by Blair Fix
Economic Development and the Death of the Free Market, Part 6
Conclusions
Peter Brown and Peter Timmerman argue that mainstream economics is an ‘orphaned discipline’. It is founded, they claim, on a “dated and unrevised metaphysical and prescientific vision” that is “incompatible with what we know about the universe and our place in it” (Brown and Timmerman, 2015). Looking at free-market theory in the context of the modern understanding of evolution, this assessment rings true.
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Adam Smith’s concept of the invisible hand was a plausible hypothesis when it was proposed more than two centuries ago (Smith, 1776). Given the state of knowledge at the time, it seemed possible that self-interest, if properly channeled, could benefit groups. But as our knowledge of evolution has progressed, this hypothesis has grown steadily less plausible. The problem is that the major transitions in evolution show a pattern that is the opposite of the invisible hand. Rather than organize decentrally, each wave of group formation seems to use at least some form of centralization. And rather than stoke the self-interest of subcomponents, successful groups seem to suppress it. And they often do so by using hierarchy.
Whether it is the symbiosis of the eukaryotic cell, the coordination in multicellular organisms, or the cooperation among eusocial animals, this pattern seems to hold. Competition among subcomponents is suppressed using some form of centralized organization. And yet, if the economic theory of free markets is correct, humans are the exception to the rule. We can organize, the theory claims, not by suppressing competition within groups, but by stoking it.
This claim becomes even more important if we consider that modern humans may be the most recent major evolutionary transition. In the last 10,000 years we have transitioned from being a social species that lived in groups of several hundred (Dunbar, 1993, 2013; Hayden, 2001), to an ‘ultrasocial’ species living in groups a million strong (Gowdy and Krall, 2013, 2014; Richerson and Boyd, 1998; Turchin, 2013). If we have accomplished this feat through decentralized competition (as free-market theory claims is possible), then the evidence should surround us. And since this transition has accelerated in the last half century (McNeill and Engelke, 2016; Steffen et al., 2015), we need not look to the deep past to study it. We can look at modern trends between nations.
Looking at these trends, the evidence suggests that human societies have developed in a way that is consistent with the major evolutionary transitions of the past. As societies industrialize (by using more energy), it seems they turn not to decentralized competition, but to increasingly large-scale hierarchy.
Where, then, does this leave the neoclassical theory of free markets? A conservative conclusion is that the theory is inconsistent with the evidence. A more radical conclusion is that free-market theory is best treated not as a scientific theory, but as a belief system – a claim that heterodox political economists have made many times (Arnsperger and Varoufakis, 2006; Backhouse, 2010; Heilbroner, 1990; Hodgson, 2019; Hoover, 2003; Hunt, 2016; Martin, 1990; Nitzan and Bichler, 2009; Samuels, 1992; Söderbaum, 2008).
If this more radical interpretation is true, then we must grapple with a paradox. Free-market theory advocates the autonomy of individuals. Yet the spread of free-market thinking has happened at the very time that hierarchy seems to have increased. A plausible explanation is that when implemented, free-market ideas actually promote the growth of hierarchy. This idea is speculative, but worth investigating further.
Given the evidence discussed in this paper, it may be time for evolutionaryminded scientists to stop treating neoclassical economics as a competing framework, and instead view it as a cultural artifact to be explained by evolutionary theory
Sources and methods
All data and code for this paper are available at the Open Science Framework: https://osf.io/gbvnh/. Code for the hierarchy model is available at github: https://github.com/blairfix/energy_hierarchy_mod. R versions of the hierarchy-model functions are available at https://github.com/blairfix/hmod.
6.1 Data sources
Communist/non-communist status. I classify a country as ‘communist’ if it has, or once had, a regime that claimed to be Marxist – Leninist. See the supplementary materials for a detailed list of sources.
Cultural tightness Data for cultural ‘tightness’ comes from Gelfand et al. (2020) and can be downloaded from the Open Science Framework: https: //osf.io/pc4ef/
Gelfand’s data was first reported in a 2010 paper. I assume that this was the date of data gathering. I match Gelfand’s data (in Fig. 13) with the average of the managers’ share of employment (within each country) over the period 1990-2010.
Energy use per capita. Data for energy use per capita comes from the World Bank, series EG.USE.PCAP.KG.OE. To these values I add an estimate for energy consumed through food (2000 kcal per day).
Firm size. Data for firm size comes from the Global Entrepreneurship Monitor (GEM), series ‘omnowjob’. To calculate firm size, I merge all data over the years 2001-2014. Because the GEM data over-represents large firms, I use only firms with 1000 or fewer employees. For method details, see the Appendix in (Fix, 2017). Power-law exponents for firm-size distributions are estimated using the R PoweRlaw package (Gillespie, 2014).
