3. _H_ 0<sup>3-differentmeasurementtechnologiesforprecipitationandtemperaturehavethesame</sup> impact on estimates of agricultural productivity.

To test the first hypothesis, we extract remote sensing weather data for LSMS-ISA survey locations using ten different combinations of spatial feature and extraction method. The spatial features represent different obfuscation techniques (aggregation and displacement) and extraction methods (simple, bilinear, and zonal statistics) represent different approaches to dealing with both coarse spatial resolution and uncertainty in location. These data are then combined with household-level data on agricultural production. Following the model specification of Deschˆene and Greenstone (2007), we then estimate agricultural yield functions. This allows us to test if there are differences in the predicted effect of a weather metric on yield across the different obfuscation procedures. Similarly, to test the second hypothesis, we calculate 22 different weather metrics that are commonly used in the economics literature. For rainfall, these include, but are not limited to, mean daily rainfall, total seasonal rainfall, deviations from the long-run average of seasonal rainfall, and the longest intra-season dry spell. For temperature, these include, but are not limited to, measurements such as mean daily temperature, GDD, and long-run deviations in GDD. By testing each of these weather metrics individually and in combination with each other, we can determine which measure of rainfall or temperature is a consistent predictor of yields. And, by extension, which have poor predictive power or are predictive for only a certain crop or in a certain country. Finally, to test the third hypothesis, we conduct all of the above analysis on data from six different remote sensing precipitation data sets and three different remote sensing temperature data sets. This allows us to see if all data sources provide essentially the same results, or if results vary by data source. All told, we run more than 129,600 regressions to identify which weather metrics have strong predictive power over a large set of crops, countries, obfuscation methods, and data sources.

While our approach allows us to compare various combinations of obfuscation or metric or source to another, it does not allow us to compare any combination to the objective fact that a data source is trying to measure. This is because there is no data source that records the objective fact for the households in our data set - or in most data sets used by economists. Unlike with studies that seek to define mismeasurement in land area, harvest, or seed variety planted, we are unable to measure the objective fact of precipitation and temperature. The equivalent to GPS traces of a plot, crop cutting of harvest, or DNA fingerprinting of seed would, in our case, be a rain gauge and thermometer at every household with data recorded daily. While it is clearly technically feasible to collect this sort of data, it is highly atypical data for collection as part of economic research. Hence the reason why economists have come to rely on remote sensing weather data.

As we lack a record of the objective facts of precipitation and temperature for each household, all of our comparisons of mismeasurement are comparisons of one obfuscation/metric/source combination to another. In order to make these comparisons meaningful, we adopt the prior that both rainfall and temperature have a significant impact on crop production. Some metrics, such 5