, formalized in the 'first fundamental theorem of welfare economics'.

The theorem claims that under conditions of perfect competition (in which all firms are 'price takers'), markets will allocate resources in a way that is 'Pareto efficient' (Mas-Colell et al., 1995). In this situation, no person can be made better off without making at least one person worse off.

With their welfare theorem in hand, neoclassical economists look at hierarchical organization and see an 'inefficient' system. Yet when biologists look at the same system, they see an 'effective' group-level adaptation. So it seems that we have a clash of theories. Given this clash, it is easy to get bogged down in debates about which form of organization (hierarchy or market) is 'best'. I think that is a mistake. Instead, we should ask an a priori question: when it comes to human social evolution, what is the trend? Towards less hierarchy? Or more?

(3) The growth of hierarchy with economic development

To shed light on the debate between economic theory and evolutionary theory, I attempt to measure how human social hierarchy varies with economic development. Ideally, we could study this variation in three steps:

  1. Postulate a measure of social hierarchy
  2. Apply this measure to human society
  3. See how hierarchy varies with economic development

In principle, this method is straightforward. We treat human relations as a network, and then measure the structure of this network. The more 'tree-like' the network structure, the greater the 'degree of hierarchy'.

While simple in principle, this straight-ahead approach is difficult in practice. The problem is that the relevant data - the network structure of an entire society - does not exist. Yes, we have data for many social networks, especially those on modern social media. But this data is insufficient for the task I propose.

Instead, what we need is detailed information about the chain of command within every firm and every level of government. It is these formal work relations, I argue, that are most important for measuring the hierarchical structure of society.

Unfortunately, we do not have this chain-of-command information - not for a single country, let alone many. Given this lack of data, how can we proceed? My solution is to use an indirect approach:

  1. Postulate a metric of social hierarchy
  2. Apply this metric to human society by simulating the required data
  3. Infer how hierarchy varies with economic development

The difference here is in step 2. Rather than using direct data for the network structure of society (which does not exist), I use an evidence-based model to simulate this data.

Here, then, is the road ahead. After clarifying my choice of social network (Sec. 3.1), I outline two metrics of hierarchy (Sec. 3.2). I then discuss how I measure 'economic development' (Sec. 3.3). Next, I look at empirical trends that plausibly relate to social hierarchy (Sec. 3.4). I then use this evidence to build a formal model of how social hierarchy varies with economic development (Sec. 3.5). Finally, I use this 'energy-hierarchy model' to simulate the network structure of real-world societies. The result is a model-based inference of how hierarchy varies with economic development (Sec. 3.6).

(3.1) Which social network to measure

To investigate how social hierarchy varies with economic development, we must first define the social network we want to quantify. Since humans form many types of social relations, there are a variety of ways to define this network. (Some possibilities include networks of family, friends, social media followers, colleagues, travel, trade, etc.) How should we decide which network is relevant?

Since my focus is on hierarchy as it applies to neoclassical economics, it is this theory that (rightly or wrongly) defines the social network of interest. In neoclassical economics, there are two basic units of organization - one for 'production' and one for 'consumption'. Production is done by firms. Consumption is done by consumers. The loose network that binds these two forms of organization is called the 'market'.

Now here is what interests me. Between these two units of organization (firms and consumers), there is an asymmetry. Consumers are individuals. But firms are groups. Even more interesting is the fact that in neoclassical theory, the internal structure of firms goes undescribed. Firms are treated as 'black boxes' - featureless organizations defined only by their inputs and outputs. This asymmetry leads to two questions:

  1. Why is the default unit of production the firm, not the individual?
  2. Why is the internal structure of firms left undescribed?

The first question has a simple answer. Economists focus on firms (as a unit of production) because this is simply how humans organize. While it is conceivable to have capitalism without firms, such a society has never existed. So economists take the real-world as a given. Firms exist.

This practical response, however, leads to more questions. Why do firms exist? To answer this question, we need to open up the firm. Yet neoclassical economics refuses to do so. Why? The answer, I believe, is sociological. When you open up a firm, you realize that it is not a market. It is a hierarchy (Leibenstein, 2013; Marglin, 1974).

It is by studying this hierarchical structure of firms (and governments) that I propose we measure the 'degree of hierarchy' in human society. Think of firms as islands of hierarchy in a free-market sea. If firms did not exist, all business relations would be organized via the market. Hence there would be no hierarchy. But as firms (and governments) emerge and grow larger, we find islands of hierarchy within the market. It is this patchwork of firm and governmental hierarchy that I wish to quantify.

