Problems with the kdensity function

[Memetteoman]

I am using firm-level data over 2015-21 to identify and analyse high-growth firms. When I draw a kernel density function with data on firm growth rates (firm growth distribution), the values on the vertical exis (density function) are comprised between 0 and 4. I know that what is important is that the area under the kernel function equals 1 . But I would like to obtain values on the vertical axis that are less than 1 (that is what several papers published on the same issue obtain). How should I write the kdensity command to achieve this end? Thank you

[Nick Cox]

You can't change the rules governing probability densities which as you imply are that densities are non-negative and integrate to 1 over the support of a variable. Those rules allow density estimates above 1 whenever as in your case probability densities are not themselves probabilities. A simple example is that a variable uniformly distributed between 0 and 1 must have density of 1; if we halved the variable to range between 0 and 0.5 the density would automatically change to 2.

Papers with "densities" modified to be below 1 always may be correct for their data but necessarily not otherwise.

If you get flak on this from reviewers or editors, you are on solid ground fighting back or just taking your submission to a journal with higher standards.

[Memetteoman]

Dear Nick, thank you so much for the clarification.