The author has declared that no competing interests exist.
Why do institutions grow? Despite nearly a century of scientific effort, there remains little consensus on this topic. This paper offers a new approach that focuses on energy consumption. A systematic relation exists between institution size and energy consumption per capita: as energy consumption increases, institutions become larger. I hypothesize that this relation results from the interplay between technological scale and human biological limitations. I also show how a simple stochastic model can be used to link energy consumption with firm dynamics.
Throughout the last century, there has been a recurrent desire to connect human social evolution to changes in energy consumption [
This paper is concerned with one particular aspect of social change: the growth in size of the
I pursue two avenues for understanding the relation between energy and institution size. The first approach draws on the rich history of stochastic modelling within firm size theory. Stochastic (random) models have been successfully used to link firm
The second approach is more speculative, and aims to offer a general explanation of why rates of energy consumption are related to institution size. I propose two factors that mediate this relation:
This paper is organized as follows. After a brief review of the strengths and weaknesses of various theories of institutional size (Sec. 1.1), Section 2 discusses the empirical evidence connecting energy consumption with institution size. Section 3 then uses a stochastic model to further illuminate the relation between energy use and firm dynamics. Finally, Section 4 presents and tests a series of hypotheses linking institution size to technological scale and social hierarchy.
Theories of institution size can be divided into two classes: those that concern themselves with the
All ‘how’ theories of institutional size can be traced back to the work of the French economist Robert Gibrat, who discovered that the rate of growth of business firms seemed to be
Despite their success, ‘how’ theories are not particularly satisfying because they do not explain
The theory of the firm has been dominated by Ronald Coase’s
Other theories propose that management talent is the driver of firm growth. For instance, Robert Lucas assumes that the firm size distribution results from “allocat(ing) productive factors over managers of different ability so as to maximize output” [
Still other theories propose that firm growth is the result of a resource-driven competitive advantage [
In terms of measurability, theories of government size have faired no better than theories of firm size. One approach is to apply the rational-choice model to the behavior of voters. Government size is treated as a reflection of the preferences of utility maximizing voters [
Another approach is to assume that government bureaucracies (or government as a whole) are self-serving entities that attempt to maximize their budgets, but are restrained by voters and/or an institutional framework such as the constitution [
The lack of measurable variables has consistently plagued ‘why’ theories of institution size. If a new theory is to be successful, it must demonstrate a connection between institution size and some universally measurable quantity. Energy consumption is just such a quantity.
To study the relation between energy and institution size, I compare variations in energy use per capita to variations in the size of firms and government over both space and time. For firms, I investigate how changes in the base, tail and mean of the firm size distribution are related to changes in energy use per capita. I use self-employment data to investigate the base of the firm size distribution (relying on the assumption that self-employer firms are very small). To investigate the tail of the firm size distribution, I look at the employment share of the largest firms. To quantify the relative size of government, I measure the government share of total employment.