(3.2) Measuring the degree of hierarchy

To measure variation in social hierarchy, we need a way to quantify the 'degree of hierarchy' in a network. I use two different metrics: 1. the concentration of hierarchical power (CHP) 2. global reaching centrality (GRC) Before describing these metrics, it is worth visualizing what a simple hierarchy looks like. As illustrated in Figure 1, a hierarchy is a type of network that has a tree-like structure. The more a network converges to this tree-like structure, the greater its degree of hierarchy.

The concentration of hierarchical power (CHP)

In a hierarchy, decision-making authority flows from the top down. The result is that individuals at the top of the hierarchy have more power than those at the bottom - they have more ability to impose their will upon others (Bendix, 1998).

The Growth Of Hierarchy With Economic Development

Figure 1: A social network with a hierarchical structure As illustrated here, a hierarchy is a form of network that has a tree-like structure. In a human hierarchy, this network delineates a chain of command, in which 'superiors' command 'subordinates'. As one moves up the hierarchy, the total number of subordinates under one's control tends to increase. Here, for instance, the red individual has 6 subordinates in total. The leader of the hierarchy, in contrast, has 30 subordinates.


The concept of 'power' provides a way to quantify the degree of hierarchy in a social network. We start by noting that within a network, an individual's power increases as they accumulate more subordinates (people who obey their command). I propose that the distribution of control over subordinates indicates the 'degree of hierarchy' in the network. The idea is simple. When no one has any subordinates, there is no hierarchy. But when a few individuals have many subordinates, the network is extremely hierarchical.

With this thinking in mind, I use the concentration of 'hierarchical power' as a measure of the degree of hierarchy. I start by defining 'hierarchical power' as an individual's control over subordinates. Formally, the hierarchical power (P) of the ith person in a network is proportional to the total number of subordinates (Ns ) they control:

The Growth Of Hierarchy With Economic Development

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.

I add '1' to the number of subordinates to symbolize that all individuals retain control of at least one person - themselves.

For an example calculation, let's return to Figure 1. Here the red individual has 2 direct subordinates and 4 indirect subordinates. With 6 subordinates in total, this person has a hierarchical power of P = 7. Individuals higher up the hierarchy have still more power. In Figure 1, the leader of the hierarchy has 30 subordinates, giving a hierarchical power of P = 31.

Having defined the hierarchical power of an individual, we can apply this measure to everyone in a network. The result will be a distribution of hierarchical power. We can then use this distribution to quantify the 'degree of hierarchy'. The more concentrated the distribution of hierarchical power, the more hierarchical the network.

To measure the concentration of hierarchical power, I use the Gini index - a standard measure of inequality. Formally, the 'concentration of hierarchical power' (CHP) is the Gini index of the hierarchical power (P) of all N individuals in a network:

The Growth Of Hierarchy With Economic Development

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.

The CHP varies between 0 (no hierarchy) and 1 (absolute hierarchy). As an example, the network in Figure 1 has CH P = 0.57, indicating that it is quite hierarchical.

Global reaching centrality (GRC)

Another approach to measuring hierarchy is to define something called 'global reaching centrality' (Mones et al., 2012; Nepusz and Vicsek, 2013). When applied to human networks, this metric again involves counting subordinates. To measure 'global reaching centrality', we first define 'local reaching centrality' (CR ). This is the number of subordinates Ns controlled by the ith individual, expressed as a portion of the total number of other people (N 1) in the network:

The Growth Of Hierarchy With Economic Development

.

.

Returning to Figure 1, let's calculate CR for the red individual. This person has 6 subordinates within a network of N = 31 people. Their local reaching centrality is therefore CR = 6/30 = 0.2. The 'global reaching centrality' (GRC) of the network is then defined as the sum of the differences between the local reaching centrality of each person subtracted from the maximum reaching centrality of the network:

The Growth Of Hierarchy With Economic Development

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The GRC can range from 0 (no hierarchy) to 1 (absolute hierarchy). As an example, the network in Figure 1 has a GRC = 0.92, suggesting that it is quite hierarchical.

