metadata: authors: 0: author: Beyer,Robert Carl Michael
1: author: Hu,Yingyao
2: author: Yao,Jiaxiong
count: World
docna: 0: docna: Measuring Quarterly Economic Growth from
            Outer Space
docty: Policy Research Working Paper
subtopic: Food Security,Industrial Economics,Economic Theory & Research,Economic Growth,International Trade and Trade Rules
teratopic: Macroeconomics and Economic Growth,Industry,Agriculture,International Economics and Trade
abstracts: cdata!: This paper presents a novel framework to
            estimate the elasticity between nighttime lights and
            quarterly economic activity. The relationship is identified
            by accounting for varying degrees of measurement errors in
            nighttime light data across countries. The elasticity is
            1.55 for emerging markets and developing economies, with
            only small deviations across country groups and different
            model specifications. The paper uses a light-adjusted
            measure of quarterly economic activity to show that higher
            levels of development, statistical capacity, and voice and
            accountability are associated with more precise national
            accounts data. The elasticity allows quantification of
            subnational economic impacts. During the COVID-19 pandemic,
            regions with higher levels of development and population
            density experienced larger declines in economic activity.
repnme: repnme: Measuring Quarterly Economic Growth from
            Outer Space
display_title: Measuring Quarterly Economic Growth
            from Outer Space
listing_relative_url: /research/2022/01/33698540/measuring-quarterly-economic-growth-outer-space
topicv3: Agriculture and Food Security m1326205 435,Economic Growth m1326241 471,Trade m1326924 698,Population, Aging and Health m1327736 640,Coronavirus (COVID-19) m1939478 4828
publishtoextweb_dt: 2022-01-06T00:00:00Z
dois: 10.1596/1813-9450-9893
historic_topic: Macroeconomics and Economic Growth,Industry,Agriculture,International Economics and Trade
origu: EFI-SAR-MTI-MacroFiscal (ESAMU)
no_of_pages: 44
author_keys: 0: author_key: 1501628
1: author_key: 480714
2: author_key: 1299358
model_extractions: Policy Research Working Paper 9893 Measuring Quarterly Economic Growth from Outer Space _Robert C. M. Beyer Yingyao Hu Jiaxiong Yao_ Macroeconomics, Trade and Investment Global Practice January 2022
Policy Research Working Paper 9893

# **Abstract**

This paper presents a novel framework to estimate the elasticity between nighttime lights and quarterly economic activity. The relationship is identified by accounting for varying degrees of measurement errors in nighttime light data across countries. The elasticity is 1.55 for emerging markets and developing economies, with only small deviations across country groups and different model specifications. The paper uses a light-adjusted measure of quarterly economic activity to show that higher levels of development, statistical capacity, and voice and accountability are associated with more precise national accounts data. The elasticity allows quantification of subnational economic impacts. During the COVID-19 pandemic, regions with higher levels of development and population density experienced larger declines in economic activity.

This paper is a product of the Macroeconomics, Trade and Investment Global Practice. It is part of a larger effort by the World Bank to provide open access to its research and make a contribution to development policy discussions around the world. Policy Research Working Papers are also posted on the Web at http://www.worldbank.org/prwp. The authors may be contacted at rcmbeyer@worldbank.org, yhu@jhu.edu, and jyao@imf.org.

_The Policy Research Working Paper Series disseminates the findings of work in progress to encourage the exchange of ideas about development issues. An objective of the series is to get the findings out quickly, even if the presentations are less than fully polished. The papers carry the names of the authors and should be cited accordingly. The findings, interpretations, and conclusions expressed in this paper are entirely those of the authors. They do not necessarily represent the views of the International Bank for Reconstruction and Development/World Bank and its affiliated organizations, or those of the Executive Directors of the World Bank or the governments they represent._ Produced by the Research Support Team
Measuring Quarterly Economic Growth from Outer Space<sup>∗</sup> Robert C. M. Beyer<sup>†</sup> Yingyao Hu<sup>‡</sup> Jiaxiong Yao<sup>§</sup>

**Keywords:** Nighttime lights, economic measurement, quarterly GDP, national accounts, COVID-19

**JEL Classification:** C10, E01, R12

> ∗The views expressed here are those of the authors and do not necessarily represent the views of the IMF or the World Bank, their Executive Boards, or their respective managements.

> †World Bank (email: rcmbeyer@worldbank.org).

> ‡Department of Economics, Johns Hopkins University (email: yhu@jhu.edu).

> §International Monetary Fund (e-mail: jyao@imf.org).
# **1 Introduction**

Satellite-recorded nighttime light data are used extensively as a proxy for economic activity. However, surprisingly little economic analysis employs data from the Visible Infrared Imaging Radiometer Suite (VIIRS).<sup>1</sup> These new nighttime light data, with a better resolution and a higher frequency than the previous generation of data, have the potential to facilitate our understanding of rapid and spatially heterogeneous economic changes, such as those during the COVID-19 pandemic.<sup>2</sup> One reason for the hesitancy to use these data in the economic literature may be the difficulty of converting changes in nighttime light intensity into changes in economic activity. To the best of our knowledge, no properly estimated and widely accepted quarterly elasticity between VIIRS nighttime lights and economic activity exists to date.<sup>3</sup> In this paper, we attempt to fill this gap.

VIIRS nighttime light data are an imprecise measure of man-made lights. Even after aggregating the data to the country level and to quarterly frequency, substantial statistical noise remains. It mainly stems from atmospheric conditions like cloud cover that impact the effective number of observations. For instance, there are only five effective observations at the pixel level on average each month for a median developing country. Equally important, missing observations in the summer months and occasional satellite sensor recalibrations contribute to the noise as well.

In this paper, we provide a novel framework to estimate the elasticity between nighttime light intensity and gross domestic product (GDP) at quarterly frequency that takes measurement errors of nighttime lights explicitly into account. The elasticity can be identified because countries exhibit varying noise in their nighttime light growth. Using information from the average number of effective observations, we provide a regression equation that estimates the elasticity precisely. In emerging markets and developing economies (EMDEs), a 1 percent change in GDP is associated with a 1.55 percent change in nighttime lights. While the elasticity varies somewhat with a country’s income status and economic structure, it does not deviate much from this

> 1A recent survey by Gibson, Olivia, and Boe-Gibson (2020) reviews more than 150 economic studies using nighttime lights and argues that economists seem slower than others to switch to VIIRS data.

> 2For a detailed explanation of the superiority of the VIIRS data, see Elvidge, Baugh, Zhizhin, and Hsu (2013) and Gibson, Olivia, Boe-Gibson, and Li (2021).

> 3The use of nighttime light data from the Defense Meteorological Program Operational Line-Scan System (DMSP-OLS) picked up only after Henderson, Storeygard, and Weil (2012) provided such an elasticity.

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average estimate. In addition, our estimates are robust to different model specifications.

Using this elasticity, we construct a new measure of economic activity that is based on the optimal linear combination of light-predicted GDP growth and GDP growth as reported in national accounts. The new measure has optimal weights of 67 percent on light-predicted GDP growth and 33 percent on official GDP growth. This new measure can be especially informative during periods in which official data are less likely to capture economic activity properly, such as during the COVID-19 pandemic.<sup>4</sup> As expected, higher levels of development and statistical capacity reduce both overand underestimation of GDP. A higher score on voice and accountability, one of the World Bank’s Worldwide Governance Indicators, reduces overestimation, in line with a crucial cross-checking function of stakeholders. During COVID-19, the new measure suggests that official statistics may have overstated the negative economic impact for countries with large manufacturing and service sectors. Finally, we employ the spatial granularity of the data and the estimated elasticity to understand subnational heterogeneity of the COVID-19 impact. We find that economic activity declined more in richer districts, likely because services and industrial activity suffered more than agricultural activity. Areas with a higher population density were also hit harder, in line with containment measures being more disruptive for them.

