“The Difference-of-Log-Normals Distribution is Fundamental in Nature” [PDF]
I describe a hitherto obscure statistical distribution – the Difference-of-Log-Normals – and make the case that it is a fundamental distribution in nature. I show how it arises from first principles, and why it describes a plethora of natural phenomena, such as population growth in standard birth-death models; firm income, growth, and equity returns; city growth; etc. I present implications for the functional form of neo-classical production functions.
“The Difference-of-Log-Normals Distribution: Properties, Estimation, and Growth” [PDF]
This paper describes the Difference-of-Log-Normals (DLN) distribution. Parham (2022) makes the case that the DLN is a fundamental distribution in nature, and shows how a simple application of the CLT gives rise to the DLN. Here, I characterize its PDF, CDF, moments, and parameter estimators; describe methods to deal with its signature “double-exponential” nature; and use it to generalize growth measurement to possibly-negative variates distributing DLN. I also conduct Monte-Carlo experiments to establish some properties of the estimators and measures described.
“Facts of US Firm Scale and Growth 1970-2019: An Illustrated Guide” [PDF]
This work analyzes data on all public US firms in the 50 year period 1970-2019, and presents stylized facts of their scale, income, growth, return, investment, and dynamism. Special attention is given to (i) identifying distributional forms; and (ii) scale effects – systematic difference between firms based on their scale of operations. The Difference-of-Log-Normals (DLN) distribution has a central role in describing heavy-tailed firm data, and scale effects are rampant.