Difference-of-Log-Normals

“Growth and Differences of Log-Normals” [PDF]

Growth rates and net flows in economics are empirically heavy-tailed across settings as diverse as firms, cities, regional output, epidemics, and wages. This paper provides a simple unifying explanation and a single theoretically motivated distributional form that fits and organizes these disparate phenomena. The key observation is that many economic variables of interest are net outcomes shaped by two opposing multiplicative forces: sales and expenses, creation and destruction, inflows and outflows. When each side is itself the product of many small shocks, the multiplicative CLT implies each component is approximately log-Normal, while their net outcome follows a Difference-of-Log-Normals (DLN) distribution.

I develop a CLT-based taxonomy of limiting distributions for economic data, and show how DLN variables admit a natural hyperbolic representation that decomposes outcomes into two interpretable separable components: productive magnitude and productive efficacy. I then test the distributional predictions in a large panel of U.S. public firms (1970–2019). Firm magnitudes are well described by Skew-Normals, with Normal upper tails. In contrast, firm cashflows, payouts, investment, key ratios, growth rates, and stock returns at multiple frequencies exhibit remarkable fit to the DLN. Finally, I embed these findings in a tractable firm model via a difference-of-log-linears profit production function, which makes the (magnitude,efficacy) state space operational for estimation and counterfactuals.

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

Firm income, growth, and return distributions are heavy-tailed. Accounting for the interplay of sales and expenses is sufficient to explain this fact without relying on time-varying volatility or factors external to the firm. Embedding the implied production function into a standard q-theory model yields novel and specific predictions regarding the distributions of income, growth, and returns. The predictions are supported by the data. The model proposes novel definitions of firm income scale, efficiency, and growth.

“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.

Publications

“Is News Really News: The Effects of Selective Disclosure Regulations”, with Brent Kitchens and Chris Yung, Review of Finance (2024) [SSRN, PDF]

Before regulation enacted to prevent such practices, information leaked via selective disclosure incorporated into markets prior to public release of news. “news days” did not deliver news to the market. Now they do. We provide novel evidence of changes in returns & turnover behavior around the enactment of regulation barring selective disclosure practices in the US and in the EU. We conversely document lack of such changes in Australia and Japan, which did not implement similar measures. We conclude selective disclosure resolves Roll’s R-squared puzzle.

“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.

“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.