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### Key findings: electricity consumption, night light, and temperature
- Night light is highly correlated with electricity consumption and reflects both its extensive and intensive margins.
- At the country level, the functional relationship between night light and electricity consumption is linear; linear prediction with country and year fixed effects attains adjusted R^2 up to 0.99.
- The relationship between annual average temperature and night light (as proxy for electricity consumption) is U-shaped above 0°C and uncertain below 0°C.
- Estimated world critical point (minimum electricity consumption) of annual average temperature: 14.6°C.
- 95% confidence interval for the world critical point: [14.1,15.3].
- When temperature is below 14.6°C, an increase in temperature reduces electricity consumption; when temperature is above 14.6°C, an increase in temperature increases electricity consumption.
- Augmenting the empirical relationship to allow for both level and growth effects indicates temperature increase raises electricity consumption growth, but the growth effect is small relative to the level effect.
- Using the composite functional relationship, a 1°C increase in temperature is estimated to drive up electricity demand in sub-Saharan Africa by 6.7%.

### Data, proxy validity, and empirical approach
- Night light data: Operational Linescan System (OLS) DMSP-OLS annual cloud-free composites, gridded at 30 arc second resolution (approximately 1 kilometer), values between 0 and 63, years 1992-2013.
- Temperature data: University of Delaware monthly-mean air temperature and monthly-total precipitation station-based gridded data, annual averages used for 1992-2013, 0.5 by 0.5 degree grid resolution (about 55.5km).
- Population mask: Gridded Population of the World (GPW), v4, using 2015 to discard cells with no more than 100 people per grid.
- Granularity and sample size: nearly 700,000 grid-level observations spanning different locations and years; total year-cell observations with both temperature and night lights available: 848340, covering 166 countries.
- Methodology: nonparametric degree-by-degree examination followed by estimation of a quadratic function to characterize the relationship; aggregation of 30 arc second night light cells to match 0.5°×0.5° temperature cells by averaging.
- Proxy caveat: elasticity d log E / d log L = 0.583 is estimated at country level; mapping country-level elasticity to grid-level f′X(T) introduces uncertainty.

### Summary statistics (grid-level)
- Main-sample (population>100 per 0.5°×0.5° grid) mean temperature: 13.62°C; overall main-sample mean referenced frequently: 13.6°C.
- Main-sample (population>100) night light mean: 2.17.
- Main sample with temperature≥0°C (N = 692794): Temperature mean 15.77°C; Night light mean 2.34.
- Table highlights (Entire sample N = 848340):
  - Temperature: mean 12.86, min -23.38, p25 3.57, p50 13.48, p75 23.23, max 35.77.
  - Night light: mean 2.00, min 0.00, p25 0.03, p50 0.33, p75 1.95, max 56.38.
- Regional notes:
  - Africa: smaller temperature range, median temperature 23.5°C; darkest continent by median grid cell luminosity.
  - Europe: brightest continent by median grid cell luminosity.

### Conceptual framework: mapping night lights to electricity consumption
- Lighting at night assumed a normal good with respect to income spent on electricity: log L = h_X(log E), where X are location-specific, time-invariant factors and h_X(·) is monotonic.
- If log E = g(T), then log L = f_X(T) = h_X(log(g(T))).
- Chain rule used to infer electricity response to temperature:
  - d log E / d T = (d log E / d log L) * (d log L / d T) = (d log E / d log L) * f′_X(T).
- Key elasticity from country-level regressions: d log E / d log L = 0.583 (Table 3, Column (3)).

### Empirical relationship: night lights predict electricity consumption (country level)
- OLS regressions of log night light on log electricity consumption show positive, statistically significant coefficients across specifications.
- Table 2 coefficients on log electricity consumption range (examples):
  - 0.888 ∗∗∗ (standard error 0.00594), Adjusted R^2 0.8970, Obs 2575.
  - With fixed effects, Adjusted R^2 up to 0.9910.
- Table 3 regressions of log electricity consumption on log night light yield preferred elasticity 0.583 ∗∗∗ (standard error 0.0798), Adjusted R^2 0.9900, Obs 2575 (with year and country fixed effects).

### Extensive and intensive margins
- Extensive margin (number of electric equipments):
  - Night light positively related to income (GDP), imports of heating and cooling equipments (SITC codes 7415 and 7416), and electricity access.
  - Examples of country-level coefficients (with year and country fixed effects):
    - (log) electricity consumption: 0.488 ∗∗∗ (0.0565) in one specification.
    - (log) GDP: 0.373 ∗ (0.174) in one column; 0.212 ∗∗ (0.0737) in another.
    - (log) imports of heating and cooling equipments: 0.0485 ∗ (0.0187) in one column; 0.0525 ∗∗ (0.0169) in another.
    - electricity access: 0.00990 ∗∗∗ (0.00244) in one specification.
- Intensive margin (usage intensity of existing equipment):
  - Grid-level regressions with degree days and temperature indicate temperature and temperature squared significant, supporting a U-shaped pattern.
  - Examples of grid-level coefficients:
    - temperature: -0.186 ∗∗∗ (0.0141); temperature squared: 0.00634 ∗∗∗ (0.000462) (Table 6, World, column 1).

