## htnea2023005 - References

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---

### Introduction and Scope
- Third edition of the IMF SDG Costing Tool (completed late 2022) estimates additional spending needs in 2030 to achieve strong performance in selected SDGs for human capital development (health and education) and physical capital development (water and sanitation, electricity, and roads).
- Countries covered: expanded from 155 to 173.
- Reference/base years and data vintage: latest observations mostly pertaining to 2020; GDP 2020 from April 2022 World Economic Outlook; population projections from 2022 UN World Population Prospects.
- The tool benchmarks 2030 input targets to current levels of strongly performing income peers and/or SDG-related targets; estimates expressed in percentage points of GDP and in constant dollars where applicable.
- Key numerical references:
  - Income-basket GDP per capita thresholds (three-year average 2018–2020): lowest basket below $4,000; middle basket $4,000 to $7,000; highest basket $7,000 to $20,000; countries above $20,000 benchmarked to third basket peers.
  - Depreciation rate used for infrastructure maintenance: 5 percent per year.

### Methodological Framework (cross-cutting)
- General nonsectoral data sources (examples):
  - Population in 2020 and 2030: 2022 UN World Population Prospects.
  - Rural population: 2018 UN World Urbanization Prospects.
  - GDP 2020 (nominal US$): April 2022 World Economic Outlook.
  - GDP 2030 (in 2020 US$): GDP 2020 * real growth factor of GDP (product of annual growth factors Y_[t], with specified multiplication/exponentiation scheme).
- Aggregation rules:
  - Total additional spending TS_i in 2030 (percent of 2030 GDP) for country i equals sum over five sectors S_ij.
  - If any of the four sectors (other than WASH) has missing additional cost, TS_i set to missing.
  - WASH missing for AE countries treated as zero.
  - If TS_i < 0, total additional spending for country i set to zero.
  - Cross-country and sectoral averages are 2030 GDP-weighted (in 2020 prices).
  - Desk estimates can be replaced by in-depth country studies where available.

### Human Capital Development — Health (SDG 3)
- Benchmarking:
  - SDG 3 index thresholds (basket-specific): lowest = 75, middle = 79, highest = 86, resulting in 5, 6, and 6 good performers respectively.
  - Direct cost drivers benchmarked: doctors per 1,000 population, doctors’ salaries (ratio to GDP per capita), share of spending on other health areas.
  - Other factors: demographic distribution (share under 1 year old and age 60 and above).
- Identity-based expenditure formulation:
  - Total health expenditure expressed via identity (equations (3)–(5)) linking doctors per 1,000, other medical personnel per 1,000, doctor wage ratio wr, wage ratio of other medical personnel a, and OHsh (percent of capital and other recurrent expenditures in total health spending).
- Demographic adjustment of staff needs:
  - High-cost (HC) and low-cost (LC) population decomposition: pop = LC + HC.
  - Parameter from Clements and others (2015): Dpop_HC = 3.2 Dpop_LC (equation (13)).
  - Target doctors per 1,000 for country i adjusted via equation (16) preserving benchmarked peer intensity while accounting for country i’s current and 2030 share of high-cost population.
- Health-staff salary ratios:
  - Average salary ratios (ratio to GDP per capita), from Serje and others (2018) and Table 2:
    - Physicians wr_D = 4.4; D = 12,375,346
    - Nurses and midwives wr_N = 3.6; N = 30,199,490
    - Other health workers wr_OW = 2.1; OW = 17,398,962
  - Computed wage ratio a = 0.68 (equation (18)).
- Sectoral data sources (Table 3) include:
  - SDG3 Index: SDG Index and Dashboards, 2022.
  - Health spending, recurrent and capital: Health Nutrition and Population Statistics (accessed 2022).
  - Doctors and other medical staff per 1,000: Global Health Workforce Statistics, 2022.
  - Medical personnel compensation shares: WHO World Health Report 2006 (region averages).

