Grouped together here are links to downloadable copies of working papers, draft reports, historical data and working models. Take the data and test your own hypotheses. Simulate the past and anticipate the future!

Models and Data  

The REXS Model

The REXS model - written using the system dynamics software Vensim. An introductory paper is available for download below. Alernatively take a tour of the model components and review certain selected results. Links to useful system dynamics resources can be found on the links page.

To run the models you will want two things. First the Vensim model reader which will let you simulate but not alter the model. Alternatively you can download the equations and import them into DYNAMO and STELLA softwares (or simply Excel). Secondly the empirical data to convince yourself of the validity of the model predictions. Model and meddle - we want your feedback!

REXS Level 1.1 c Vensim Model (as text)
and model notes.

Empirical data for theUS 1900-2000, described in
greater detail here



INSEAD R&D Working Papers and Reports

An introduction to the REXS system dynamics model
Benjamin Warr and Robert U. Ayres, INSEAD R&D Working Paper 2003

This paper describes the development of a forecasting model called REXS (Resource EXergy Services) capable of accurately simulating the observed economic growth of the US for the 20th century. The REXS model requires no exogenous assumptions for continuous exponential growth. It is a simple model representing the dynamics of endogenous technological change, that results from learning and production experience. In this introductory paper we present new formulations of the important components of most economy-energy models the capital accumulation, resource use (energy) and technology-innovation mechanisms. Robust empirical trends of capital and resource intensity and the technical efficiency of exergy conversion were used to parameterise a parsimonious model of economic output, resource consumption and capital accumulation. Exogenous technological progress assumptions were replaced by two learning processes: a) cumulative output and b) cumulative energy service production experience. The initial results of simulation for the period 1900-2000 shed light on the historical causes of economic growth and downturn. They also have considerable implications when simulating future output for scenario analysis. Over the past century, the dominant long-term productivity improvements can be associated with efficiency improvements of primary exergy use. Economic downturns were the result of strong and sudden depreciation during the 1930s due to overcapacity and a similar rapid drop in the level of investment end energy consumption in the early 1970s. The REX modules are the focus of ongoing research. In this first presentation of REXS we discuss briefly the many possibilities for elaboration of each module that will enrich the feedback dynamics, policy levers and post-scenario analyses.

Useful Work and Information as Drivers of Growth
Robert U. Ayres and Benjamin Warr, INSEAD R&D Working Paper 2002/

The history of growth theories is reviewed. A semi-empirical endogenous growth theory is proposed. It is based on a model of the economy as a multi-stage materials processing system. Growth is simulated by a two-parameter production function with two traditional factors, labor and capital, and a non-traditional factor. The non-traditional factor can be interpreted as
`useful’ (physical) work output, as distinguished from energy (exergy) inputs. It is calculated from energy (exergy) inputs multiplied by the average energy conversion efficiency, which is a function of time. This theory `explains’ past US growth from 1900 through 1973-74 with satisfactory accuracy but it slightly underestimates subsequent growth ( leaves a small unexplained residual) for the period after 1975. However, by subdividing capital stock (and services) into traditional and information-technology components, we are able to extend the theory to explain US economic growth accurately through 1998. The revised production function has only three independent parameters, determined by statistical fitting. The new theory also has implications for future economic growth, energy and environmental policy that differ significantly from the traditional growth theory. These implications are discussed.

Accounting for Growth
Robert U. Ayres and Benjamin Warr, INSEAD R&D Working Paper 2002/70

It is argued that the consumption of exergy (available useful energy) has been, and still is, an important driver of economic growth. This paper tests several related hypothesis for explaining US economic growth since 1900. The authors show that if raw exergy inputs are included with capital and labor in a production function, the historical growth trajectory cannot be reproduced without an exogenous 'technical progress' multiplier (the Solow residual). However, introducing the sum total of all types of physical work (by animals, prime movers and heat transfer systems) as a factor of production, the actual growth path is reproduced with high accuracy from 1900 until the mid 1970s and with fair accuracy since then. The unexplained residual during this recent period amounts to about 12% of total growth during the recent quarter century and it is suggested that information technology is mainly responsible. Nevertheless only 'useful available work' powers the economy, wasted exergy may hinder growth.

Exergy, power and work in the US economy
Robert U. Ayres, Leslie W. Ayres and Benjamin Warr, INSEAD R&D Working Paper 2002/52.

Much of the natural resource exergy that is consumed is wasted. In this paper the concept of work is elaborated in detail and many examples of how the efficiency of work delivery, the technical exergy conversion eficiency, can be estimated are presented. We present data showing the significant improvements over the period observed in the US over the last century (1900-2000). The historical data used to estimate the total primary natural resource exergy and exergy services (useful work) are described in considerable detail. This paper is key to understanding how exergy services, the new factor of production, are estimated.

Economic growth models and the role of physical resources
Robert U. Ayres and Benjamin Warr, INSEAD R&D Working Paper 2002/53.

Conventional economic growth theory assumes that technological progress is exogenous and that resource consumption is a consequence, not a cause, of growth. This assumption is built into most, if not all of the largescale models used for policy guidance by governments. The reality is more complex. A 'growth engine' is a positive feedback loop involving declining costs of inputs and increasing demand for outputs. The most important 'growth engine' of the first industrial revolution was based on coal and steam power, through its impact on rapidly declining fossil fuel and mechanical power costs, and their relationship with scale of production on the one hand and demand for end use products, on the other. The growth impetus due to fossil fuel discoveries and applications, and continued cost reductions, continued through the 19th century and into the 20th with petroleum, internal combustion engines, and - most potent of all - electrification. The advent of cheap electricity in unlimited quantities has triggered the development of a whole range of new products and industries, including electric light, radio and television, moving pictures, and new materials such as aluminum and superalloys without which the aircraft and aerospace sectors could not exist. In effect, energy consumption within the economy is as much a driver of economic growth as it is a consequence of growth.

Draft reports and work in progress
Energy conversion efficiency learning curves for the US 1900-2000

Learning or experience curves were fit to historical time series of the technical efficiency of primary exergy conversion from the US 1900-2000, for the major fossil fuels energy carriers, coal , oil gas and for all natural resource primary exergy(U/R). The logistic and the bi-logistic models were compaerd the bilogistic is useful for characterising a system, whcih pauses betwen growth phases, and is therefore suitable to describe the aggregate technical efficiency, the sum of technological progress in many (un)related processes. Each of the time series and fitted curves shows quite distinct behaviour, which can be interpreted in light of historical technological progress and the specific ways in which each energy carrier is and has historically been used by society. An overview of the subject is a good place to start learning more about the subject. Links to related website can be found in links.

Experiments varying the exergy intensity of output (Environmental Kuznets Curve - EKC)

I'll think of a more imaginative title for this set of work soon. These graphics represent the preliminary results of simulations of plausible futures using REXS. We identified the average decay rate of the exergy intensity of output (R/GDP) for the period 1900-1998 for the US, as being a constant 1.2%, by fitting the REXS model to historical empirical data. The simulations involved increasing and decreasing thsi parameter from 1998 onwards, while keeping the values of all other parameters fixed. The illustrations provide a summary of the results. For further detail visit the REXS presentation.


This site was created by Dr.Benjamin Warr,
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