Nathaniel Rooney
A Brief Introduction to System Dynamics
Nathaniel Rooney
Abstract:
This paper is a culmination of work done at MIT’s System Dynamics Group under Professor John Sterman in updating data for Professor Sterman’s seminal textbook in System Dynamics (SD), Business Dynamics. SD is a relatively new and powerful field of thought that offers a straightforward framework for understanding complex systems. While mainly used for management and sustainability, SD is generalizable to aid understanding and decision-making in many fields. This paper aims to familiarize the reader with the basic concepts of SD through updated versions of figures from Business Dynamics, with each figure demonstrating an important concept in SD.
Introduction:
Invented in the 1960s by Jay Forrester, System Dynamics (SD) and Systems Thinking are schools of thought that use formal modeling (i.e. graphical, mathematical, and computer) to better understand and manage complex, dynamic systems. They combine tangible data typically used in other fields of STEM with intangible things like how humans think to create models of complex systems. This unique approach provides extra insight into understanding complex systems that make SD incredibly useful.
Complex systems are dynamic, interconnected, selforganizing, and evolving. They can be as vast as an ecosystem or a climate, or as small as an individual deciding what to get for lunch. SD models of complex systems are built using several simple components: stocks, flows, and reinforcing and balancing feedback loops (or positive and negative feedback loops, respectively), as shown in Figure 1. One of the most common ways of explaining stocks and flows is by thinking about a bathtub (Forrester 2009).
The water in the bathtub acts as a stock as it can increase or decrease in amount. The water through the faucet and drain act as an in-flow and an out-flow of the bathtub respectively, as flows increase or decrease the amount of the stock. Feedback loops are loops of variables where the outcome of one variable affects the outcome of the next, and so on and so forth until the original variable is affected and the loop starts again. A reinforcing feedback loop is a feedback loop in which a change in the original variable is amplified through each cycle of the loop. Interest on bank savings, for example, is reinforcing feedback since an increase in the amount of money in the bank account leads to an increased amount of interest which leads to more money in the bank and an even higher amount of interest. A balancing feedback loop is one where the system over time approaches equilibrium.
Homeostatic processes, like sweating, are balancing feedback loops since an increase in body temperature leads to the production
of sweat, which lowers body temperature through evaporative cooling.
Figure 1: New Product Adoption model (Sterman 2001).
The ability to break complex systems down into smaller, easily understood parts is incredibly useful, especially in a more and more interconnected world with more and more interconnected problems. We humans think we’re much more capable of understanding complex systems in our heads than we actually are. In fact, even well-educated, technically capable people exhibit shortcomings in mentally simulating how even the most basic systems behave (Cronin 2009). Other studies suggest that we can only simulate interactions between 2-3 variables mentally, and beyond 4 variables our understanding is no better than chance (Halford 2005). SD modeling allows us to not only think about the simpler components that make up complex systems but also predict and simulate many variables at once. SD modeling also helps determine how a change to one part of the system impacts the overall behavior of the system.
With the knowledge of the effects of each component, one can also determine how best to manage that system. Common examples of this include policymaking and its implications, business management, and mitigating climate change. MIT’s System Dynamics Group, for example, is a part of the MIT Sloan School of Management. Many of the models and work from the SD group are about figuring out how a company should best manage a given situation. That being said, Professor John Sterman has said that SD, and his textbook, Business Dynamics, are really a Trojan horse for sustainability. MIT’s SD group collaborates with many climate change organizations including Climate Interactive to make models like En-ROADS, a “global climate simulator that allows users to explore the impact that dozens of policies such as electrifying transport, pricing carbon, and improving agricultural practices have on hundreds of factors like energy prices, temperature, air quality, and sea level rise,” which has been used to
inform “more than 130 members of the US Congress” about climate change (Climate Interactive 2023).
Even with its powerful applications, there are several limitations of SD. As George Box famously said, “All models are wrong, but some are useful.” This certainly holds for SD models. One will never create a model that is a hundred percent accurate. There will always be some unpredictable behavior or event, and even if there isn’t, “the data you need to build and test your model are rarely available without significant cost and effort” (Sterman 2002). But, as Sterman argues in “All models are wrong: reflections on becoming a systems scientist,” there are “assumptions at the root of everything we think we know.”