The rest of the paper is organized as follows. Section 2 discusses related literature. Sections 3 and 4 describe the VIIRS nighttime light data and important stylized facts, respectively. In Section 5, we present our approach to estimate the elasticity between nighttime light intensity and GDP growth. Section 6 constructs a new measure of economic activity using nighttime lights and compares it with national accounts data. Section 7 analyzes the impact of COVID-19 at the subnational level. Section 8 concludes.

# **2 Related Literature**

Nighttime light data from the Defense Meteorological Satellite Program (DMSP), available at annual frequency from 1992 to 2013, have been used extensively in a wide array of economic studies. Among others, the data have proven helpful to monitor economic activity (Henderson, Storeygard, and Weil, 2012; Keola, Andersson, and Hall, 2015; Henderson, Squires, Storeygard, and Weil, 2018), to assess the quality of national ac-

> 4During the COVID-19 pandemic, official surveys used to estimate GDP could not be conducted in many countries due to stringent lockdown measures.

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counts statistics (Pinkovskiy and Sala-i-Martin, 2016a; Clark, Pinkovskiy, and Sala-i Martin, 2017; Morris and Zhang, 2019), and to approximate economic activity at small spatial units (Nordhaus and Chen, 2015; Heger and Neumayer, 2019; Chanda and Kabiraj, 2020). A recent survey by Gibson, Olivia, and Boe-Gibson (2020) reviews more than 150 economic studies using nighttime lights and finds that they overwhelmingly use DMSP data.

While more recent VIIRS nighttime light data are understudied in comparison, there are some noticeable exceptions. For example, the higher frequency of these data allowed analysis of India’s demonetization in November 2016 (Beyer, Chhabra, Galdo, and Rama, 2018; Chodorow-Reich, Gopinath, Mishra, and Narayanan, 2020). They have also been used to predict GDP in metropolitan statistical areas in the United States (Chen and Nordhaus, 2019) and to analyze the impact of the recent tariff war between the United States and China on China’s economy (Chor and Li, 2021). More recently, in response to COVID-19, a growing literature uses VIIRS nighttime lights as a subnational indicator of economic activity at high frequency. Among others, the data have been used to assess the impact of COVID-19 in India (Beyer, Jain, and Sinha, 2020; Ghosh, Elvidge, Hsu, Zhizhin, and Bazilian, 2020; Beyer, FrancoBedoya, and Galdo, 2021), China (Elvidge, Ghosh, Hsu, Zhizhin, and Bazilian, 2020), and Morocco (Roberts, 2021). All these studies struggle to convert changes in VIIRS nighttime lights to changes in economic activity. Chodorow-Reich, Gopinath, Mishra, and Narayanan (2020), for example, use an elasticity estimated with annual DMPSOLS data (Henderson, Storeygard, and Weil, 2012), even though their study uses monthly VIIRS data. Most others are abstaining from the conversion and instead focus on differences between subnational entities (Beyer, Franco-Bedoya, and Galdo, 2021), thwarting quantitative economic conclusions.

So far, to the best of our knowledge, no cross-country study of the quarterly relationship between VIIRS nighttime lights and GDP exists. However, to exploit the full potential of VIIRS data for economic analysis, an elasticity to convert changes in nighttime lights into changes in economic activity is fundamental. This paper fills this important gap. In terms of the econometric framework, it is closely related to the seminal contribution of Henderson, Storeygard, and Weil (2012) and the more recent work of Hu and Yao (2021), which both estimate the annual elasticity between DMSP lights and GDP in a global sample. The elasticity estimated by the former has become the standard elasticity used to date, but its validity for higher-frequency VIIRS data is limited. In addition, identification and estimation of the elasticity depend crucially on assumptions about the signal-to-noise ratios of GDP data. Hu and Yao (2021) 4
address this issue in a non-classical and non-linear measurement error model, allowing for a general relationship between measurement errors of GDP and nighttime light growth, statistical capacity, and geographic locations.<sup>5</sup> In this paper, we develop a novel approach to estimate the quarterly elasticity between VIIRS nighttime lights and GDP, employing the effective number of nighttime light observations to identify the relationship. The latter provides information to quantify the measurement errors in the lights data, which greatly simplifies the estimation.

In our applications, we construct a light-adjusted measure of economic activity to cross-check official estimates similar to Henderson, Storeygard, and Weil (2012) and Martinez (2021). We check whether measurement errors in the long-term, short-term, and during the COVID-19 pandemic vary systematically with country characteristics. In addition, we study the spatially heterogeneous impact of the pandemic and hence contribute to the large and growing empirical literature on the economic impact of COVID-19.<sup>6</sup>

# **3 Data**

## **3.1 Nighttime Lights**

Nighttime light data have changed over two different generations of satellites. The first generation of nighttime light data, based on the Operational Linescan Sensor (OLS) onboard the DMSP satellites, covers 1992 to 2013 at annual frequency. The second generation, based on the VIIRS Day Night Band (DNB) onboard the Joint Polar Orbiting Satellite System, covers April 2012 to the present at monthly frequency. Compared with DMSP-OLS, VIIRS nighttime lights have higher resolution and benefit from much improved low light imaging (Elvidge, Baugh, Zhizhin, and Hsu, 2013).<sup>7</sup> This paper focuses on VIIRS nighttime lights at quarterly frequency. To obtain quarterly nighttime lights, we use the monthly version of the cloud-free DNB composites, which excludes data impacted by stray light between April 2012 and December

> 5In the working paper version, Hu and Yao (2021) also provide an elasticity for VIIRS data. However, different from this paper, they aggregate the data to annual frequency, which leaves very few observations for their estimation and requires estimating the model in levels, which weakens the

> 6Miguel and Mobarak (2021) provide a good overview of this literature with a focus on low- and middle-income countries.

> 7For more details on different versions of VIIRS nighttime light data, please visit `https: //eogdata.mines.edu/products/vnl/` .

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in aggregation.<sup>10</sup> Throughout this paper, we use a threshold of zero, implying that we sum over all pixels with a value greater than zero.<sup>11</sup> Third, satellite sensor recalibration and decay may affect the nighttime lights captured across countries. For example, a recalibration of satellite sensors in the first quarter of 2017 reduced background light and resulted in a worldwide increase in recorded nighttime lights.<sup>12</sup> Countries across the planet all show an increase in nighttime lights, albeit to different extents. Since sensor recalibration and decay pertain to all countries, controlling for time and country fixed effects helps to mitigate the issue.<sup>13</sup> Last but not least, despite all the noise removal, nighttime light growth rates still exhibit large fluctuations. For example, year-on-year quarterly nighttime light growth can exceed 200 percent in some countries in some quarters. Those countries are either very poorly lit because of low electricity access or their nighttime lights are poorly captured because of atmospheric conditions and interference by the sun. A small change in the sum of nighttime lights can then lead to large percentage changes. To mitigate this issue, we winsorize the data by removing the tails of the nighttime light growth distribution. In the following, we report results after removing the top and bottom 5 percent of nighttime light growth rates.<sup>14</sup>

# **3.2 GDP Growth and Other Data**

# _GDP Growth, GDP per Capita, and Sectoral Shares_

For quarterly GDP growth, we use all the available data from the World Economic Outlook database from the International Monetary Fund (IMF), which covers mostly advanced economies. We complement these data with national accounts data for EMDEs compiled by Haver Analytics. We remove the top and bottom 1 percent of

> 10Panel (a) in figure B.1 in the appendix shows that the threshold of zero reduces the volatility of the sum of nighttime lights in Sierra Leone and ensures that the sum is always positive.