### Human Capital Development — Education (SDG 4)
- Benchmarking:
  - SDG 4 index thresholds: lowest = 87, middle = 92, highest = 97.
  - Direct cost drivers benchmarked: number of teachers relative to students (student-per-teacher ratio STR), teachers’ salaries as ratio to GDP per capita.
  - Other factors: enrollment rate and student-age population.
- Identity-based expenditure formulation:
  - Education expenditure identity (equation (19)) links teacher wages wr, student-per-teacher ratio STR, school-age population SAPp (share of population), and OEsh (share of capital and other recurrent expenditures).
- Enrollment targets and projections:
  - Benchmark enrollment rate for 2030: universal enrollment for primary and secondary; 50 percent for preprimary and tertiary—resulting in target enrollment ~80 percent depending on age distribution.
  - School-age population defined as ages 2–21 (averaging entry to primary at 6 preceded by 4 years preprimary).
- Sectoral data sources (Table 4) include:
  - SDG4 index: SDG Index and Dashboards, 2022.
  - Enrolment counts and teacher counts: EdStats, 2022; World Development Indicators, 2022.
  - Public expenditure on education (% of GDP): World Development Indicators, 2022.
  - Student-age population 2020 and 2030: World Population Prospects, 2022.

### Physical Capital Development — Water, Sanitation, and Hygiene (SDG 6)
- Tool origins and scope:
  - WASH tool developed by the World Bank in collaboration with UNICEF and WHO; unit costs calibrated at the country level (Hutton and Varughese 2016).
  - Targets assessed: SDG 6.1 (universal and equitable access to safe and affordable drinking water) and SDG 6.2 (adequate and equitable sanitation and hygiene; end open defecation).
- Coverage and technology assumptions:
  - Baseline coverage year: 2015.
  - Population to be served 2015–2030 divided into 15 equal annual tranches for capital and O&M estimation.
  - Population disaggregated by rural/urban and by wealth quintile; lower-coverage quintiles assumed to be served faster.
  - Technology mix allowed (e.g., community wells, improved latrines, piped water and sewerage).
  - Baseline assumption: half of unserved population goes straight to higher-level services; half passes through basic services first.
- Reference to detailed methodology: Hutton and Varughese (2016) and SWA (n.d.).

### Physical Capital Development — Electricity (SDG 7)
- Target: SDG 7.1 universal access to affordable, reliable, modern energy services (first indicator: proportion of population with access to electricity).
- Coverage and consumption modeling:
  - Additional unserved population to be connected in 2030: E_unserved = E_T * ACC_T − E_t0 * ACC_t0 (equation (21)), with default target ACC_T = 1 (universal coverage).
  - Current electricity consumption per user = per-capita consumption / access rate (equation (22)).
  - Elasticity β of electricity consumption with respect to GDP per capita estimated via regression (equation (23)); regression results (Table 5):
    - Coefficient on ln(gdp_cap): 1.060*** (0.0453)
    - Constant: −2.072*** (0.413)
    - Observations: 183
    - R^2: 0.799
  - Target consumption per user in 2030: d_user_T = d_user_t0 * [1 + β * gdp_cap_per_person_pr] (equation (24)), with growth factor defined in (25).
- Unit cost and cost components:
  - Unit cost per kW (including generation, transmission, distribution): UC = $2,258 (World Bank 2013).
  - Assumed investment cost shares: 60 percent generation, 10 percent transmission, 30 percent distribution (following Fay and Yepes 2003).
- Cost computations:
  - Cost to connect new users at current per-user consumption (equation (26)): R_cost_nu = E_unserved * d_user_t0 * UC.
  - Cost to raise consumption for whole target population in 2030 consistent with income growth (equation (27)): R_cost_pr = (E_iT * ACC_iT) * (d_user_T − d_user_t0) * UC.
  - Total cost = sum of the two components (equation (28)).
- Data sources (Table 6): Electricity access (% population) from World Development Indicators (accessed 2022); electricity consumption kWh from World Energy Statistics 2020, IEA-OECD; unit cost UC from World Bank (2013).

