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Urban Start-up Agglomeration and Venture Capital Investment (view source)
Revision as of 19:59, 1 December 2020
, 19:59, 1 December 2020→Formalizing Jim's Notes
The concavity measure in col6 is therefore the -1 times central first difference divided by the central second difference, but the central first isn't computable for a step of 1 (and gives a weird answer anyway, as it straddles the observation in question). The central second difference isn't defined for either the first or last layer, and the backward first difference isn't defined for the first layer. It seems likely that we don't want the last layer and might get it because D1 is small and drives the ratio.
We could instead use the forward first difference - this isn't available for the last observation (for which we can't compute a second central anyway) but is available for the first observation - and increment the answer, much as Jim proposes decrementing it when using the backward layer. But seeing as we can't use the first observation we've gained nothing anyway! So we'll do Jim's method verbatim, and declare the result null if it comes out as either the first or last layer.
{{Colored box|title=Specification|content=For layer <math>l</math>, I will compute the concavity as -1 times the backward first difference from layer <math>l+1</math> divided by the central second difference from <math>l</math>. The first and last layers are forbidden results.}}
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