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### Introduction — Purpose and Key Contributions
- Satellite-recorded nighttime light data (VIIRS) used as proxy for economic activity; VIIRS provides higher resolution and higher frequency than DMSP-OLS.
- Main gap addressed: no properly estimated and widely accepted quarterly elasticity between VIIRS nighttime lights and economic activity.
- Core contribution: framework to estimate the quarterly elasticity between nighttime light intensity and GDP that explicitly accounts for measurement noise using the average number of effective nightly observations per quarter for each country.
- Key empirical estimates:
  - Baseline elasticity for EMDEs: "a 1 percent change in GDP is associated with a 1.55 percent change in nighttime lights."
  - Elasticity range across countries: "varies from 1.36 to 1.81."
  - Optimal linear combination for a new measure of economic activity: 67 percent weight on light-predicted GDP growth and 33 percent weight on official GDP growth.
- Practical applications:
  - New measure is especially informative when official data may poorly capture activity (e.g., COVID-19).
  - Official statistics may have overstated negative COVID-19 impacts for countries with large manufacturing and service sectors.
  - Subnational: economic activity declined more in richer districts and in areas with higher population density.

### Data — Nighttime Lights, GDP, and Controls
- Nighttime lights:
  - VIIRS Day Night Band (DNB) monthly cloud-free composites excluding stray light between April 2012 and December 2020.
  - Quarterly aggregates: sum of nighttime lights within each country administrative boundary using monthly data.
  - Thresholding: lower threshold of zero applied to pixel-level values (sum over all pixels with a value greater than zero).
  - Sensor recalibration example: recalibration in the first quarter of 2017 reduced background light and resulted in a worldwide increase in recorded nighttime lights.
  - Winsorization: remove top and bottom 5 percent of nighttime light growth rates for main results.
- GDP and other country-level data:
  - Quarterly GDP growth: IMF World Economic Outlook database for many AEs; Haver Analytics for EMDEs.
  - Remove top and bottom 1 percent of GDP growth.
  - Level of development: World Development Indicators (WDI) — PPP-adjusted GDP per capita in constant 2017 international dollars.
  - Country groupings: AEs, EMs, LIDCs; main analysis combines EMs and LIDCs into EMDEs.
  - Sectoral shares: agriculture, manufacturing, services from WDI.
- Statistical capacity and governance:
  - World Bank’s Statistical Capacity Indicator and Voice and Accountability from the Worldwide Governance Indicators used as covariates.
- Additional geospatial inputs:
  - Cloud cover: Climatic Research Unit (CRU TS version 4.03) area-weighted averages (1901-2018).
  - Subnational population: Gridded Population of the World, version 4.
  - Administrative boundaries: simplified GAUL 2015 and GADM v2.8.

### Summary Statistics and Stylized Facts
- Sample coverage: 117 countries from 2013Q2 to 2020Q4, including 33 advanced economies and 84 EMDEs.
- Selected statistics (2013Q2–2020Q4) — Night light growth, GDP growth, Avg. nightly obs. (p10, p25, p50, p75, p90 shown where provided):
  - AEs (33): Night light growth Mean 3.0 p10 -15.6 p25 -6.2 p50 2.1 p75 11.3 p90 23.7; GDP growth Mean 1.6 p10 -1.9 p25 0.8 p50 2.1 p75 3.3 p90 4.5; Avg. nightly obs. Mean 25.6 p10 5.9 p25 15.7 p50 27.5 p75 35.1 p90 40.8.
  - EMs (61): Night light growth Mean 6.7 p10 -15.7 p25 -4.1 p50 5.0 p75 16.9 p90 33.6; GDP growth Mean 1.9 p10 -3.2 p25 0.7 p50 2.8 p75 4.5 p90 6.1; Avg. nightly obs. Mean 28.5 p10 9.5 p25 17.2 p50 29.6 p75 39.0 p90 46.3.
  - LIDCs (23): Night light growth Mean 5.2 p10 -27.3 p25 -13.4 p50 4.3 p75 23.1 p90 40.6; GDP growth Mean 3.7 p10 -1.3 p25 2.5 p50 4.6 p75 6.2 p90 7.4; Avg. nightly obs. Mean 24.9 p10 12.0 p25 16.4 p50 24.6 p75 32.8 p90 38.8.
  - Total (117): Night light growth Mean 5.5 p10 -18.3 p25 -6.0 p50 4.1 p75 16.2 p90 32.1; GDP growth Mean 2.1 p10 -2.7 p25 1.0 p50 2.8 p75 4.5 p90 6.2; Avg. nightly obs. Mean 27.2 p10 9.4 p25 16.6 p50 27.9 p75 36.7 p90 44.0.
- Stylized facts:
  - Nighttime lights grew faster than GDP on average and are much more volatile.
  - Effective nightly observations per quarter are often low: Average AE ≈ 26 nights per quarter; Average EM ≈ 29 nights per quarter; 90th percentile ~39 nights per quarter.
  - Temporal noise (cloud cover, solar illumination, sensor recalibration) generates month-to-month coverage variation; year-on-year quarterly growth rates mitigate seasonality.
  - Annual nighttime lights averaged from monthly data are strongly correlated with annual VIIRS products at levels (0.997), but growth rates differ meaning annual vs. monthly elasticities are not interchangeable.

