There is a picture of the Korean peninsula at night, with the South full of light and the North almost black. I have used it many times when someone asked whether satellite lights can measure an economy. It always worked in conversation. This year night lights came up again in economics. Luis Martinez published a paper that uses them to check how much autocracies inflate their GDP growth. I realized I had never looked at the numbers behind the picture. I only knew that lights and money go together. How well they go together I did not know.
So I took a place where the official numbers are good and checked the lights against them. On December 8 BEA published GDP by county for 2021. Others did this before me. Henderson, Storeygard and Weil built the method on countries in 2012. John Gibson did almost exactly this comparison for US counties in 2021, in a paper with his coauthor in Remote Sensing. I read their abstract and wanted to see the rest with my own eyes.
The data
The lights are the annual VIIRS composites from the Colorado School of Mines, VNL version 2.1. It is the masked average radiance, with background and short lived lights like fires removed. The grid is 15 arc seconds, about 500 metres. For every county I summed the radiance over all its pixels, weighted by pixel area, since pixels get smaller towards the north. GDP is the BEA release from December 8, real GDP by county in chained 2012 dollars. Virginia reports some independent cities together with their counties, so I merged those shapes the same way. That leaves 3080 units in the 48 states and DC. Alaska and Hawaii I did not cut from the raster.
Before counting I wrote down what I expected. Levels will match well, a correlation of 0.8 or more. Growth will match weakly, under 0.3. Year to year changes will be close to noise. And in 2020 the lights will fall less than GDP or not at all, because people stayed home with the lights on.
Levels
For 2019 the correlation between log light and log GDP over 3080 counties is 0.92. The slope is 1.03, so 10% more light goes with about 10% more GDP. In 2013 and 2021 it is the same. In the middle 80% of counties GDP per unit of light differs about 4 times.
The pair at the extremes is what I would put in a talk instead of Korea. Manhattan produced $641 billion in 2019. McKenzie County in North Dakota produced $4.9 billion. McKenzie gives off 17 times more light in total, but it is also 120 times larger, so per square kilometre it is darker. Per dollar of GDP the difference is about 2300 times. McKenzie sits in the middle of the Bakken oil field. I assume most of that light is gas flares and lit drilling pads, but I did not separate them in the image.
The 124 counties where mining is more than 30% of GDP make 1.1% of the GDP in my sample in current dollars and 7.8% of the light. Not every mining county glows: the median one has about the same GDP per unit of light as an ordinary county. The light comes from a few giants in the Bakken and the Permian basin.
Growth
Between 2013 and 2019 the correlation between the change in light and the change in GDP is 0.33, slightly above what I expected. Then I removed those 124 mining counties and it fell to 0.12. Most of the growth signal came from oil fields, where a boom means more flares and more money at the same time. In an ordinary county the light went up or down mostly on its own, at least at this scale.
A simpler test says the same. Whether a county grew faster than the median county, by light and by GDP, agreed in 54% of counties, a coin with a small bias. Year to year it is worse. For each pair of neighbouring years the correlation stays between −0.02 and 0.15.
Adding counties into states did not help me. Over 49 states the growth correlation is 0.10, while the levels still give 0.81. I expected the noise to average out at the state level but it did not.
Where I was wrong about the series
Then I summed the light over the whole country. It fell for 3 years while GDP grew.
From 2013 to 2016 the total fell by 9.5%, while GDP grew by 7%. In 2017 it jumped almost back. 95.6% of counties became brighter in one year, with the median county up by 19%.
My first explanation was oil. Prices collapsed from mid 2014 to early 2016 and the 4 biggest Bakken counties lost about 38% of their light between 2014 and 2016. It fit nicely, so I checked it. It was wrong. Mining counties explain less than 5% of the national drop to 2016. The dashed line without them falls just as deep. Between 2013 and 2016 the light went down in 45 of 49 states. Among them were Vermont and Maryland, which have no oil at all. I do not know what caused it. It could be the processing of the composites or the sensor. I doubt any economy makes 95.6% of counties brighter in one year.
This also changed how I read 2020. Light fell by 4.2% and GDP by 2.8%, so the lights fell more than GDP, the opposite of what I expected. But 63% of that drop came from the mining counties, mostly the oil fields of Texas and North Dakota. There the light probably fell with flaring, when the oil price fell. Without them light fell by 1.7% and GDP by 2.8%. That is my expectation again, for ordinary counties. The median county was even 1.9% brighter in 2020, while Manhattan lost 8% of its light. But the same series fell by 9.5% to 2016 with no recession at all. A difference of one percentage point in it does not prove much.
What it gives me
Lights tell which county is big quite well. For growth they mostly worked in oil counties, where the boom itself is visible as flares. For a country without honest statistics a level is still better than nothing. The Korean picture shows levels, but I used it in arguments about growth.
What I did not check
I did not compare my numbers with the tables of the Gibson paper. BEA revises county GDP every year, so the next release will move single numbers. The raster I summed stores radiance rounded to whole units, so pixels fainter than half a unit are zero. How much light rural counties lose this way I did not check.
Gas flares stay in, although Colorado School of Mines publishes a separate flare catalogue. Population and area are not controlled for. The growth correlations are computed across counties, so a jump shared by all counties does not move them. Other units I did not try either. Cities or 10 km cells could behave differently from counties, whose borders were drawn long before anyone measured light.
2022 is not in the comparison, because its annual composite and its county GDP are not published yet.