The Energy-Environment -Economy (E3) System
To compensate for the inability of social agents to maintain relative stability in a complex system like E3 (let alone act optimally), it is becoming increasingly obvious that some sort of coordinated policy guidance is needed. Examples abound: from the global drive to end the current economic crisis that has gripped the world and could turn out to be the worst on record, to the implementation of a transition process from fossils to renewables, to the quest for effective moderation of human activity to avert irreversible damage to the environment, governmental / intergovernmental initiatives play an ever more visible role (e.g. economic stimulus package, Kyoto protocol, California energy initiatives, Copenhagen process, etc). Large-scale initiatives, by exerting commensurate leverage, have potentially the capacity to steer a system toward a desired macroscopic state via safe evolutionary corridors. Yet the collective super-entities that drive initiatives of scale are themselves social agents, susceptible to misjudgment and other perils to which their elemental counterparts are also exposed; most significantly, when it comes to foresight they are just as myopic. While the intent of collaborative endeavors can by no means guarantee the outcome, their scale can reasonably be expected to have a bearing on their impact; therefore a possible failure of large-scale initiatives can have devastating consequences and safeguarding against it is vital.
Our aspiration is to develop a comprehensive platform that supports good-intentioned policy initiatives of scale by enabling rigorous safeguarding: monitoring the state of the E3 system; detecting early signals of straying from stability toward chaos; setting feasible targets that improve system performance compatible with physical constraints; designing, testing, and ameliorating policies before launch, aimed to facilitate attaining the set targets; assessing and adjusting policies continuously as conditions change after launch. Prerequisite for a program of this scope is a comprehensive E3 model grounded on empirical facts that enables realistic simulations.
Our E3 work for DOE
In simulations of this preliminary E3 model, sensible ‘government’ intervention has positive effects: scenarios of carbon-tax / cap & trade funded R&D on renewables results in higher growth rates and less turbulent economic cycles (lower unemployment and less fluctuating growth) relative to the baseline scenario (which results in lower growth rate, extremely high unemployment during the transition from fossils to renewables, shortened lifecycles for firms, and difficulty to adapt to new energy sources). If we take for granted that some sort of centralized regulatory mechanism will eventually come into effect to help address major challenges posed by the E3 system, then the following important findings come out of our preliminary simulations: In the presence of a central policy whose net effect is to promote a certain energy source (or class of sources) relative to another, the combination of this central policy and individual policies (i.e. exercised by firms) is only effective if the latter are synergistic rather than antagonistic to the former. For example: E3 scenarios that use carbon-tax / cap & trade money to fund R&D on renewables do much better than baseline scenarios without a carbon tax or R&D. If on top of that individually funded R&D investment by the firms in renewables is also implemented, the end result is an even higher growth rate, faster innovation and new technology adoption rates, and smoother growth patterns.
If, however, individual R&D by the firms is invested equally in all the energy sources of the current energy portfolio, while public R&D is exclusively allocated to renewables, then the end result is a marked deterioration relative to even the baseline scenario with no R&D (large unemployment rates, much reduced growth rate, prolongation of the use of oil and gas, turbulent economic cycles). As importantly, the mere presence of a central policy is not in itself panacea even if its effect is amplified by synergistic individual policies: in a simulated environment of finite natural reserves of fossils, central policies that promote prolonging the dependence on fossil fuels into an era of severe depletion amplify both the frequency and the intensity of turbulence in the economy and result often in catastrophic collapse, characterized by the massive closure of firms, explosion of unemployment, and perpetual subsequent stagnation with no sign of recovery.
The lesson is that individually driven investments need to be synergistic to central policies if they are to both succeed in themselves (on average), as well as to help rather than stall the overall economy, and that both public and private investments must be mindful of and compliant to hard physical constraints. It follows that informed consensus grounded on empirical evidence and the dictates of physical constraints needs to be built between institutional investors and governmental/intergovernmental regulatory bodies, so that they both pull in the same sensible direction toward a feasible goal, rather than take erratic steps that can escalate to a crisis or impede the objectives of each other. For these benefits to be realized membership in some sort of mutual collaborative makes sense (i.e. green Silicon Valley) to leverage resources toward attaining a desired goal; parallel to this, the implementation of a scientifically reliable system for monitoring collective performance, anticipating failures, and facilitating corrective steps, could go a long way toward ensuring a match between objectives and outcome.
