Granularity

What it means to be granular

Granularity can mean multiple things:

High concentration or skewness ⇒ individual units matter
Finite or small number of units ⇒ we live in world of pre-asymptotics
High idiosyncratic volatility ⇒ units do their own thing

Phenomena associated with high granularity

Faster growth
- Fat-tailedness is associated with faster growth because positive idiosyncratic shocks to large firms make the size distribution more skewed and lead to faster growth
- See Large Firm Dynamics and the Business Cycle
Increasing returns to scale
- In granular, fat-tailed variables, aggregating over larger quantities of underlying units increases the sample mean. Thus, a doubling of units leads to a more than doubling of the variable of interest
- See Statistical Consequences of Fat Tails, Enterprise Software Monetization is Fat-Tailed, Sample means change with sample size in fat-tailed distributions
Mean reversion
- Granular/idiosyncratic shocks tend to mean revert much more quickly and forcefully
- See Granular Comparative Advantage, A Demand System Approach to Asset Pricing
Cross-sectional variance
- Granularity drives larger variance across the cross-section
- See Granular Comparative Advantage
Volatility over time
- Idiosyncratic dynamics account for large share of the evolution of a variable associated with a unit over time
- See Granular Comparative Advantage, Large Firm Dynamics and the Business Cycle
Predictability
- Lagged idiosyncratic shocks can be used to forecast economic variables
- See The Granular Origins of Aggregate Fluctuations, A Demand System Approach to Asset Pricing
Concentrated, attributable growth
- If the variable in question is concentrated, growth or changes in that variable will be attributable to particular subcomponents
- See Which Investors Matter for Equity Valuations and Expected Returns?, The Granular Origins of Aggregate Fluctuations