> 11Threshold values greater than zero yield very similar results.

> 12As shown in Panel (b) in figure B.1 in the appendix. The calibration occurred at 14:18 Coordinated Universal Time on January 12, 2017. For more details, see `https://ncc.nesdis.noaa.gov/ VIIRS/` .

> 13Since changes in recorded nighttime lights are at the pixel level, there is a stronger increase in lights of larger countries. However, this is of no concern for growth rates of nighttime lights.

> 14We find that not winsorizing nighttime light data at all leads to poor correlation between nighttime light growth and GDP growth. However, winsorizing the tail end of the distribution from 1 to 10 percent yields similar results.

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GDP growth, effectively limiting the disproportionate influence of very large swings in quarterly growth.

For the level of economic development, we rely on the World Development Indicators (WDI) database from the World Bank and use purchasing power parity-adjusted GDP per capita in constant 2017 international dollars. For the income status of countries, we use the IMF’s definition of advanced economies (AEs), emerging markets and middle-income countries (EMs), and low-income developing countries (LIDCs) to divide countries into mutually exclusive groups. For the main analysis, we combine the last two into a single group: emerging market and developing economies (EMDEs).

For the shares of agriculture, manufacturing, and services in each economy, we also rely on the WDI database.

# _Statistical Capacity and Voice and Accountability_

We use the World Bank’s Statistical Capacity Indicator, which measures a nation’s ability to collect, analyze, and disseminate high-quality data about its population and economy. It is a composite score assessing the capacity of a country’s statistical system based on the methodologies and data used, as well as the periodicity and timeliness of data releases. It uses publicly available information and country inputs to score countries against 25 criteria.

From the World Bank’s Worldwide Governance Indicators, we obtain a measure for voice and accountability. It captures perceptions about citizens’ ability to select their government, the extent of freedom of expression and association, as well as the presence of a free media.

# _Cloud Cover, Subnational Population, and Spatial Aggregation_

The Climatic Research Unit at the University of East Anglia provides monthly highresolution gridded data sets on cloud cover (Harris, Osborn, Jones, and Lister, 2020). For the analysis of elasticities, we take the area-weighted average of cloud cover (CRU TS version 4.03) within each country and across time between 1901-2018.

For our subnational analysis, we use population data from the fourth version of the Gridded Population of the World from the Socioeconomic Data and Applications Center.

Throughout, when aggregating variables by country boundaries, we use the simplified version of Global Administrative Unit Layers 2015 from the Food and Agriculture Organization of the United Nations. When aggregating variables by the first adminis8
trative boundaries, we use the Database of Global Administrative Areas version 2.8.

# **4 Summary Statistics and Stylized Facts**

## **4.1 Summary Statistics**

Our main analysis focuses on a merged data set of nighttime light growth and GDP growth at quarterly frequency. It covers 117 countries from 2013Q2 to 2020Q4, including 33 advanced economies and 84 EMDEs. Table 1 presents the summary statistics. Across all countries, nighttime lights grew faster than GDP and both nighttime lights and GDP grew on average slower in AEs than in EMDEs. Nighttime light growth is an order of magnitude more volatile than GDP growth, as is clear from the much wider interquartile range of nighttime light growth rates. As can be seen from the 25th percentile, nighttime light growth can be negative even when GDP growth is moderately positive. This is likely a result of the remaining noise in nighttime lights dwarfing the positive contribution from GDP growth to nighttime light growth.

Table 1: Nighttime Lights and GDP Summary Statistics at Quarterly Frequency

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

_Notes_ . This table presents summary statistics of year-on-year night light growth and GDP growth between 2013Q2-2020Q4 for different country groups. The mutually exclusive country groups are advanced economies (AEs), emerging markets and middle-income countries (EMs), and low-income developing countries (LIDCs).

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Table 1 also provides the average number of nightly observations each quarter that is used to construct the nighttime light data. Nighttime lights of AEs, most of which are located in the northern part of the Earth, are affected by late sunsets in summer months and therefore have on average a lower number of effective observations than EMs. The average AE has about 26 nights of observations each quarter, compared with 29 in an average EM. LIDCs, many of which are situated in tropical areas, also have relatively low numbers of observations due to frequent cloud cover. Even at the 90th percentile, the number of nightly observations is just 39, and hence less than half of a quarter. The variation in the number of nightly observations across countries and over time can be used to quantify the measurement errors in nighttime lights, which allows us to identify the elasticity between nightlight growth and GDP growth.

A country’s annual nighttime lights averaged across the monthly data are very strongly correlated with those from alternative annual VIIRS data.<sup>15</sup> However, the correlation of the annual growth rates averaged across the monthly data with the direct annual growth rates is weaker, suggesting that elasticity estimates from annual and monthly data should not be used interchangeably.<sup>16</sup>

# **4.2 Cross-Sectional and Temporal Relationships**

The recording of nighttime lights is affected by extraterrestrial and atmospheric conditions. As a result, temporal fluctuations in the data can be large, making it problematic to use time-series changes in nighttime lights as a proxy for changes in economic activity directly. However, because the noise is often common to all countries at a point in time, the relationship between nighttime lights and economic activity is strong and relatively stable when the analysis controls for time-specific factors.

Table 2 examines the roles of country- and time-specific factors in the relationship between nighttime light growth and GDP growth. Without any fixed effects, the correlation coefficient of 0.32 is statistically significant only at the 10 percent level, as shown in column (1). With country fixed effects, as shown in column (2), the average temporal correlation between nighttime light growth and GDP growth is not statistically different from zero, suggesting that time-series changes in nighttime lights are a poor proxy for changes in economic activity if time-specific factors are ignored. Columns (3) and (4) show that when the analysis controls for time specific factors, the relationship between nighttime light growth and GDP growth is strong and statistically

> 15Separate annual VIIRS data (VNL-V2) provided by Earth Observation Group have undergone an additional filtering and outlier removal processes.

> 16 Appendix C provides more details.

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significant at the 1 percent level.

Table 2: VIIRS Nighttime Lights: Cross Section and Temporal Relationships

||N|ight light|growth (yo|y)|
|---|---|---|---|---|
||(1)|(2)|(3)|(4)|
|GDP growth (yoy)|0.318*|0.320|0.495***|0.467***|
||(0.176)|(0.198)|(0.129)|(0.138)|
|Country fxed efects|-|Yes|-|Yes|
|Date fxed efects|-|-|Yes|Yes|
|Obs|2957|2957|2957|2957|
|Adjusted _R_<sup>2</sup>|0.00438|0.00543|0.277|0.286|

_Note_ . This table presents the regression results of nighttime light growth on GDP growth, incrementally controlling for time and country fixed effects. Throughout, standard errors are clustered by time and in parentheses.yoy=year-over-year.<sup>_∗_</sup> _p <_ 0 _._ 10,<sup>_∗∗_</sup> _p <_ 0 _._ 05,<sup>_∗∗∗_</sup> _p <_ 0 _._ 01.

# **4.3 Relationship for Different Country Groups**

In table 3, we further examine the relationship between nighttime light growth and GDP growth across different country groups. We group countries by their income status as discussed above.