Overview of the current E3 model
- The FREE model , a macroscopic model encompassing the economy, energy, and the environment, which focuses on the exploration of the impact of policies (e.g. taxation) on the patterns of energy consumption and in turn on the environment and the economy.
- A hybrid model of the economy , with individual firms as the basic units of the economy represented by agents, and some macroscopic aspects (e.g. labor). The motivation was to probe the apparent constraints to growth, triggered by the observation that wealthy economies have grown at a rather stable rate since the onset of the industrial revolution, despite major technological changes and shifts in dominant energy sources.
These basic attributes evolve through a firm’s life deliberately or spontaneously, in response to perceived signals from the environment and a firm’s current internal state. Synthetic features further characterize firms – e.g. their workforce size, volume of capital, or portion of newly built capital committed to any one energy source – molded by interactions with the environment.
At the present preliminary stage of implementation, in order to maintain a controllable number of agents, firms are more akin to vertical sectors than conventional businesses: they produce output both as products for delivery in the market and as production capital for their own use. This output embeds characteristics that mirror the firms’ respective attributes: essentially instantaneous for products, integrated over time for capital that takes longer to complete.
The market rewards or punishes the individual firms depending on their overall perceived quality, efficiency, prevalence in market share, and environmental friendliness relative to the ambient mood – which is endogenous, reflecting macroscopic averages across the model. Firms that are well perceived in the context of their contemporary environment see their revenues rise and their credit-worthiness go up. The firms respond to good fortune by deliberate expansion, boosting their capital, labor force and production output; or, on the contrary, by deliberate shrinkage in size and output, as well as by spontaneous changes under the pressures of perceived failure. Occasionally poorly performing firms become extinct with a probability that grows as a firm’s performance rank falls, tuned semi-empirically to attain firm lifetime distributions in accord with empirical data.
Accounting and resource management mechanisms are implemented in the model, invoked by each individual firm at each time step (currently one year). These rational mechanisms comprise assessing a firm’s relative performance, its stock of capital with its embedded properties, the size of its labor force, its personality and efficiency traits, as well as the availability of resources in the environment. The resources that are currently monitored in the model are cash, energy, labor, and primary materials. On the basis of these processes each firm individually both sets immediate goals and revises long-term targets for production and capital.
A rudimentary banking system is also implemented which monitors cash flows across the economy and for each individual firm, and includes some banking policy levers that regulate interest rates, can somewhat control inflation, or trigger the injection of new cash to when needed to sustain the economy. Stocks of used capital discarded by defunct firms are recycled alongside new capital, depending on demand. A population model is implemented, and stocks of unemployed workforce are tracked. An energy sector delivers various sources of energy at prices compatible with market conditions, depending on the state of associated technologies, availability, and demand. At each time-step each firm bids for the resources it needs in order to meet its immediate production targets as well as long-term capital needs: cash drawn from a firm’s own deposits or loans, energy depending on the embodied production capital and availability, labor, and materials which are other firm’s products. Overall resource availability and a firm’s effectiveness determine the portion of desired resources secured in a time-step. Constraints in resource availability are accounted for, resulting in necessary adjustments in long-term forecasts and targets that the firms set for themselves.
Similar processes are implemented for startup firms, which begin as candidates assessed on their promise as reflected by their attributes in the context of their contemporary environment. A candidate startup must secure a threshold of desired resources relative to its target in order to be promoted to a startup firm, which initiates a stage of exclusive capital building. On attaining a fraction of their target capital, determined probabilistically, they start production and are granted a grace period over which they are assessed leniently relative to mature firms. On reaching a threshold size or exceeding an amount of time allocated for buildup, they begin to be treated as mature firms and can subsequently fail.
An aggregate household sector is also implemented, currently characterized by passive attributes that mirror macroscopically the part of the economy comprised by the firms. The households are funded by the business sector via labor, build their own stock tuned semi-empirically to account for housing and durable goods, consume energy in proportion to their stocks of capital, and are the primary consumers of the firm products. The rates at which households consume products and energy or build capital in the model are subject to availability constraints similar to the firms.