According to Sterman, much of our knowledge is based on mental models and assumptions. This isn’t to say that we must uproot the fundamentals of our very way of thinking since it is based on assumptions but to prove that just because something isn’t
completely accurate doesn’t mean it can’t be useful to enrich our understanding.
Data Collection and Visualization:
Numerous datasets were found and researched for the updated textbook. The datasets all demonstrated a common behavior or idea in SD, and the idea was to use these datasets to help explain these common behaviors to strengthen the reader’s fundamental understanding of SD.
Examples of Exponential Growth:
The first behavior is exponential growth. Figure 2-1 shows the most basic underlying structure of exponential growth and Figures 2-2, 2-3, 2-4, and 2-5 are several real-world examples representative of exponential growth. Applying the world population example (2-2) to the causal loop diagram, we see that a greater number of people leads to a higher birth rate which leads to
an even greater number of people, etc. The “+” symbol under the arrows on causal links designates that a change in one variable leads to a change in the same direction in the next variable (increase leads to increase; decrease leads to decrease). The “-” symbol designates a change in one variable leads to the opposite change in the next variable (increase leads to decrease; decrease leads to increase). In 2002, the year of the original publication of Business Dynamics, each one of these datasets was representative of exponential growth. However, in the 20 years following, many of these graphs have become less demonstrative of exponential growth. For example, the world population recently slowed its rate of increase, and the US prison population has been decreasing since around 2015. Though these graphs no longer demonstrate exponential growth, they still convey an important message about exponentiality: in a finite world, there cannot be exponential growth forever.
Figure 2-1: Simple causal loop diagram of exponential growth from Business Dynamics.
Figure 2-2: Graph of world population over time (United Nations 2023).
Figure 2-3: Graph of US real GDP over time (Measuring Worth 2023).
Figure 2-4: Graph of US prison population over time (Bureau of Justice Statistics 2023)
Figure 2-5: Graph of log base 10 of transistors per microchip over time (Martin 2023).
The graph demonstrates Moore’s Law, which is that the number of transistors per microchip doubles every 2 years. Note that the graph looks roughly linear but is exponential because of the logarithm.
Linear growth is rather rare in complex systems (Sterman 2000). This is because linear growth means that the state of the system has a constant rate of change – speaking in SD terms, this means that the state of the system has absolutely no impact on the rate at which the state of the system changes. “What appears to be linear growth is often actually exponential but viewed over a time horizon too short to observe the acceleration” (Sterman 2000). This might seem counterintuitive - but other than age and distance traveled at a constant speed, it’s hard (not impossible) to think of something that increases truly linearly. For example, suppose a farmer buys a cow and every year, with the profit the farmer makes from selling milk, the farmer buys more cows. At first, the farmer can only afford to buy one cow each year. This fixed initial rate
does not represent linear growth. In fact, given the farmer is reinvesting profits into buying more cows, this could be the early stages of exponential growth. Every year, the farmer will have more cows producing more profit than the previous year, allowing the farmer to purchase two, four, eight, and exponentially more cows each year.
Example of Goal-Seeking Behavior:
Another important type of system behavior is goal-seeking. Goal-seeking behavior occurs when a system trends toward some equilibrium. For instance, US traffic fatalities per vehicle mile traveled illustrate a downward goal-seeking trend, as seen in Figure 3-1. This behavior is easily explained by an increase in safety regulations and safety technology of cars.
Figure 3-1: Graph of US traffic fatalities per vehicle mile traveled over time (NHTSA 2023).
Using system dynamics, the general behavior of a goalseeking structure can be expressed rather simply, as seen in Figure 3-2. In the traffic fatalities example, the desired state of the system would be as few traffic fatalities as possible. If there is any discrepancy between the actual state of the system (the number of fatalities) and the goal (the desired number of fatalities), there will be some corrective action on the state of the system. In this
example, corrective action could include seatbelt laws and improved airbags. After these actions are implemented, the discrepancy between the goal and the state of the system decreases. This lower discrepancy means that less action is needed to achieve the goal state. Given this context, the state of the system can’t go beyond the goal, so corrective action in the opposite direction won’t occur. However, in goal-seeking situations where overachieving the goal is undesirable (for example, the number of guests at a restaurant, where the goal is a certain number of guests), corrective action would occur. In the restaurant example, having more than the goal number of guests would mean longer wait times to get a table, decreased quality of service and food since the restaurant is rushed, and a generally worse experience.