### Global functional form and heterogeneity (U-shaped relationship)
- Nonparametric local slopes by 1°C bins show U-shaped pattern: for 0–9°C slopes negative; for >14°C slopes mostly positive; below 0°C estimates highly uncertain.
- Parametric quadratic specification (cells with annual average temperature ≥ 0°C) yields:
  - World (Table 6, column 1): temperature -0.186 ∗∗∗ (0.0141); temperature squared 0.00634 ∗∗∗ (0.000462). Implied critical point T∗ = 14.6°C. Average T = 15.8°C. Obs = 691660. Adjusted R2 = 0.9430.
  - 95% confidence interval for the World critical point based on 400 bootstraps: [14.1,15.3].
  - Continent examples:
    - Africa: temperature -0.247 ∗ (0.0963); temperature squared 0.00697 ∗∗ (0.00222). Critical point 17.7°C. Average T = 23.5°C. Obs = 112143. Adjusted R2 = 0.904.
    - Europe: temperature -0.0963 ∗∗∗ (0.0121); temperature squared 0.00208 ∗ (0.000854). Critical point 23.1°C. Average T = 6.1°C. Obs = 124266. Adjusted R2 = 0.957.

### Heterogeneous patterns by population density and NO2 (urban/rural and industrial differences)
- First-level administrative regions ranked by population density (year 2000) and by average daily tropospheric NO2 density (2005–2013) show:
  - Population density quartiles critical points:
    - 1st quartile (lowest density): T∗ = 12.9°C; temperature -0.142 ∗∗∗ (0.0246); temperature squared 0.00550 ∗∗∗ (0.000890). Obs = 186838.
    - 4th quartile (highest density): T∗ = 15.6°C; temperature -0.259 ∗∗∗ (0.0239); temperature squared 0.00833 ∗∗∗ (0.000755). Obs = 166312.
  - NO2 density quartiles critical points increase with NO2:
    - 1st quartile: T∗ = 12.4°C.
    - 4th quartile: T∗ = 16.3°C.
- Interpretation: more densely populated and more industrial regions have higher critical points; rural and less industrial areas have lower critical points and may be more sensitive to warming crossing those points earlier.

### Level and growth effects: persistence and medium-term implications
- Growth-specification regressions on Δ log night light (Table 8) indicate a positive and statistically significant sum of temperature coefficients (γ), implying temperature increases raise electricity consumption growth persistently.
- Examples of results (Δ log night light regressions; year and grid-cell fixed effects):
  - Column (1): temperature -0.0691 ∗∗∗ (0.00734); temperature (1st lag) 0.0811 ∗∗∗ (0.00714); temperature squared diff 0.00205 ∗∗∗ (0.000194). Obs = 638239. Adjusted R2 = 0.0818. γ = 0.012. F test p-value = 0.0001.
  - Column (3): γ = 0.027 (sum of temp. coeffs). Obs = 574956. Adjusted R2 = 0.0833. F test p-value = 0.00000.
- Specific statement from the paper: "Specifically, a 1° increase in temperature is estimated to increase electricity consumption growth by at least 1 percentage point."
- Policy implication: persistent growth effects mean temporary fixes (e.g., power ships) are insufficient; long-term capacity expansion and planning required.

### Challenging future for Sub-Saharan Africa (SSA) and regional impacts
- d log E / d log L = 0.583 (Section III.C).
- Point estimates of regression (6) imply f′X(T) = −0.186 + 2×0.00634 T.
- For SSA countries in the sample, average temperature of all year-cell observations: 23.7°C.
- Derived impact: d log E / d T = 6.7% — a 1°C increase in temperature increases electricity consumption of all SSA countries by 6.7%.
- 95% confidence interval for d log E / d T: 6.0% to 7.5%.
- Regional vulnerability:
  - West Africa, particularly the Sahel, could experience more than 10% increase in electricity demand for a 1°C increase.
  - A 1°C increase in SSA is characterized as "about adding the electricity consumption of Nigeria, the second largest electricity consumption country in sub-Saharan Africa in 2014."
- Contextual projection mention: global mean temperature could increase by about 1°C from the 2010s to the 2050s and by about 3°C to 2100 without substantial mitigation of greenhouse gas emissions.

