# Firm size distribution under horizontal and vertical innovation

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## Abstract

This paper studies the firm size distribution arising from an endogenous growth model of quality ladders with expanding variety. The probability distribution function of a given cohort is a Poisson distribution that converges asymptotically to a normal of log size. However, due to firm entry propelled by horizontal R&D, the *total *distribution—i.e., when the entire population of firms is considered—is a mixture of overlapping Poisson distributions which is systematically right skewed and exhibits a fatter upper tail than the normal distribution of log size. Our theoretical results qualitatively match the empirical evidence found both for the cohort and the total distribution, and which has been presented as a challenge for theory to explain. Moreover, by obtaining a total distribution with a gradually increasing average over a long time span, the model is able to address complementary empirical evidence that points to a total distribution subtly evolving over time.

## Keywords

Firm size distribution Skewness Heavy tails Endogenous growth Horizontal and vertical R&D## JEL Classification

O41 O38 L11## Notes

### Acknowledgement

We would like to thank an anonymous referee for his comments and suggestions, which we found extremely helpful and constructive.

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