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International Futures Help System

Equation Notation

Variable names are shown in all capitals, as in the display functions of the model. Parameters are shown in lower case and boldface. Empirically-based initial conditions of variables are in capitals with boldface. Internal computed variables, which are not available for display, are shown in mixed upper and lower case.

At one time the project used a superscript of "t" to indicate time/year. Although it has mostly moved that to subscripts, it may sometimes still be found in project documentation. Superscripts other than "t" indicate exponentiation. Subscripts or superscripts with "t" indicate time, but will be omitted when a reference is contemporary to model year "t."

Subscripts show dimensionality and there are a number of standard ones in the model:

  • r for region/country r = 1,2,... (e.g., United States, European Union, Japan, Brazil...)
  • c (sometimes the project uses j) for age cohort c/j = 1,2,...,22 (infant, 0-4 years,...95-99 years, 100+ years; abbreviated set for World Value Survey variables)
  • s for economic sector s = 1,2,3,4,5,6 (agriculture, energy, materials, manufactures, services, ICT)
  • f for food types f = 1,2 (crops, meat/fish)
  • l for land types l = 1,2,3,4,5 (crop, grazing, forest, unused, urban/industrial)
  • e for energy types e = 1,2,3,4,5,6,7 (oil, gas, coal, hydroelectric, nuclear, other renewable, unconventional oil)
  • g for govt spending g = 1,2,3,4,5,6 (military, health, education, R&D, other, foreign aid)
  • p for population sex p=1,2 (male, female)
  • ss for safe water and sanitation ladder categories
  • d for cause of death (15 in total)
  • dg for cause of death group dg=1,2,3 (communicable, non-communicable, injuries/accidents)
  • h for household types h=1,2 (unskilled, skilled)

Individual equations specify a range of dimensionality only if it differs from that above.