### Uncertainties, limitations, and robustness
- Main limitations:
  - Night light is a proxy for electricity consumption; country-level elasticity may not hold at grid-level disaggregation.
  - Complex interactions and endogeneity between electricity consumption, economic growth, and climate change remain unresolved.
  - Nonparametric estimates imprecise and statistically insignificant when temperature < 0°C or > 26°C; focusing on 0–26°C (roughly 80% of sample) reinstates U-shaped relationship.
- Robustness checks:
  - Two-way clustering of standard errors (by year and first administrative region) preserves statistical significance of quadratic temperature term for the whole sample and most continent-level subsamples.
  - Controlling for region-specific time trends leaves quadratic temperature term significant though t-statistics decline as more local trends are added.

### Policy recommendations and implications
- Investment priorities:
  - Expand electricity access and electricity power grid capacity.
  - Increase energy efficiency and reduce carbon footprint.
  - Use geospatial electrification tools that leverage night light and other spatial data to determine cost-effective mixes of conventional and renewable technologies for specific localities.
- Urgency:
  - Given SSA’s average temperature (23.5°C to 23.7°C in reported samples) is well above the world critical point 14.6°C, warming-driven increases in demand heighten the urgency of infrastructure investment to meet Sustainable Development Goal 7.

*Source: IMF Working Paper (chapter "1. Functional relationship" and accompanying sections).*

### 1.    Functional relationship    .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .    13

### 1.    Functional relationship

### Key findings on electricity consumption and temperature
- Night light is highly correlated with electricity consumption and reflects both its extensive and intensive margins.
- At the country level, the functional relationship between night light and electricity consumption is linear.
- The relationship between annual average temperature and night light (as proxy for electricity consumption) is U-shaped above 0°C and uncertain below 0°C.
- The estimated critical point (minimum electricity consumption) of annual average temperature is 14.6°C.
- The 95% confidence interval for the critical point is between 14.1 and 15.3°C.
- When temperature is below 14.6°C, an increase in temperature reduces electricity consumption; when temperature is above 14.6°C, an increase in temperature increases electricity consumption.
- Augmenting the empirical relationship to allow for both level and growth effects indicates temperature increase raises electricity consumption growth, but the growth effect is small relative to the level effect.
- Using the composite functional relationship, a 1°C increase in temperature is estimated to drive up electricity demand in sub-Saharan Africa by 6.7%.

### Heterogeneity and spatial patterns
- The analysis uses grid-level data allowing subnational (first-level administrative region) heterogeneity assessment.
- More densely populated regions have a higher critical point of temperature for minimum electricity consumption; for the top population-density quartile of first-level administrative regions, the critical point is close to 16°C.
- More industrial regions (measured by average tropospheric nitrogen dioxide density) tend to have a higher critical point of temperature.
- Implication: electricity consumption in urban and more industrial areas may react more slowly to climate change, while rural and less industrial areas may be more sensitive and vulnerable.

### Data, proxy validity, and empirical approach
- Night light data: Operational Linescan System (OLS) DMSP-OLS annual cloud-free composites, gridded at 30 arc second resolution (approximately 1 kilometer), values between 0 and 63, years 1992-2013.
- Temperature data: University of Delaware monthly-mean air temperature and monthly-total precipitation station-based gridded data, annual averages used for 1992-2013, 0.5 by 0.5 degree grid resolution (about 55.5km).
- Population mask: Gridded Population of the World (GPW), v4, using 2015 to discard cells with no more than 100 people per grid.
- Granularity and sample size: nearly 700,000 grid-level observations spanning different locations and years.
- Methodology: nonparametric degree-by-degree examination followed by estimation of a quadratic function to characterize the relationship; aggregation of 30 arc second night light cells to match 0.5 by 0.5 degree temperature cells by averaging.

### Implications for sub-Saharan Africa and policy relevance
- Average annual temperature in sub-Saharan Africa is 24°C, well above the estimated critical point of 14.6°C, implying warming will increase electricity demand in the region.
- A 1°C increase in temperature in sub-Saharan Africa is estimated to increase electricity demand by 6.7%, an amount roughly equivalent to adding the electricity consumption of the third largest country in sub-Saharan Africa.
- Given existing electricity deficits in sub-Saharan African countries, climate-driven increases in demand heighten the urgency of building power infrastructure to meet Sustainable Development Goal 7 (ensure access to affordable, reliable, sustainable and modern energy).

*Source: IMF Working Paper (chapter "1. Functional relationship" and accompanying sections).*

### 0.5 degree grid cell is slightly more than two-thirds the size of Rhode Island at its location.

### wpiea2021022-print-pdf - 0.5 degree grid cell is slightly more than two-thirds the size of Rhode Island at its location.