### Measurement Framework and Identification
- Observation model variables:
  - y_{i,t} = measured GDP growth; z_{i,t} = measured night light growth; N_{i,t} = number of effective daily observations in quarter t for country i.
  - z_{i,t} = (1/N_{i,t}) sum_{j=1}^{N_{i,t}} z_{i,t,j}; y_{i,t} = y^*_{i,t} + ε^y_{i,t}; z_{i,t,j} = β y^*_{i,t} + ε^z_{i,t,j}.
- Key derived equations:
  - var(z_{i,t}) = β^2 var(y^*_{i,t}) + (1/N_{i,t}) σ^2_{ε_z}    (equation (5))
  - cov(y_{i,t}, z_{i,t}) = β var(y^*_{i,t})                      (equation (6))
  - Combined: var(z_{i,t}) = β cov(y_{i,t}, z_{i,t}) + σ^2_{ε_z} (1/N_{i,t}) (equation (7))
- Identification novelty: exploit observed, time-varying N_{i,t} across countries to identify β without imposing signal-to-noise assumptions on GDP.
- Estimation approach: partition each country's time series into K periods, compute σ^2_{z;i,k}, σ_{yz;i,k}, average 1/N_{i,k}, and estimate σ^2_{z;i,k} = β σ_{yz;i,k} + α (1/N_{i,k}) + ζ_{i,k} (equation (8)).
- Measurement noise sources: cloud cover, seasonal illumination, background noise (negative pixel values), sensor recalibrations (e.g., January 12, 2017 recalibration at 14:18 UTC), extreme percentage changes in low-lit countries (could exceed 200 percent) — winsorization used.

### Elasticity Estimates and Robustness
- Baseline sample: 84 EMDEs between 2013Q2 and 2020Q4; variances/covariances computed over two-year windows (2013-14, 2015-16, 2017-18, 2019-20).
- Table 4 point estimates (cov(y,z) coefficient estimates across columns): 1.46***, 1.55***, 1.51***, 1.60***, 1.64*** with standard error (0.55), (0.54), (0.54), (0.54), (0.54) respectively.
- Baseline elasticity selected: β = 1.55 (column (2) in Table 4).
- Elasticity heterogeneity (Table 5): elasticities by subgroup range from 1.36 to 1.81 across splits by GDP per capita and sectoral shares; example subgroup estimates include 1.52** (GDP per capita below median), 1.61 (above median), 1.45 (agriculture below), 1.52** (agriculture above), 1.66** (industry below), 1.36 (industry above), 1.36** (services below), 1.81 (services above).
- Robustness checks:
  - Winsorization sensitivity: elasticity more sensitive to trimming of nighttime light growth distribution than to GDP growth trimming.
  - Grouping length sensitivity: using three-year grouping retains statistical significance at 5 percent; four-year grouping reduces significance though magnitudes similar.
  - Alternative estimation windows and specifications produce elasticities in the range 1.51–1.64.

### Combining Nighttime Lights and National Accounts — Light-Adjusted GDP
- Light-predicted GDP growth specification: ̃y_{i,t} = γ z_{i,t} + γ_d d_t + γ_c c_i  (equation (9)).
- New combined measure: ȳ = (1 − λ) y + λ ̃y  (equation (10)); optimal weight λ^* minimizes mean squared prediction error:
  - λ^* = var(ε_y) / [ var(ε_y) + (γβ − 1)^2 var(y^*) + γ^2 var(ε_z) ]  (equation (11)).
- Empirical inputs (Table 6 intermediate calculations):
  - β = 1.55; γ = 0.0157 (t-statistic 4.01, significant at the 1 percent level); cov(y,z) = 4.05; var(y^*) = 2.62; var(y) = 7.90; var(ε_y) = 5.29; var(z) = 5952; var(ε_z) = 5925.
  - Optimal weight λ^* = 0.67 (point estimate).
  - Variance decomposition: For var(y): Signal = 3%, Noise = 97%; For var(z): Signal = 2%, Noise = 98%.
- Interpretation: majority of variance in nighttime light growth attributed to noise; with identified β and estimated γ, substantial weight (67 percent) placed on nighttime light-predicted GDP growth when forming light-adjusted GDP.

### Long-Run Differences Between Official National Accounts and Light-Adjusted GDP
- Long-run averages constructed over 2012Q4–2020Q4:
  - y^L_i = long-run average official GDP growth; z^L_i = long-run average nighttime light growth; ̃y^L_i = γ^L z^L_i (equation (15)).
  - Light-adjusted long-run GDP: ȳ^L_i = (1 − λ) y^L_i + λ ̃y^L_i (equation (16)), using λ from Table 6.
- Regression: ȳ^L_i − y^L_i = x^L_i β^L + ξ^L_i (equation (17)); covariates include income, statistical capacity, voice and accountability, sectoral structure.
- Findings on long-run differences:
  - Aggregate example: 0.74 percentage points (0.19 from voice and accountability and 0.55 from the level of development), close to actual difference of 0.63 percentage points.
  - Overestimation of GDP (nighttime lights implying higher activity than national accounts) associated with:
    - Lower level of development (statistically significant at the 10 percent level).
    - Lower statistical capacity (statistically significant at the 10 percent level).
    - Lower voice and accountability (statistically significant at the 10 percent level).
  - For countries where nighttime lights suggest underestimation of GDP, no meaningful relationships with explanatory variables were found.