Corrective action would be taken by the restaurant to decrease the number of guests to the goal amount through methods such as changing rules for reservations and controlling the flow of guests in and out of the restaurant.
Figure 3-2: Simple goal-seeking model from Business Dynamics.
The Challenge of Forecasting: Oil Prices
A complex system that plays an important role in the global economy and human impact on the environment and climate is the production and consumption of oil. The price of oil is influenced by many factors, including oil demand, supply, and policies that constrain its extraction and use. Because of its economic significance, there is a long history of attempts to forecast the behavior of oil prices over time. The failure of these forecasts to accurately predict oil prices is a clear illustration of how the
behavior of complex systems is difficult to predict - especially without system dynamics. To help illustrate these concepts, data about oil prices over time were collected and analyzed to determine how accurate forecasts were.
The Department of Energy’s Energy Information Agency (EIA) produces yearly Annual Energy Outlooks (AEO), which include forecasts for oil prices as well as data on actual oil prices. They also include forecasts from other reputable energy organizations, including the International Energy Agency (IEA), Energy Ventures Analysis (EVA), IHS Global Insight (IHSGI), and Petroleum Economics Ltd. (PEL). Datasets were compiled using digitized versions of the AEOs and Excel’s “importing data from a picture” tool. Excel’s image analysis tool is still in development, so each entry also required meticulous doublechecking. As seen in the example AEO table in Figure 4, the forecasts from the other agencies only included forecasts in 5-year increments. The EIA produced forecasts for every year, so a
dataset of only the EIA’s predictions was also made. For simplicity’s sake, the following discussion of oil prices refers to the EIA’s “reference” price forecasts.
Figure 4: Table of Oil Price Forecasts from AEO from 1998.
There are several important nuances and details that need to be mentioned. First and foremost, the AEO’s report their forecasts in USD from a year or two before the year of publication. The value of a 1979 US dollar is very different from the value of a 2022 US dollar, so the data were standardized to 2022 US dollars using a GDP deflator from the Federal Reserve’s Economic Data (FRED 2023). The changes in the way the oil prices are reported are also noteworthy. Until 2006, AEOs used the average imported refiner acquisition cost of crude oil to the United States (IRAC) to report oil prices. However, IRAC started to deviate from other common oil price indices like West Texas Intermediate (WTI; used by EVA and IHSGI) and Brent (used by PEL), so from 2006-2012 AEOs used imported low-sulfur crude oil to U.S. refiners prices to lessen discrepancies between the AEOs and other organizations oil data. According to the EIA, imported low-sulfur crude oil and WTI prices are "approximately the same” (AEO 2006). As they moved to a digital format, from 2013 to present the AEOs also include
WTI and Brent price forecasts. As seen in Figure 5-1, the different oil price indices largely agree with small exceptions around 2006, 2010-2013, and 2017. Since there was the largest sample for imported crude oil price, that data was used to compare to the forecast data as it gave more insight into the behavior of oil prices over time. As shown in Figure 5-2, not all of the forecasts' starting year data match up to the actual oil price of that year, which is likely due to the fact that forecast data used WTI whenever possible and WTI and imported crude oil price vary slightly.
Figure 5-1: Actual oil prices from the EIA in WTI, Brent, Refiner
Average Crude Oil Acquisition Cost, and Imported Crude Oil
Average Price ($/barrel) over time (EIA 2023).
Figure 5-2: Graph of US EIA’s forecasts for oil prices from their Annual Energy Outlooks and the actual oil prices. The black line represents the actual oil prices while the red lines are forecasts. The year when the forecast was made is labeled at the end of each forecast timeline.
After compiling the data in Excel, ChatGPT was used to help write code in R to graph the forecasts, as seen in the dialogue in Figure 5-3. R code was iteratively edited with assistance from ChatGPT, and a PowerPoint slide deck of graphs like Figure 5-2
was created documenting the year-by-year progression of AEO forecasts. These graphs technically won’t be used in Business Dynamics, but Professor Sterman is using them as examples in his introductory course on system dynamics. These oil forecasts offer many lessons on effective forecasting in general.
