significant, indicating data manipulation. However, lights are evidently not robust to different samples, which can obscure this result. For instance, Column 2 extends the time sample through 2013, which is the end of the DMSP-OLS sample. In this case, the interaction has a gradient of zero. And, when we change the sample to 2005-2020 in Column 3 using VIIRS data, the sample we use in our baseline results, the gradient becomes negative. One possibility is that this spurious result is in some way due to the inclusion of the 2020 downturn. For example, it has been speculated is that manipulation is more likely to occur during recessions in China (Wallace, 2016). In Column 4, we investigate this possibility by including an interaction dummy for whether the year is 2009 or 2020, which we designate a crisis, and find no difference.

The results change, however, when we use NO2 as the signal of economic activity instead of lights. In Column 5, we re-estimate the same specification used in Column 3 through 2020, simply replacing lights with NO2. Again, a positive interaction appears, indicative of data manipulation previously seen in lights over 1992-2008. Moreover, in Column 6, we see that there is statistically significant evidence of misreporting during crisis years specifically, consistent with theory. Thus, using NO2 has measurable benefits in global applications.

**Trend Economic Growth.** Despite these findings supporting NO2, night lights are highly complementary, and applicable in different contexts. In Online Appendix B.2, we repeat the analysis described in Tables 2, 3, and 4, but removing country-specific time trend controls. Thus, predictive power for trend economic growth is now under consideration. One difference is that the overall explanatory power of night lights remains, regardless of what additional signals are available. Moreover, examining the differences by-grade, we find that lights now explain trend growth not only in grade D and E nations, but C as well. Finally, it is unclear how to interpret NO2-based estimates in either case, given the known differences in trends across nations that are omitted; perhaps as a result, the explanatory power of NO2 falls. Finally, we also find that there is lights-based evidence of data manipulation over 2005-2020 in terms of trend economic growth, and measurable differences in crisis years. Thus, in studies of economic growth in developing nations, lights are preferable. But in studies of global cyclical economic activity like ours, NO2 is preferable, and upon it we base the remaining analysis.

# **5.2 Identifying the Growth Elasticity of NO** 2

We are interested in annual fluctuations. Given that NO2 is a preferable signal for this purpose, we now wish to construct a composite estimate of economic activity using it, specifically. In order to do so, we need to estimate the growth elasticity of NO2, previously denoted _β_ (Equation 2). As previously discussed, to retrieve this from a regression of log NO2 ( _x_ ) on log GDP ( _z_ ), we need an instrument which is correlated with true output, but which has measurement errors uncorrelated with both GDP and NO2. Since Table 2 Columns 2-5 can be interpreted as the 19