Tax policy scenarios are implemented, including carbon taxes linked to the level of emissions. A pricing model accounts for effects of depletion, demand pressures, technological improvements, and taxation.
Science and Innovation
First, a technology index is implemented for each of the four energy sources. Its purpose is to capture the relative efficiency of each species of technology classified by energy source, due to scientific or engineering advancements. While firms in the model possess various attributes, none currently reflects technological prowess. Until such attributes become embedded in the dynamics of firms, the processes that generate innovations are absent from the agent dynamics. The artifact of a technology index offers a glimpse of how innovations could be expected to play out in the economy. The technology index improves probabilistically in increments whose frequency falls with their size, and an assumed deceleration of the rate of improvement as technologies age. Hence, technologies linked to renewables start out less efficient than their fossil fuel base counterparts, but in time can potentially catch up or surpass them. Together, the availability, price, and technology index of an energy source constitute ‘objective’ criteria of desirability that firms consider in targeting an energy consumption profile. The firms invoke these objective criteria, in conjunction with their own attributes (including environmental friendliness) and overall state, to determine in what proportion they commit newly constructed capital to each energy source. This in turn shapes the future energy consumption profile of the entire economy, as it generates future dependencies on the availability of energy and imposes constraints on the choices firms can make. Moreover, the technology indices combine with the firms’ individual efficiency attributes to determine the market attractiveness of their products – and hence revenues – as well as the efficiency of capital they build for their own production needs. The technology indices were initialized to match empirical energy consumption profiles over the first few simulation steps.
Second, while the baseline scenario includes probabilistic improvements of the technology indices as described, we implement in addition a policy lever to emulate the impact of public R&D funding on the frequency and magnitude of innovations. For purposes of illustration, we explore the use of carbon taxes that penalize fossil fuels in proportion to carbon concentrations in the environment, to fund R&D on renewables. The innovation rates that result in improvements of the technology indices are assumed to grow with the level of funding within a moderate range (as a fraction of total expenditures on a technology) and plateau asymptotically to an upper limit above that range.
Third, we also provide a qualitative mechanism to probe the effect of individual R&D investments by firms on the effectiveness of their products. The assumed dependence of firm-driven technological improvements from individual investments, as a fraction of a firm’s revenues, is assumed to be similar to that of public R&D. The precise meaning of firm-driven technological improvements is somewhat abstract and can accommodate unspecified technological progress also in aspects decoupled from the use of energy.
Calibration to the US Economy
The simulations shown here cover the period from 1960 to 2200 in time steps of one year. We use data from 1960 to 1995-2000 , and tune the model for overall agreement in population, GDP, and total energy consumption over that period (Figs 1-3). A host of other model variables are initialized for the start year (1960) using US data from various sources whenever available (e.g. capital embodied in the economy, energy capital by source aggregated as in the model, energy production rates by source, etc).
Figure 1 From left to right: total energy consumption, total GDP, and population; for the US (in black) and the rest of the world (in red). The asterisks represent data points  and the curves best fits to 3rd or 4th order polynomials as indicated in the figures.
Figure 2 a) US population data from  (bullets); fit to a 3rd order polynomial using data from 1800 (not shown before 1960), projected to the end of the simulated period (in red); the population computed by the embedded model in the simulations (in blue). b) Data for the rest of the world from  (bullets) with a fit (in red) to a 3rd order polynomial as in (a).
Figure 3 a) Total US energy consumption, b) GDP; data (bullets) from  against a typical simulation (in blue). Various model variables involve stochastic components, e.g. the initialization of startup firm attributes, so that time series produced in different simulation runs differ from one another despite identical initial conditions for macroscopic aspects of the E3 system.
While we eventually plan to include all the regional world economies, we can currently accommodate a single economy. In order to carry out this exercise we pretend that the US is an isolated, self-contained economy which produces as much energy as it consumes. However, in order to maintain the integrity of the model we preserve the dependence of global aspects on world rather than US values of certain observables – e.g. the depletion rate of the natural reserves of fossils, demand pressures and effects on energy prices, carbon concentrations in the environment etc – that depend on the world volume of energy consumption. For this we extrapolated world consumption volumes from their US counterparts which are computed by the model, using scaling estimators derived from available data (Fig 4).
