This document discusses and summarizes a paper by François Geerolf that provides a static microfoundation for the Pareto distribution of firm size and income. The paper argues that Pareto heterogeneity can emerge from very small heterogeneity in primitives, challenging theories that assume Pareto-distributed productivity variables. Geerolf's model assumes a power law production function that exhibits complementarities, leading to Pareto distributions even with homogeneous firms. The document discusses alternative views and questions whether the model can fully discriminate between Pareto and other potential distributions like log-normal that may fit the data.

1. A Static Theory of Pareto Distributions
by Fran¸cois Geerolf
Discussion by T. Mayer
BdF June 2016
Discussion by T. Mayer

2. The motivation
• Provide a static microfoundation for Pareto distribution of firm
size and income.
• Pareto-heterogeneity emerges with “very small” heterogene-
ity in primitives: challenge for enormous litterature that has
been assuming Pareto-distributed primitive performance vari-
able (“productivity”).
• In this paper, Pareto is the benchmark for perfect homogeneity!
fundamental heterogeneity gives rise to deviations from Pareto.
• Comes from production function assumption (power law) ex-
hibiting complementarities.
⇒ Fascinating, provocative and ambitious (for het. firms
literature)
Discussion by T. Mayer

3. Firm’s heterogeneity literature
Synthetized in a recent paper by Mrazova, Neary and Parenti:
1 We observe firm heterogeneity (in output, exports, wage pre-
mium...) with a certain distribution
2 Our benchmark market structure is CES (another power law)
+ monop. comp.
3 We usually infer distribution of primitive performance variable
from 1) and 2).
4 For that, we use what they call “self reflection”. Largely used
since Chaney (2008):
Pareto performance + CES → Pareto sales.
5 More generally, MNP show that self reflection occurs when per-
formance and sales are related by a power function.
Discussion by T. Mayer

4. The power of powers
MNP also give the families for which self-reflection holds
1 The Generalized Power Function (GPF) family of distributions,
that includes Pareto, truncated Pareto, log-normal, uniform,
Fr´echet, Gumbel, and Weibull.
2 “CREMR” family demand (Constant Revenue Elasticity of Marginal
Revenue):
p(x) =
β
x
(x − γ)
σ−1
σ
n.b: They maintain Dixit-Stiglitz market structure.
Discussion by T. Mayer

5. Why do we care?
Pareto gives a large number of useful results (often even without
assuming CES-MC)
1 Gravity: another “law” in economics, which started from a
vacuum of theory to end up with a crowded set of micro-
foundations.
2 A constant macro trade elasticity
3 A super simple equation for gains from trade liberalization
4 Micro shocks can have Macro effects
• Is it Pareto-distributed performance or Pareto-distributed size
of firms that matter?
• Should it be fully Pareto or just in the right tail?
Discussion by T. Mayer

6. Explaning deviations from Pareto in the lower tail
Proposition 2, and Result 2 are quite powerful: almost
independently of skill distribution assumptions, firm size is
distributed Pareto in the upper tail
• Pareto black hole (as in gravity)
• Indeed, lower tail has problems:
Figure: Distribution of French exports to Belgium in 2005
(a) Eaton et al. (2011) graph (b) simple density of the same data
Discussion by T. Mayer

7. For incomes too
For income and consumption too (Battistin, Blundell and Lewbel,
JPE09)
Discussion by T. Mayer

8. An alternative view
At least 2 views:
• Geerolf: Lower tail deviations from Pareto are the only sign of
heterogeneity in fundamentals (would be nice to have more on
that, can we quantify this in any way?)
• Alternative: Fundamentals are heterogeneous, and maybe Log-
Normal. Or a mixture with Pareto in the right tail.
Can we discriminate?
Discussion by T. Mayer

9. Remarks on Empirics
Main result:
• Inside establishment: distribution of span of control follows a
Pareto with slope 1.96 in the upper tail.
1 How is the upper tail defined?
2 How should lower tail deviations be interpreted?
3 How close is the full distribution from LN?
Does it really discriminate for other Pareto DGPs?
Discussion by T. Mayer