Figure 5-3: Dialogue with ChatGPT to help create graphs of oil prices.
Returning to Figure 5-2, the EIA’s forecasts are very inaccurate. In 1979 and 1982, they predicted that oil prices would increase sharply – but they ended up crashing. In fact, throughout the rest of the 80s, they consistently predicted that oil prices would bounce up but they ended up staying relatively flat. By the time the EIA was predicting oil prices would remain flat for a long time, like in their predictions from around 1997 to 2005, oil prices were in reality already starting to rise. After the peak, plummet from the 2008 financial crisis, and subsequent recovery to pre-crisis prices, the EIA predicted further increases for each of its next several predictions. However, in reality, there was a repeat of what happened in the 80s, where the EIA consistently predicted price increases despite oil prices plummeting.
Perhaps one might think this assessment is uncharitable. After all, the AEO predictions from 1997 to 2005 do end up being accurate for 2020. The 1991-1993 forecasts also end up predicting the oil prices well in 2005/06. While that may be true, even those
predictions do quite poorly when it comes to capturing what happens between the date of prediction and the point where the prediction becomes accurate. As another saying goes, “Even a broken clock is right twice a day.”
Another reason these forecasts seem dubious is that even after correcting for inflation (by standardizing prices to 2022 US dollars), the forecasts always predict that oil prices will rise. The only exceptions to this are during oil price plummets, where the EIA predicts prices fall a little more, level out, and then rise. Given the seemingly up-and-down nature of oil prices, filled with peaks and troughs, a good prediction should have at least some areas of decrease.
The AEO’s forecasts also exhibit surprisingly frequent linear growth. Looking closely at each line, apart from the occasional fluctuation, many of them exhibit linear growth longterm. As mentioned before, linear growth is rather rare in the real world. For oil prices to exhibit linear growth, the year-to-year price
increase would have to be independent of the original oil price at the start of that year. This can’t be true; if prices get too high, no one will buy oil, and prices must fall before oil will be sold again. This is not to say linear growth over relatively short periods is impossible. Perhaps these forecasts are exponential growth in a short enough time frame that they appear to be linear growth. Or maybe they coincidentally have net increases that look like linear growth. Nonetheless, we can still take a generalized lesson about how to make an improved forecast.
Lastly, but perhaps most importantly, we must consider oil shocks, which are sudden, sharp changes in oil production or supply. Isn’t it hard to predict what will happen to oil prices when unpredictable events, like the 2008 financial crisis, the Persian Gulf War, and the Iranian Revolution happen so often? The answer is yes and no. Some of these events, like the 2008 financial crisis, are a major cause of oil price shocks but can’t reasonably be predicted. It seems that the 2008 financial crisis didn’t have long-
term effects on oil prices, as they shot right back up after the crisis. That being said, there is research to suggest many of these “exogenous shocks,” or shocks to the oil industry from events originating outside of the industry, which often are political events in the Middle East, have less impact on oil prices than one might think (Kilian 2008). In his research of oil price shocks from 1973 to 2004, Kilian found that “Of the episodes studied, only the 1980/81 oil price increases can be attributed to exogenous oil supply disruptions.” While other exogenous events, like the Iranian revolution, resulted in oil supply disruptions, Kilian finds that “oil supply disruptions explain only a small fraction of the oil price increases” in the events studied.
An astute system dynamicist might point out that even if production doesn’t decrease during an event, that doesn’t mean that event couldn’t impact prices. They would be right: that event could cause public perception of oil and thus demand to fall, which as we will see later in Figure 8, will cause prices to decrease.
Kilian comes to the same conclusion, “Even if physical production does not move, expectations of future oil supply interruptions alone may have powerful effects, as is evident in [his] analysis of the 1990/91 Persian Gulf War episode.” Nevertheless, this doesn’t account for the majority of oil price shocks. In fact, some of the attributions of political events to oil price shocks could just be revisionist history: “Given that oil price shocks are not necessarily preceded by exogenous Middle Eastern political events, it is not clear that the observed increase in oil prices after those exogenous events was actually caused by those events” (Kilian 2008). One possible explanation for the oil price booms in 1973, 1979, and 2003/04 is that there were “capacity constraints in oil production” (Kilian 2008).
