A Static Theory of Pareto Distributionsby Francois Geerolf

Discussion by T. Mayer

BdF June 2016

Discussion by T. Mayer

The motivation

• Provide a static microfoundation for Pareto distribution of firmsize and income.

• Pareto-heterogeneity emerges with “very small” heterogene-ity in primitives: challenge for enormous litterature that hasbeen 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. firmsliterature)

Discussion by T. Mayer

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 variablefrom 1) and 2).

4 For that, we use what they call “self reflection”. Largely usedsince 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

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,Frechet, Gumbel, and Weibull.

2 “CREMR” family demand (Constant Revenue Elasticity of MarginalRevenue):

p(x) =β

x(x − γ)

σ−1σ

n.b: They maintain Dixit-Stiglitz market structure.

Discussion by T. Mayer

Why do we care?

Pareto gives a large number of useful results (often even withoutassuming CES-MC)

1 Gravity: another “law” in economics, which started from avacuum 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 sizeof firms that matter?

• Should it be fully Pareto or just in the right tail?

Discussion by T. Mayer

Explaning deviations from Pareto in the lower tailProposition 2, and Result 2 are quite powerful: almostindependently of skill distribution assumptions, firm size isdistributed 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

For incomes too

For income and consumption too (Battistin, Blundell and Lewbel,JPE09)

Discussion by T. Mayer

An alternative view

At least 2 views:

• Geerolf: Lower tail deviations from Pareto are the only sign ofheterogeneity in fundamentals (would be nice to have more onthat, 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

Remarks on Empirics

Main result:

• Inside establishment: distribution of span of control follows aPareto 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