### Administrative maps and data resolution
- 0.5 degree grid cell is slightly more than two-thirds the size of Rhode Island at its location.
- Temperature data resolution is about 55km.
- About 1% of all 2478 first administrative regions contain only one cell of temperature data at this resolution.
- First-level administrative regions (states and provinces) from GADM 2.8 are used to account for spatial correlation and to control for institutional and cultural differences.
- Population density (people per square kilometer) at the first administrative level is computed using year 2000 data to distinguish urban and rural areas; higher population density indicates more urbanized areas.
- Average nitrogen dioxide (NO2) density at the first administrative level (average of cloud-screened tropospheric NO2 between 2005 and 2013 from OMNO2d) is used to distinguish more industrial areas from less industrial areas; higher NO2 density represents more industrial areas.
- For comparisons: electricity access, electricity consumption, and GDP are taken from the World Development Indicators; imports of heating and cooling equipment from UN Comtrade; historical global gridded degree-days data from Mistry (2019).

### Summary statistics (grid-level)
- Total year-cell observations with both temperature and night lights available: 848340, covering 166 countries.
- After excluding sparsely populated cells, about 8% of observations are dropped for non-parametric analysis.
- Parametric analysis focuses on regions with annual average temperature no less than 0°, which is about 90% of the remaining observations.
- Main sample (population>100 per 0.5°×0.5° grid) mean temperature: 13.62°C; overall main-sample mean referenced frequently: 13.6°C.
- Average night lights across cells (main sample): 2.17 (mean), indicating many lighted areas are very dim at night.

- Table 1. Summary Statistics of Grid-Level Temperature and Night Light
  - Entire sample (N = 848340)
    - Temperature: mean 12.86, min -23.38, p25 3.57, p50 13.48, p75 23.23, max 35.77
    - Night light: mean 2.00, min 0.00, p25 0.03, p50 0.33, p75 1.95, max 56.38
  - population>100 per 0.5°×0.5° grid (N = 777073)
    - Temperature: mean 13.62, min -23.24, p25 4.75, p50 14.43, p75 23.54, max 35.77
    - Night light: mean 2.17, min 0.00, p25 0.05, p50 0.43, p75 2.25, max 56.38
  - population>100 per 0.5°×0.5° grid and temperature≥0°C (N = 692794)
    - Temperature: mean 15.77, min 0.00, p25 7.63, p50 16.63, p75 24.26, max 35.77
    - Night light: mean 2.34, min 0.00, p25 0.06, p50 0.54, p75 2.55, max 56.38

- Regional distributions (1992–2013)
  - Europe, the Americas, and Asia: wide range of annual average temperature (below -15°C to above 30°C).
  - Africa: smaller temperature range, median temperature 23.5°C.
  - Europe: brightest continent by median grid cell luminosity; Africa: darkest.
  - North–south divide: colder regions tend to be more developed and brighter at night.

### Relationship with electricity consumption — conceptual framework
- Lighting at night is assumed a normal good with respect to income spent on electricity; let E be electricity consumption and L the total night lights in a region.
- Causal relationship: log L = h_X(log E), where X are location-specific, time-invariant factors; h_X(·) is assumed monotonic.
- If log E = g(T) (temperature impact on electricity consumption), then log L = h_X(log(g(T))) = f_X(T).
- Monotonicity of h_X(·) implies critical points (minima/maxima) of f_X(·) correspond to those of electricity consumption.
- Inversion: log E = h_X^{-1}(f_X(T)), allowing focus on estimating f_X(·).
- Chain rule: d log E / d T = (d log E / d log L) * (d log L / d T) = (d log E / d log L) * f'_X(T).

### Empirical relationship — night lights and electricity consumption (country level)
- Country-level comparisons use electricity consumption per capita and population (World Bank) to compute total electricity consumption.
- Figure 2 (1992–2013) shows monotonic relationship between night light and electricity consumption; linear prediction of electricity consumption by night lights has adjusted R^2 = 0.99 with country and year fixed effects.

- Table 2. Night Light and Electricity Consumption (OLS regressions of log night light on log electricity consumption)
  - Dependent variable: (log) night light
  - Coefficients on (log) electricity consumption:
    - Column (1): 0.888 ∗∗∗ (standard error 0.00594), Adjusted R^2 0.8970, Obs 2575
    - Column (2): 0.888 ∗∗∗ (standard error 0.0235), Adjusted R^2 0.9010, Obs 2575
    - Column (3): 0.686 ∗∗∗ (standard error 0.0445), Adjusted R^2 0.9840, Obs 2575
    - Column (4): 0.488 ∗∗∗ (standard error 0.0565), Adjusted R^2 0.9910, Obs 2575
    - Column (5): 1.289 ∗∗∗ (standard error 0.356) on linear term, and (log) electricity consumption squared coefficient -0.0178 ∗ (standard error 0.00769); Adjusted R^2 0.991, Obs 2575
  - Notes: Year and country fixed effects are added progressively across columns; standard errors clustered at country level. Stars indicate significance levels: ∗ p<0.05, ∗∗ p<0.01, ∗∗∗ p<0.001.
  - Interpretation: Coefficient on log electricity consumption is positive and statistically significant throughout; with year and country fixed effects, a linear function with fixed effects explains the relationship well (Adjusted R^2 up to 0.99). Quadratic specification suggests night light lies on the increasing segment of the quadratic relationship over the observed domain.