### Physical Capital Development — Roads (SDG 9)
- Target: SDG 9.1.1 — proportion of rural population living within 2 km of an all-season road.
- Modeling approach:
  - Two-step approach: estimate road infrastructure gap; compute annual investment needs to close gap given unit cost per km.
  - Regression for road density (ln RoadDensity) on ln GDP per capita, ln population density, Rural Access Index (RAI), and percent rural population (equation (29)).
- Regression results (Table 7 — Estimated Coefficients from the Roads Regression):
  - RAI coefficient: 0.0105*** (0.00314)
  - ln GDP per capita coefficient: 0.553*** (0.0639)
  - ln population density coefficient: 0.589*** (0.0444)
  - percent rural population coefficient (w_rur): 0.00719** (0.00328)
  - Constant: −9.500*** (0.594)
  - Observations: 181
  - R^2: 0.760
- Interpretation of coefficients:
  - β1 (0.553) = roads to GDP per capita elasticity.
  - β2 (0.589) = roads to population density elasticity.
  - β3 (0.0105) implies road density increases by 1.05 percent with RAI increase of 1 unit.
  - β4 (0.00719) implies road density rises by 0.72 percent with a 1 point increase in percent rural population.
- Target RAI values for 2030 by income group:
  - LIDCs: 75
  - EMEs: 90
  - AEs: 100
- Unit cost and cost aggregation:
  - Unit cost used: UC = 487,168 US$/km (World Bank 2013).
  - Cumulative additional construction cost H_i computed as difference between target and current all-season road length times UC (equation (35)).
  - All-season road length includes paved and unpaved roads in good condition; unpaved portion adjusted by normalized mean speed score (Moszoro and Soto 2022).
- Data sources (Table 8): Rural Access Index from Mikou and others (2019); length of roads from International Road Federation and CIA World Factbook; unit cost UC from World Bank (2013).

### Infrastructure Investment Annualization and Netting BAU Maintenance
- Capital accumulation and additional stock:
  - Standard capital stock accumulation: K_t = K_{t-1}·(1 − d) + I_t (equation (36)); final-year T = 2030 expression developed through iterative substitution (equations (37)–(40)).
  - Additional stock K_add = K_T − K_0 derived (equations (40), (44), (48), (50)).
- Investment path assumption:
  - Yearly investment as constant fraction of that year’s GDP requires investment to grow at the GDP growth rate g: I_{t+1} = I_t·(1 + g) (equation (41)).
  - Closed-form for initial investment I_0 derived (equation (49)) and expressed as percent of today’s GDP (equation (50)).
  - C parameter: C = (1 + g) / (1 − δ) (equation (46)).
- Netting out BAU maintenance:
  - BAU depreciation cost each year initially DEP_t = K_0 · δ (equations (51)–(53)).
  - BAU depreciation cost annualized so amounts are constant as share of GDP and grow with GDP at rate g; closed-form for first year’s BAU depreciation cost constant-as-share-of-GDP: GEG_{1,con} = S·K_0·δ·g·(1 + g)^{T−1} (equation (60) formatting preserved).
  - BAU depreciation in 2030: GEG_{con,T,pg} expressed by formula derived (equations (61)–(63)).
- Final additional annual investment (percent of GDP) needed to achieve SDG targets for infrastructure sectors:
  - I_NI_con_SDG = I_con_pg − GEG_con_T_pg, with full expression given in equation (64) (numerical substitution depends on country-specific K_add, K_0, δ, g, GDP_0, GDP_T, and C).

### Aggregation and Reporting Rules
- Total additional spending TS_i in 2030 (percent of 2030 GDP) is sum of sectoral S_ij across five SDG areas.
- Adjustments before group averages:
  - If TS_i originally negative and set to zero, set S_ij = 0 for each j of that country.
  - If any S_ij missing for a country, set S_ij missing for all sectors of that country.
  - AE countries’ WASH S_ij set to 0 where WASH unit costs missing.
- Cross-country and sectoral averages S_j computed as real 2030 GDP-weighted averages of adjusted S_ij.
- Desk estimates replaced by in-depth country estimates where available.