### Short-Run Differences and COVID-19 Measurement
- Country-specific intercepts filter out long-term differences; regressions focus on quarterly differences between light-adjusted and national accounts GDP growth.
- COVID interaction specification: ̄y_i,t − y_i,t = x_i,t β_S0 + 1{t∈COVID} x_i,t β_S1 + ξ_i,t, with 1{t∈COVID} = 1 during 2020Q1–2020Q4.
- Key regression findings (Table 8 highlights):
  - Voice and accountability: coefficient -0.18*** (standard error 0.053) — higher voice and accountability ⇒ smaller absolute measurement errors.
  - Statistical capacity: coefficient -0.014*** (standard error 0.0034) — higher statistical capacity ⇒ smaller measurement errors.
  - Voice and accountability × COVID: -0.56*** (standard error 0.13) — additional large impact during the pandemic.
  - Industry share × COVID: 0.032*** (standard error 0.012) — larger industrial sector associated with larger differences during COVID-19.
  - Service share × COVID: 0.074*** (standard error 0.024) — larger service sector associated with larger differences during COVID-19.
  - Statistical capacity reduces both underestimation and overestimation in separate specifications; voice and accountability primarily reduces overestimation.
- Example country-level interpretations:
  - Kenya predicted 0.29 percentage points larger absolute deviation than Tunisia (0.07 from voice and accountability and 0.22 from statistical capacity); actual difference 0.20 percentage point.
  - Colombia predicted 0.33 percentage points larger than Chile (0.17 from voice and accountability and 0.16 from statistical capacity); actual difference 0.62 percentage point.

### Subnational Heterogeneity of COVID-19 Impacts
- Subnational regression: z_k,i,t = x_k,i β_sub0 + 1{t∈COVID} x_k,i β_sub1 + α_i + δ_t + ξ_k,i,t, where z_k,i,t = year-on-year nighttime light growth and x_k,i includes average nighttime lights per capita and population density (logs).
- Main subnational findings (Table 9 highlights):
  - Average nighttime light per capita × COVID: coefficient -11.7*** (standard error 1.36) and -12.2*** (standard error 1.45) — more developed regions experienced larger declines in nighttime light intensity during the pandemic.
  - Population density × COVID: coefficient -11.9*** (standard error 0.83) — more densely populated regions experienced much larger declines during COVID-19.
  - Quantitative translation using elasticity 1.55:
    - A 10 percent higher population density ⇒ 1.2 percent lower nighttime light growth ⇒ equivalent to 0.77 percent of GDP (1.2 / 1.55 = 0.774... presented as 0.77 percent).
    - Ten percent higher average nighttime lights per capita associated with 0.77 percentage point lower quarterly growth during COVID-19 (using elasticity mapping).
- Regional examples:
  - Thailand: Phuket predicted to darken more than Loei by 36 percentage points (12 percentage points from development level and 24 percentage points from population density); actual decline an additional 32 percentage points in 2020Q2.
  - Poland: Greater Poland predicted to darken 4.8 percentage points less than Lesser Poland; actual difference 3.0 percentage points in 2020Q2.
- Robustness: controlling for 2017Q1 sensor recalibration or excluding pre-recalibration observations leaves results nearly unchanged; emissions per capita not statistically significant.

### Policy Implications and Applications
- Strengthening statistical offices and systems in EMDEs likely reduces measurement errors in national accounts, as higher statistical capacity associated with smaller measurement deviations.
- Public scrutiny (voice and accountability) is crucial: low voice and accountability linked to higher overestimation of GDP growth, underscoring the role of debate in academia, think tanks, and media for credible GDP data.
- Monthly VIIRS nighttime light data, combined with estimated elasticity, provide a practical tool to:
  - Study short-term economic impacts of shocks (conflicts, social unrest, epidemics).
  - Translate changes in nighttime lights into changes in economic activity using elasticity β = 1.55 (or its inverse).
- Example application: with elasticity 1.55, a 10 percent decline in nighttime lights implies an economic impact of 6.5 percent of GDP for the affected group relative to control.

### Technical and Data Notes Emphasized
- Aggregation caveats: geographic coverage, extent of low-lit areas, and sensor recalibrations must be considered when aggregating nighttime light data to country level.
- Temporal noise: year fixed effects can control for temporal variations common across countries.
- Correlation pattern: quarterly correlation between VIIRS nighttime light growth and GDP growth is stronger for EMDEs than for advanced economies.
- Elasticity identification: framework exploits varying degrees of measurement errors in nighttime light data across countries to identify the elasticity.