- Table 3. Predicting Electricity Consumption by Night Light (OLS regressions of log electricity consumption on log night light)
  - Dependent variable: (log) electricity consumption
  - Coefficients on (log) night light:
    - Column (1): 1.010 ∗∗∗ (standard error 0.00676), Adjusted R^2 0.8970, Obs 2575
    - Column (2): 0.468 ∗∗∗ (standard error 0.0766), Adjusted R^2 0.8980, Obs 2575 (with year fixed effects)
    - Column (3): 0.583 ∗∗∗ (standard error 0.0798), Adjusted R^2 0.9900, Obs 2575 (with year and country fixed effects)
    - Column (4): 0.645 (standard error 0.396) on linear term and (log) night light squared 0.0206 ∗∗∗ (standard error 0.00290) in column (1) and -0.00264 (standard error 0.0160) in column (4); Adjusted R^2 0.990, Obs 2575
  - Key value used for chain rule: Column (3) implies d log E / d log L = 0.583 at the country level.

### Key empirical implications
- Night lights provide a strong, monotonic predictor of electricity consumption at the country level; with country and year fixed effects, linear predictions achieve adjusted R^2 = 0.99.
- The elasticity of electricity consumption with respect to night lights (d log E / d log L) is estimated at 0.583 in the preferred specification (Table 3, Column (3)).
- Given monotonicity of h_X(·), estimating f_X(T) using granular night light and temperature data can identify temperatures associated with minima and maxima in electricity consumption.

*Source: wpiea2021022-print-pdf - 0.5 degree grid cell is slightly more than two-thirds the size of Rhode Island at its location.*

### 2.  Extensive and Intensive Margins

### 2.  Extensive and Intensive Margins

### Extensive margin: determinants and empirical findings
- Concept: extensive margin reflects the number of electric equipments in use.
- Factors considered: income (measured by GDP), adaptation to climate change (proxied by imports of heating and cooling equipments, SITC codes 7415 and 7416), and electricity access (share of population with electricity access).
- Empirical relationships (country-level, annual frequency; all regressions contain year and country fixed effects; standard errors clustered at the country level):
  - (log) electricity consumption: 0.488 ∗∗∗ (0.0565) in column (1); 0.433 ∗∗∗ (0.0626) in column (2); 0.486 ∗∗∗ (0.0553) in column (3); 0.430 ∗∗∗ (0.0551) in column (4).
  - (log) GDP: 0.373 ∗ (0.174) in column (5); 0.212 ∗∗ (0.0737) in column (6).
  - (log) imports of heating and cooling equipments: 0.0485 ∗ (0.0187) in column (5); 0.0525 ∗∗ (0.0169) in column (6).
  - electricity access: 0.00990 ∗∗∗ (0.00244) in column (3); 0.00102 (0.00269) in column (6).
  - Observations by column: 25753, 13432, 31328, 25249, 32481, 22481, 2206 (as listed).
  - Adjusted R2 by column: 0.9910, 0.9920, 0.9910, 0.9940, 0.9920, 0.9910, 0.993.
- Interpretation:
  - Night light is positively related to income, imports of heating and cooling equipments, and electricity access at the country level, indicating night light reflects the extensive margin.
  - Income and adaptation to climate change influence night light beyond total electricity consumption; such region-specific factors captured in X(·).

### Intensive margin: temperature-driven intensity and empirical findings
- Concept: intensive margin reflects the usage intensity of existing electric equipments.
- Measure: heating degree days (threshold 10°C) and cooling degree days (threshold 25°C) at the grid level; degree days measure cumulative degrees below/above threshold in a year. Cooling/heating degree days normalized by 1000 in regressions.
- Empirical relationships (grid-level; all regressions contain year and grid-cell fixed effects; standard errors clustered by first administrative region):
  - temperature: -0.186 ∗∗∗ (0.0141) in column (1); -0.207 ∗∗∗ (0.00328) in column (2); -0.186 ∗∗∗ (0.00241) in column (3).
  - temperature squared: 0.00634 ∗∗∗ (0.000462) in column (1); 0.00678 ∗∗∗ (0.0000899) in column (2); 0.00634 ∗∗∗ (0.0000804) in column (3).
  - heating degree days: 0.215 ∗∗∗ (0.0328) in column (2); -0.0752 ∗∗∗ (0.00798) in column (4).
  - cooling degree days: 0.150 ∗∗ (0.0478) in column (2); 0.00934 (0.00996) in column (5).
  - Observations: 691626, 686973, 686973, 686973, 686973 (as listed).
  - Adjusted R2: 0.943, 0.942, 0.942, 0.943, 0.943.
- Interpretation:
  - Night light is positively related to the intensive margin at grid level.
  - Including annual temperature can change signs (e.g., heating degree days coefficient turns negative), suggesting substitution (gas may be more important than electricity for heating) and weaker correlation between night light and electricity at low annual average temperatures.
  - For capturing cooling demand at annual frequency, average temperature can be adequate.

