the NBS,<sup>29</sup> and allow for region-specific optimal weights _λ_ . We find that the variation of the estimate of _λ_ is quite small, ranging from 0.576 to 0.594. Finally, the derived measure of over-reporting is winsorized at the 0.1th and 99.9th percentiles. See Appendix C for how we apply the modified version of Henderson, Storeygard, and Weil (2012) to our analysis of GDP manipulation of Chinese cities.<sup>30</sup> Figure 3 displays the relationship between ln(GDP) and ln(Lights) net of city and year FEs across the eight economic regions. A linear specification in the lights growth appears to be adequate. For all the regions except Northwest, real GDP’s elasticity with respect to nighttime lights is positive and statistically significant, ranging from 0.046 to 0.191. The adjusted _R_<sup>_2_</sup> indicates that the light intensity and city and year FEs explain more than 99.5% of the variation in official real GDP. The regional distribution of the estimated over-reporting of GDP growth ranges from -6.2 to 7.2 percentage points, with a standard deviation of 1.4 percentage points (Table 1).<sup>31</sup> By construction, our measure of over-reporting centers around zero, and can take both positive and negative values.<sup>32</sup> As a result, our measure of GDP manipulation should be viewed as capturing the extent of manipulation only in relative terms. If all the cities manipulate their growth rates upward, the slope will become steeper whereas cities lying on the fitted line will still get a zero over-reporting. In this sense, cities lying above (below) the fitted line are thus predicted to have more (less) overreporting than those lying on the fitted line. Therefore, while negative values of our measure could indicate under-reporting in some cases (especially when the magnitude is large), we should not take the negative sign literally as under-reporting.

To gain intuition for whether our measure is an appropriate proxy of the extent of manipulation, we link it with cities’ annual growth targets, typically set at the beginning of the year. We expect that cities that have achieved the yearly target (i.e., reported growth more than the target growth) are more likely to exaggerate their growth figures compared to those that have failed to do so—the former group should have more manipulators than the latter group. Figure 4 plots the distribution of our manipulation measure for these two groups. Indeed, the distribution of the target-reaching group (solid line) lies to the right of the distribution of the target-failing group (dashed line). In fact, nearly 60% of cities in the

> 29 The eight economic regions are: Northeast, North Coast, Eastern Coast, Middle Yellow River, Middle Yangtze River, Southwest, Northwest, and South Coast.

> 30 Gibson et al. (2021) show that the performance of DMSP data in predicting GDP is worse for lower-level spatial units, for lower density areas, and for smaller areas. Given the size and population density of Chinese cities, their results suggest our use of DMSP data to predict city-level GDP growth is appropriate and relatively accurate. 31 In robustness checks, we also use more sophisticated specifications (e.g., province-specific slopes or a quadratic specification) and add more controls when predicting GDP growth in Eq. (1), such as electricity consumption, bank loans and freight volume. However, we do not incorporate these into the baseline regression Eq. (1) since the current specification already explains more than 99.5% of variation in official real GDP. Including more terms leads to overfitting, which will make the light-predicted real GDP growth very close to officially reported one, resulting in the loss of useful information in nighttime lights.

> 32 It is essentially the first-differenced residuals from Eq. (1) multiplied by a constant between 0 and 1.

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