Figure 4 From left to right: total energy consumption, energy consumption per capita, and GDP per capita; for the US (in black), and the rest of the world (in red). The curves are the fits of Fig 1 extended to 2200, from which the model extrapolates world consumption volumes used to estimate the depletion rate of fossil fuel reserves and carbon concentrations in the environment.
Calibration of the Firm Dynamics
In the above sense our early work focused on getting right the dynamics of growth at the individual firm level as key to explaining patterns of growth in the aggregate economy, guided by data that impose stringent constraints and vet unrealistic assumptions. Specifically, we required that our multi-agent model of the economy be able to generate distributions of sizes, growth rates, and ages of firms consistent with empirical data (Fig 5), besides reproducing macroscopic indicators compatible with the US economy (Fig 3). Several empirical studies find the size distribution of the relatively few large firms in the industrial sector to be consistent with a lognormal (see e.g. ), while that of the entire (much larger) population of tax-paying US firms obeys a power law . The distribution of growth rates of firms is found to exhibit a characteristic tent-like shape in log-log scale (see e.g. [7, 8]) and the age distribution is described by a lognormal . For models of economic growth the ability to generate statistical signatures of genuine firms is broadly regarded as a critical test of validity, one which conventional macroeconomic models have been criticized for failing on account of assuming optimal behavior that cannot account for the shape of empirical firm growth distributions.
Figure 5 Top, from left to right: empirical distributions of firm sizes , ages and growth rates ; Bottom, from left to right: the corresponding model distributions at the final simulation step, having evolved driven by the model dynamics. The histograms shown combine 100 runs differing only in the seed of the random number generator for stochastic assignments. Each run incorporates 100 firms and is tuned to the US economy in the start year 1960, subsequently running up to 2200 in time steps of one year. Any run in the set yields results similar to those of Figs 2-3, 6-9. Due to current limitations the firm population is far lower in the model than in the US economy (~5.5 x 106 ), so tuning the former to the latter assigns the total US production capital to a few firms, in effect yielding a model more akin to an industrial sector than a full economy. This may be the cause of lognormal shaped size distributions in the model, which describe small samples of large industrial firms . We aim to address distortions of the capital intensity profile of firms in the model, which may lead to size distributions with the power-law shape of the full population of US firms .
All three cases in the long run converge to an average per capita growth rate of 1.6 – 1.9 %, exhibiting the same ‘glass ceiling’ attribute and ‘catch-up’ mode as empirical data . The two R&D scenarios induce less fluctuating and somewhat faster growth, attaining by 2200 about 50% higher GDP relative to the baseline scenario (Fig 6b). The impact of carbon taxes and R&D on the energy consumption profile is dramatic (Figs 6a, 7): though oil/gas consumption in all three cases peaks around 2030 and then falls (Fig 7b) as the natural reserves of oil/gas become deeply depleted (Fig 8), significant differences emerge in which energy sources gain the share shed by oil/gas and eventually become dominant in the economy (Fig 7).
In the two cases that promote the renewables the total energy consumption (Fig 6a) is quadrupled (b) and doubled (c) to back faster growth relative to the baseline scenario (a), with the scenario that includes private R&D (c) being the less energy intensive. The renewable sources are the main beneficiary of the higher demand in (b, c). The use of Coal in (b, c) is generally suppressed relative to (a), but in (b) it is prolonged, declining slowly. Carbon emissions in the long run mirror coal consumption for all three cases (Fig 9), none of which considers explicit reductions policies like emissions quota. Overall case (c) is the most advantageous, inducing higher growth rate and earlier transition from fossils to renewables. The consumption of hydro and nuclear energy – neither carbon polluters nor R&D beneficiaries in the model – rises over time roughly in proportion to the overall energy demand.
Figure 6 a) Total US energy consumption; b) US annual GDP. Simulation scenarios: no carbon taxes or R&D (in green); modest carbon taxes funding R&D on renewables (in red); as in (b) plus firm-funded R&D at 2% of total revenues (in blue). The impact of carbon taxes combined with R&D on renewables is modest on GDP and significant on energy consumption.