*Italic source: wpiea2022109-print-pdf - References, https://www.imf.org/-/media/files/publications/wp/2022/english/wpiea2022109-print-pdf.pdf*

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

### wpiea2022109-print-pdf - References

### Appendices and Supporting Materials
- Appendix topics listed:
  - A. More Details on VIIRS Nighttime Light Data
  - B. Zero Threshold and Sensor Recalibration
  - C. Comparing Monthly with Annual Nighttime Lights
  - D. Country Characteristics and Variance of Light Growth
  - E. Data Winsorization
  - F. Alternative Elasticity Estimation
  - G. Light-Predicted GDP
  - H. Summary Statistics for Regressions (17) and (18)
  - I. COVID-19 Impact: Official and New GDP Growth
  - J. Summary Statistics for Regression (19)
  - K. Population Density and COVID-19 Impact

- List of Tables (selected):
  - 1. Nighttime Lights and GDP Summary Statistics at Quarterly Frequency
  - 2. VIIRS Nighttime Lights: Cross-Section and Temporal Relationships
  - 3. VIIRS Nighttime Lights and Economic Growth at Quarterly Frequency
  - 4. Elasticities between Nighttime Lights and GDP
  - 5. Elasticities between Nighttime Lights and GDP, by Economic Structure
  - 6. Optimal Weight on Nighttime Lighted-predicted GDP Growth
  - 7. Systematic Difference between New and Official Growth Measures
  - 8. Difference between New and Official Growth Measures
  - 9. Differentiated Impact of COVID-19 at the Subnational Level

- List of Figures (selected):
  - 1. VIIRS Nighttime Lights: June versus December
  - A.1. VIIRS Nighttime Lights and Average Number of Observations
  - B.1. Sum of VIIRS Nighttime Lights at the Country Level
  - C.1. VIIRS Nighttime Lights, 2013-2019: Monthly versus Annual
  - D.1. Country Characteristics and Variance of Nighttime Light Growth
  - K.1. Nighttime Light Growth during COVID-19 and Population Density

### Introduction — Purpose and Key Contributions
- Satellite-recorded nighttime light data are used extensively as a proxy for economic activity; VIIRS data have higher resolution and higher frequency than prior DMSP-OLS data.
- Main gap addressed: no properly estimated and widely accepted quarterly elasticity between VIIRS nighttime lights and economic activity exists to date.
- Core contribution: novel framework to estimate the elasticity between nighttime light intensity and GDP at quarterly frequency that explicitly accounts for measurement noise by using the average number of effective nightly observations per quarter for each country.

- Key empirical estimates:
  - Baseline elasticity for EMDEs: "a 1 percent change in GDP is associated with a 1.55 percent change in nighttime lights."
  - Elasticity range across countries: "varies from 1.36 to 1.81" depending on income status and economic structure.
  - Optimal linear combination for a new measure of economic activity:
    - 67 percent weight on light-predicted GDP growth
    - 33 percent weight on official GDP growth

- Practical applications highlighted:
  - The new measure is especially informative when official data may poorly capture activity (e.g., COVID-19).
  - Findings on COVID-19: official statistics may have overstated the negative impact for countries with large manufacturing and service sectors.
  - Subnational findings: economic activity declined more in richer districts and in areas with higher population density.

### Related Literature — Positioning and Gaps
- DMSP-OLS based literature widely used historically; VIIRS understudied despite advantages.
- Prior efforts:
  - Henderson, Storeygard, and Weil (2012) provided an annual elasticity for DMSP-OLS widely used in the literature.
  - Hu and Yao (2021) address measurement error in a non-classical, non-linear model but aggregate VIIRS to annual frequency.
- Novelty of current approach: identification leverages variation in the effective number of nighttime light observations to quantify measurement error in lights and thus estimate the quarterly elasticity.

### Data — Nighttime Lights, GDP, and Controls
- Nighttime lights:
  - VIIRS Day Night Band (DNB) monthly cloud-free composites excluding stray light between April 2012 and December 2020.
  - Quarterly aggregates: sum of nighttime lights within each country administrative boundary using monthly data.
  - Thresholding: apply a lower threshold of zero to pixel-level values (sum over all pixels with a value greater than zero).
  - Sensor recalibration example: recalibration in the first quarter of 2017 reduced background light and resulted in a worldwide increase in recorded nighttime lights.
  - Winsorization: remove top and bottom 5 percent of nighttime light growth rates for main results.

- GDP and other country-level data:
  - Quarterly GDP growth: IMF World Economic Outlook database for many AEs; Haver Analytics for EMDEs.
  - Remove top and bottom 1 percent of GDP growth.
  - Level of development: World Development Indicators (WDI) — PPP-adjusted GDP per capita in constant 2017 international dollars.
  - Country groupings: advanced economies (AEs), emerging markets and middle-income countries (EMs), low-income developing countries (LIDCs); main analysis combines EMs and LIDCs into EMDEs.
  - Sectoral shares: agriculture, manufacturing, services from WDI.

