Research

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.

Conventional income growth is undefined for transitions involving losses and can magnify ordinary revenue–cost movement near break-even. I show that income growth is two-dimensional: scale and balance changes reconstruct revenue and cost growth throughout the signed domain. No informative endpoint-only scalar has the same additive, unit-invariant properties through zero; conventional growth omits 19 percent of operating and 28 percent of economic-income transitions. Gaussian revenue–cost dynamics generate heavy-tailed income and income growth. The representation reinterprets growth persistence and valuation and shows that omitted transitions are concentrated in equity-return tails, placing profit, loss, and recovery in one growth system.

We show that, for any stochastic discount factor (SDF), the log expected gross excess return is an exact sum of joint return-SDF cumulants. The sum nests the familiar covariance channel at order two, co-skewness at order three, and co-kurtosis at order four. When the SDF is affine in a few observable risk factors, one structural parameter per factor prices the entire implied library of cumulant factors. The factor “zoo” is therefore consistent with a low-dimensional SDF. In our tests, three structural parameters generate 31 cumulant prices, and the resulting 28 overidentifying restrictions are not rejected. The restricted model also forecasts held-out returns as well as the unrestricted one. Out of sample on 284 long-short anomaly portfolios, our cumulant models match the Fama–French benchmarks on mean absolute alpha and cut unexplained average returns by a third.

Dynamic firm models commonly combine capital with one firm-specific operating factor. Conditional on aggregate conditions, an ordered factor places revenue-cost balance on a smooth surface of capital and scale intensity. In 142,480 firm-years, the best outcome-free surface leaves 82 percent of balance dispersion. This missing margin persists and organizes investment, value, losses, and adverse CRSP exit. In a common q-theory environment, fixed-balance and deterministic-manifold technologies generate virtually no losses, while allowing balance to move independently spans the observed region and reproduces much of the observed signed-income variation. Persistent balance is a second operating state in q-theory.

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-dependant heteroskedasticity is rampant, and small firms are systematically different from large firms.

Before regulations were enacted to prevent such practices, information leaked through selective disclosure was incorporated into markets prior to the public release of news. “News days” did not deliver news to markets; now they do. We provide novel evidence of changes in returns and turnover behavior around the enactment of regulations barring selective disclosure practices in the United States and the EU. We conversely document lack of such changes in Australia and Japan, which did not implement similar measures. We conclude that selective disclosure resolves Roll’s R2 puzzle.

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% 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 seven 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.

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.