temperature metrics perform the best. Based on R<sup>2</sup> and _p_ -values, mean and median daily temperature appear to be the best predictors of outcomes across many different cases. However, neither do particularly well in being consistently positively or negatively correlated with outcomes. Coefficients on both variables are as likely to be associated with better outcomes as worse outcomes. The different signs do not appear to be more or less likely in one country over another, suggesting the reason for the inconsistency is measurement error and not aggregation over regions, countries, or crops. While not as strong as mean or median in explaining variance in outcomes or correlating with outcomes, coefficients on variance of daily temperature are consistently negative, making it among our preferred measure for temperature. Somewhat surprisingly, given its frequency of use in the economics literature, GDD and deviations from GDD are poor metrics for temperature as measured by our heuristics. While GDD may be appropriate for predicting crop yields in temperate climates such as the United States, it appears to be a poor choice for use in the tropical regions of Sub-Saharan Africa.

Based on this evidence, we proceed to analyze measurement error in remote sensing products focusing on four rainfall metrics and three temperature metrics. These are mean rainfall, total rainfall, number of rainy days, share of rainy days, mean temperature, median temperature, and variance of temperature. Without additional evidence, these appear to be the best metrics for measuring precipitation and temperature. When researchers are considering how to include precipitation or temperature in their economic analysis (at least in Sub-Saharan Africa), we recommend they use one or more of the above seven metrics.<sup>22</sup> The choice of a different weather metric should be accompanied by a theoretical or agronomic justification and likely warrant robustness checks to ensure results are not driven by the choice of any one specific weather metric.

# **4.3 Remote Sensing Products**

By narrowing in on a single extraction method and a subset of weather metrics that are correlated with outcomes, we can better investigate which remote sensing products mismeasure precipitation and temperature. Specifically, we want to examine the evidence around Hypothesis 3 ( _H_ 0<sup>3- different</sup> measurement technologies for precipitation and temperature have the same impact on estimates of agricultural productivity). As noted previously, mismeasurement in the objective fact of precipitation and temperature may be introduced by inaccuracies in the sensor (e.g. infrared, microwave, optical), the algorithm used to convert sensor data into rainfall or temperature (e.g. reanalysis, interpolation), or the resolution of the data (e.g. spatial, temporal). Our null hypothesis rests on the assumption that these inaccuracies either do not exist (that all remote sensing products accurately report the objective facts) or that any mismeasurement is insubstantial and will not impact the analysis. The alternative hypothesis is that there is substantial mismeasurement in remote sensing weather data, as Figures 1 and 2 seem to imply. If the alternative is true, then care must be taken

> 22See Appendix F for an exploration of linear combinations of rainfall and temperature metrics.

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