Free-market word frequency. Word frequency of free-market jargon is from the Google Ngram corpus for American English.
Government employment. Data for government employment comes from ILOSTAT series GOV_LVL_PSE (all public sector employees). I divide this series by the size of the labor force reported in World Bank series SL.TLF.TOTL.IN. Data for US government employment share (Fig. 12A) comes from:
- 1890 to 1928: Historical Statistics of the United States, Table Ba 470-477
- 1929 to present: Bureau of Economic Analysis series 6.8A-D (total persons engaged in production)
Individualism Index. Data for the ‘individualism index’ comes from Hofstede et al. (2010). In addition to measures for specific countries, Hofstede reports measures for the following regions: (1) Arab countries; (2) East Africa; and (3) West Africa. Based on Hofstede’s notes, I disaggregate these regions as follows:
- Arab countries = Egypt, Iraq, Kuwait, Lebanon, Libya, Saudi Arabia, United Arab Emirates
- East Africa = Ethiopia, Kenya, Tanzania, Zambia
- West Africa = Ghana, Niger, Sierra Leone, Togo
I assign each country Hofstede’s metric for the region.
According to Hofstede, most of his data was gathered in the late 1960s and early 1970s (the dataset does not specify years). However, data for the management share of employment does not begin until 1990. To match Hofstede’s data with the management data (Fig. 13), I average the latter (within each country) over the period 1990-2010.
6.2 Hierarchy-model equations
The hierarchy model used in this paper is based on equations derived independently by Herbert Simon (1957) and Harold Lydall (1959). In this model, hierarchies have a constant span of control. We assume that there is one person in the top rank. The total membership in the hierarchy is then given by the following geometric series:
Here n is the number of ranks, s is the span of control, and NT is the total membership. Summing this geometric series gives:
In my model of hierarchy, the input is the hierarchy size NT and the span of control s. To model the hierarchy, we must first estimate the number of hierarchical ranks n. To do this, we solve Eq. 13 for n:
Here
denotes rounding down to the nearest integer.
Next we need to calculate N1 – the employment in the bottom hierarchical rank. To do this, we rewrite Eq. 12, this time building the hierarchy from the bottom up. Starting with the bottom rank N1 , membership in each consecutive rank declines by a factor of 1/s. That means the hierarchy’s total membership (NT ) is given by the following geometric series:
Summing this series gives:
Solving for N1 gives:
Given N1 , membership in each hierarchical rank h is:
Sometimes rounding errors cause total employment of the modeled hierarchy to depart slightly from the size of the original inputted institutions. When this happens I add/subtract members from the bottom rank to correct the error. The model is implemented numerically in C++, using the Armadillo linear algebra library (Sanderson and Curtin, 2016).
6.3 Modeling Managers
I model managers as all individuals in and above rank 3. In a firm with n hierarchical levels, the number of managers is equivalent to the membership in a hierarchy with n−2 levels. Using Eq. 13, we find that the number of managers M is:
By dividing Eq. 19 by Eq. 13, we can find the management share of employment (M/NT ) in the firm:
6.4 Finding the best-fit energy-hierarchy model
To find the model parameters that best fit the trends in empirical data (inset Fig. 9 and Fig. 10), I first group the model results in log-spaced bins by energy use. (This smooths the stochastic noise that is built into the model.) In each bin, I calculate the average energy use and the average of the statistic of interest (either the management share of employment or the government share of employment). I then interpolate linearly between these averaged points, creating a function that relates energy use to the government/management share of employment. I use this numerical function to compute the error between the model and the raw empirical data. The error function is:
Here Sr is the real-world statistic (either government or management share of employment) and Sm is the model statistic. The best-fit model minimizes this error.
6.5 Fitting the energy-hierarchy model to individual countries
To infer the degree of hierarchy within countries (Fig. 11), I first fit the energyhierarchy model to data for individual countries. For each country-year observation, I chose the model iteration that minimizes the following error function:
Here Er and Em are energy use per capita in the real-world country and the model, respectively. Mr and Mm are the management share of employment in the real-world country and model, respectively. Because the energy-hierarchy model is stochastic, I choose the 10 best-fit iterations, and average the measured degree of hierarchy across these models. I then infer that the degree of hierarchy found in the real-world country is the same as found in the model.
6.6 Calculating the degree of hierarchy in the energy-hierarchy model
To calculate the degree of hierarchy in the energy-hierarchy model, I assume that power relations exist only within institutions. In other words, there are no power relations between institutions.
It is worth noting that this assumption is not realistic. Studies of corporate ownership suggest that between firms, there is an interlocking network of power (Fichtner et al., 2017; Glattfelder and Battiston, 2009; Vitali et al., 2011). I ignore this complexity here for two reasons:
- First, it is beyond the scope of the energy-hierarchy model to simulate the network of power between firms.