Table 3 presents the results of regressions of nighttime light growth on GDP growth controlling for country and year fixed effects. Column (1) shows that nighttime light growth is weakly correlated with GDP growth for AEs. Columns (2) and (3) indicate that the relationship is much stronger for EMs and especially LIDCs. Grouping EMs and LIDCs together in column (4), the coefficient on GDP growth is statistically significant at the 1 percent level. Column (5) shows that the coefficient is slightly smaller when estimated using the entire sample, albeit still statistically significant at the same level.

While table 3 provides insightful information on the relationship between nighttime light growth and GDP growth, the estimated coefficients cannot be used directly as the elasticity of nighttime lights with respect to GDP, because both variables contain measurement errors. In the next section, we develop a framework to estimate the elasticity properly.

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Table 3: VIIRS Nighttime Lights and Economic Growth at Quarterly Frequency

|||night|light grow|th (yoy)||
|---|---|---|---|---|---|
||(1)|(2)|(3)|(4)|(5)|
||AE|EM|LIDC|EMDE|All|
|GDP growth (yoy)|0.266|0.492**|0.710**|0.513***|0.467***|
||(0.249)|(0.216)|(0.321)|(0.140)|(0.138)|
|country fxed efects|Yes|Yes|Yes|Yes|Yes|
|date fxed efects|Yes|Yes|Yes|Yes|Yes|
|No. of observations|799|1676|482|2158|2957|
|No. of countries|33|61|23|84|117|
|Adjusted _R_<sup>2</sup>|0.217|0.381|0.464|0.353|0.286|

_Notes_ . This table presents the regression results of nighttime light growth on GDP growth for different country groups between 2013Q2 and 2020Q4. Mutually exclusive country groups include advanced economies (AEs), emerging markets and middle-income economies (EMs), and low-income developing countries (LIDCs). Emerging markets and developing economies (EMDEs) is the union of EMs and LIDCs. Throughout, standard errors are clustered by date and in parentheses.<sup>_∗_</sup> _p <_ 0 _._ 10,<sup>_∗∗_</sup> _p <_ 0 _._ 05, _∗∗∗ p <_ 0 _._ 01.

# **5 Elasticity between Nighttime Lights and Economic Activity**

The elasticity between nighttime lights and GDP is key to quantify the link between nighttime lights and economic activity. However, both nighttime lights and GDP are measured with errors, complicating the estimation of the elasticity. In this section, we provide a novel framework to identify this elasticity, employing varying measurement errors in nighttime lights across countries.

## **5.1 Identification of the Elasticity: A Novel Approach**

Let _yi,t_ and _zi,t_ be the measured GDP growth and night light growth of country _i_ in quarter _t_ , respectively. Both _yi,t_ and _zi,t_ are observable. In particular, _zi,t_ is the average of monthly nighttime lights that are in turn predicated on daily observations. While daily observations are not accessible in our data, the number of effective days used to construct monthly observations is known. Let _Ni,t_ be the number of effective daily observations of nighttime lights for country _i_ in quarter _t_ , and _zi,t,j_ be the nighttime light growth in day _j_ . Then the relationship between quarterly and daily observations follows: 12
We assume that _yi,t_ is equal to true GDP growth _yi,t_<sup>_∗_plus an additive measurement</sup> error _ε_<sup>_y_</sup> _t_<sup>,and</sup><sup>_zi,t,j_islinearlyrelatedto</sup><sup>_y_</sup> _i,t_<sup>_∗_withanadditivemeasurementerror</sup><sup>_εz_</sup> _i,t,j_<sup>:</sup> _β_ is the elasticity between nighttime lights and true GDP. Daily nighttime light observations _zi,t,j_ can be thought of as a snapshot of economic performance in quarter _t_ , reflecting true GDP growth _yi,t_<sup>_∗_throughtheelasticity</sup><sup>_β_.Measurementerrorsin</sup> GDP growth and nighttime light growth are assumed to be independent of true GDP growth and each other.

Let _σε_<sup>2</sup> _z_<sup>bethevarianceof</sup><sup>_εz_</sup> _i,t,j_<sup>.Substitutingequation(3)intoequation(1),we</sup> have Taking the variance of both sides of equation (4) and the covariance between equations (2) and (4) yields With equations (5) and (6), we arrive at The relationship in equation (7) is the basis for identification and estimation of elasticity _β_ . The novelty in this approach is that we bring in additional information, the number of nightly observations for each country in each quarter, to achieve identification and precise estimation. Such information is objectively measured, time-varying, and available for all countries.

Henderson, Storeygard, and Weil (2012) use statistical capacity as additional information, but because it is not available for advanced economies, identification must rely 13
on assumptions about the signal-to-noise ratios of the GDP data. Without invoking assumptions about any signal-to-noise ratios, Hu and Yao (2021) use statistical capacity and geographic locations as additional information, allowing for a general relationship between measurement errors of GDP and nighttime light growth, statistical capacity, and geographic location in a non-classical and non-linear measurement error model. Compared with those two approaches, using the number of nightly observations avoids additional assumptions and greatly simplifies the estimation.

To estimate equation (7), we first divide the sample into country-period groups to obtain var( _zi,t_ ) and cov( _yi,t, zi,t_ ) and then estimate _β_ through a regression based on equation (8). Specifically, for each country _i_ , we divide the observations into _K_ time periods. Within each time period _k_ , we calculate the variance and covariance in equation (8) with quarterly observations as _σz_<sup>2</sup> ; _i,k_<sup>and</sup><sup>_σ_</sup> _yz_<sup>2</sup> ; _i,k_<sup>,aswellastheaverage</sup> 1 _/Ni,k_ . We then estimate the following regression to obtain _β_ : where _β_ and _α_ are coefficients and _ζi,k_ is the residual. In equation (8), 1 _/Ni,k_ is proportional to the variance of measurement errors in nighttime light growth. Other factors, such as the area of a country or its average cloud cover, affect measurement errors in nighttime light growth in a similar way. As a robustness check, we hence also estimate equation (8) by replacing 1 _/Ni,k_ with the area of a country or its average cloud cover.

# **5.2 Baseline Estimates**

First, we remove country and time fixed effects by regressing nighttime light growth and GDP growth on country and time dummies, respectively. Working with the residuals, we use two years of data for each country to calculate the variances and covariances. The weak correlation between nighttime light growth and GDP growth in advanced economies would reduce the efficiency of our estimation, so that we only include EMDEs.<sup>17</sup> In addition to the number of valid observations each quarter, we consider the area of each country and the annual average cloud cover as additional control variables. Both are likely to affect the variance of nighttime light growth, since larger and cloudier countries tend to have larger noise in nighttime light growth (see figure D.1 in the appendix).

> 17Nighttime lights are also a more important source of information in EMDEs, since they typically have less accurate national accounts and fewer subnational measures of GDP.

14
Table 4 presents the estimation results of elasticity regression (8). Columns (2)-(5) show that the elasticity is around 1.55. The coefficient of 1 _/N_ is statistically significant at the 1 percent level in column (2) and at the 10 percent level in column (5), supporting our identification assumption with the number of effective observations capturing cross-country variability in the variance of nighttime light growth. The coefficients of area and cloud cover are also statistically significant at the 1 percent level when included alone, indicating that they also affect the noise in nighttime light growth. Across the different specifications, the estimated elasticity stays nearly the same, varying from 1.51 to 1.60 when the controls are included separately and rising to 1.64 when they are included together. The elasticity is hence higher than suggested by the simple regression presented in table 3. It is also higher than the central unity estimate in Henderson, Storeygard, and Weil (2012) and the 1.3 estimated in Hu and Yao (2021), both of which use annual DMSP nighttime light data from 1992.<sup>18</sup> However, our estimate is somewhat below the implied elasticity between VIIRS nighttime lights and GDP per capita in China, which Chor and Li (2021) estimate to be 2.1.