Especially in market-dependent commodities, there are many variables that impact the state of the system. Some will be unpredictable, and no amount of modeling will change that. Many, like public perception/demand and capacity constraints, are much
more predictable. A good model should maximize instances of predictable behaviors to minimize the impact of unpredictable ones on the state of the system. We will see these implementations further in Figure 8.
Examples of Market-influenced
Commodities:
Many of the datasets researched pertained to commodity data compiled from the Commodity Research Bureau’s (CRB) annual Commodity Yearbooks. These datasets included data on hogs (slaughter rate, price, frozen pork storage, hog-corn ratio, and number of hogs), cattle (stocks, slaughter rates, and price), and copper (price and production). These commodities all exhibit cycles, which are common in market-affected commodities mostly because of supply and demand. To see these cycles, locally estimated scatterplot smoothing (LOESS) graphs were created in R with the help of ChatGPT. These LOESS graphs create a trend line of the commodity based on the values of close-by points. Since the
trend line is calculated from a range of local points, the trend line is corrected for any smaller cycle such as seasonality. By creating a graph of the ratio of the commodity graph to its trend line, then one can see the smaller cycles. As seen in Figure 6-1, the trend line of US cattle stocks increases and decreases with the broader trend of cattle stocks, while the ratio to trend line seen in Figure 6-2 oscillates above and below the trend line every 10 or so years. A similar behavior can be seen in Figures 7-1 and 7-2, with the US production of refined copper. Copper production has large amplitude cycles of around 15 years, but it also has smaller amplitude cycles every few years.
Figure 6-1: Graph of US cattle stocks over time. The blue line is the raw data and the red line is the LOESS trend line (CRB 2023).
Figure 6-2: Graph of the ratio of cattle stocks to the trend line, showing clear cycles of approximately 10 years (CRB 2023).
Figure 7-1: Graph of US production of refined copper over time (CRB 2023).
Figure 7-2: Graph of the ratio of US production of refined copper to its trend line (CRB 2023).
Figure 7-3: Graph of copper price over time (CRB 2023).
Business Dynamics includes a general model of commodities subject to the invisible hand of market forces like supply and demand. Figure 8 depicts both the underlying supply and demand structure (top right of Figure 8) as well as several other market feedbacks (loops B1, B2, and B3). Loop B1, “Substitution,” accounts for the effect competition has on the relative value of and thus demand for a certain commodity. For
example, if Chile produced refined copper that US companies could buy for less than it would cost if the US produced it, then demand for US-produced copper would decline since its relative value declines. It’s also important to note that as demand decreases, the expected profitability of current operations will also decrease causing the production rate to decrease. Copper is highly conductive and used frequently in electronics so as demand for technology continues to increase in the future, copper production will likely increase globally if not locally.
As seen in loop B2, price also has a delayed effect on production: if a commodity can be sold for more money then profitability rises, which causes capacity utilization and then production rate to rise. Capacity utilization is the actual output over the maximum potential output of a commodity–so if the profitability increases, the producer will increase its output to maximize profit. This increased output can only happen if the production rate also increases. Figures 7-1 and 7-3 show the
relationship between price and production well. After leveling out from the plummet from the start of the Great Depression, copper price has steadily trended upwards. Copper production has a similar upward trend up until around 2000. Understanding why copper production doesn’t continue to rise even though copper prices rise goes beyond the scope of this model. Decreases in copper production could be caused by the continual decrease in copper ore grade, which would decrease expected profitability and thus production rate (Calvo 2016). Decreases might also be from the fact that copper mining can be dangerous, and if workers can find other relatively safer jobs, production will go down. All of this is to say that no model will be completely perfect.
Loop B2 also explains the aforementioned relationship between capacity constraint and oil price. If capacity is constrained, that means capacity utilization is lowered, causing production and thus inventory to be lowered, which causes price to increase.