### Summary Results (high-level findings from third edition)
- Income-group performance patterns:
  - AEs perform distinctly better on average across the 17 SDGs than EMEs; EMEs are ahead of LIDCs.
  - SDG index gaps: median gap of 10 points between EMEs and AEs; 15 points between median LIDC and EME (SDG index range 0–100).
- Improvements since first edition (2018):
  - All income groups saw improvements up to pandemic; largest improvements for EMEs.
  - Improvements mainly prior to the pandemic; health crisis caused partial backsliding.

### 1. Performance in 2018 (Gaspar and others 2019) — Key quantitative findings (2030 additional spending)
- Global additional spending required to achieve a strong performance in the selected SDGs in 2030: $3 trillion (3.4 percent of 2030 world GDP).
- Average additional SDG cost for LIDCs: 16.1 percent of 2030 LIDC GDP.
- Average additional SDG cost for EMEs: 4.8 percentage points of their GDP in 2030.
- Additional cost for AEs: less than 0.2 percent of their 2030 GDP.
- Regional averages (additional spending requirement, percentage points of GDP):
  - SSA (sub-Saharan Africa): 19.4 percentage points of GDP.
  - CCA (Caucasus and Central Asia): 11.7 percentage points of GDP.
  - LAC (Latin America and the Caribbean): 2.5 percentage points of GDP.
- Sectoral balance: human versus physical capital
  - Global additional spending split:
    - Human capital development: 1.70 percentage points of GDP.
    - Physical capital (infrastructure) development: 1.71 percentage points of GDP.
  - By income group:
    - LIDCs will need to expend relatively more on human capital development.
    - EMEs’ additional costs are somewhat higher in the infrastructure sectors.
  - By region:
    - MENAP (Middle East, North Africa, Afghanistan, and Pakistan): additional costs for human development are more than double those for infrastructure.
    - LAC and Emerging and Developing Europe: need to concentrate a larger share of efforts on expanding infrastructure (the reverse of MENAP).
- Regional and income-group disparities (interpretation of results)
  - Disparities in SDG outcomes across income groups are mirrored in additional spending needs to close the performance gap.
  - Updated results show a moderate rise in added spending needs for EMEs and LIDCs compared with previous prepandemic estimates.
  - Across regions, SSA continues to have by far the largest additional expenditure burden to achieve a good performance in the SDGs.
- Methodology and appendix notes
  - Target performance in 2030 for a given country is determined by a combination of absolute targets derived from SDG target indicators and the use of values from income peers with the highest SDG outcomes (example provided for education: student-to-teacher ratio and target gross enrollment rate).
  - All cross-country averages of additional spending needs presented are weighted by 2030 GDP, following Gaspar and others (2019).
  - The Appendix table presents the third edition desk estimates for countries’ additional spending needs to achieve outcomes in line with well-performing peers and selected SDG targets.
  - Total additional spending needs in 2030 for each country (percent of 2030 GDP) is the sum of all five sectors’ additional spending; summing applies even when additional sectoral needs are negative (a country cross-sector total may be lower than the sum of shown positive estimates if some sectoral estimates are negative).
  - Desk estimates are robust at the country group level; in-depth country-level assessments are needed for sound and reliable results at the country level. Country-level desk estimates should not be used for drawing policy conclusions for the country in question.
  - Appendix Table A1 reports the positive additional costs; results already published based on in-depth analyses are highlighted bold and in blue.

*Source: IMF | How to Note NOTE/2023/005 — How to Assess Spending Needs of the Sustainable Development Goals, The Third Edition of the IMF SDG Costing Tool (Prepared by Piergiorgio Carapella, Tewodaj Mogues, Julieth Pico-Mejía, and Mauricio Soto, December 2023).*

### References .............................................................................................................