- Statistical capacity and governance:
  - World Bank’s Statistical Capacity Indicator used as a measure of a nation’s ability to collect, analyze, and disseminate high-quality data.
  - Voice and Accountability from the Worldwide Governance Indicators used to capture perceptions about civil liberties and media freedom.

- Additional geospatial inputs:
  - Cloud cover: Climatic Research Unit (CRU TS version 4.03) area-weighted averages within countries (1901-2018) used to inform effective observation counts.
  - Subnational population: Gridded Population of the World, version 4.
  - Administrative boundaries: simplified GAUL 2015 and GADM v2.8 for first-level aggregation.

### Summary Statistics and Stylized Facts
- Sample coverage:
  - 117 countries from 2013Q2 to 2020Q4, including 33 advanced economies and 84 EMDEs.

- Table 1 — Nighttime Lights and GDP Summary Statistics at Quarterly Frequency (2013Q2-2020Q4)
  - AEs (33 countries)
    - Night light growth: Mean 3.0 p10 -15.6 p25 -6.2 p50 2.1 p75 11.3 p90 23.7
    - GDP growth: Mean 1.6 p10 -1.9 p25 0.8 p50 2.1 p75 3.3 p90 4.5
    - Avg. nightly obs.: Mean 25.6 p10 5.9 p25 15.7 p50 27.5 p75 35.1 p90 40.8
  - EMs (61 countries)
    - Night light growth: Mean 6.7 p10 -15.7 p25 -4.1 p50 5.0 p75 16.9 p90 33.6
    - GDP growth: Mean 1.9 p10 -3.2 p25 0.7 p50 2.8 p75 4.5 p90 6.1
    - Avg. nightly obs.: Mean 28.5 p10 9.5 p25 17.2 p50 29.6 p75 39.0 p90 46.3
  - LIDCs (23 countries)
    - Night light growth: Mean 5.2 p10 -27.3 p25 -13.4 p50 4.3 p75 23.1 p90 40.6
    - GDP growth: Mean 3.7 p10 -1.3 p25 2.5 p50 4.6 p75 6.2 p90 7.4
    - Avg. nightly obs.: Mean 24.9 p10 12.0 p25 16.4 p50 24.6 p75 32.8 p90 38.8
  - Total (117 countries)
    - Night light growth: Mean 5.5 p10 -18.3 p25 -6.0 p50 4.1 p75 16.2 p90 32.1
    - GDP growth: Mean 2.1 p10 -2.7 p25 1.0 p50 2.8 p75 4.5 p90 6.2
    - Avg. nightly obs.: Mean 27.2 p10 9.4 p25 16.6 p50 27.9 p75 36.7 p90 44.0

- Key stylized facts:
  - Nighttime lights grew faster than GDP on average across countries; nighttime light growth is much more volatile than GDP growth.
  - Effective number of nightly observations per quarter is often low:
    - Average AE: about 26 nights per quarter
    - Average EM: about 29 nights per quarter
    - Even at the 90th percentile, nightly observations are just 39 nights per quarter.
  - Temporal noise (cloud cover, solar illumination, sensor recalibration) leads to substantial month-to-month coverage variation; year-on-year quarterly growth rates mitigate some seasonality.
  - Annual nighttime lights averaged from monthly data are strongly correlated with other annual VIIRS products, but annual growth rates from monthly-averaged series correlate less well with direct annual growth rates — implying annual vs. monthly elasticities are not interchangeable.

- Cross-sectional and temporal relationships:
  - Without fixed effects, correlation of nighttime light growth and GDP growth: 0.32 (statistically significant only at the 10 percent level).
  - With country fixed effects only: average temporal correlation not statistically different from zero.
  - Controlling for time-specific factors yields a strong and statistically significant relationship at the 1 percent level.

### Measurement and Estimation Considerations
- Sources of measurement noise in VIIRS:
  - Atmospheric conditions (cloud cover) reduce effective observations.
  - Seasonal solar illumination prevents data collection in polar regions at certain months.
  - Background noise can produce negative pixel values; threshold of zero applied when aggregating.
  - Sensor recalibrations and decay (example: recalibration in the first quarter of 2017) affect levels across countries; controlled using country and time fixed effects.
  - Extreme percentage changes in low-lit countries can exceed 200 percent in a quarter; winsorization (top and bottom 5 percent) used to mitigate.

- Identification strategy:
  - Use variation in the average number of effective nightly observations by country-quarter to quantify measurement error in lights and identify the quarterly elasticity between nighttime light growth and GDP growth.

*Italic source: wpiea2022109-print-pdf - References, https://www.imf.org/-/media/files/publications/wp/2022/english/wpiea2022109-print-pdf.pdf*

### Appendix C provides more details.

### 0.74 percentage points (0.19 from voice and accountability and 0.55 from the level of de-

### wpiea2022109-print-pdf - 0.74 percentage points (0.19 from voice and accountability and 0.55 from the level of de-

### Elasticity estimate between nighttime lights and GDP
- Estimated elasticity for EMDEs: 1.55.
- Elasticity range across country groups: from 1.36 to 1.81.
- Translation example provided: a 10 percent decline of nighttime lights in the treated group with respect to the control group reflects an economic impact of 6.5 percent of GDP.