Loop B3, “Capacity Acquisition,” factors in the acquisition of new investments –whether they be in the form of resources, information, technology, or something else. For copper mining, this could mean finding a new mine, getting more mining tools, or getting new mining technology. If acquiring these investments will boost profitability, they’ll be acquired and production will increase.
8: “Generic structure of commodity markets” model from Business Dynamics.
Figure
Conclusion:
SD is a simple but powerful tool that helps one understand a system–a group of interacting components–better. It compensates for our limited mental capacities for comprehending interactions between variables. Stock-flow diagrams allow for an easy understanding of how each variable affects not only another variable but the entire state of the system. Graphs and predictions generated by the models further aid in understanding what will happen to the system. SD models like En-ROADS allow you to alter each variable and produce graphs that demonstrate the effect of that alteration on each part of the system.
No matter how complex a model is, from En-ROADS to the basic new product adoption model in Figure 1, every SD model can be broken down into the same underlying parts like stocks, flows, and feedback loops (there are several more complicated parts which go beyond the scope of this paper). This paper covered several of the simple interactions these parts can have with each
other such as exponential growth and goal-seeking behavior through several real-world examples.
Making predictions based on a model is perhaps the most useful component of SD. Graphs that a model produces plainly show how the system is change over time. However, these predictions are difficult to make accurately. This paper reviewed predictions made about the price of oil over time to demonstrate how one can tell a prediction is inaccurate. This review also explained some of the limits of SD, as your predictions will never be completely accurate and there will always be some element of the model to be tweaked or added.
Finally, this paper discusses the basics of modeling commodities subject to market forces. Many commodities, like copper and hogs, undergo cycles - sometimes, even multiple concurrent cycles. These cycles are partially explained by the interactions of supply and demand as they relate to the commodity. The real-world example of copper is used to explain a general
commodity model from Business Dynamics that can be adapted to model virtually any other commodity.
This paper introduced some of the basic concepts in SD as Business Dynamics does, using many real-world examples and easily understandable concepts. This paper aims to promote people to implement systems thinking and SD into their own life and fields of study. As a stand-alone theoretical field, SD doesn’t serve much purpose–by design, the foundational concepts of SD are straightforward so that it is easily explained and understood. It is its applications to numerous other fields and its usefulness as a way of thinking that give it incredible value.
References:
Calvo, G.; Mudd, G.; Valero, A.; Valero, A. Decreasing Ore Grades in Global Metallic Mining: A Theoretical Issue or a Global Reality? Resources 2016, 5, 36. https://doi.org/10.3390/resources5040036
Climate Interactive, (2023). The En-ROADS Climate Solutions Simulator. https://www.climateinteractive.org/en-roads/. Accessed January 12, 2024
Commodity Research Bureau (1960-2023). Commodity Yearbooks. https://www-mergentarchivescom.libproxy.mit.edu/modules/CRB/openReport.php?year =CRB%20Commodity%20Yearbook%201992, Accessed July 10, 2023.
Cronin, M. A., et al. (2009). "Why don't well-educated adults understand accumulation? A challenge to researchers, educators, and citizens." Organ. Behav. Hum. Dec. 108(1): 116-130.
Forrester, J. W. (2009). "Some basic concepts in System Dynamics." Sloan School of Management–MIT.
Halford, G. S., et al. (2005). "How many variables can humans process?" Psychol Sci 16(1): 70-76.
Kilian, Lutz (2008). "Exogenous Oil Supply Shocks: How Big Are They and How Much Do They Matter for the U.S. Economy?". The Review of Economics and Statistics. Measuring Worth (2023). What Was the U.S. GDP Then? https://www.measuringworth.com/datasets/usgdp/. Accessed February 20, 2023.
Sterman, J. D. (2000). Business Dynamics: Systems Thinking and Modeling for a Complex World. McGraw-Hill Education
Sterman, J. D. (2001). System Dynamics Modeling: Tools for Learning in a Complex World. California Management Review, Vol. 43, No. 4.
Sterman, J. D. (2002). "All models are wrong: reflections on becoming a systems scientist." System Dynamics Review 18(4): 501-531.