### Night light and temperature: global functional form (U-shaped relationship)
- Nonparametric evidence:
  - Local slopes β1 by 1°C bins show a U-shaped pattern: for temperature between 0°C and 9°C the 95% confidence intervals for β1 are below zero; for temperature greater than 14°C the 95% confidence intervals are mostly above zero; below 0°C estimates are highly uncertain.
  - Critical point for minimum night lights roughly between 9°C and 15°C.
- Parametric specification: quadratic panel regression logLit = β0 + β1Tit + β2Ti,t^2 + μi + αt + εi,t (cells with annual average temperature ≥ 0°C).
- Table 6 (grid-level, year and grid-cell fixed effects; standard errors clustered by first administrative region):
  - World (column 1): temperature -0.186 ∗∗∗ (0.0141); temperature squared 0.00634 ∗∗∗ (0.000462). Implied critical point T∗ = 14.6°C. Average T = 15.8°C. Obs = 691660. Adjusted R2 = 0.9430.
  - With precipitation (column 2): temperature -0.185 ∗∗∗ (0.0141); temperature squared 0.00639 ∗∗∗ (0.000470). Critical point 14.5°C.
  - Asia (column 3): temperature -0.185 ∗∗∗ (0.0394); temperature squared 0.00553 ∗∗∗ (0.00122). Critical point 16.7°C. Average T = 15.8°C. Obs = 207379. Adjusted R2 = 0.923.
  - Americas (column 4): temperature -0.156 ∗∗∗ (0.0212); temperature squared 0.00514 ∗∗∗ (0.000667). Critical point 15.2°C. Average T = 16.1°C. Obs = 215931. Adjusted R2 = 0.956.
  - Africa (column 5): temperature -0.247 ∗ (0.0963); temperature squared 0.00697 ∗∗ (0.00222). Critical point 17.7°C. Average T = 23.5°C. Obs = 112143. Adjusted R2 = 0.904.
  - Europe (column 6): temperature -0.0963 ∗∗∗ (0.0121); temperature squared 0.00208 ∗ (0.000854). Critical point 23.1°C. Average T = 6.1°C. Obs = 124266. Adjusted R2 = 0.957.
  - Oceania (column 7): temperature -0.0211 (0.0698); temperature squared 0.000508 (0.00188). Critical point 20.8°C. Average T = 18.3°C. Obs = 22651. Adjusted R2 = 0.928.
  - 95% confidence interval for the World critical point: [14.1,15.3] (based on 400 bootstraps; each bootstrap draws a random sample with replacement that has one-fifth the size of the original sample).
- Interpretation:
  - The quadratic (U-shaped) relationship holds globally: night light first decreases with temperature up to a minimum (T∗), then increases for higher temperatures.
  - The world average temperature between 1992 and 2013 is 15.8°C, exceeding the world critical point 14.6°C.
  - Africa’s average temperature 23.5°C is well above the critical point, implying many African cells lie firmly on the increasing portion of the U-shaped curve.

