Fig 1.
Institution size vs. energy use per capita at the international level.
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 S1 Appendix (part A).
Fig 2.
Institution size vs. energy use per capita in the United States.
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 S1 Appendix (part A).
Fig 3.
Synthesizing evidence—firm size vs. energy use per person/worker.
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 person, while at the sectoral level, it is measured per worker. In panel A, self-employment data (for nations and US Industry) is merged with the data for the employment share of firms with 0–4 employees in US manufacturing subsectors. In panel B, data for the employment share of the largest 25 firms (for nations and US Industry) is merged with data for the employment share of firms with more than 5000 employees in US manufacturing subsectors. Panel C shows mean firm size data at the national and sectoral level. Grey regions indicate the 99% confidence region of each model. For sources and methodology, see S1 Appendix (part A).
Fig 4.
Using firm age data to estimate international firm dynamics.
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 (Fig 1C), modelled mean firm size is then transformed into an estimate for energy use per capita. The resulting relation between μ and b vs. energy use per capita (for data in the fitted zone only) is plotted in panel D.
Table 1.
Scale increase of various industrial technologies.
Fig 5.
Technological scale and social coordination in electricity generation.
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 S1 Appendix (part A).
Fig 6.
The growth of management as a function of the firm size distribution.
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.
Fig 7.
Testing the hierarchical model of the firm using managment share of total employment.
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 single firm. Blue boxplots indicate aggregate studies and show the span of control distribution across many different firms. The span of control distribution across all 12 studies is shown on the right. For sources and methodology, see S1 Appendix (part A).
Fig 8.
A case study in causality: The collapse of the soviet union.
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.