The primary equations in the infrastructure model in IFs are those for estimating the expected levels of infrastructure stocks or access. Each of the estimated equations relates one aspect of physical infrastructure to specific economic, structural, and demographic drivers; in some cases these equations also include other types of infrastructure, creating explicit linkages across those infrastructures. While a number of earlier studies did provide equations for forecasting future levels of some of the types of physical infrastructure we include, we chose to undertake our own analyses for the purposes of this volume. This allowed us to use more recent data to drive the relationships than earlier studies and to better integrate the resulting relationships within the broader IFs system.
Our choices of the driving variables ultimately included in the equations were influenced by theoretical considerations, previous efforts, the availability of data, and, of course, the analytical results themselves. These factors also influenced our choices of functional forms. In particular, for variables that have natural minimums and maximums, such as the percentage of population with access to electricity, we use functional forms that guarantee that the forecasted values fall in this range.
The basic equations shown below provide only the initial estimates of the expected levels of the specific infrastructure stock or access. The final values are adjusted based upon a number of algorithmic and scenario-specific processes, including the use of shift factors, multipliers, extrapolative formulations, targeting processes. Some key aspects of these algorithmic processes, including key parameters available to the user for scenario development, are provided below the definitions of the variables used in the basic equations. Finally, the nature of the data used for estimation, the model fitted, and the R-squared values for a fit of the predicted against the actual historical values used for our estimations are also provided.
As with the flow charts, this section presents the equations grouped by the four categories of infrastructure: transportation, electricity, water and sanitation, and ICT. Unless specified otherwise, in all of the following equations, the subscripts r and t refer to region/country and time/year, respectively.
For help understanding the equations see Notation.