Table 4: Elasticities between Nighttime Lights and GDP

||Var|iance of nig|ht light g|rowth: va|r(_z_)|
|---|---|---|---|---|---|
||(1)|(2)|(3)|(4)|(5)|
|cov(_y, z_)|1.46***|1.55***|1.51***|1.60***|1.64***|
||(0.55)|(0.54)|(0.54)|(0.54)|(0.54)|
|1_/N_||522.0***|||341.4*|
|||(139.8)|||(198.6)|
|Area|||0.12***||0.026|
||||(0.045)||(0.061)|
|Cloud cover||||4.32***|3.47***|
|||||(1.14)|(1.19)|
|Obs|327|327|327|319|319|
|Adjusted _R_<sup>2</sup>|0.018|0.056|0.036|0.058|0.074|

_Note_ . This table presents the results of regression (8) and its variants with other covariates. The first row represents estimates of the elasticity between nighttime lights and GDP. The sample includes 84 emerging markets and development economies between 2013Q2 and 2020Q4. Each time period that is used to estimate the variances and covariances covers two years, i.e., 2013-14, 2015-16, 2017-18, and 2019-20. Throughout, standard errors are in parentheses.<sup>_∗_</sup> _p <_ 0 _._ 10,<sup>_∗∗_</sup> _p <_ 0 _._ 05,<sup>_∗∗∗_</sup> _p <_ 0 _._ 01.

> 18However, it is within the range of elasticities presented in table 5 of Henderson, Storeygard, and Weil (2012).

15
We choose the elasticity estimate of 1.55 in column (2) as our baseline for subsequent analysis since 1 _/N_ varies across countries and over time and contains more observations than area and cloud cover. However, the difference between the estimated elasticities in columns (2)-(4) is small compared with their standard errors. In practice, one could use any one of them.

# **5.3 Robustness**

Our estimated elasticity is very similar whether differences in the variance in nighttime light growth are explained by the number of effective observations, the average cloud cover of countries, or by their country size. In this section, we test the model’s robustness to data winsorization, estimation choices, and the inclusion of different country groups.

# _Data Winsorization_

As mentioned in section 3, we winsorized the data by removing the top and bottom 5 percent of the nighttime light growth distribution as well as the top and bottom 1 percent of the GDP growth distribution. Such winsorization is useful because growth rates at the extreme ends have disproportionate influence on the estimated relationship. Since nighttime light growth is much more volatile than GDP growth, we chose a higher truncation threshold for nighttime light growth than for GDP growth.

Figure 2 shows how the removal of the extreme ends of the nighttime light growth and GDP growth distributions affects the estimated relationship. In line with the baseline, we exclude the top and bottom 5 percent of the nighttime light growth when focusing on the role of extreme GDP growth. Equivalently, to investigate the impact from varying the threshold for light, we exclude the top and bottom 1 percent of GDP growth.

Panel (a) shows that winsorization of GDP growth has only a very small impact on the estimated elasticity, which fluctuates around 1.74, with our baseline choice resulting in an elasticity closer to the lower bound. For nighttime light growth, winsorization plays a much larger role. The elasticity and its standard error are considerably higher for lower thresholds, but stabilizes around 1.5 for higher ones. Summarizing, data winsorization impacts the results but our baseline results are relatively robust to changing the threshold for GDP growth in any direction and for excluding more observations for nighttime light growth.<sup>19</sup>

> 19Table E.1 in the appendix provides detailed estimates with various winsorization thresholds.

16
<!-- Start of picture text --> 4<br>23<br>E<br>FE<br>>?<br>s<br>no<br>oO<br>oO 1<br>0a<br>51 £15 2 25 3 35 4 45 5<br>winsorization threshold<br>(top and bottom % of GDP growth)<br><!-- End of picture text --> <!-- Start of picture text --> 6<br>2<br>E4<br>FE<br>><br>= 2<br>no<br>oO<br>xo)<br>(@) iO<br>1 2 3 4 5 6 7 8 9 10<br>winsorization threshold<br>(top and bottom % of night light growth)<br><!-- End of picture text -->
## _Heterogeneity across Countries_

Next, we investigate whether the elasticity depends on the income level and the economic structure. To do so, we estimate the elasticity separately for countries with below and above median GDP per capita, share of agriculture, share of industry, and share of services. Table 5 shows the different relationships. First and foremost, we only find modest differences between the relationships among the different groups. However, with fewer observations in the different groups, the elasticity is not statistically significant even at the 10 percent level in some cases. Somewhat surprisingly, the elasticity is statistically significant at the 5 percent level for the poorer countries with a higher share of agriculture (and a lower share of industry and services). This could reflect the better measurement of nighttime lights in low-lit areas with VIIRS compared with DMSP-OLS sensors and suggests that VIIRS data offer great opportunities for economic analysis even in the least developed countries and regions.

Table 5: Elasticities between Nighttime Lights and GDP, by Economic Structure

||||Va|riance of ni|ght light|growth:|var(_z_)|||
|---|---|---|---|---|---|---|---|---|---|
||(1)|(2)|(3)|(4)|(5)|(6)|(7)|(8)|(9)|
||EMDEs|GDP p|er capita|Agricultu|re share|Indust|ry share|Service|s share|
|||Below|Above|Below|Above|Below|Above|Below|Above|
|cov(_y, z_)|1.55***|1.52**|1.61|1.45|1.52**|1.66**|1.36|1.36**|1.81|
||(0.54)|(0.62)|(1.21)|(1.09)|(0.64)|(0.70)|(0.86)|(0.61)|(1.49)|
|1_/N_|522.0***|1056.0|565.0***|531.3***|1049.4|1390.2|513.6***|2168.0***|526.8***|
||(139.8)|(990.8)|(136.5)|(136.7)|(925.9)|(972.9)|(136.7)|(750.0)|(119.8)|
|Obs|327|173|151|161|166|169|158|175|152|
|Adjusted _R_<sup>2</sup>|0.056|0.029|0.097|0.081|0.029|0.031|0.082|0.058|0.11|

_Note_ . This table presents the results of regression (8) by economic structure. The first row represents estimates of the elasticity between nighttime lights and GDP. The sample includes 84 EMDEs between 2013Q2 and 2020Q4. Column (1) replicates column (2) in table 4 as our baseline estimate of elasticity. Columns (2)-(9) consider grouping countries based on their GDP per capita and sector share relative to the median of the sample. For each variable, below (above) indicates below (above) the median of that variable in the sample. For example, column (2) includes countries whose GDP per capita is below the median. Each time period used to estimate the variances and covariances covers two years, 2013-14, 2015-16, 2017-18, and 2019-20. Throughout, standard errors are in parentheses.<sup>_∗_</sup> _p <_ 0 _._ 10,<sup>_∗∗_</sup> _p <_ 0 _._ 05,<sup>_∗∗∗_</sup> _p <_ 0 _._ 01.