U.S. Bureau of Economic Analysis (2023). Gross Domestic Product: Implicit Price Deflator [GDPDEF], retrieved from FRED, Federal Reserve Bank of St. Louis; https://fred.stlouisfed.org/series/GDPDEF, Accessed July 24, 2023.
U.S. Energy Information Administration (1979-2023). Annual Energy Outlooks and Annual Energy Outlook Retrospectives.
https://www.eia.gov/outlooks/aeo/archive.php, Accessed July 24, 2023.
Data Sources:
Cattle Data Source: Commodity Research Bureau, The CRB Commodity Yearbook, https://www.mergentarchives.com/search.php Accessed
July 10, 2023
1. Cattle Stocks (in thousands): CRB Yearbook Years: 1939, 1948, 1957, 1966, 1973, 1982, 1985, 1992, 1999, 2005, 2013, 2018, 2023
2. Federally Inspected Cattle Slaughter (in thousands): CRB Yearbook Years: 1939, 1941, 1949, 1959, 1969, 1979, 1984, 1988, 1990, 1992, 1997, 2002, 2008, 2014, 2023
3. Cattle Price (in $/100 lbs): CRB Yearbook Years: 1949, 1959, 1969, 1978, 1983, 1987, 1998, 2000, 2007, 2014, 2023 Adjusted Cattle Price PPI Data: US Bureau of Labor Statistics, https://data.bls.gov/pdq/SurveyOutputServlet, Series Id: WPU041, Accesed July 13, 2023
Copper Data Source: Commodity Research Bureau, The CRB Commodity Yearbook, https://www.mergentarchives.com/search.php Accessed
July 11, 2023
1. Copper Prices (cents/pound): CRB Yearbook Years: 1939, 1949, 1959, 1969, 1975, 1977, 1983, 1984, 1988, 1997, 2007, 2015, 2023
2. Adjusted Copper Price PPI Data: 1974-2022: US Bureau of Labor Statistics, https://data.bls.gov/pdq/SurveyOutputServlet, Series Id: WPUSI019011, Accessed July 13, 2023
3. Refined Copper Production (in millions of metric tons): CRB Yearbook Years: 1939,1949, 1959, 1969, 1977, 1984, 1988, 1997, 2007, 2016, 2023
Actual Oil Prices, Adjusted for Inflation: U.S. Energy Information Administration, Short-term Energy Outlook Data Browser, https://www.eia.gov/outlooks/steo/data/browser/#/?v=8&f= A&s=0&start=1997&end=2024&id=&ctype=linechart&ma ptype=0&linechart=WTIPUUS~RACPUUS~BREPUUS~R AIMUUS&map=, Accessed July 24, 2023
EIA Forecasts. Unadjusted for Inflation.
1982-1997 and 2016-2023 forecasts are in dollars 1 year prior to forecast year (AEO 2017 data is in 2016 USD), 1998-2015 forecasts are in dollars 2 years prior to forecast year (AEO 2005 data is in 2013 USD). Forecasts from 1979-1985: U.S. Energy Information Administration, Annual Energy Outlook (from years 1979-1985), https://www.eia.gov/outlooks/aeo/archive.php, Accessed July 24, 2023; Forecasts from 1982-1993: U.S. Energy Information Administration, Retrospective Review Annual Energy Outlook 2010, https://www.eia.gov/outlooks/aeo/retrospective/archive/201 0/pdf/retrospective.pdf, Accessed July 24, 2023; Forecasts from 1994-2009: U.S. Energy Information Administration, Annual Energy Outlook 2022 Retrospective: Evaluation of Previous Reference Case Projections, https://www.eia.gov/outlooks/aeo/retrospective/pdf/retrosp ective.pdf, Accessed July 24, 2023; Forecasts from 2010-
2022: U.S. Energy Information Administration, Data Browser, https://www.eia.gov/outlooks/aeo/data/browser/, Accessed July 24, 2023
US Prison Population:
State and Federal Sources: 1925 - 1977: Bureau of Justice Statistics, Historical Statistics on Prisoners in State and Federal Institutions, Yearend 1925-86, Table 3 https://www.bjs.gov/content/pub/pdf/hspsfiy2586.pdf#page=17, Accessed 02/20/23, 1978 - 2015: Bureau of Justice Statistics, Corrections Statistical Analysis Tool (CSAT) – Prisoners Quick Tables, "Sentenced prisoners under the jurisdiction of state or federal correctional authorities, December 31, 1978-2016"
