Government expenditures in IFs fall into two categories: direct consumption (GOVCON) and transfers (GOVHHTRN). The direct expenditures fall the following categories: military, health, education, research and development, infrastructure (the core types elaborated in the infrastructure model), other infrastructure (all non-specified infrastructure types), and other (including administrative and implicitly foreign aid of donor countries). IFs divides total government consumption (GOVCON) into these destination sectors (GDS) in a process described below. The user can change that default pattern of government spending over time with a multiplier parameter ( gdsm ). The model normalizes the allocation to assure that the money spent is no more or less than total government consumption.

There are several issues that complicate the calculation of GDS, while simultaneously assuring that the sum of it across all categories equals GOVCON. These issues are:

1. In the cases of education, health, and infrastructure (core types), IFs contains models that produce calculations of expenditure needs or demands. Attempts to satisfy these demands in whole or part require adjustments in GDS for other spending categories.
2. In the cases of health, infrastructure and R&D categories, the model represents private as well as public spending (it should eventually also do this for education, but does not at this time). These private expenditures need tracking also and can, as in health, affect the ability of the government to meet total bottom-up health cost demands.
3. In the case of military spending, the model uses an action-reaction formulation that links spending of some countries to that of others (see the documentation of international politics). This is the reason that IFs code for GDS calculation was initially placed into and sits in the international political model (it should be moved to a separate function at some point).
4. In the case of education and health, financial flows into or out of countries from international financial institutions (IFIs) such as the World Bank need to adjust the values of GDS.

Preliminary GDS Calculations (Top Down Except for Infrastructure)

The first stage in the computation of government spending by category (GDS) is the computation of a ratio of government spending in each category to GDP (Gk). In the sequencing of the code, in both first and subsequent years the first steps of that stage are the use of cross-sectionally estimated analytical functions that compute expected military, education, health and other infrastructure expenditures as a percent of GDP as a function of GDP per capita at PPP (GkComp). A similar analytical function is used to compute total (public and private) R&D expenditures. In the first year there are actually data on such expenditures, so a country-specific "shift" vector is computed (GkRI) that saves the ratios of the actual values to those computed in the functions. In the subsequent years, the values in that shift vector converge to 1 over 200 years, meaning that the pattern generated by the expected values from the functions very gradually take over from the pattern in the initial conditions. In the first year the other category is available as a residual (the preprocessor keeps it from going to zero or negative) and the ratio of that value to GDP (Gk) is maintained as the expected value over time. Note that there is no function or process to compute an expected value for infrastructure spending as a portion of GDP per capita; the data for infrastructure led model developers to conclude that it was better to use only bottom-up information on infrastructure costs and expenditures. So in general:

where

After the initial calculation of the ratio of government spending to GDP in each category, a number of adjustments are made that vary by expenditure category in order to get an initial estimate of actual expenditures (GDS). First, for military spending the estimate use the Gk variable, but modifies it by both an exogenous multiplier ( gdsm ) and a multiplier for it (GkMul) computed in the action-reaction process around military spending (described in documentation of the international political model).

For health, R&D, and other, the equation is a variant in which funds coming from international financial institutions (GDSWB) are added to the basic calculation; in reality, such funds affect GDS only for education and health and at this point they are added only for health (nothing augments R&D and Other). 

For education the equation is the same, except for the exogenous multiplier. That multiplier is used only later in the process, when the initial GDS estimate is being reconciled with the bottom-up cost calculation from the education model.

The process is slightly more complicated for R&D because there are both private and public expenditures to account for. The code first computes a ratio of the expected share of public expenditures within GDP in the current year relative to the first year, a term that will be used as a multiplier in the next step (RandDMul).

That term is used to adjust the initial ratio of public R&D expenditures as a portion of GDP (RandDI) in order to compute the current time step's value, which is allowed to converge, but at minimal speed (1000 years) to the estimated value for the current time step:

where

Finally, this allows the computation of the initial estimate of GDS for R&D:

At this point, then, initial estimates of GDS are available for all government spending categories except core infrastructure, other infrastructure, and education.

For the two infrastructure terms the process depends on value of a parameter that turns on government finance for them ( infrafinon ) and the default value is for it to be on (=1). In that case, for other infrastructure the process is essentially the same as for the military or health spending, except that there are no exogenous multipliers or other terms affecting the basic calculation. That basic calculation is:

where

For core infrastructure, when the infrafinon parameter has its default value, the value of GDS comes completely from a function (CalcInfraBudgetDemand) that adds up the public portions of the new construction and maintenance costs for various types of infrastructure for the current year as already calculated in the infrastructure model. For reasons said above, infrastructure GDS calculation, unlike other GDS categories, do not use any reference to either initial values of infrastructure spending or any expected value relative to GDP per capita at PPP. It is the only preliminary GDS value that is not calculated using a top-down logic.

where

In the equations above, infct stands for the index number of various infrastructure types included in the IFs model, for example, road, electricity, water connections etc.; INFRAINVESTNEW and INFRAINVESTMAINT are total costs of new construction and maintenance respectively and infrainvnewpubshrm and infrainvmaintpubshem are shares of the costs borne by the government.