Comparison of these institution size metrics with energy use per capita are shown in Figs
This figure shows how different metrics of institution size vary with energy consumption per capita. Panels A-C analyze variations in firm size by looking at the base, tail, and estimated mean of the firm size distribution. Panel D analyzes variations in government size. In order to show as much evidence as possible, panels A, B and D are a mix of time series and scatter plot. Lines represent the path through time of individual countries while points represent a country with a single observation. Error bars in panel C represent the 95% confidence interval of mean firm size estimates. Variations in self-employment, large-firm, and government employment share vs. energy are modelled with log-normal cumulative distribution functions. Mean firm size vs. energy is modelled with a power law. Grey regions indicate the 99% confidence region of each model. For sources and methodology, see
This figure shows the trends for various measures of institution size in the United States over the last century. Trends mirror those found at the global level. As energy consumption per capita increases, self-employment rates decline (panel A, note reverse scale), the large firm employment share increases (panel B), mean firm size increases (panel C), and the government employment share increases (panel D). Note that government regressions exclude World War II (dotted line). For sources and methodology, see
This figure combines data from 3 different units of analysis (nations, sectors, and sub-sectors) to offer a comprehensive picture of the relation between firm size and energy use per capita (or per worker). ‘US Industry’ consists of construction and manufacturing sectors, while ‘US Manufacturing Subsectors’ are the smallest subdivisions of the manufacturing sector. At the national level, energy use is measured per
To summarize our findings, the evidence in Figs
The small firm employment share
The large firm employment share
The mean firm size
The government employment share
Findings 1–3 suggest that increases in energy consumption are associated with a shift in employment from small to large firms. This indicates that the firm size distribution becomes more
Assuming a correlation between energy use and GDP, then the evidence presented here is consistent with previous research that has focused on the relation between firm size and GDP per capita [
Following the long-standing division in institution size theory between ‘how’ and ‘why’ theories, I adopt two separate approaches for understanding the relation between institution size and energy consumption. The first approach deals with the ‘how’ question:
Beginning with the work of Gibrat [
Ideally, we would look at this relation directly by investigating international variations in the firm growth rate distribution and comparing them to variations in energy consumption. Unfortunately, data constraints make such a comparison difficult. Calculating international firm growth rate distributions would require longitudinal data for a large, representative sample of firms in many countries. I am not aware of the existence of any such data at the present time. However, we can use what little data
Firm age data provides an indirect window into firm dynamics. If we assume that new firms start at a small size, then we can infer the historic rate of growth of any firm, given its current age and size (i.e. a new, large firm likely grew rapidly, while an old, small firm likely grew slowly).
This figure demonstrates how firm age and mean size data can be used to restrict the parameter space of a stochastic model. This allows predictions to be made about the relation between energy use and firm dynamics. Panel A shows the country-level relation between the fraction of firms under 42 months old vs. energy use per capita (the grey region indicates the 99% confidence region of the regression). Panel B shows the country-level relation between the fraction of firms under 42 months old and mean firm size (error bars indicate 95% confidence intervals). The ‘Fitted Zone’ in Panel B shows the age-size relation produced by a stochastic model with a parameter range specifically chosen to capture the empirical data. Panel C shows the model’s parameter space with the resulting mean firm size indicated by color. Using the regressed relation between mean firm size and energy use per capita (
This data clearly hints that a systemic relation exists between energy consumption and firm dynamics. In the following section, I use a stochastic model to make specific predictions about the form of this relation.
The essence of all stochastic firm models is that growth is treated probabilistically. Each firm begins with some arbitrary initial size
This basic Gibrat model is unstable unless additional stipulations are added (see
The firm size distribution is a power law.
Firm growth rates are independent of size.
New firms are all born at size
The firm birth rate is equal to the firm death rate.
Firm growth rates come from a
The firm size distribution exists in an equilibrium.
Assumption 1 is necessary because the model produces a power law distribution (see
Assumption 2 is a property of most stochastic firm growth models, and dates back to the work of Gibrat [
Assumptions 3 and 4 give meaning to the reflective lower bound. We can interpret this boundary as a firm birth/death zone. Any firm that passes below
Regarding assumption 5, it is well established that the firm growth distribution has a tent-shape that can be modelled with the Laplace distribution [
Assumption 6 justifies testing the model against empirical data. Given some arbitrary initial conditions, the model will always approach a stable firm size distribution that is a function of only the growth rate distribution (provided that the stability conditions are met). Prior to arriving at equilibrium, there is
The goal of this analysis is to estimate how firm dynamics (i.e. growth rate distributions) change with levels of energy consumption per capita. This estimation involves three steps. First, we must use appropriate empirical data to restrict the parameter space of the model. Second, we analyze how this parameter space relates to mean firm size. Finally, we extrapolate, from mean firm size, the relation between model parameters and energy use per capita.