### htnea2023005 - References

### Introduction and Scope
- Third edition of the IMF SDG Costing Tool (completed late 2022) estimates additional spending needs in 2030 to achieve strong performance in selected SDGs for human capital development (health and education) and physical capital development (water and sanitation, electricity, and roads).
- Countries covered: expanded from 155 to 173.
- Reference/base years and data vintage: latest observations mostly pertaining to 2020; GDP 2020 from April 2022 World Economic Outlook; population projections from 2022 UN World Population Prospects.
- The tool benchmarks 2030 input targets to current levels of strongly performing income peers and/or SDG-related targets; estimates expressed in percentage points of GDP and in constant dollars where applicable.

*Key numerical references:*
- Income-basket GDP per capita thresholds (three-year average 2018–2020): lowest basket below $4,000; middle basket $4,000 to $7,000; highest basket $7,000 to $20,000; countries above $20,000 benchmarked to third basket peers.
- Depreciation rate used for infrastructure maintenance: 5 percent per year.

### Methodological Framework (cross-cutting)
- General nonsectoral data sources summarized in Table 1 (examples):
  - Population in 2020 and 2030: 2022 UN World Population Prospects.
  - Rural population: 2018 UN World Urbanization Prospects.
  - GDP 2020 (nominal US$): April 2022 World Economic Outlook.
  - GDP 2030 (in 2020 US$): GDP 2020 * real growth factor of GDP (product of annual growth factors Y_[t], with specified multiplication/exponentiation scheme).
- Aggregation rules:
  - Total additional spending TS_i in 2030 (percent of 2030 GDP) for country i equals sum over five sectors S_ij.
  - If any of the four sectors (other than WASH) has missing additional cost, TS_i set to missing.
  - WASH missing for AE countries treated as zero.
  - If TS_i < 0, total additional spending for country i set to zero.
  - Cross-country and sectoral averages are 2030 GDP-weighted (in 2020 prices).
  - Desk estimates can be replaced by in-depth country studies where available.

### Human Capital Development — Health (SDG 3)
- Benchmarking:
  - SDG 3 index thresholds (basket-specific): lowest = 75, middle = 79, highest = 86, resulting in 5, 6, and 6 good performers respectively.
  - Direct cost drivers benchmarked: doctors per 1,000 population, doctors’ salaries (ratio to GDP per capita), share of spending on other health areas.
  - Other factors: demographic distribution (share under 1 year old and age 60 and above).
- Identity-based expenditure formulation:
  - Total health expenditure expressed via identity (equations (3)–(5)) linking doctors per 1,000, other medical personnel per 1,000, doctor wage ratio wr, wage ratio of other medical personnel a, and OHsh (percent of capital and other recurrent expenditures in total health spending).
- Demographic adjustment of staff needs:
  - High-cost (HC) and low-cost (LC) population decomposition: pop = LC + HC.
  - Parameter from Clements and others (2015): Dpop_HC = 3.2 Dpop_LC (equation (13)).
  - Target doctors per 1,000 for country i adjusted via equation (16) preserving benchmarked peer intensity while accounting for country i’s current and 2030 share of high-cost population.
- Health-staff salary ratios:
  - Average salary ratios (ratio to GDP per capita), from Serje and others (2018) and Table 2:
    - Physicians wr_D = 4.4; D = 12,375,346
    - Nurses and midwives wr_N = 3.6; N = 30,199,490
    - Other health workers wr_OW = 2.1; OW = 17,398,962
  - Computed wage ratio a = 0.68 (equation (18)).
- Sectoral data sources (Table 3) include:
  - SDG3 Index: SDG Index and Dashboards, 2022.
  - Health spending, recurrent and capital: Health Nutrition and Population Statistics (accessed 2022).
  - Doctors and other medical staff per 1,000: Global Health Workforce Statistics, 2022.
  - Medical personnel compensation shares: WHO World Health Report 2006 (region averages).