Bottom-Up Cost Calculation

The equation just above used a bottom-up cost calculation from the infrastructure model to compute an initial estimate of GDS for core infrastructure. In the case of both education and health, the models also provide a bottom-up cost calculation foundation and we turn to that next before proceeding to reconciliation of the Top-Down and Bottom-Up values.

We begin with education. The basic logic of that cost calculation is that in the first year of the forecast a ratio (EdCostGDSEdRI) is calculated of the public expenditures on education (GDS from data and the preprocessor) and a variable from the education model representing bottom-up costs (EdTotCost). A modeling decision was made to make this ratio converge to 1.1 over time.

The bottom-up educational expenditure demand (DemandCalc) used in the budget reconciliation process below is calculated as the bottom-up calculation in the preceding year times this ratio. In addition, a small adjustment is made to the bottom-up calculation from the previous year in order to make it grow somewhat over time; the initial growth rate is set equal to the initial growth rate of GDP ( igdpgr ) and allowed to converge to 0 over time.

where

This would be logical place to discuss bottom up health cost wrap around from previous year - at this point I would simply wrap it with a moving average growth term, not using anything like the 1.1 stuff above which I don't understand. Health might logically precede education given their sequence in the GDS matrix.

Reconciling Top-Down Expenditure Availability with Bottom-Up Cost Calculation

At this point the initial values of GDS have been calculated and the bottom-up cost calculations for health, education, and infrastructure have been identified. But the preliminary GDS values will almost certainly not sum to GOVCON, which is what the model has determined is available. Nor will the bottom-up (EDTOTCOST and HLCOST) and top-down estimates for costs of and expenditures on health and education be equivalent. The two reconciliation issues are interactive and must be addressed to some degree simultaneously.

For education the first step in the reconciliation process (focusing on the bottom-up and top-down aspects) is a recalculation of GDS for education that determines a refined value taking into account both the bottom-up demand calculation (DemandCalc) and the earlier preliminary top-down version of GDS. The parameter for budget balancing ( edbudgon ), with a default value of 0.4 and constrained to be between 0 and 1, provides a weighted average of the two input terms.

Because the model computes the value of total (public and private) research and development expenditures (RANDDEXP) and the normalization process will change the public portion of that, the value of RANDDEXP is temporary changed to remove the public expenditures. After GDS for R&D is recalculated below, the revised version of GDS for R&D will be added back into the total.

The next step in the process is to normalize the sum of all GDS terms across categories to GOVCON. This process has the potential, however, of setting GDS values for health, education, and infrastructure that are very different from the bottom-up costs. Thus the normalization process includes a mechanism for avoiding that. It protects some or all of the bottom-up calculations during the normalization.

The mechanism for protecting some or all of the bottom-up calculations involves "set asides". The extent of set asides for education, core infrastructure and other infrastructure is determined by parameters ( budbal and infrabudsdrat ) that take on values between 0 and 1; values of 0 protect none of the bottom-up value and values of 1 protect it all. The default value of infrabudsdrat is 0.

There is another step before the normalization process begins, namely adjusting GDS for education, core infrastructure, and other infrastructure by an exogenous multiplier ( gdsm ), the default value for which is 1.0.

The sum of all GDS values (GTOT) can now be compared with GOVCON. If there are more than enough funds to provide all of the GDS requested (that is, GOVCON exceeds GTOT), the final calculation of GDS simply assigns proportional shares of the surplus to each GDS category. 

If there is a shortage of funds to meet all demand (that is, GTOT exceeds GOVCON), it would be possible to proportionately reduce each GDS accordingly. But the set aside values allow protection of some or all of the GDS values for education, infrastructure and other infrastructure. In the normalization process when there is a shortage of funds, each potentially or actually protected GDS is reduced by the set aside, as are both GTOT and GOVCON (using a GOVCONRed or GOVCON reduced). Then the normalization of all GDS occurs and the protected or set aside values are added back in.

At this point it is possible to add the public R&D expenditures back into the variable RANDEXP from which they had earlier been removed (leaving that variable temporarily to hold only private expenditures).

There are a number of forward linkages from GDS that are important elsewhere in the model. The most important of these are linkages to multifactor productivity from human capital. Those are discussed elsewhere in this documentation. Here we note only two such forward linkages, both of which are set up in the same section of code as the computation of GDS.

The first is of a mortality multiplier (MORTMG) that is computed for the demographic model, using changes in health spending from the initial year and a parameter of the impact of that spending ( elashc ). This multiplier is now not typically used in the IFs system because the calculation of mortality that it feeds in the population model has been replaced in the default model mode by the entire health model.

The second forward linkage at this point is in the calculation of a saved value of health expenditures as a portion of GDP to be used in the calculation of water and sanitation in the infrastructure model. In the formulation below, if the exogenous multiplier gdsm for health spending is greater than or equal to 1 (the default), the value of sHlthExpPcntGDP is not allowed to decline over time.