Modelled growth rates are determined by the Laplace probability density function below, where
To do this, I use the empirical relation between the proportion of firms under 42 months of age and mean firm size (
The final step in the analysis is to use the regressed relation between mean firm size and energy use per capita (
Our restricted stochastic model predicts the following: (1)
Any attempt to explain why institutions grow must first settle on the appropriate scale: do we attempt to explain why
The very success of stochastic firm growth models—in which
My explanation of the energy versus institution size relation builds on the ‘social brain’ hypothesis proposed by Dunbar [
To connect social coordination to energy consumption, I explore the connection between energy use and technological scale. I argue that increases in energy consumption are associated with the use of increasingly large technologies. The construction, operation, and maintenance of these larger technologies, in turn, requires greater social coordination.
I formalize this reasoning in the joint hypotheses below. The order of these hypotheses is meant to show a line of reasoning, not necessarily a direction of causality.
Increases in per capita energy consumption are accomplished (in part) through increases in technological
Increases in technological scale require increases in
Humans have a
Institutions (firms and governments) are dedicated social hierarchies.
In the following sections, I review the empirical evidence in support of each of these hypotheses.
My focus on technology (hypothesis A) is motivated both by theoretical arguments and by the empirical results in
From a theoretical (thermodynamic) perspective, energy ‘consumption’ is best thought of as a
On the empirical side, the fact that firm size scales with energy consumption both at the national and
To illuminate the relation between energy and technology, consider the definitional statement that energy per capita (
In terms of social coordination, there is a fundamental difference between increasing energy consumption through technological density versus technological scale: the former is a
As an example of a technological
As an example of a technological
Type | Early Prototype | Largest Today | Unit | Scaling Factor |
---|---|---|---|---|
Electric Power Plant | 0.0125 | 2 2500 | megawatts | 1.80 × 106 |
Oil Refinery | 5.5 | 1 240 000 | barrels per day | 2.24 × 105 |
Aluminium Smelter | 5.7 | 1 060 000 | tonnes per year | 1.86 × 105 |
Internal Combustion Engine | 0.75 | 107 390 | horsepower | 1.43 × 105 |
Mining Excavator | 380 | 2 324 0000 | cubic meters per day | 6.12 × 104 |
Blast Furnace | 0.3 | 5 500 | cubic meters | 1.83 × 104 |
Tanker Ship | 1809 | 260 859 | gross tonnage | 1.44 × 102 |
This table shows the size of 7 selected industrial technologies at their earliest stage of development (‘Early Prototype’) and at the largest scale existing today. Column 5 shows the scaling factor between the largest and early technologies (largest/early). Technologies are ranked in descending order of scaling factor. For data sources, see
But to what degree are increases in energy use per capita actually achieved through increases in technological scale? Given the complexity of technological change, this question is difficult to answer at a general level (for all technologies). Instead of a general test of hypothesis A, I present here a case study of electricity production and consumption in the United States (
Panel A shows the time-series relation between the mean capacity of US power plants and US electricity use per capita. Both series are indexed to 1 in the year 1920 in order to show relative growth. Power plants tend to get larger as electricity use per capita increases increases. Panel B shows the fraction of US per capita electricity use growth (since 1920) that was met by increases in mean plant size. The dashed line indicates the mean over the period 1920–2015, while the shaded region shows the standard deviation. Panel C shows the relation between power plant capacity and the estimated construction labor time. The entire range of electricity generation technology is included in this plot—from the smallest gasoline generators to the largest hydroelectric power plants. Different primary energy sources are indicated by color. Data is modelled with a power law. Grey regions indicate the 99% confidence region of the regression. For sources and methodology, see
In the US electricity generation sector, increases in technological scale obviously played a major role in meeting increases in per capita electricity consumption. Was this increase in scale accompanied by a corresponding increases in the scale of social coordination (hypothesis B)? Answering this questions requires that we first define what we mean by the ‘scale’ of social coordination, and specify how this relates to a given technology.