### Human Capital Development — Education (SDG 4)
- Benchmarking:
  - SDG 4 index thresholds: lowest = 87, middle = 92, highest = 97.
  - Direct cost drivers benchmarked: number of teachers relative to students (student-per-teacher ratio STR), teachers’ salaries as ratio to GDP per capita.
  - Other factors: enrollment rate and student-age population.
- Identity-based expenditure formulation:
  - Education expenditure identity (equation (19)) links teacher wages wr, student-per-teacher ratio STR, school-age population SAPp (share of population), and OEsh (share of capital and other recurrent expenditures).
- Enrollment targets and projections:
  - Benchmark enrollment rate for 2030: universal enrollment for primary and secondary; 50 percent for preprimary and tertiary—resulting in target enrollment ~80 percent depending on age distribution.
  - School-age population defined as ages 2–21 (averaging entry to primary at 6 preceded by 4 years preprimary).
- Sectoral data sources (Table 4) include:
  - SDG4 index: SDG Index and Dashboards, 2022.
  - Enrolment counts and teacher counts: EdStats, 2022; World Development Indicators, 2022.
  - Public expenditure on education (% of GDP): World Development Indicators, 2022.
  - Student-age population 2020 and 2030: World Population Prospects, 2022.

### Physical Capital Development — Water, Sanitation, and Hygiene (SDG 6)
- Tool origins and scope:
  - WASH tool developed by the World Bank in collaboration with UNICEF and WHO; unit costs calibrated at the country level (Hutton and Varughese 2016).
  - Targets assessed: SDG 6.1 (universal and equitable access to safe and affordable drinking water) and SDG 6.2 (adequate and equitable sanitation and hygiene; end open defecation).
- Coverage and technology assumptions:
  - Baseline coverage year: 2015.
  - Population to be served 2015–2030 divided into 15 equal annual tranches for capital and O&M estimation.
  - Population disaggregated by rural/urban and by wealth quintile; lower-coverage quintiles assumed to be served faster.
  - Technology mix allowed (e.g., community wells, improved latrines, piped water and sewerage).
  - Baseline assumption: half of unserved population goes straight to higher-level services; half passes through basic services first.
- Reference to detailed methodology: Hutton and Varughese (2016) and SWA (n.d.).

### Physical Capital Development — Electricity (SDG 7)
- Target: SDG 7.1 universal access to affordable, reliable, modern energy services (first indicator: proportion of population with access to electricity).
- Coverage and consumption modeling:
  - Additional unserved population to be connected in 2030: E_unserved = E_T * ACC_T − E_t0 * ACC_t0 (equation (21)), with default target ACC_T = 1 (universal coverage).
  - Current electricity consumption per user = per-capita consumption / access rate (equation (22)).
  - Elasticity β of electricity consumption with respect to GDP per capita estimated via regression (equation (23)); regression results (Table 5):
    - Coefficient on ln(gdp_cap): 1.060*** (0.0453)
    - Constant: −2.072*** (0.413)
    - Observations: 183
    - R^2: 0.799
  - Target consumption per user in 2030: d_user_T = d_user_t0 * [1 + β * gdp_cap_per_person_pr] (equation (24)), with growth factor defined in (25).
- Unit cost and cost components:
  - Unit cost per kW (including generation, transmission, distribution): UC = $2,258 (World Bank 2013).
  - Assumed investment cost shares: 60 percent generation, 10 percent transmission, 30 percent distribution (following Fay and Yepes 2003).
- Cost computations:
  - Cost to connect new users at current per-user consumption (equation (26)): R_cost_nu = E_unserved * d_user_t0 * UC.
  - Cost to raise consumption for whole target population in 2030 consistent with income growth (equation (27)): R_cost_pr = (E_iT * ACC_iT) * (d_user_T − d_user_t0) * UC.
  - Total cost = sum of the two components (equation (28)).
- Data sources (Table 6): Electricity access (% population) from World Development Indicators (accessed 2022); electricity consumption kWh from World Energy Statistics 2020, IEA-OECD; unit cost UC from World Bank (2013).

