“The Difference-of-Log-Normals Distribution is Fundamental in Nature” [PDF]

The growth of many natural and social phenomena including pandemics, firms, cities, and various economic indices, is known to be heavy-tailed. Most growth is modest, but we often observe explosive growth rates, such as firms doubling or halving in size within a short period. Neither a simple explanation nor a well-fitting distributional form for these growth phenomena is known. Here I show that a hitherto obscure statistical distribution — the Difference-of-Log-Normals (DLN) — describes a plethora of growth phenomena remarkably well, and discuss why it arises as a natural consequence of the Central Limit Theorem (CLT). The results demonstrate how growth phenomena subject to opposing random exponential forces are likely to distribute DLN. This provides both a framework for scientifically modeling these phenomena and a simple distributional form to be used when empirically modeling observed heavy-tailed growth. I hence posit that the DLN is a fundamental distribution in nature, in the sense that it emerges in many disparate natural phenomena, especially growth phenomena, similar to the repeated disparate emergence of the Normal and log-Normal distributions.

“The Difference-of-Log-Normals Distribution: Properties, Estimation, and Growth” [arXiv]

This paper describes the Difference-of-Log-Normals (DLN) distribution. A companion paper 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 in many disparate phenomena. Here, I characterize its PDF, CDF, moments, and parameter estimators; generalize it to N-dimensions using spherical distribution theory; 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” [arXiv]

This work analyzes data on all public US firms in the 50 year period 1970-2019, and presents 18 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. Notable findings are that the Difference-of-Log-Normals (DLN) distribution has a central role in describing firm data, scale-dependent heteroskedasticity is rampant, and small firms are systematically different from large firms.

“Why Are Firm Growth Distributions Heavy-tailed?” []

Coming soon.

“The Growth of Cities” []

Coming soon.

“Are Firms Really Investment Constrained? Evidence From Firm Scale” []

Coming soon.


“WSJ Category Kings – the Impact of Media Attention on Consumer and Mutual Fund Investment Decisions”, with Ron Kaniel, Journal of Financial Economics (2017), 123(2), 337-356 [SSRN]

We exploit a novel natural experiment to establish a causal relation between media attention and consumer investment behavior, independent of the conveyed information. Our findings indicate a 31 percent local average increase in quarterly capital flows into mutual funds mentioned in a prominent Wall Street Journal “Category Kings” ranking list, compared to those funds which just missed making the list. This flow increase is about 7 times larger than extra flows due to the well-documented performance-flow relation. Other funds in the same fund complex receive substantial extra flows as well, especially in smaller complexes. There is no increase in flows when the Wall Street Journal publishes similar lists absent the prominence of the Category Kings labeling. We show mutual fund managers react to the incentive created by the media effect in a strategic way predicted by theory, and present evidence for the existence of propagation mechanisms including increased fund complex advertising subsequent to having a Category King and increased efficacy of subsequent fund media mentions.

“Fitting the errors-in-variables model using high-order cumulants and moments”, with Timothy Erickson and Toni M. Whited, Stata Journal (2017), 17(1), 116-129 [PDF]

In this article, we consider a multiple mismeasured regressor errors-in-variables model. We present xtewreg, a command for using two-step generalized method of moments and minimum distance estimators that exploit overidentifying information contained in high-order cumulants or moments of the data. The command supports cumulant or moment estimation, internal support for the bootstrap with moment condition recentering, an arbitrary number of mismeasured regressors and perfectly measured regressors, and cumulants or moments up to an arbitrary degree. We also demonstrate how to use the estimators in the context of a corporate leverage regression.

Other Working Papers

“Knowledge Constraints and Firm Scale” [SSRN]

I propose a resolution to the high-returns-to-R&D puzzle. The R&D investments of small and medium firms (lower 2/3 of the firm scale distribution) exhibit evidence of bunching below an upper-bound. No such bunching exists for physical investment. I show that a constraint on knowledge accumulation rationalizes this pattern and resolves the R&D puzzle. Structural estimation indicates the constraint is binding for the 20%-25% highest growth R&D-performing small and medium firms. Counter-factual analysis shows slackening the constraint significantly increases firm growth rates and the total size of the economy. A validation test indicates the constraint is related to frictions in human-capital accumulation within firms.

“Revisiting Roll’s R2 Puzzle”, with Brent Kitchens and Chris Yung [SSRN]

We resolve Roll’s R2 puzzle. Before Reg FD, “news days” did not deliver news to the stock market. Now they do.

“Innovation, competition, and market structure – evidence from Bitcoin’s mining market“, with Einar Kjenstad [SSRN]

We construct and estimate a dynamic oligopoly model of the Bitcoin mining market. Mining equipment manufacturers produce differentiated durable capital goods and endogenously choose optimal investments in R&D. Miners make dynamic purchase decisions based partly on beliefs regarding manufacturers’ future choices. We show that policy-relevant values, such as aggregate R&D investment by manufacturers and network energy consumption, are predictable given only a Bitcoin price-path. We further show the industry is uniquely suited to test the impact of product market competition on innovation, a much-debated subject in the economics of R&D literature.

“Whose attention is it, anyway?”

Abstract unavailable.