# **6 Combining Nighttime Lights and National Accounts**

GDP growth as reported in national accounts may not always be an accurate measure of economic activity, in particular if statistical capacity is weak or if there is political pressure on statistical authorities. These concerns may be aggravated during periods 18
of large economic disruptions. Since the measurement error in nighttime lights is plausibly independent of the measurement error in GDP, we can use nighttime lights as an independent benchmark to assess existing measures of economic activity (Pinkovskiy and Sala-i-Martin, 2016a; Pinkovskiy and Sala-i Martin, 2016b; Aruoba, Diebold, Nalewaik, Schorfheide, and Song, 2016). Nighttime light adjusted GDP, a measure that optimally combines GDP growth from national accounts with GDP growth predicted by nighttime lights, provides a complementary view of changes in economic activity.

# **6.1 A Light-Adjusted GDP Measure**

Let _y_ ̃ be a linear prediction of GDP growth by nighttime light growth, where _dt_ ’s are temporal changes in nighttime light growth common to all countries and _ci_ ’s are time-invariant, country-specific factors that affect nighttime light growth. We consider a linear combination of _y_ and _y_ ̃ as a new measure of GDP growth,<sup>21</sup> where _λ_ is the weight on nighttime lighted-predicted GDP growth.

The expected mean squared prediction error of the new measure follows: The optimal linear combination that minimizes the expected mean squared prediction error therefore has the following weight: Empirically, since we have identified _β_ already, the remaining terms can be computed as follows:

> 21For ease of presentation and without loss of clarity, we have omitted the subscripts.

19
For the estimate of _β_ , we use the result in column (2) in table 4. Regression equation (9) yields a point estimate of _γ_ of 0.0157, with t-statistic 4.01 and significance at the 1 percent level.<sup>22</sup> We estimate var( _z_ ), var( _y_ ), and cov( _y, z_ ) directly from the sample. With those estimates, we arrive at an optimal weight of 0.67. The first row in table 6 presents from left to right the intermediate calculation results of equations (12)-(14). The second row presents some useful statistics. Notably, the majority of the variance of nighttime light growth can be attributed to noise.

Table 6: Optimal Weight on Nighttime Lighted-Predicted GDP Growth

||_β_<br>_γ_|cov(_y, z_)|var(_y_<sup>_∗_</sup>)|var(_y_)|var(_ε_<sup>_y_</sup>)|var(_z_)<br>var(_ε_<sup>_z_</sup>)|
|---|---|---|---|---|---|---|
|Point estimate|1.55<br>0.0157|4.05|2.62|7.90|5.29|259<br>252|
||optimal weight||var(_y_) de|composition||var(_z_) decomposition|
||||signal|noise||Signal<br>Noise|
|Point estimate|0.67||33%|67%||2%<br>98%|

_Note_ . This table presents detailed calculations of the optimal weight based on equation (11). The sample includes 84 EMDEs between 2013Q2 and 2020Q4. _β_ is estimated in column (2) in table 4 and _γ_ in column (4) in table G.1.

# **6.2 Shedding Light on National Accounts**

# _Long-Run Differences between National Accounts and Nighttime Lights_

Following Henderson, Storeygard, and Weil (2012), we start by analyzing long-run differences between GDP growth as reported in national accounts and adjusted GDP growth incorporating information from nighttime light growth. To do so, let _yi_<sup>_L_and</sup> _zi_<sup>_L_belong-runaverageofficialGDPgrowthandnighttimelightgrowth,respectively,</sup> between 2012Q4 and 2020Q4 for country _i_ . We first construct a linear prediction of long-run average GDP growth by long-run average nighttime light growth: Analogous to equation (10), we then construct a new measure of long-run GDP growth using the predicted long-run average GDP growth from equation (15), _y_ ̃ _i_<sup>_L_, and</sup> the optimal weight obtained in table 6:

> 22The regression table and further explanation are included in appendix G.

20
To examine the difference between our new measure and the official measure of longrun GDP growth and the factors behind such discrepancies, we conduct the following regressions: where _y_ ̄ _i_<sup>_L−y_</sup> _i_<sup>_L_isthedifferencebetweenthenewandofficialmeasures.Apositive</sup> (negative) difference implies that nighttime light growth suggests an underestimation (overestimation) by the official data. We also consider the absolute difference, _|y_ ̄ _i_<sup>_L−y_</sup> _i_<sup>_L|_,</sup> which indicates the overall discrepancy. **_x_**<sup>_L_</sup> _i_<sup>isavectorofcovariatesthatmayexplain</sup> the discrepancy, including economic, political, and statistical factors. Specifically, we consider income, statistical capacity, voice and accountability, and the structure of the economy.<sup>23</sup> _ξi_<sup>_L_istheresidual.</sup> We first analyze absolute differences. As column (1) in table 7 shows, more developed countries tend to have smaller long-run differences (statistically significant at the 10 percent level). Higher voice and accountability reduces the difference as well (statistically significant at the 10 percent level). This result is very much in line with recent findings that the elasticity between nighttime lights and GDP is higher in more authoritarian regimes and especially with weak constraints on GDP exaggeration (Martinez, 2021).

Comparing two countries can provide some intuition for these regression results. For example, since Lesotho is less developed than South Africa and scores lower in terms of voice and accountability, the results suggest a larger deviation of Lesotho’s reported and nighttime light-adjusted GDP growth compared to South Africa. Based on the regression coefficients and underlying data, the predicted difference between the two countries is 0.74 percentage points (0.19 from voice and accountability and 0.55 from the level of development), which is very close to the actual difference between them (0.63 percentage points).

Next, we analyze countries separately depending on whether nighttime light growth suggests an under- or overestimation of GDP in the long run. For the former, we do not find meaningful relationships with the explanatory variables, which hence cannot explain whether countries underestimate a lot or a little. By contrast, larger overestimation is associated with a lower level of development, lower statistical capacity, and lower voice and accountability (all statistically significant at the 10 percent level).

> 23A table of summary statistics is included in appendix H.

21
Table 7: Systematic Difference between New and Official Growth Measures

||Absolute diference|Underestimation|Overestimation|
|---|---|---|---|
||(1)|(2)<br>diference_>_0|(3)<br>diference_<_0|
|(log) GDP per capita|-0.36*|-0.22|0.54*|
||(0.21)|(0.30)|(0.30)|
|Statistical capacity|-0.0029|0.00093|0.032*|
||(0.0094)|(0.013)|(0.018)|
|Voice and accountability|-0.33*|-0.32|0.44*|
||(0.18)|(0.28)|(0.22)|
|Agriculture share|-0.019|-0.0077|0.062|
||(0.027)|(0.048)|(0.039)|
|Industry share|-0.0080|-0.011|-0.016|
||(0.021)|(0.039)|(0.025)|
|Service share|0.0091|0.042|0.018|
||(0.025)|(0.046)|(0.029)|
|Constant|4.58*|1.21|-9.79**|
||(2.71)|(4.75)|(4.05)|
|Obs (number of countries)|76|32|44|
|Adjusted _R_<sup>2</sup>|0.042|-0.044|0.20|

_Note_ . The sample includes 76 EMDEs between 2013Q2 and 2020Q4. Throughout, standard errors are in parentheses.<sup>_∗_</sup> _p <_ 0 _._ 10,<sup>_∗∗_</sup> _p <_ 0 _._ 05,<sup>_∗∗∗_</sup> _p <_ 0 _._ 01.

# _Short-Run Differences between National Accounts and Nighttime Lights_

Next, we abstract from long-run differences and focus on short-run differences. While systematic differences between official GDP growth and nighttime light-adjusted GDP growth are revealed in the long run, short-run differences can provide insights into GDP growth measurement errors in extraordinary episodes when official measures might be inadequate, such as during conflicts, social unrest, and epidemics. By allowing for country-specific intercepts in equation (9), long-term differences are filtered out. The nighttime light-adjusted GDP measure fluctuates around GDP as measured in the national accounts, but there are no differences on average over the estimation period. Large absolute differences between the two imply both strong under- and overestimation of GDP.