### Physical Capital Development — Roads (SDG 9)
- Target: SDG 9.1.1 — proportion of rural population living within 2 km of an all-season road.
- Modeling approach:
  - Two-step approach: estimate road infrastructure gap; compute annual investment needs to close gap given unit cost per km.
  - Regression for road density (ln RoadDensity) on ln GDP per capita, ln population density, Rural Access Index (RAI), and percent rural population (equation (29)).
- Regression results (Table 7 — Estimated Coefficients from the Roads Regression):
  - RAI coefficient: 0.0105*** (0.00314)
  - ln GDP per capita coefficient: 0.553*** (0.0639)
  - ln population density coefficient: 0.589*** (0.0444)
  - percent rural population coefficient (w_rur): 0.00719** (0.00328)
  - Constant: −9.500*** (0.594)
  - Observations: 181
  - R^2: 0.760
- Interpretation of coefficients:
  - β1 (0.553) = roads to GDP per capita elasticity.
  - β2 (0.589) = roads to population density elasticity.
  - β3 (0.0105) implies road density increases by 1.05 percent with RAI increase of 1 unit.
  - β4 (0.00719) implies road density rises by 0.72 percent with a 1 point increase in percent rural population.
- Target RAI values for 2030 by income group:
  - LIDCs: 75
  - EMEs: 90
  - AEs: 100
- Unit cost and cost aggregation:
  - Unit cost used: UC = 487,168 US$/km (World Bank 2013).
  - Cumulative additional construction cost H_i computed as difference between target and current all-season road length times UC (equation (35)).
  - All-season road length includes paved and unpaved roads in good condition; unpaved portion adjusted by normalized mean speed score (Moszoro and Soto 2022).
- Data sources (Table 8): Rural Access Index from Mikou and others (2019); length of roads from International Road Federation and CIA World Factbook; unit cost UC from World Bank (2013).

### Infrastructure Investment Annualization and Netting BAU Maintenance
- Capital accumulation and additional stock:
  - Standard capital stock accumulation: K_t = K_{t-1}·(1 − d) + I_t (equation (36)); final-year T = 2030 expression developed through iterative substitution (equations (37)–(40)).
  - Additional stock K_add = K_T − K_0 derived (equations (40), (44), (48), (50)).
- Investment path assumption:
  - Yearly investment as constant fraction of that year’s GDP requires investment to grow at the GDP growth rate g: I_{t+1} = I_t·(1 + g) (equation (41)).
  - Closed-form for initial investment I_0 derived (equation (49)) and expressed as percent of today’s GDP (equation (50)).
  - C parameter: C = (1 + g) / (1 − δ) (equation (46)).
- Netting out BAU maintenance:
  - BAU depreciation cost each year initially DEP_t = K_0 · δ (equations (51)–(53)).
  - BAU depreciation cost annualized so amounts are constant as share of GDP and grow with GDP at rate g; closed-form for first year’s BAU depreciation cost constant-as-share-of-GDP: GEG_{1,con} = S·K_0·δ·g·(1 + g)^{T−1} (equation (60) formatting preserved).
  - BAU depreciation in 2030: GEG_{con,T,pg} expressed by formula derived (equations (61)–(63)).
- Final additional annual investment (percent of GDP) needed to achieve SDG targets for infrastructure sectors:
  - I_NI_con_SDG = I_con_pg − GEG_con_T_pg, with full expression given in equation (64) (numerical substitution depends on country-specific K_add, K_0, δ, g, GDP_0, GDP_T, and C).

### Aggregation and Reporting Rules
- Total additional spending TS_i in 2030 (percent of 2030 GDP) is sum of sectoral S_ij across five SDG areas.
- Adjustments before group averages:
  - If TS_i originally negative and set to zero, set S_ij = 0 for each j of that country.
  - If any S_ij missing for a country, set S_ij missing for all sectors of that country.
  - AE countries’ WASH S_ij set to 0 where WASH unit costs missing.
- Cross-country and sectoral averages S_j computed as real 2030 GDP-weighted averages of adjusted S_ij.
- Desk estimates replaced by in-depth country estimates where available.