https://www.bjs.gov/nps/resources/documents/QT_total%2 0jurisdiction%20count_total.xlsx, Accessed 02/20/23, 2016-2019: Bureau of Justice Statistics, Corrections Statistical Analysis Tool (CSAT) – Prisoners Quick Tables, "Sentenced prisoners under the jurisdiction of state or federal correctional authorities, December 31, 1978-2019" https://www.bjs.gov/nps/resources/documents/QT_sentence d%20jurisdiction%20count_total.xlsx, Accessed 02/20/23, 2020-2021: 2020-2021 Prisoners in 2021 - Statistical Tables https://bjs.ojp.gov/sites/g/files/xyckuh236/files/media/docu ment/p21st.pdf, Accessed 02/20/23
Local Jail Sources: 1940, 1950, 1960, 1970, 1978: Bureau of Justice Statistics, Historical Corrections Statistics in the United States, 1850 – 1984, Table 4-1 "Total Number of Jail Inmates by State: 1880-1983"
https://www.bjs.gov/content/pub/pdf/hcsus5084.pdf#page= 91, Accessed 02/20/23, 1983-1999: Bureau of Justice Stastics, Sourcebook of Criminal Justice Statistics, Table 6.14 "Number of jail inmates, average daily population, and rated capacity,"
https://www.albany.edu/sourcebook/pdf/section6.pdf, Accessed 02/20/23, 2000-2009: Bureau of Justice Statistics, Jail Inmates at Midyear 2014, Table 1 "Inmates confined in local jails at midyear, average daily population, and incarceration rates, 2000-2014"
https://www.bjs.gov/content/pub/pdf/jim14.pdf#page=2, Accessed 02/20/23, 2010-2020: Bureau of Justice Statistics, Jail Inmates in 2020, Table 1 "Inmates confined at midyear, average daily population, annual admissions, and incarceration rates, 2010-2020"
https://bjs.ojp.gov/content/pub/pdf/ji20st.pdf, Accessed: 02/20/23, 2021: Bureau of Justice Statistics, Jail inmates in 2021, Table 1 "Inmates confined at midyear, average daily population, annual admissions, and incarceration rates, 2011–2021"
https://bjs.ojp.gov/sites/g/files/xyckuh236/files/media/docu ment/ji21st.pdf, Accessed: 02/20/23
Transistors per Microchip: Eric Martin, "Moore's Law is Alive and Well," Medium.com, https://medium.com/predict/moores-law-is-alive-and-welleaa49a450188, Accessed 02/20/23
US Real GDP: Samuel H. Williamson, https://www.measuringworth.com/datasets/usgdp/result.ph
p 'What Was the U.S. GDP Then?' MeasuringWorth, 2023. Accessed 02/20/23
US Traffic Fatalities per VMT: 1899 - 2020: NHTSA, CDAN, "Motor Vehicle Traffic Fatalities and Fatality Rates, 18992020." Accessed March 19, 2023.
https://cdan.nhtsa.gov/tsftables/Fatalities%20and%20Fatalit y%20Rates.pdf., 2021 Fatalities: NHTSA, "Crash Stats: Early Estimate of Motor Vehicle Traffice Fatalities in 2021." Accessed March 20, 2023.
https://crashstats.nhtsa.dot.gov/Api/Public/ViewPublication /813283. 2021 VMT: US DoT, Federal Highway Administration, "Traffic Volume Trends." Accessed March 20, 2023.
https://www.fhwa.dot.gov/policyinformation/travel_monito ring/21dectvt/21dectvt.pdf.
World Population: United Nations, of Economic and Social Affairs, Population Division (2022). World Population Prospects 2022, https://population.un.org/wpp/Download/Standard/MostUs ed/, "Complete (estimates and all projection scenarios)," (for direct download: https://population.un.org/wpp/Download/Files/1_Indicators %20(Standard)/EXCEL_FILES/1_General/WPP2022_GE N_F01_DEMOGRAPHIC_INDICATORS_REV1.xlsx), Accessed 02/14/23