sensing products mismeasure precipitation and temperature.

# **4.1 Extraction Method**

We begin by examining extraction method, following Hypothesis 1 ( _H_ 0<sup>1-differentobfuscation</sup> procedures implemented to preserve privacy of farms or households have no impact on estimates of agricultural productivity). Our null hypothesis rests on two assumptions. First, existing publicly available remote sensing weather products are too coarse a resolution for any of the extraction methods to make a substantial difference in which pixel a household ends up in. Second, even if the obfuscation technique moves a household location from one pixel to another, weather is sufficiently spatially correlated that the shift will not matter. The alternative hypothesis is that obfuscating a household’s true GPS coordinates introduces substantial mismeasurement resulting in researchers matching the obfuscated coordinates with gridded remote sensing data that does not accurately reflect the true weather experienced by the household.

To test Hypothesis 1, we pool the results from the 77,760 regressions (those that do not include linear combinations) and then divide the pool into ten bins, one for each extraction method. We then calculate descriptive statistics for each bin of results. These include the mean adjusted R<sup>2</sup> value and the share of coefficients ( _β_ 1) with _p_ -values of _p >_ 0 _._ 90 _, p >_ 0 _._ 95 or _p >_ 0 _._ 99. For each of these values, we calculate the 95% confidence interval on the mean.<sup>12</sup> We then compare mean adjusted R<sup>2</sup> values or the share of _p >_ 0 _._ 95s across all ten extraction methods and use the 95% confidence interval on the mean to evaluate differences using our weak and strong test criteria. This allows us in turn to make a determination about our Hypothesis: if the preponderance of evidence is such that we see no differences in our heuristics, then we fail to reject the null and conclude that obfuscation of household GPS coordinates does not introduce substantial mismeasurement into the analysis. Alternatively, if the preponderance of evidence is such that our heuristics are either weakly or strongly different, then we reject the null and conclude that obfuscation does introduce measurement error into the analysis.

## **4.1.1 Adjusted R**<sup>2</sup>

We use a specification chart to examine adjusted R<sup>2</sup> values across the ten types of extraction method. Figure 8 shows the mean adjusted R<sup>2</sup> and the 95% confidence interval on the mean by extraction method. We further disaggregate results by model specification, since a model with covariates or fixed effects will have a different adjusted R<sup>2</sup> value than a model without covariates or fixed effects. The northwest panel of Figure 8 displays results from model specifications (2a) and (3a), which are the linear and quadratic models without covariates and without household

> 12 We also create graphs which examine the differences in coefficients ( _β_ 1) and their relative significance by extraction method. For parsimony, as these do not reveal any further information, they are presented in the Appendix, Figure C1 through Figure C6.

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