(3.3) Measuring economic development

Having defined how I measure hierarchy, I turn now to how I measure economic development. When economists speak of 'development', they usually mean the growth of 'real GDP'. In this paper, however, I use a different metric. I measure economic development in terms of energy use per person.

I have two reasons for using energy to measure development. First, there are many 'aggregation problems' inherent in the calculation of real GDP (Fix, 2019a; Fix et al., 2019). These problems occur largely (but not exclusively) because real GDP is based on the unit of prices, which are unstable. This instability introduces ambiguity in the value of real GDP.

Second, I use energy consumption to measure 'economic development' because I want a method that generalizes beyond human societies. If the growth of human hierarchy is an extension of a general evolutionary process, then we want a metric of 'development' that is universal. Since real GDP has no meaning outside the human economy, it is not helpful. Energy, however, is a 'universal currency' in the natural sciences (Chaisson, 2005).

The importance of energy stems from basic thermodynamics. It is the flow of energy that makes complex structure possible. Without energy flows, natural systems converge to equilibrium - a state where nothing happens on the macro scale. But when there is an energy gradient, macro-level structures tend to emerge - structures that dissipate energy more rapidly (Kondepudi and Prigogine, 1998).

A convection cell, driven by a temperature gradient within a fluid, is a simple example of such a 'dissipative structure'. Living organisms are a more complex example, driven by the energy flow from the sun (Annila and Annila, 2008; Boltzmann, 2011; Chaisson, 2002; Schrodinger, 1992). The human economy is still more complex, but obeys the same principle. It is a dissipative structure driven by flows of energy (Georgescu-Roegen, 1971; Giampietro et al., 2012).

Because of its role in driving complex systems, I use energy consumption as a measure of economic development.4

(3.4) Evidence for the growth of hierarchy

My goal is ultimately to use my metrics of hierarchy (Sec. 3.2) to measure how the 'degree of hierarchy' varies with economic development. Unfortunately, the data needed to achieve this goal does not yet exist. As such, I will take an indirect route to measuring hierarchy.

I will first review evidence suggesting that hierarchy varies with economic development. In the section that follows, I show that as societies use more energy, governments tend to get larger and the number of managers tends to increase. I then use this evidence to build a formal model of hierarchy (Sec. 3.5), which I use to infer how the 'degree of hierarchy' varies with economic development (Sec. 3.6).

The size of government

In neoclassical economics, government is a necessary evil. It is a form of hierarchical organization that must exist, but should not grow too large.

Government must exist, Milton Friedman observes, to

"do something that the market cannot do for itself, namely, to determine, arbitrate, and enforce the rules of the game" (1962).

But while government is a prerequisite for markets, it is also the market's enemy. That is because, as Franklin Fisher notes:

"the principal policy insight of economics [is] that a competitive price system produces desirable results and that government interference will generally lead to an inefficient allocation of resources" (1987).

In neoclassical theory, then, government is a necessary form of hierarchy, but one that should remain as small as possible. It seems, however, that real-world societies do not listen to this 'small government' principle. Instead, economic development goes hand in hand with larger governments.

Figure 2 shows the evidence across (and within) countries. I plot here the employment share of government as it relates to energy use per capita. ('Government' is defined as the entire public sector. Each line in Fig. 2 represents the path through time of a specific country.) While country-level trends vary, the overall pattern is clear. As energy use increases, governments tend to get larger.

From a neoclassical standpoint, this result is unexpected. If markets are 'efficient', why does economic development involve government encroachment on the private sector? One possibility is that governments are not heeding economists' advice, and that societies would be better off if government remained small. If so, then it is politics that are driving the growth of government.

To investigate the role of politics, let us turn to Figure 3. Here I replot the data from Figure 2, but this time I differentiate between two types of countries:

  1. Countries that have (or once had) a communist government
  2. Countries that have never had a communist government

It is easy to see the difference between the two types of countries. Those that have had communist regimes tend to have larger governments than those that have not.5

Given the intense 20th-century battle between capitalism and communism, it is unsurprising that politics affect the size of government. What is surprising, however, is that regardless of politics, governments tend to get larger as energy use increases. The inset panel in Figure 3 shows this fact. Here I smooth the raw data (within each type of country) using a local polynomial regression. The results are interesting. In both communist and non-communist countries, governments tend to grow larger with energy use.