### Heterogeneous impacts by population density and NO2 (urban/rural and industrial differences)
- Method: first-level administrative regions ranked by population per square kilometer (population in year 2000) and by average daily tropospheric NO2 density (2005–2013). Regressions are grid-level, with year and grid-cell fixed effects; standard errors clustered at first administrative level.
- Table 7 findings:
  - By population density quartile (1st = lowest, 4th = highest):
    - 1st quartile: temperature -0.142 ∗∗∗ (0.0246); temperature squared 0.00550 ∗∗∗ (0.000890). Obs = 186838. Adjusted R2 = 0.920. Critical point T∗ = 12.9°C.
    - 2nd quartile: temperature -0.176 ∗∗∗ (0.0340); temperature squared 0.00617 ∗∗∗ (0.00108). Obs = 162287. Adjusted R2 = 0.942. Critical point T∗ = 14.3°C.
    - 3rd quartile: temperature -0.194 ∗∗∗ (0.0271); temperature squared 0.00596 ∗∗∗ (0.000905). Obs = 171222. Adjusted R2 = 0.946. Critical point T∗ = 16.3°C.
    - 4th quartile: temperature -0.259 ∗∗∗ (0.0239); temperature squared 0.00833 ∗∗∗ (0.000755). Obs = 166312. Adjusted R2 = 0.952. Critical point T∗ = 15.6°C.
  - By NO2 density quartile (1st = lowest, 4th = highest):
    - 1st quartile: temperature -0.158 ∗∗∗ (0.0281); temperature squared 0.00637 ∗∗∗ (0.00102). Obs = 189752. Adjusted R2 = 0.931. Critical point T∗ = 12.4°C.
    - 2nd quartile: temperature -0.197 ∗∗∗ (0.0209); temperature squared 0.00661 ∗∗∗ (0.000733). Obs = 169437. Adjusted R2 = 0.939. Critical point T∗ = 14.9°C.
    - 3rd quartile: temperature -0.197 ∗∗∗ (0.0293); temperature squared 0.00641 ∗∗∗ (0.000968). Obs = 169227. Adjusted R2 = 0.943. Critical point T∗ = 15.3°C.
    - 4th quartile: temperature -0.212 ∗∗∗ (0.0387); temperature squared 0.00652 ∗∗∗ (0.00105). Obs = 162497. Adjusted R2 = 0.950. Critical point T∗ = 16.3°C.
- Interpretation:
  - All quartiles exhibit a U-shaped relationship.
  - As population density or industrial activity (NO2) increases, the critical point T∗ tends to increase.
  - Implication: global warming’s effect on electricity demand may be felt more strongly in rural and less industrial areas because their critical points are lower and average temperatures may rise above those points earlier.

### Level and growth effects of temperature on night lights (and implied electricity consumption)
- Modeling approach:
  - Allow a growth component for baseline electricity consumption: E = e^{g(T)} * Ē and permit temperature to affect growth rate: dĒ/Ē = g_E + γ_E T.
  - For night lights L (assumed proportional to E), derive growth specification: Δ log L = (β1 + γ) Tt − β1 Tt−1 + β2 (Tt^2 − Tt−1^2).
  - Presence of γ ≠ 0 indicates temperature has a growth impact on electricity consumption/night lights.
- Table 8 regression results (Δ log night light; year and grid-cell fixed effects; standard errors clustered at first administrative level):
  - Column (1): temperature -0.0691 ∗∗∗ (0.00734); temperature (1st lag) 0.0811 ∗∗∗ (0.00714); temperature squared diff 0.00205 ∗∗∗ (0.000194). Obs = 638239. Adjusted R2 = 0.0818. sum of all temp. coeff. (γ) = 0.012. F test p-value = 0.0001.
  - Column (2): temperature -0.0800 ∗∗∗ (0.00702); temperature (1st lag) 0.0894 ∗∗∗ (0.00717); temperature (2nd lag) 0.00180 (0.00256); temperature squared diff 0.00228 ∗∗∗ (0.000188). Obs = 606460. Adjusted R2 = 0.0804. γ = 0.011. F test p-value = 0.0045.
  - Column (3): temperature -0.0814 ∗∗∗ (0.00695); temperature (1st lag) 0.0929 ∗∗∗ (0.00728); temperature (2nd lag) -0.00332 (0.00277); temperature (3rd lag) 0.0191 ∗∗∗ (0.00380); temperature squared diff 0.00229 ∗∗∗ (0.000188). Obs = 574956. Adjusted R2 = 0.0833. γ = 0.027. F test p-value = 0.00000.
  - Column (4): temperature -0.0686 ∗∗∗ (0.00705); temperature (1st lag) 0.0840 ∗∗∗ (0.00725); temperature (2nd lag) -0.0133 ∗∗∗ (0.00287); temperature (3rd lag) 0.0222 ∗∗∗ (0.00415); temperature (4th lag) -0.00824 ∗ (0.00356); temperature squared diff 0.00196 ∗∗∗ (0.000187). Obs = 544299. Adjusted R2 = 0.0814. γ = 0.016. F test p-value = 0.0001.
- Interpretation:
  - The sum of temperature coefficients (γ) is positive and statistically significant across specifications, indicating a growth effect: temperature increases lead to persistent rises in electricity consumption/night lights over the medium term.
  - Specific statement: "Specifically, a 1° increase in temperature is estimated to increase electricity consumption growth by at least 1 percentage point."
  - Policy implication: temporary measures (e.g., bringing power ships) are insufficient; long-term solutions are needed to address electricity challenges posed by climate change.