### Long-run differences: systematic measurement biases
- Aggregate long-run difference example: 0.74 percentage points (0.19 from voice and accountability and 0.55 from the level of development), close to the actual difference of 0.63 percentage points.
- Overestimation of GDP (nighttime lights implying higher activity than national accounts) is associated with:
  - Lower level of development (statistically significant at the 10 percent level).
  - Lower statistical capacity (statistically significant at the 10 percent level).
  - Lower voice and accountability (statistically significant at the 10 percent level).
- For countries where nighttime lights suggest underestimation of GDP, no meaningful relationships with the explanatory variables were found.

### Short-run differences and measurement during extraordinary episodes (COVID-19)
- Method: country-specific intercepts filter out long-term differences; analysis focuses on quarterly differences between nighttime light-adjusted GDP growth and national accounts GDP growth.
- Regression specification for COVID interaction: ̄y_i,t − y_i,t = x_i,t β_S0 + 1{t∈COVID} x_i,t β_S1 + ξ_i,t, where 1{t∈COVID} = 1 during 2020Q1–2020Q4.
- Key regression findings (Table 8 highlights):
  - Voice and accountability (column (1)): coefficient -0.18*** (standard error 0.053) — higher voice and accountability ⇒ smaller absolute measurement errors.
  - Statistical capacity (column (1)): coefficient -0.014*** (standard error 0.0034) — higher statistical capacity ⇒ smaller measurement errors.
  - Voice and accountability × COVID (column (2)): coefficient -0.56*** (standard error 0.13) — additional large impact of voice and accountability during the pandemic.
  - Industry share × COVID (column (2)/(3)): coefficient 0.032*** (standard error 0.012) — larger industrial sector associated with larger differences during COVID-19.
  - Service share × COVID (column (2)/(3)): coefficient 0.074*** (standard error 0.024) — larger service sector associated with larger differences during COVID-19.
  - For under- and overestimation separately:
    - Statistical capacity reduces both underestimation and overestimation (columns (3)/(4)/(5)/(6) show negative and significant coefficients for statistical capacity).
    - Voice and accountability primarily reduces overestimation (overestimation column coefficient 0.30*** with standard error 0.11 indicates voice and accountability relates to differences directionally; context in paper notes voice and accountability reduces overestimation).
- Country examples from regression intuition:
  - Predicted absolute average deviation: Kenya 0.29 percentage points larger than Tunisia (0.07 from voice and accountability and 0.22 from statistical capacity); actual difference is 0.20 percentage point.
  - Predicted absolute average deviation: Colombia 0.33 percentage points larger than Chile (0.17 from voice and accountability and 0.16 from statistical capacity); actual difference is 0.62 percentage point.

### Subnational heterogeneity of COVID-19 impacts (nighttime lights at regional level)
- Regression specification: z_k,i,t = x_k,i β_sub0 + 1{t∈COVID} x_k,i β_sub1 + α_i + δ_t + ξ_k,i,t, with z_k,i,t = year-on-year nighttime light growth, x_k,i includes average nighttime lights per capita and population density (logs), COVID dummy for 2020Q1–2020Q4.
- Main subnational findings (Table 9 highlights):
  - Average nighttime light per capita × COVID: coefficient -11.7*** (standard error 1.36) in column (2) and -12.2*** (standard error 1.45) in column (3) — more developed regions experienced larger declines in nighttime light intensity during the pandemic.
  - Population density × COVID: coefficient -11.9*** (standard error 0.83) in column (3) — more densely populated regions experienced much larger declines in nighttime lights during COVID-19.
  - Quantitative interpretation:
    - A 10 percent higher population density is associated with 1.2 percent lower nighttime light growth.
    - Using elasticity 1.55, a 1.2 percent lower nighttime light growth is equivalent to 0.77 percent of GDP.
    - Ten percent higher average nighttime lights per capita is associated with 0.77 percentage point lower quarterly growth during COVID-19 (using the elasticity mapping).
- Regional examples:
  - Thailand: Phuket predicted to darken more than Loei by 36 percentage points (12 percentage points from development level and 24 percentage points from population density); actual decline was an additional 32 percentage points in 2020Q2.
  - Poland: Greater Poland predicted to darken 4.8 percentage points less than Lesser Poland; actual difference was 3.0 percentage points in 2020Q2.
- Robustness:
  - Controlling for the 2017Q1 sensor recalibration leaves results nearly unchanged.
  - Excluding observations before recalibration yields minimal changes and conclusions hold.
  - Controlling for emissions per capita: not statistically significant even at the 10 percent level and no impact on other results.

### Implications for measurement and policy
- Strengthening statistical offices and systems in EMDEs is likely to reduce measurement errors in national accounts, as higher statistical capacity is associated with smaller measurement deviations.
- Public scrutiny (voice and accountability) plays a crucial role: low voice and accountability is linked to higher overestimation of GDP growth, implying the importance of debate in academia, think tanks, and the media for credible GDP data.
- Monthly VIIRS nighttime light data, with estimated elasticity, provide a practical tool to:
  - Study short-term economic impacts of shocks (conflicts, social unrest, epidemics).
  - Translate changes in nighttime lights into changes in economic activity using the inverse elasticity (1/β) or the elasticity β, as appropriate.
- Example application: with elasticity 1.55, a 10 percent decline in nighttime lights implies an economic impact of 6.5 percent of GDP for the affected group relative to control.

