The major objective of this simplified version of the REXSF model is to estimate the gap (GDP fraction) between a target country and the leading country (the USA for our purposes). The GDP fraction variable is the country's GDP, in purchasing power parity (PPP) per capita, as a fraction of the US GDP in the same year. The larger the fraction, the smaller the gap with respect to the USA. The standard source of GDP data in PPP since 1950 is the so-called Penn World tables (Heston et al. 2006). In principle, we would need international historical data on labor and capital as well as useful work, to account for GDP. The World Bank Development Indicators (WDI) is the standard source for employment data by economic activity (World Bank 2006). However, there is no readily accessible standard source of international data on capital stock. The best available source is the work of Angus Maddison, but his published work primarily concerns a few individual OECD countries (Maddison 1995b). Hence we focus in this work on the search for an alternative proxy, namely 'useful work'.

It is well-known that the US GDP from 1900 to the present cannot be explained by the growth of capital stock or labor force alone, whence an exogenous multiplier, total factor productivity (TFP), is generally introduced. However Hypothesis II above is that a third factor, called 'useful work' (U), combined with the other two can explain economic growth in developing countries, at least those in Groups A and B. As noted above, useful work (U) is the product of the input energy (actually exergy) flow multiplied by the energy to work conversion efficiency for the economy as a whole (Ayres and Warr 2002; Ayres 2002; Ayres and Warr 2003; Ayres et al. 2003; Ayres and Warr 2005).

Electrification and urbanization are both fairly well documented variables that are also correlated with economic development. In fact, they are also closely correlated with each other, which means that they are not independent. (See Appendix C.1). Of the two, electrification is far better documented. Statistics on electric power production are widely available on a year by year - rather than decennial - basis. The efficiency of the energy conversion process is easily calculated and widely published. Electric power per se is also a form of useful work. It is by far the most flexible and adaptable, hence desirable, form of work, inasmuch as it can easily be reconverted to heat, light, motive power, or electromagnetic signals.

On the other hand, electricity is not the only, or even the most important, form of work in some countries. Human and animal muscles are still important in some of the less developed parts of the world where electricity is not yet widely available. Solar heat is still quite important for certain purposes - such as salt production, food and crop preservation and biomass desiccation prior to combustion - in some countries. Biomass combustion is a primary source of heat for cooking and space heating in many of the same countries. Finally, mobile mechanical power for transport, mining, agriculture and construction are not suitable for electrification except in a few exceptional cases.

The contribution of human and animal muscles to 'work' (in the thermo-dynamic sense) is largely a rural phenomenon. In cities, there is little need for human muscles and virtually none for animals. Hence the substitution of machine-work for muscle-work is closely correlated with urbanization. This is, essentially, the logic of suggesting urbanization as a proxy for work. As noted, urbanization is also closely correlated with electrification. As people move to cities they get electric light, TVs and other services. But space heat and hot water are mostly non-electric, while transportation and construction are almost entirely driven by mobile power sources based on internal combustion engines. Hence the simplest alternative (to using electricity consumption alone) is to add a fraction of petroleum (oil) consumption in order to reflect the non-electric types of work, especially transportation. Because of the low combined thermodynamic and mechanical efficiency of most internal combustion engines, we multiply total oil consumption by a fraction (typically around 0.1) before adding it to electricity consumption. The coefficient factor 0.1 might not be optimal. We test its sensitivity later. The symbol EP (energy proxy) is used to represent this new variable, also expressed as a fraction of the US value.

Of course, it is not to be expected that a single factor, such as EP, would explain all of the divergences among countries in regard to economic growth. There must be other factors affecting economic growth that are omitted from our simple hypothesis. Sources of divergence include: (1) the structure of the economy; (2) the form of government, (3) social and ethnic homogeneity, (4) bureaucracy, law and corruption, (5) the geographic location (and its influence on climate and energy consumption), (6) macroeconomic management, (7) openness to foreign investment, (8) educational level and capacity to absorb advanced technologies, (9) petroleum and gas exports in relation to consumption, and so on. Luckily, as emphasized later, some of these variables tend to occur in combination, which suggests the possibility of grouping.

All the other data are obtained from the IEA (OECD) database (2003) (Organization for Economic Cooperation and Development and International Energy Agency 2005). The periods that the IEA database covers are 1960-2001 for OECD countries and 1971-2001 for the others. There are 131 countries with reasonably good data records in the database.

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