product. And again, as with rainfall, coefficient ordering shifts across models. This is more evident with the smaller number of EO sources used in the temperature regressions. Most frequently, countries follow a trend of one set of ordering for the weather only model specification, which shifts to a different ordering for the models which include fixed effects. Consider, as an example, Niger in Figure 10: in the first panel ERA5 produces large negative and significant coefficients while MERRA-2 produces small coefficients that are either negative and significant or not significant. In the models with FE, MERRA-2 produces the largest negative coefficient while ERA5 produces the largest coefficient, now positive and significant. While we see that similar reorderings appear in other countries for other temperature metrics, the most striking element of the temperature results are that we see strong patterns in the specification charts for a couple countries, specifically Nigeria and Uganda. As we saw in the descriptive statistics, there is less variation in the temperatures that the different EO products report relative to the temperature products and thus less changes to the ordinality of coefficients.

Before moving to a closer examination of changes in ordinality in regression results, two other regularities in the specification charts bear commenting upon. First, for both rainfall and temperature, regardless of the EO product or the weather metric, weather becomes much less important in predicting agricultural productivity once household FEs are included. Over and over again, regressing output on just rainfall or temperature shows a significant relationship between the two. But once household FEs are included to control for time-invariant unobservables, the relationship goes away. Weather is a time varying phenomenon, often considered exogenous or as good as randomly determined. It is not immediately obvious why the inclusion of a time-invariant control destroys the relationship between weather and agricultural production. A likely reason, which we leave unexplored, is that weather in a given location does not vary that much over time. Thus, including household FEs, assuming a household does not move, is essentially a location FE. Once location is controlled for, weather varies very little year-to-year and small deviations from the time average in a location has little to no impact on agricultural production in the year. This raises questions about the use of weather as an instrument (as it is correlated with time-invariant household heterogeneity, specifically location) as well as the ability of economists to use weather to predict the effects of climate change (by definition, a slow process) on economic indicators.

A second regularity is that the sign on the weather coefficients can vary substantially. This is related to, but distinct from the ordinality issue. Within a single econometric specifications, rainfall from one EO product will be positively correlated with agricultural production while in rainfall from another product will be negatively correlated. Shifts in significance across specification can be the result of changes in relative size (cardinality). But what should raise concerns among applied economists is that in every country a researcher could produce whatever relationship they wanted between weather and the dependent variable by judiciously choosing the EO product, the weather metric, and the econometric specification. Essentially, a researcher using EO weather data has 19