### Challenging future for Sub-Saharan Africa (SSA)
- Context: SSA is one of the hottest and most climate-vulnerable regions.
- Using derivative relationship (repeated): d log E / dT = (d log E / d log L) * d log L / dT = (d log E / d log L) f′_X(T).
- Empirical context from prior sections:
  - World critical point T∗ = 14.6°C (95% CI [14.1,15.3]); world average temperature 15.8°C.
  - Africa average temperature = 23.5°C, above both the world and Africa-specific critical points.
- Implication:
  - Many locations in SSA are on the increasing portion of the temperature–electricity relationship, implying that further warming will raise electricity demand.
  - Given the growth effect and persistence, SSA faces a challenging future in meeting increased electricity demand driven by rising temperatures.

*Source: IMF working paper chapter — "2.  Extensive and Intensive Margins" (from wpiea2021022-print-pdf).*

### Section III.C shows thatdlogE/dlogL=0.583. The point estimates of regression (6) for

### wpiea2021022-print-pdf — Section III.C (Electricity consumption, temperature, and SSA)

### Key empirical estimates
- dlogE/dlogL = 0.583.
- The point estimates of regression (6) for the entire sample imply f′X(T) = −0.186 + 2×0.00634T.
- For SSA countries in the sample, the average temperature of all year-cell observations is 23.7°C.
- From the above, dlogE/dT = 6.7%: a 1°C increase in temperature increases electricity consumption of all SSA countries by 6.7%.
- The 95% confidence interval for dlogE/dT ranges from 6.0% to 7.5%.
- World-level critical point for minimum electricity consumption is about 14.6°C (the world has already surpassed this point).

### Regional impacts and vulnerabilities
- West Africa, particularly the Sahel region, is more sensitive to climate change and could experience more than 10% increase in electricity demand for a 1°C increase in temperature.
- A 1°C increase in temperature in SSA is characterized as "about adding the electricity consumption of Nigeria, the second largest electricity consumption country in sub-Saharan Africa in 2014."
- Recent projections cited: global mean temperature could increase by about 1°C from the 2010s to the 2050s and by about 3°C to 2100 without substantial mitigation of greenhouse gas emissions.

### Uncertainties and limitations
- Night light is used as a proxy for electricity consumption; the relationship between night light and temperature is estimated on grid-level data, while the elasticity of electricity consumption to night light is based on country-level data. Whether this relationship holds across spatial disaggregation levels remains unverified.
- The response of electricity consumption to temperature increase has "great uncertainties" including:
  - Potential mismatches between grid-level and country-level relationships.
  - Complex interactions among electricity consumption, economic growth, and climate change: solving electricity capacity constraints could spur economic growth (raising demand), while warming could negatively impact growth (reducing demand).
  - Economic growth trajectories (and their greenness) affect the speed of climate change, implying endogeneity among variables.
- A general equilibrium model addressing endogeneity of these variables is needed for more precise forecasting; this is left for future research.

### Robustness and related empirical notes (from appendices)
- Two-way clustering of standard errors (by year and first administrative region) preserves statistical significance of the quadratic temperature term for the whole sample and most continent-level subsamples.
- Controlling for region-specific time trends (UN region×year, country×year, state×year fixed effects) leaves the quadratic temperature term statistically significant, though t-statistics decline as more local time trends are added.
- Nonparametric estimates show imprecise and statistically insignificant impacts when temperature is below 0°C or above 26°C; focusing on 0–26°C (roughly 80% of sample) reinstates the U-shaped relationship and statistical significance for the quadratic term in relevant specifications.

### Policy implications and recommendations
- Investment in basic infrastructure, such as the electricity power grid, is essential to:
  - Expand electricity access.
  - Increase energy efficiency.
  - Reduce carbon footprint.
- Geospatial electrification tools that use data such as night light to determine cost-effective conventional and renewable technologies for specific localities are recommended as quantitative tools for assessing sustainable development policy options.
- Given projected warming scenarios and SSA’s vulnerability, meeting Sustainable Development Goals for electricity access will be made more difficult without substantial investment and planning.

### Conclusion (summary takeaways)
- The paper uncovers a U-shaped relationship between night light (proxy for electricity consumption) and temperature, with a global critical temperature of about 14.6°C.
- Sub-Saharan Africa is identified as the most vulnerable region: a 1°C rise could increase regional electricity consumption by about 6.7% (95% CI: 6.0% to 7.5%), with some subregions (e.g., the Sahel) potentially experiencing increases exceeding 10% for a 1°C rise.
- Significant uncertainties remain due to data proxies and endogenous interactions among electricity demand, growth, and climate; policy responses should prioritize infrastructure investment and spatially targeted electrification planning.

*Source: wpiea2021022-print-pdf — Section III.C*

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_Source: https://www.imf.org/-/media/files/publications/wp/2021/english/wpiea2021022-print-pdf.pdf_