### Technical and data notes emphasized in the chapter
- Aggregation caveats: geographic coverage, extent of low-lit areas, and sensor recalibrations must be considered when aggregating nighttime light data to country level.
- Temporal noise: year fixed effects can control for temporal variations unrelated to economic activity if such noise is common across countries.
- Correlation pattern: quarterly correlation between VIIRS nighttime light growth and GDP growth is stronger for EMDEs than for advanced economies.
- Elasticity identification: framework exploits varying degrees of measurement errors in nighttime light data across countries to identify the elasticity.

*Source: https://www.imf.org/-/media/files/publications/wp/2022/english/wpiea2022109-print-pdf.pdf*

### REFERENCES

### REFERENCES

### Key bibliographic scope
- Lists empirical and methodological literature on nighttime lights, GDP measurement, and COVID-19 economic impacts, including journal articles, Working Papers, and National Bureau of Economic Research papers.
- Representative authors and topics include Aruoba et al. (measurement error and GDP), Henderson, Storeygard, and Weil (measuring economic growth from outer space), Elvidge and colleagues (VIIRS nighttime lights data properties), Pinkovskiy and Sala-i-Martin (night lights and income), and multiple World Bank and IMF-related analyses of economic activity during COVID-19.

### VIIRS nighttime lights: data characteristics (Appendix A)
- Uses the vcm configuration of VIIRS nighttime lights, which starts from April 2012.
- VIIRS has two layers:
  - avg_rad: average radiance (brightness of lights).
  - cf_cvg: cloud-free coverages (total number of observations per pixel).
- Pixel-level average of monthly nighttime lights examined for April 2012–December 2020.
- Geographic observation patterns noted:
  - United States and Europe much brighter than Latin America and Africa at night.
  - Canada and Europe have fewer observations due to high latitudes.
  - Tropical areas (e.g., Gulf of Guinea) have fewer observations due to higher cloud cover.
  - Sahara Desert and most of Australia have the most observations owing to dry weather, despite low population density.

### Zero-threshold and sensor recalibration (Appendix B)
- Background noise can yield negative pixel-level monthly values in low-lit areas; summing pixels can produce negative country-level sums in some months (example: Sierra Leone negative in some months before 2017).
- Applying a threshold of zero:
  - Reduces volatility of country-level sums.
  - Ensures the sum of nighttime lights is always positive.
- VIIRS underwent a calibration at 14:18 Coordinated Universal Time on January 12, 2017, which produced increases in summed nighttime lights across regions (magnitude varies by region).

### Monthly versus annual nighttime lights (Appendix C)
- Comparison between annual average of monthly vcm data and annual VNL-V2 for 185 countries (2013–2019):
  - Level correlation: 0.997 between sums of monthly averages and VNL-V2.
  - Growth rates: VNL-V2 exhibits larger variations on average, likely due to reduced background noise from additional filtering and outlier removal.
- Conclusion: Additional cleaning in annual data has limited impact on country-level sums but can meaningfully alter implied growth rates; elasticity estimates from annual and monthly data may not be interchangeable.

### Country characteristics and variance of light growth (Appendix D)
- Three country characteristics used to proxy variance of measurement errors in nighttime light growth:
  - Inverse of the number of valid observations each quarter (time-varying).
  - Area of the country (fixed).
  - Annual average cloud cover (fixed).
- Empirical relationships:
  - Variance of nighttime light growth correlates strongly with number of valid observations and cloud cover (similar correlations).
  - Correlation with country area is much weaker.
- Baseline control uses the inverse of the number of valid observations.

### Data winsorization robustness checks (Appendix E)
- Baseline winsorization: remove top and bottom 5 percent of nighttime light growth distribution and top and bottom 1 percent of GDP growth distribution.
- Sensitivity checks summarized in Table E.1:
  - Winsorization by GDP growth (columns with thresholds 0.5%, 1%, 2%, 5%): reported cov(y,z) estimates 1.89***, 1.55***, 1.85***, 1.69** with standard errors (0.56), (0.54), (0.57), (0.69); 1/N estimates 525.9***, 522.0***, 499.6***, 560.4*** with standard errors (141.1), (139.8), (143.9), (146.5); Obs 327, 327, 325, 320; Adjusted R2 0.063, 0.056, 0.057, 0.053.
  - Winsorization by nighttime light growth (thresholds 1%, 2%, 5%, 10%): cov(y,z) 2.38**, 3.07***, 1.55***, 1.29*** with standard errors (1.21), (1.02), (0.54), (0.38); 1/N 586.0***, 562.4***, 522.0***, 205.7* with standard errors (164.5), (171.2), (139.8), (109.6); Obs 327, 327, 327, 321; Adjusted R2 0.044, 0.050, 0.056, 0.038.
- Finding: elasticity estimate (coefficient before covariance term) is more sensitive to extreme ends of nighttime light growth distribution than to GDP growth distribution.