The Growth Of Hierarchy With Economic Development

Figure 2: Government's share of employment vs. energy use per capita I define 'government' here as employment in the entire public sector. Lines represent the path through time of individual countries (from 1990 to the present). Points represent countries with a single observation. Select countries are labeled with alpha-3 codes. The black line shows the trend across all countries, smoothed with a LOESS regression. For data sources, see Section 6.


The Growth Of Hierarchy With Economic Development

Figure 3: Government's share of employment vs. energy use per capita by political spectrum I reproduce here the data in Fig. 2, but now distinguish between communist and noncommunist countries. 'Communist countries' are those that have (or once had) a communist regime. Lines represent the path through time of individual countries. Communist countries are labeled with alpha-3 codes. The inset panel shows the smoothed trends, calculated with a local polynomial regression. For data sources, see Section 6.


So yes, politics do affect the size of government. But there is also a secular trend that is independent of political ideology - a fact that does not sit well with the neoclassical theory of free markets. As societies develop, government tends to grow larger.

The number of managers

Let's turn now from the public sector to the whole economy. When describing the economy, neoclassical economists see competition between firms. But what about within firms? There, competition seems less salient. Once an employee has a position within a firm, they are expected to cooperate with their coworkers. And that usually involves taking and/or giving orders - a sign of hierarchy.

If we were to grossly simplify the structure of a firm's hierarchy, we might reduce it to two classes: those who take orders and those who give orders. The order givers are usually called managers. Their job is to command the activity of other people - a job that is unique to hierarchies. I propose, then, that the relative number of managers in a society provides a window into the degree of hierarchy. A society with no managers has no hierarchy. A society with many managers has lots of hierarchy.

With this thinking in mind, Figure 4 plots the evidence. Here, I look at how the relative number of managers (within countries) varies with energy use per capita. As with the size of government, I find that the number of managers tends to increase with economic development.

This evidence seems to contradict the neoclassical theory of free markets. As societies develop, they turn increasingly to top-down management. It could be, though, that this trend is ultimately political. In that case, politics induce the growth of hierarchy, which then 'distorts' free-market efficiency.

The Growth Of Hierarchy With Economic Development

Figure 4: Managers' share of employment vs. energy use per capita I plot here the international trend between the number of managers in a country (as a share of total employment) and energy use per capita. Lines represent the path through time of individual countries (from 1990 to the present). I have labeled select countries with alpha-3 codes. The black line shows the trend across all countries, smoothed with a LOESS regression. For data sources, see Section 6.


To investigate the role of politics, let us look at Figure 5. Here I replot the trend between the number of managers and energy use per capita. But this time I differentiate between communist/non-communist politics. The results are telling. Unlike with the size of government, politics seems to have no effect on the number of managers. The inset panel in Figure 5 emphasizes this nondistinction. Here I show the smoothed trend across countries, differentiated by political regime.

The Growth Of Hierarchy With Economic Development

Figure 5: Managers' share of employment vs. energy use per capita by political spectrum I reproduce here the data in Fig. 4, but now distinguish between communist and noncommunist countries. 'Communist countries' are those that have (or once had) a communist regime. Lines represent the path through time of individual countries. Communist countries are labeled with alpha-3 codes. The inset panel shows the smoothed trends, calculated with a local polynomial regression. For data sources, see Section 6.


There is virtually no difference between communist and non-communist countries. So whatever is driving the growth of managers, it is not overtly political.

Next time we will look more explicitly at the role of energy.


Notes

4 If one is skeptical of this choice, note that there is strong correlation between energy use and real GDP (Brown et al., 2011). As such, should we measure economic development using real GDP, the results in this paper would likely remain unchanged.

5 On a historical note, the data in Figure 3 captures the collapse of the Soviet Union in action. The data begins in 1990, just when the Soviet Union disbanded. Former Soviet states like the Ukraine, Estonia, Moldova and Armenia begin (in 1990) with almost 100% government employment - a relic of their communist history. But over the next decade, governments in these countries shrank drastically, collapsing to levels similar to their non-communist counterparts. With this government collapse came a decline in energy use.


This article is part of a new research paper draft ("Economic Development and the Death of the Free Market ") being presented serially. Here are the parts:

  1. Evolution of Free Markets and Hierarchy
  2. The Growth of Hierarchy with Economic Development
  3. Energy and Hierarchy
  4. Rethinking Free-Market Theory
  5. Conclusions and Methods
  6. References

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