An unintuitive observation worth noting is that the imposition of carbon taxes to fund R&D on renewables does not generally drive the prices of fossils up in the model, but rather for the most part down. This is the combined effect of two synergistic processes: First, R&D on renewables induces the associated technologies to mature faster and become cheaper and more efficient, which in turn boosts the attractiveness of renewables and accelerates the transition from fossils. Second, the speedy shift eases demand on oil/gas and slows down their depletion rate, which in the era of severely depleted natural reserves is the main driver of price hikes in the model. Consequently scenarios (b, c) maintain lower oil/gas prices than the baseline scenario (a) over time.
Figure 7 For the set of simulations of Fig 6, clockwise from top left: Coal, Oil/Gas, Renewables, Hydro/Nuclear.
Figure 8 For the set of simulations of Fig 6, the remaining world natural reserves of Coal (left) and combined Oil/Gas (right).
Work in Progress
The mathematical modeling track involves both microscopic and macroscopic aspects. On the one hand we are expanding the agent representation to include (besides firms) other species of entities whose role is vital in the E3 system, such as households, banks, laboratories and research institutions (as hubs of innovation), universities (as disseminators of knowledge), and regulatory bodies (as implementers of policy) to name a few. Additionally we are extending the scope of macroscopic components like climate and the environment to incorporate complementary work we pursue in parallel (C-ROADS). On the other hand we aim to devise appropriate metrics for monitoring long-range aspects of the E3 system, to facilitate detecting warning signals and exploring policies aimed at maintaining stability and averting chaotic transitions into disorderly and unpredictable regimes. We expect that the resulting system representation will enable effective troubleshooting in a wide range of crucial issues: from asset bubbles, market meltdowns, and all-out economic crises, to resource constraints, energy policy dilemmas, and imminent environmental threats.
The data analysis track mirrors modeling. Microscopic data will be used to assemble statistical profiles of attribute distributions for the various species of agents, as well as to calibrate their respective interaction dynamics for agreement with observations (see e.g. Fig 5 and the related discussion, currently for a number of attributes of firms). Macroscopic data will likewise be used to tune the aggregate aspects of the model, but also to validate the emergent system-level behavior against observed patterns. A model that can be depended upon for high-stakes decisions and strategic planning must be able to pass stringent tests of validity, including a demonstrable ability to maintain quantitative consistency with the body of empirical data at both the microscopic and macroscopic levels, under conditions of either normalcy or extreme crises.
Implementing an integrated software platform capable of accommodating the outlined program poses technical challenges. Our prototype is once again efforts of comparable scope in physics research, where multifaceted environments are typically built from scratch expressly to enable probing a complex physical system. Such platforms are unified, yet modular rather than monolithic, and incorporate: utilities for the acquisition of empirical data; models for the generation of simulated data; mathematical and statistical libraries for the analysis of both types of data on equal footing; fitting algorithms for the calibration/validation of models and the optimization of processes; file systems and databases for effective data storage and retrieval; interfaces for the display of data at the microscopic, statistical, or aggregate level; automated consistency checks and output generation for safeguarding the integrity of models and processes; and meta-analysis utilities, for the aggregation of detailed results into instructive summary insights. Such environments are designed for flexibility and maintainability by integrating reusable self-contained modules suited for multi-layered analyses, allowing from rapid online snapshots of the overall system status and detection of issues as they arise, to detailed offline computations for the systematic probing of the dynamics and optimal design of controllable conditions suited to a task. Moreover, requiring agent models to capture physical entities realistically as self-contained units with individual attributes and methods of interacting entails tight coupling of mathematical and computational aspects, to a point that renders the implementation an integral part of the model. The natural choice for modular simulation/analysis environments of large scale and for agent representations is the Object Oriented (OO) programming and software architecture paradigm, which we have adopted for our work in development. Specifically we develop the next generation E3 model and supporting software environment in C++ which combines computational performance with portability and graphical versatility. A further important advantage of C++ is that, by virtue of being the most extensively used modern OO language in the physical sciences for systems of similar scope, numerous open-source libraries of data structures and mathematical/statistical utilities that suit our purposes are available, having been developed and tested thoroughly by a large scientific community, and can be readily integrated into our system.
In the course of this phase of our program, which is manifestly of considerable scope that requires significant resources, we will be seeking to build partnerships with collaborators and sponsors who can contribute to our effort and speed up its pace.
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