fixed effects. The northeast panel displays results from model specifications (2b) and (3b), which include household fixed effects, but not covariates. The southwest panel displays results from model specifications (2c) and (3c), which include fixed effects and covariates. At the top of each “column” in the specification chart is the mean adjusted R<sup>2</sup> and the 95% confidence interval on the mean for the set of 1,296 regressions run. Below, the chart indicates the extraction method and model specification associated with the statistics.

Considering first the northwest panel: mean adjusted R<sup>2</sup> values are not substantially different across extraction method within model specifications (2a). The mean adjusted R<sup>2</sup> value for any one extraction method passes neither our weak nor strong difference test when compared to any of the other extraction methods. Similarly, when comparing across extraction method within model specification (3a), no mean adjusted R<sup>2</sup> is weakly or strongly different from any other. Though not a formal statistical test, our heuristic fails to reject the null for these two model specifications.

We conduct the same exercise for results from the extraction methods and model specifications presented in the northeast and southwest panels. As with the first panel, the mean adjusted R<sup>2</sup> value for any one extraction method is neither weakly nor strongly different than any other method. Our heuristic fails to reject the null for any model specification. Based on this, we conclude that remote sensing weather data from any one extraction method does not explain a substantially larger amount of the variance in our outcome variables relative to any other extraction method.

Despite the failure to reject the null based on either the strong or weak criteria, the pattern of which extraction methods result in the largest adjusted R<sup>2</sup> values is remarkably consistent. Bilinear extraction methods for household coordinates, EA centerpoint, and modified EA centerpoint always make up three of the top four models. Recall that the bilinear method computes the distance weighted average of values at the four nearest cell centers. Thus, unlike the simple extraction method, the bilinear method accounts for the point location within the arbitrary cell boundaries of the gridded data product. This approach seems to produce better results than the simple extraction method or the zonal means for small areas (households or EAs). Administrative area appears to be too large of an area to produce strong results, as using Administrative area, regardless of extraction method (simple, bilinear, or zonal mean), tends to produce the smallest adjusted R<sup>2</sup> values. While the pattern is consistent, it should be remembered that differences between each extraction method is not substantial enough to pass even our weak test, and we fail to reject the null.

# **4.1.2** _p_ **-values**

Next, we consider if different extraction methods produce substantially different numbers of significant coefficients. Recall that our maintained assumption is that the weather metrics we examine are significantly correlated with the outcome variables as these weather metrics are commonly used in the literature for just such a purpose. While when examining adjusted R<sup>2</sup> values we disaggregated each bin of regression results by model specification, when examining _p_ -values we disaggregate by 22