Our light-adjusted measure derived from equation (10) may be especially insightful 22
during episodes with large economic disruptions. For example, lockdown measures during COVID-19 severely disrupted economic activity in 2020. All countries struggled to capture the extent of the disruption with official statistics, especially those with large informal service sectors. To understand which factors contribute to larger measurement errors in normal times and during COVID-19, we estimate the following regression model: ̄ where _yi,t − yi,t_ is the difference between nighttime light-adjusted and official GDP growth at the quarterly frequency; **_x_** _i,t_ is a row vector of covariates; **1** _{t∈_ COVID _}_ is a time indicator function that equals 1 during COVID-19 starting in 2020Q1 and 0 otherwise; and _ξi,t_ is the residual. The interaction term, **1** _{t∈_ COVID _}_ **_x_** _i,t_ **_β_**<sup>_S_</sup> 1<sup>,inequation</sup> (18) captures the difference between two measures of GDP growth during COVID-19. **_β_**<sup>_S_</sup> 0<sup>and</sup><sup>**_β_**</sup><sup>_S_</sup> 1<sup>arecolumnvectorsofcoefficients.</sup> Table 8 presents the results. In addition to the variables in the table, we also control for GDP per capita and the share of GDP generated by agriculture, industry, and services, although none of these variables is statistically significant at least at the 10 percent level.

Column (1) in table 8 shows that higher statistical capacity and higher voice and accountability result in smaller measurement errors. Some examples can again help to strengthen the intuition. The results predict that Kenya has a 0.29 percentage points larger absolute average deviation than Tunisia (0.07 from lower voice and accountability and 0.22 from lower statistical capacity). And indeed, the actual average absolute difference between official and nighttime light-adjusted GDP growth is 0.20 percentage point larger in Kenya than in Tunisia. Similarly, the regression predicts a 0.33 percentage point larger average absolute deviation in Colombia than in Chile (0.17 from voice and accountability and 0.16 from statistical capacity). The actual absolute average deviation between official and nighttime light-adjusted GDP growth is indeed larger in Colombia than in Chile, but at 0.62 percentage point the difference between the two countries is even larger than the regression suggests.

Column (2) allows a different impact in normal times and during the COVID-19 pandemic. It confirms that the results from column (1) hold in normal times and that voice and accountability had an additional, large impact during the pandemic. The results in column (2) also show that countries with larger industrial and service sectors exhibited larger differences between official and nighttime light-adjusted GDP growth during the pandemic.

23
We next analyze periods of under- and overestimation separately. While statistical capacity reduces both, voice and accountability only reduces overestimation. The nighttime light-adjusted measure suggests a smaller decline in economic activity than reported in the national accounts for countries with a higher share of value added by industry and especially services (and a lower share of value added by agriculture). COVID-19 hit economies with a large service sector especially hard, because the sector relies heavily on human-to-human contact and it was partially shut down to prevent the transmission of the virus. Table I.1 in the appendix shows that both reported as well as nighttime light-adjusted GDP growth during the pandemic declined more with higher shares of services. However, the deviations between the two measures suggest that these countries may have overestimated the impact of COVID-19 (and hence underestimated GDP growth more).

It might seem that the result could reflect a different elasticity of value added in manufacturing and services compared with agriculture. However, we showed in table 5 that the elasticity between countries with above and below median agriculture is nearly the same. Moreover, the elasticity was higher for countries with an above-median share of services, suggesting that a possible bias would not weaken but strengthen the finding.<sup>24</sup>

# **7 Heterogeneous Subnational COVID-19 Impacts**

With our estimated elasticity, we can quantify different impacts of COVID-19 at the subnational level. Subnational data on economic activity are not often available for EMDEs, especially not at quarterly frequency. Nighttime lights provide an alternative way of measuring spatially disaggregated economic activity (see Section 5). Our elasticity estimate from Section 5.2 allows us to translate changes in nighttime lights into changes in economic activity.

We regress regional changes in nighttime lights at quarterly frequency on population density and a region’s average nighttime lights per capita, which is a proxy for its level of development. We estimate the following regression model:

> 24To make the argument work would require arguing that the elasticity between nighttime lights and value added in industry and services declined much less (or increased much more) than the elasticity between nighttime lights and value added in agriculture. However, we are not aware of any reasons to think that this happened.

24
Table 8: Difference between New and Official Growth Measures

||Absolute|diference|Underes|timation|Overest|imation|
|---|---|---|---|---|---|---|
||(1)|(2)|(3)|(4)|(5)|(6)|
||||difere|nce_>_0|difere|nce_<_0|
|Voice and accountability|-0.18***|-0.11**|-0.083|-0.094|0.30***|0.12*|
||(0.053)|(0.043)|(0.079)|(0.083)|(0.11)|(0.061)|
|Statistical capacity|-0.014***|-0.017***|-0.017***|-0.018***|0.0099*|0.015***|
||(0.0034)|(0.0030)|(0.0037)|(0.0040)|(0.0049)|(0.0044)|
|Voice and accountability _×_ COVID||-0.56***||-0.11||0.96***|
|||(0.13)||(0.29)||(0.31)|
|Statistical capacity _×_ COVID||0.016||0.013||-0.032|
|||(0.016)||(0.012)||(0.020)|
|Agriculture share _×_ COVID||0.020||-0.0054||-0.0053|
|||(0.014)||(0.035)||(0.029)|
|Industry share _×_ COVID||0.032***||0.067**||0.010|
|||(0.012)||(0.029)||(0.011)|
|Service share _×_ COVID||0.074***||0.12**||0.015|
|||(0.024)||(0.046)||(0.017)|
|Constant|2.11***|2.01***|2.73**|2.76**|-1.60*|-1.94**|
||(0.61)|(0.53)|(1.22)|(1.14)|(0.85)|(0.75)|
|Date fxed efects|Yes|Yes|Yes|Yes|Yes|Yes|
|Controls|Yes|Yes|Yes|Yes|Yes|Yes|
|Obs|1965|1965|887|887|1078|1078|
|Adjusted _R_<sup>2</sup>|0.11|0.12|0.100|0.11|0.14|0.18|
|Number of countries|76|76|76|76|76|76|

_Note_ . The sample includes 76 EMDEs between 2013Q2 and 2020Q4. COVID is a time dummy that equals 1 between 2020Q1 and 2020Q4 and 0 otherwise. Throughout, standard errors are in parentheses. _∗p <_ 0 _._ 10, _∗∗ ∗∗∗ p <_ 0 _._ 05, _p <_ 0 _._ 01.

where _zk,i,t_ is year-on-year nighttime light growth in region _k_ in country _i_ at time _t_ . **_x_** _k,i_ is a row vector of average nighttime lights per capita and population density.<sup>25</sup> **1** _{t∈_ COVID _}_ is a time dummy indicating the COVID-19 period. _αi_ are country fixed effects and _δt_ are time fixed effects. _ξk,i,t_ is the residual term. **_β_**<sup>_sub_</sup> 0 and **_β_**<sup>_sub_</sup> 1 are column vectors of<sup>26</sup> Column (1) in table 9 shows that higher average nighttime lights per capita are associated with faster growth of nighttime lights over the estimation period. This suggests that regions within countries diverged and spatial inequality rose. The result strengthens when we control for the COVID-19 period (see column (2)) because more

> 25Neither is time-varying as we use the average for nighttime lights per capita and population density in 2015. Both are in logs.

