Appendix
A graphical depiction of need, demand, and supply
Figure 2 shows the demand and supply of doctors though this could apply to nurses or other health workers as well. Demand is related to the spending on health by the government, private insurance, and outofpocket payments. The supply of health workers is a function of the training capacity in a country, net migration, deaths, and retirements. In a perfectly functioning labor market, the market clears when the supply of health workers equals the demand at point E. When this happens, the wage would be W* and N* doctors would be employed. However, countries, particularly in resourceconstrained low and middleincome settings, often face binding constraints on the amount of financing that is available for paying health workers as well as rigidities such as government salaries that are set by law across civil servant categories and often do not fully relate to the value of a health worker’s productivity. Thus, the wage offered will be lower, W^{L} rather than W*, resulting in a shortage of doctors represented by length AB. The supply of doctors willing to work at W^{L} is A while the demand for doctors at this wage is B. If the lack of government resources and/or policy prevent wages from rising to W*, the shortage will persist.
The need for doctors is shown as the vertical line which passes through point C though it could be further to the right of C—which is the case in very lowincome countries. At a wage W^{L}, the number of doctors employed will be A but the need is C, so the needsbased shortage is length AC. In this case, the needsbased shortage is larger than the demandbased shortage by BC (AC minus AB). For highincome countries and uppermiddleincome countries, the situation is often reversed. The need line moves to the left inside the demand curve, and the demandbased shortage is often larger than the needsbased shortage (Fig. 3).
Regression equations used to estimate need, demand, and supply
Need
$$ \mathrm{SDG}\ \mathrm{composite}\ {\mathrm{score}}_i={\beta}_0+{\beta_1}^{\ast}\mathit{\ln}\left(\mathrm{health}\ \mathrm{workers}\ \mathrm{per}\ 1000\ {\mathrm{population}}_i\right)+{\xi}_i $$
(1)
where ξ_{
i
} is the disturbance term, and β_{0} and β_{1} are unknown parameters to be estimated from the model.
Demand
$$ {\displaystyle \begin{array}{l}\mathit{\ln}\left(\mathrm{physicians}\ \mathrm{per}\ 1000\ {\mathrm{population}}_{it}\right)={\beta}_0+{\beta_1}^{\ast}\mathit{\ln}\left(\mathrm{GDP}\ \mathrm{per}\ {\mathrm{capita}}_{it1}\right)+\\ {}{\beta_2}^{\ast}\mathit{\ln}\left(\mathrm{GDP}\ \mathrm{per}\ {\mathrm{capita}}_{it4}\right)+{\beta_3}^{\ast}\mathit{\ln}\left(\mathrm{GDP}\ \mathrm{per}\ {\mathrm{capita}}_{it5}\right)+{\beta_4}^{\ast}\mathit{\ln}\left({\mathrm{OOPPC}}_{it2}\right)+\\ {}{\beta_5}^{\ast}\mathit{\ln}\left( Pop{65}_{it3}\right)+{\mu}_i+{\xi}_{it}\end{array}} $$
(2)
where μ_{
i
} represents a vector of country fixed effects, ξ_{
it
} is the disturbance term, and β coefficients are unknown parameters to be estimated from the model. A generalized linear model (GLM) with a normal distribution and identity link function was used to fit a linear regression using a maximum likelihood estimator. Predicted values of logged physician densities from this model were then transformed with an antilog and multiplied by a correction factor \( {e}^{\sigma^2/2} \) to account for the skewed distribution.
To avoid endogeneity, GDP per capita, OOP spending per capita (OOPPC), and the size of the population aged 65 or over (Pop65) were all lagged up to 5 years to allow time for such factors to work through the economy and affect the labor market, as other authors have done in previous projection exercises [18, 29]. A stepwise approach was used to select the specific combination of year lags that maximized the predictive power of each variable. Lagged variables that achieved a minimum 1% level of significance after repeated iteration were kept within the model.
Supply
WHO separately estimated the growth rate of physician and nurses/midwives density for each country from 1990 to 2013 using the following equations:
$$ \mathrm{Physicians}\ \mathrm{per}\ 1000\ {\mathrm{population}}_t={\alpha}_0+{\alpha_1}^{\ast }{\mathrm{year}}_t+{\varepsilon}_t $$
(3)
$$ \mathrm{Nurses}/\mathrm{midwives}\ \mathrm{per}\ 1000\ {\mathrm{population}}_t={\beta}_0+{\beta_1}^{\ast }{\mathrm{year}}_t+{\varepsilon}_t $$
(4)
where ε_{
t
} is the random disturbance term and α_{0}, β_{0}, α_{1}, and β_{1} are unknown parameters, with the last two parameters representing the linear growth rates to be estimated from the model.
Strengths and weaknesses of the demand and supply model
Demand model:

Strengths:

Builds on previous models of health worker demand (see [18]) and adds in two factors not previously accounted for but that can have a large effect on demand: outofpocket expenditures (i.e., as an indicator for the generosity of health insurance, and thus social protection against catastrophic healthcare spending) and the size of the population aged 65 or over (as an indicator for population aging, which is likely to drive greater demand for care).

Inclusion of country fixed effects to account for timeinvariant unobservable heterogeneity across countries (i.e., differences in baseline characteristics between countries).

Sensitivity analyses showed that the final specification yielded the best predicted values in terms of having the lowest mean error compared to alternative specifications using differently calculated input variables (i.e., percentage of the population aged 65+, outofpocket expenditures as a percentage of total per capita health expenditures).

Predicted values were also relatively stable using alternative estimates of future values of GDP per capita and size of the population aged 65 or over.

Weaknesses

Cannot take other factors into account that also affect demand, such as changing epidemiology of disease (e.g., epidemiological transition from infectious diseases to noncommunicable diseases in many lowerincome countries), increased productivity (through technological advance, which can also affect skills mix), changes in the organization of health care delivery

Only had sufficient data for physicians to do predictions, had to make global assumptions about nurses/midwives and other types of health care workers. Can build these other cadres in as more data become available.
Supply model:

Strengths:

Weaknesses

Assumes no change in either the entry or exit of workers into the market, which may be unrealistic (as reviewer mentions example about the aging workforce). Linear trend assumes rate of aging will stay the same when it actually may be increasing, resulting in an overestimate of future supply.

Other factors, such as changes in certification/licensing rules, migration, and education capacity could also affect the supply. In many countries, these policy and programmatic changes are enacted to augment the production of health workers, some of which may actually become employed in service delivery. Ignoring these factors would likely result in underestimating future supply.

In the end, it is not known what the net effect of these various factors might be on supply without more detailed data on graduation rates, in/out migration of health workers across countries, and retirement to include in the model.