### Summary Results (high-level findings from third edition)
- Income-group performance patterns:
  - AEs perform distinctly better on average across the 17 SDGs than EMEs; EMEs are ahead of LIDCs.
  - SDG index gaps: median gap of 10 points between EMEs and AEs; 15 points between median LIDC and EME (SDG index range 0–100).
- Improvements since first edition (2018):
  - All income groups saw improvements up to pandemic; largest improvements for EMEs.
  - Improvements mainly prior to the pandemic; health crisis caused partial backsliding.

*Italic source attribution line:*  
*Source: IMF | How to Note NOTE/2023/005 — How to Assess Spending Needs of the Sustainable Development Goals, The Third Edition of the IMF SDG Costing Tool (Prepared by Piergiorgio Carapella, Tewodaj Mogues, Julieth Pico-Mejía, and Mauricio Soto, December 2023).*

### 1. Performance in 2018 (Gaspar and others

### 1. Performance in 2018 (Gaspar and others 2019)

### Key quantitative findings (2030 additional spending)
- Global additional spending required to achieve a strong performance in the selected SDGs in 2030: $3 trillion (3.4 percent of 2030 world GDP).
- Average additional SDG cost for LIDCs: 16.1 percent of 2030 LIDC GDP.
- Average additional SDG cost for EMEs: 4.8 percentage points of their GDP in 2030.
- Additional cost for AEs: less than 0.2 percent of their 2030 GDP.
- Regional averages (additional spending requirement, percentage points of GDP):
  - SSA (sub-Saharan Africa): 19.4 percentage points of GDP.
  - CCA (Caucasus and Central Asia): 11.7 percentage points of GDP.
  - LAC (Latin America and the Caribbean): 2.5 percentage points of GDP.

### Sectoral balance: human versus physical capital
- Global additional spending split:
  - Human capital development: 1.70 percentage points of GDP.
  - Physical capital (infrastructure) development: 1.71 percentage points of GDP.
- By income group:
  - LIDCs will need to expend relatively more on human capital development.
  - EMEs’ additional costs are somewhat higher in the infrastructure sectors.
- By region:
  - MENAP (Middle East, North Africa, Afghanistan, and Pakistan): additional costs for human development are more than double those for infrastructure.
  - LAC and Emerging and Developing Europe: need to concentrate a larger share of efforts on expanding infrastructure (the reverse of MENAP).

### Regional and income-group disparities (interpretation of results)
- Disparities in SDG outcomes across income groups are mirrored in additional spending needs to close the performance gap.
- Updated results show a moderate rise in added spending needs for EMEs and LIDCs compared with previous prepandemic estimates.
- Across regions, SSA continues to have by far the largest additional expenditure burden to achieve a good performance in the SDGs.

### Methodology and appendix notes
- Target performance in 2030 for a given country is determined by a combination of absolute targets derived from SDG target indicators and the use of values from income peers with the highest SDG outcomes (example provided for education: student-to-teacher ratio and target gross enrollment rate).
- All cross-country averages of additional spending needs presented are weighted by 2030 GDP, following Gaspar and others (2019).
- The Appendix table presents the third edition desk estimates for countries’ additional spending needs to achieve outcomes in line with well-performing peers and selected SDG targets.
- Total additional spending needs in 2030 for each country (percent of 2030 GDP) is the sum of all five sectors’ additional spending; summing applies even when additional sectoral needs are negative (a country cross-sector total may be lower than the sum of shown positive estimates if some sectoral estimates are negative).
- Desk estimates are robust at the country group level; in-depth country-level assessments are needed for sound and reliable results at the country level. Country-level desk estimates should not be used for drawing policy conclusions for the country in question.
- Appendix Table A1 reports the positive additional costs; results already published based on in-depth analyses are highlighted bold and in blue.

*Source: Gaspar and others (2019); IMF SDG Costing Tool; IMF SDG Performance Tool, based on Sachs and others (2022).*

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_Source: https://www.imf.org/-/media/files/publications/howtonotes/2023/english/htnea2023005.pdf_