> 26A table of summary statistics is included in appendix J.

25
developed regions experienced larger declines in nighttime light intensity during the pandemic. Next, we add population density, which is positively related with the level of development and negatively associated with nighttime light growth during COVID19.<sup>27</sup> Column (3) shows that more populated regions indeed experienced a much larger decline in nighttime lights with the effect being statistically significant at the 1 percent level. A 10 percent higher population density is associated with 1.2 percent lower nighttime light growth.<sup>28</sup> Using an elasticity of 1.55, this is equivalent to 0.77 percent of GDP. The inclusion of population density makes the negative relationship between the level of development and the impact of the pandemic statistically significant at the 1 percent level. During COVID-19, wealthy regions had more options for remote working and therefore might have weathered the impact of COVID-19 better. Ten percent higher average nighttime lights per capita is associated with 0.77 percentage point lower quarterly growth.

Comparing a few regions shows that these results are plausible. For example, the regression results predict that Phuket darkened more during COVID-19 than Loei (two regions in Thailand), since the former is more developed (nighttime lights per capita are nearly three times as high) and more densely populated (population density is seven times higher).<sup>29</sup> The regression result predicts a 36 percentage point larger decline in nighttime lights in Phuket compared with Loei (12 percentage points for the level of development and 24 percentage points for population density), and indeed, nighttime lights declined by an additional 32 percentage points in the second quarter of 2020. Similarly, the regression results predict that Greater Poland darkened less during COVID-19 than Lesser Poland. While the former is somewhat more developed (by 15.3 percent based on official estimates of GDP per capita and by 21.6 percent based on nighttime lights per capita), the latter has a much higher population density (46 percent higher). Based on the former, we expect nighttime lights in Greater Poland to decline somewhat more (by 2.5 percentage points). However, based on the latter, we expect them to decline much less (by 7.3 percentage points). The net effect of the predicted 4.8 percentage points lower decline in Greater Poland is close to the actual difference of 3.0 percentage points in the second quarter of 2020.

We conduct two robustness checks to see whether the results hold if we control for

> 27See figure K.1 in the appendix.

> 28A 10 percent higher population density is about 0.1 in log difference. Multiplied by -11.9, which is the coefficient of the interaction term between population density and COVID-19 in column (3), this implies -1.19 percent in nighttime light growth.

> 29According to official statistics, GDP per capita in Phuket is 3.6 times as large as in Loei, very much in line with the 2.8 times higher nighttime lights per capita.

26
the 2017Q1 sensor recalibration (see section 4). First, we include a dummy for the period before the recalibration and column (4) shows that the results remain nearly unchanged. Next, we exclude all observations before the recalibration and even then, the changes are minimal and all conclusions hold. We also checked whether controlling for emissions per capita changes the findings, but they are not statistically significant even at the 10 percent level and have no impact on the other results.

Table 9: Differentiated Impact of COVID-19 at the Subnational Level

|||Night|time light gr|owth||
|---|---|---|---|---|---|
||(1)|(2)|(3)|(4)|(5)|
|Avg. nighttime light per capita|0.47*|0.78*|0.20|0.31|-0.40|
||(0.27)|(0.40)|(0.32)|(0.33)|(0.57)|
|Avg. nighttime light per capita _×_ COVID||-1.71|-11.7***|-12.2***|-11.9***|
|||(1.61)|(1.36)|(1.45)|(1.57)|
|Population density|||0.31|0.35|0.15|
||||(0.21)|(0.22)|(0.34)|
|Population density _×_ COVID|||-11.9***|-12.2***|-12.1***|
||||(0.83)|(0.89)|(0.98)|
|Constant|8.77***|8.84***|0.63|0.70|-4.78***|
||(0.88)|(0.89)|(0.91)|(0.90)|(1.12)|
|Country fxed efects|Yes|Yes|Yes|-|Yes|
|Date fxed efects|Yes|Yes|Yes|Yes|Yes|
|2017Q1 adjustment|-|-|-|Yes|-|
|Starting period|full sample|full sample|full sample|Full sample|_≥_2017Q1|
|Obs|39176|39176|39176|39176|23301|
|Adjusted _R_<sup>2</sup>|0.27|0.27|0.32|0.33|0.41|

_Note_ . The sample includes 2165 first administrative regions of 116 EMDEs between 2020Q1 and 2020Q4. Nighttime light growth is in percent. Both average nighttime light per capita and population density are in logs. Throughout, country and date fixed effects are included. Standard errors are clustered at the country level and in parentheses.<sup>_∗_</sup> _p <_ 0 _._ 10,<sup>_∗∗_</sup> _p <_ 0 _._ 05,<sup>_∗∗∗_</sup> _p <_ 0 _._ 01.

# **8 Conclusion**

Annual DMSP nighttime light data have already contributed greatly to deepening our economic understanding (Donaldson and Storeygard, 2016). With the availability of monthly VIIRS data at an even finer spatial grid and with greatly improved measurement of low-light areas, nighttime lights are becoming an even more important source of information.

In this paper, we initially provided some stylized facts about global VIIRS nighttime light data at quarterly frequency. We documented the need to consider a few technical details when aggregating the data at the country level, including its ge27
ographic coverage, the extent of low-lit areas, and sensor recalibrations. Temporal variations unrelated to economic activity give rise to large noise in nighttime light data, but year fixed effects in regression analyses can control for such noise if it is common across countries. We found that the quarterly correlation between VIIRS nighttime light growth and GDP growth is stronger for EMDEs than for advanced economies.

Different from annual DMSP nighttime light data, monthly VIIRS nighttime light data can be used to study economic short-term impacts of different shocks. Efforts in this direction are already leading to very interesting new insights. Among others, studies have looked into the impact natural disasters like the 2017 earthquakes in Nepal (Beyer, Chhabra, Galdo, and Rama, 2018), domestic policy measures like the demonetization in India (Chodorow-Reich, Gopinath, Mishra, and Narayanan, 2020) or lockdown measures during the COVID-19 pandemic (Beyer, Jain, and Sinha, 2020), and trade shocks like the recent tariff war between China and the United States (Chor and Li, 2021). Other possible applications are too numerous to list. For all of them, it is necessary to translate changes in nighttime lights measured in nanowatts into changes in economic activity measured in US dollars (or any other currency).

In this paper, we presented a novel framework to estimate the elasticity between nighttime lights and GDP, which is fundamental for this translation. Our framework uses varying degrees of measurement errors in nighttime light data across countries to identify the elasticity. We estimate it to be 1.55 for EMDEs and find only small differences across model specifications and country groups. This elasticity can now be used to translate changes in nighttime lights into changes in economic activity. For example, if the economic impact of a shock is studied with a difference-in-differences approach, 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.<sup>30</sup> We concluded the paper with two applications. First, we constructed a nighttime light-adjusted measure of GDP growth and showed that more developed countries and those with higher statistical capacity tend to have smaller measurement errors in their national accounts. Widespread efforts to strengthen statistical offices and systems in EMDEs are hence indeed likely to contribute to better economic measurement. However, we also found that low voice and accountability results in higher overestimation of GDP growth, highlighting a crucial role for public scrutiny in ensuring proper measurement. A proper debate about GDP growth in academia, think tanks, and the media is

> 30To translate changes in nighttime lights to changes in GDP, the inverse elasticity, that is 1 _/β_ , needs to be used.

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hence important for credible GDP data. Second, we assessed the economic impact of the COVID-19 pandemic and showed that regions with higher levels of development and population density experienced larger declines in economic activity.

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