### Alternative elasticity estimation and grouping choices (Appendix F)
- Trade-off: grouping length used to compute var(z) and cov(y,z) affects number of observations available to estimate β.
- Grouping by three years (periods: 2013-15, 2016-2018, 2019-20) and by four years (2013-16, 2017-20) reported in Table F.1.
- Selected estimates (cov(y,z) shown):
  - Grouping by three years, column (1) cov(y,z) 1.01 (0.72); column (2) 1.38** (0.70); column (3) 1.18* (0.71); column (4) 1.40* (0.73); column (5) 1.56** (0.71). 1/N estimates and other covariates reported; Obs 246 (or 240), Adjusted R2 vary.
  - Grouping by four years, cov(y,z) 0.96 (0.95), 1.04 (0.91), 1.03 (0.94), 1.18 (0.95), 1.08 (0.92). Obs 166 (or 162), Adjusted R2 vary.
- Conclusion: Point estimates are similar to baseline (table 4), indicating robustness to grouping, but statistical significance declines as grouping length increases and number of observations for β estimation falls.

### Light-predicted GDP (Appendix G)
- Estimation of γ from equation (9) reported in Table G.1 for EMDEs:
  - Coefficient on nighttime light growth (yoy) across columns: 0.0123* (0.00717), 0.0110 (0.00646), 0.0225*** (0.00599), 0.0157*** (0.00392).
  - Models incrementally control for country fixed effects and date fixed effects.
  - Obs across specifications: 2158; Adjusted R2 across columns: 0.0027, 0.2030, 0.3770, 0.586.
- Used coefficient from column (4) for optimal weight calculation.

### Summary statistics for regressions (Appendix H)
- Control variables (average 2013-2020) distributional statistics in Table H.1:
  - Statistical capacity: Mean 74.55; p10 55.8; p25 68.1; p50 76.4; p75 83.8; p90 88.5.
  - Voice and accountability: Mean -0.2; p10 -1.1; p25 -0.6; p50 -0.1; p75 0.3; p90 0.6.
  - GDP per capita: Mean 12.42; p10 2.25; p25 5.3; p50 11.9; p75 17.5; p90 25.8 (in thousands of constant 2017 international dollar PPP).
  - Agriculture share: Mean 11.7; p10 3.4; p25 5.0; p50 8.3; p75 15.8; p90 25.9.
  - Industry share: Mean 26.6; p10 16.1; p25 21.6; p50 25.5; p75 30.7; p90 36.2.
  - Service share: Mean 52.9; p10 41.1; p25 47.4; p50 54.1; p75 58.9; p90 61.9.

### COVID-19 impact: official versus light-adjusted GDP (Appendix I)
- Regression results in Table I.1 for 76 EMDEs (2013Q2–2020Q4), comparing Official and Light-adjusted GDP measures with COVID dummy (1 for 2020Q1–2020Q4):
  - Statistical capacity: coefficients 0.039*** (0.0073), 0.039*** (0.0078), 0.038*** (0.0037), 0.038*** (0.0042).
  - Voice and accountability: coefficients -0.14 (0.17), 0.11 (0.092), -0.13** (0.055), -0.063 (0.041).
  - Interaction Voice and accountability × COVID: -1.78** (0.66) and -0.45** (0.20) in respective specifications.
  - Interaction Statistical capacity × COVID: -0.017 (0.015) and -0.0093* (0.0050).
  - Service share × COVID: -0.15*** (0.040) and -0.023 (0.021).
  - Constant terms: -5.21** (2.03), -4.45** (1.82), -4.24*** (0.96), -4.08*** (0.91).
  - Obs 1949 across specifications; Adjusted R2 0.45, 0.47, 0.71, 0.71.
- Note: standard errors in parentheses; significance indicators used: * p<0.10, ** p<0.05, *** p<0.01.

### Subnational summary statistics and population density effects (Appendices J–K)
- Admin-1 region properties and controls (Table J.1):
  - Number of regions per country: Mean 19; p10 5; p25 9; p50 14; p75 24; p90 34.
  - Area of regions (1000 km2): Mean 43.5; p10 1.7; p25 3.6; p50 9.8; p75 35.7; p90 101.7.
  - Average nighttime lights per capita: Mean 0.053; p10 0.012; p25 0.022; p50 0.041; p75 0.069; p90 0.11 (winsorized; log versions reported).
  - Population density (100 per km2): Mean 2.03; p10 0.13; p25 0.33; p50 0.69; p75 1.40; p90 3.55 (winsorized; log versions reported).
- Finding on population density and COVID-19 (Appendix K):
  - Scatter plot of nighttime light growth in 2020 quarters versus population density in 2015 at subnational level shows a strong negative correlation.

*Source: wpiea2022109-print-pdf - REFERENCES*

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_Source: https://www.imf.org/-/media/files/publications/wp/2022/english/wpiea2022109-print-pdf.pdf_