<h3 id="Aggregation-before-transformation">Aggregation-before-transformation<a class="anchor-link" href="#Aggregation-before-transformation"> </a></h3><p>When an economic process is occurring at the county level, we need to first do the weather variable aggregation at the county level. We do the weather variable transformation after we have aggregated it to the county level using weighted averaging method, and then run our estimation on the county level data. For example, to estimate the effect of storm events on public service employment at the administrative block level, we need to take into account the fact that hiring/firing of public service employees happens at the block level only. Estimating grid-level effects will lead to wrong estimation, as it would result in zero estimate for those (almost all) grid cells which do not have the block office coordinates, and extremely large values for those (very few) cells, which comprise of the block office coordinates. The mathematical formulation for aggregation-before-transformation can be learned through transformation-before-aggregation formulation described above, with a change that the aggregation step precedes the transformation step. Weather data products can have temporal resolution finer than scale of daily observations. Like spatial aggregation, we can do temporal aggregation to month, year, or decade; however, unlike spatial aggregation, the averaging process is standard in all general cases.</p>
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