I define the ‘scale’ of social coordination as the number of people required to construct, maintain, and operate a specific technology. For measurement purposes, however, I limit my analysis only to
To estimate construction labor time from costs, I first note that by the rules of double-entry accounting, all costs eventually become someone’s
To summarize, our case study of the electricity generation sector is consistent with both hypothesis A and B. We find that increases in power plant scale have played an important role in meeting increases in US per capita electricity consumption (hypothesis A). Furthermore, we find that power plant size is strongly related to construction labor time—our measure of the scale of social coordination (hypothesis B).
Admittedly, a case study of a single technology represents limited evidence. However, the vast scaling of the other technologies shown in
Social coordination can conceivably be achieved in many different ways (customs, markets, institutions, etc.). Thus, an increase in social coordination does not necessarily imply an increase in firm and government size. Why, then, have these institutions increased in size as energy consumption increases? Hypotheses C-E propose a chain of reasoning explaining why institutions are the most effective way of organizing large groups of people. The key to this reasoning is hypothesis C: humans have a
The evidence for this hypothesis comes primarily from the work of anthropologist Robin Dunbar, who has uncovered a startling relation between primate brain size and mean group size [
The implication of Dunbar’s findings is that the size of the human brain places limitations on the number of social relations that an individual is able to maintain. Dunbar uses his primate data to predict a mean human group size of about 150. While this number should be considered exploratory, Dunbar notes that early egalitarian societies had group sizes around this order of magnitude [
A key feature of egalitarian organization is that any member of a group may maintain relations with any other member of the group. Thus, the number of possible social relations increases linearly with group size. Given the hypothesized limitations in the human ability to maintain social relations, it follows that egalitarian social organization is not an effective method for coordinating large numbers of people.
One way of increasing group size beyond Dunbar’s number is to organize groups in a way that
As evidence for this line of reasoning, Turchin and Gavrilets demonstrate that a strong correlation exists between the population of historical agrarian empires and the number of administrative (hierarchical) levels within their respective governments. Similarly, Hamilton et al. find a strong relation between population size and the number of hierarchical levels with various hunter-gatherer societies [
Social hierarchies have taken many different forms at different points in human history. For instance, in many pre-state societies, social hierarchy took the form of the chiefdom. In middle-ages Europe, the feudal manor was the principle unit of hierarchy. In the modern era, I argue that business firms and governments are the principle unit of social hierarchy (hypothesis E). To test this hypothesis, I focus only on firms.
The implication of hypothesis E is that increasing firm size constitutes an
Since the upper echelons of a hierarchy are almost exclusively involved in managing the activities of other people, it seems sensible to use the
To refine this prediction, I develop a hierarchical firm model of society (
All firms are ‘ideal’ hierarchies with a single span of control.
All individuals in and above the third hierarchical level are considered ‘managers’.
The firm size distribution is a power law.
This figure graphically demonstrates how the management fraction increases with firm size (assuming firms are ‘ideal hierarchies’). Firms are indicated by boxes (with the exception of single-person firms) with a worker’s hierarchical position shown vertically. The span of control—defined as the size ratio between adjacent hierarchical levels—is constant for all firms. In this picture, the span of control is 2. Managers (red) are assumed to be all individuals in and above the third hierarchical level. To maintain simplicity, this graphic does not use a power law firm size distribution.