- Second, this network is ignored by the neoclassical theory of free markets. In the neoclassical model, firms interact only by buying and selling, so there are no power relations between them.
In my energy-hierarchy model, then, I give neoclassical theory the benefit of the doubt. I assume that power-relations exist only within firms, not between them. Were we to add power relations between firms, the inferred degree of hierarchy would increase.
One more caveat. The energy-hierarchy model does not directly simulate the chain of command within hierarchies. Instead, it simulates aggregate hierarchical structure – the number of people in each rank. To calculate the number of subordinates controlled by an individual, I assign each modeled person the average number of subordinates below their rank, defined as:
Here h is the hierarchical rank, N is the membership in each rank, and {Ns-bar} is the average number of subordinates. I then input the distribution of Ns into the formulas for the concentration of hierarchical power (Eqs. 1 – 2) and global reaching centrality (Eqs. 3 – 4).
6.7 Differences between CHP and GRC
My two metrics of hierarchy – the concentration of hierarchical power (CHP) and global reaching centrality (GRC) – both agree that the ‘least hierarchical’ network is one in which nobody has subordinates. But the two metrics disagree about what type of network is the ‘most hierarchical’.
The GRC assumes that the most hierarchical network is one in which all people are directly under the command of a single person. This is a society consisting of a single hierarchical firm, in which the CEO directly commands everyone else.
Whether such a society is indeed the ‘most hierarchical’ is a matter of definition. In an engineering scenario (where the GRC is derived), it makes sense to define the most hierarchical network as one in which a single node directly controls all other nodes. But in human networks, this idea makes less sense. The problem is that in practice, as humans accumulate more direct subordinates, their ability to actually command any single person diminishes. An army general may easily command 10 officers. But can the same general manage 10,000 soldiers directly? Unlikely.
As humans try to directly manage more people, their subordinates become more autonomous. We have a word for this tendency. As the span of control increases, we say that the hierarchy becomes ‘flatter’. To many people, a flatter organization is ‘less hierarchical’. But the GRC assumes the reverse is true. That is why my other metric – the ‘concentration of hierarchical power’ (CHP) – is useful. In contrast to the GRC, the CHP views a steeper organization as more hierarchical.
Because the CRC and CHP disagree about what constitutes the ‘most hierarchical network’, they could give conflicting results for the trend in social hierarchy. One metric might increase while the other decreases. Fortunately, I do not find such a conflict (Fig. 11). The reason the two metrics agree is because their differing definitions matter only when societies approach a single hierarchy. Since no real-world society is close to this limit, the CHP and GRC show a consistent trend.
6.8 Verifying the energy-hierarchy model’s span of control
In the energy-hierarchy model, the span of control is a free parameter that varies between model iterations. One way to test the model is to see if the fitted values for the span of control are consistent with observations from real-world firms.
To conduct this test, I use Eq. 22 to find the model iteration that best fits the observed relation (within countries) between energy use and the management share of employment. I then take the fitted values for the span of control and compare them to real-world studies of hierarchy within firms. Figure 14 shows the results. The model’s estimates for the span of control have a range that is consistent with the real-world observations. A t-test (p = 0.77) and ks-test (p = 0.08) both indicate that the two distributions are statistically indistinguishable at the 5% level.
Figure 14: Span of control – empirical data and model estimates
The red distribution shows density estimates for the span of control in the available studies of firm hierarchy. Data is from Ariga et al. (1992); Audas et al. (2004); Baker et al. (1993); Bell and Van Reenen (2012); Dohmen et al. (2004); Eriksson (1999); Heyman (2005); Lima (2000); Morais and Kakabadse (2014); Mueller et al. (2016); Rajan and Wulf (2006); Treble et al. (2001). Because these studies report data over differing timeframes, I first average the spans reported by each study. I then plot the distribution of these averages. The black points on the x-axis show the individual averages. The blue distribution shows density estimates for the span of control fitted by the energy-hierarchy model. The two distributions are statistically identical at the 5% level.
Funding
This research was funded in part by John Medcalf, Mike Tench, Robin Shannon, Brent Gulanowski, Tom Ross, Steve Keen, Hilliard MacBeth, Joe Clarkson, Grace and Garry Fix, Pierre, Norbert Hornstein, and Ed Zimmer.
Conflicts of Interest
The author has no conflicts of interest to declare that are relevant to the content of this article.
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:
- Evolution of Free Markets and Hierarchy
- The Growth of Hierarchy with Economic Development
- Energy and Hierarchy
- Rethinking Free-Market Theory
- Does Free-Market Thinking Motivate Hierarchy?
- Rethinking the Free Market: Conclusions and Methods
- References
Caption graphic photo credit: Clip from image by David Mark from Pixabay. Full image:
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