Why assume that management begins at the third hierarchical level? Obviously, individuals within the lowest hierarchical level have no management responsibilities. Those in the second hierarchical level can be thought of as ‘working supervisors’—individuals who have some supervisory responsibilities but who spend a majority of their time engaged in ‘production’ [
This model predicts that the management fraction of employment should grow non-linearly with firm size, eventually approaching an asymptote defined only by the span of control. If the span of control is
In
Panels A and B plot the country-level relation between the management fraction and mean firm size. Modelled data is also shown in the background, with the span of control indicated by color. Panels A and B use different (incommensurable) classification methodologies for ‘management’. Panel A uses ISCO-88 (which includes legislators, senior officials and managers) while panel B uses ISCO-1968 (which includes administrative and managerial workers). Error bars indicate the 95% confidence intervals for mean firm size. Panel C compares the span of control range from the model to the span distribution found by 12 different empirical studies. Red boxplots indicate case studies, and show the span of control distribution within a
The model nicely reproduces the observed relation between mean firm size and the management fraction of employment. However, this fit is achieved by freely manipulating the span of control parameter. Thus, it is important to check that the modelled span of control range is consistent with the span range for
Ideally we would be able compare the span range of the model to the span distribution of a large, global sample of firms. Unfortunately, data constraints make this impossible. Due to the proprietary nature of firm personnel data, only a handful of studies have analyzed firm hierarchies.
Boxplots in
To summarize these findings, a simple hierarchical firm model of society is able to replicate the observed relation between mean firm size and the management share of employment. The changes in mean firm size are achieved by varying the exponent of a firm size power law distribution, while the management fraction of employment is fitted by ‘tuning’ the span of control range (assumed to be the same both within and between all modelled firms). Importantly, the resulting fitted span range is consistent with the existing empirical data on the internal structure of the firm. The success of this model gives support to hypothesis E, and suggests that increases in mean firm size are characteristic of a generalized increase in social hierarchy.
I have proposed hypotheses A-E as a chain of reasoning connecting energy consumption to institution size. But which way does causation run? Do increases in energy consumption
Although hypotheses A-E are framed in terms of
However, recent history (the collapse of the Soviet Union) suggests that causality can operate in the
This figure tracks the path through time of six nations that emerged after the collapse of the Soviet Union (in 1990–91). As the collapse unfolded, the fraction of people employed by the government shrank rapidly, as did energy use per capita. Since the USSR collapse was an institutional crisis (not an energy crisis), this suggests that at least in this case, causality runs from institution size to energy consumption.
This case is illustrative because the Soviet economy relied on an unusually high degree of government control of production, placing an enormous amount of power in the hands of a single institution. Not surprisingly, the collapse of this institution led to social chaos and widespread economic decline. I think this shows quite clearly that institutional collapse can cause a decline in energy consumption.
The argument that causation can operate in
It is also important to note that changes in energy use and institution size occur alongside other social changes, the two most obvious being urbanization and changes in sector composition [
All life on earth is united by a common struggle—a “struggle for free energy available for work” [
Based on this line of reasoning, a branch of scholarship has emerged that studies the role of energy in human societies [
I have offered a new theory of institution size that is rooted in human biology, and the theorized limitations of our ability to maintain social relations. I have proposed that institutions (firms and governments) are social hierarchies that serve to increase the scale of social coordination beyond that which is possible through egalitarian relations. I have argued that increases in energy consumption require a general increase in the scale of social coordination, and that increases in technological scale are a plausible reason for this connection. There is, of course, no need for increases in technological scale to be the
An important prediction of this theory is that increases in energy consumption are associated with a general increase in social hierarchy, meaning power is concentrated in the hands of fewer and fewer people. Although this starkly contradicts neoclassical economic theory, it is consistent with the power-based approach to political economy offered by Nitzan and Bichler [
Contains information on data sources and methods. It also contains extra analysis referenced in the main paper.
(PDF)
This zip file contains raw and final data for all analysis conducted in this paper. It also includes R code used for modelling.
(ZIP)
The method used in this paper owes a great deal to the work of Jonathan Nitzan, who encouraged me to abandon the use of real GDP, and who made me aware of many of the databases used in this paper. I would also like to thank Ellie Perkins and Mark Thomas, as well as the two anonymous reviewers, for their helpful comments on drafts of this paper. I would also like to thank Garry and Grace Fix for their proofreading skills.