This document discusses and critiques the paper "Large Firm Dynamics and the Business Cycle" by Vasco Carvalho and Basile Grassi. It notes that the paper develops a new framework for modeling firm dynamics that incorporates heterogeneity and granularity. The document discusses some of the model's results, like endogenous fluctuations in equilibrium and characterization of aggregate dynamics under certain assumptions. It also raises several critiques, questioning aspects of the model like the competitive firm assumption, how well it documents industry structure, and implications of the production function specification. Measurement issues in applying the model to data are also raised.

1. Discussion of
“Large Firm Dynamics and the Business Cycle”
by Vasco Carvalho and Basile Grassi
Claire Lelarge
RITM and CREST

2. A new quantification framework
for the granularity hypothesis
Paper motivation :
The main empirical contributions until now start from rather static
frameworks :
featuring firm level heterogeneity/ concentration of output among firms
in which shocks are incorporated
This paper takes a different route :
Starts from intrinsically dynamic framework : Hopenhayn 1992
Makes clear that the growth process of firms (“shocks”) and the firm size
distribution (concentration of output among firms) are related.
Also their response to shocks...
(These aspects are lost in the existing empirical frameworks).
also featuring firm level heterogeneity
and incorporating granularity (instead of the “continuum” assumption)
Content of the paper :
How does this model behave ?
No stationary (firm size) distribution when granularity :
Endogenous fluctuations in equilibrium.
Under Gibrat’s law : gets complete characterization of aggregate dynamics
Quantification exercises

3. Pushing Hopenhayn’s model to its limits
1. Assumption of competitive firms more difficult to sustain with
granularity
both on the output market and input market (no strategic interaction)
"A mathematical model appropriate to the intuitive notion of perfect
competition must contain infinitely many participants. We submit that the
most natural for this purpose contains a continuum of participants"
Nobel Prize laureate R. Aumann (Ecta, 1964)
2. Standard aspects of the Hopenhayn model not documented :
granularity and overall industry structure ?
e.g. comparative statics for entry cost, driving (long term) market
concentration, productivity (size) dispersion, industry turnover.
3. Large labor demand elasticity
The Cobb-Douglas specification implies :
Ld (wt , ϕs ) = α.ϕs
wt
1
1−α
=⇒ ∂Ld
∂wt
= −5
Does it matter ?
(generates fat tails but increases GE smoothing of shocks via wages)

4. Elasticity of Labor Demand
Fig. 1. Distribution of Labor Demand Elasticities.
Lichter, Andreas, Andreas Peichl and Sebastian Siegloch,
The Own-Wage Elasticity of Labor Demand: A Meta-Regression Analysis,
IZA DP No. 7958.

5. Quantification exercises
Measurement aspects : what definition of firms ?
Analysis of the firm size distribution
You seem to predict too few large firms, and too high FSD fluctuation ?
Argument that FSD is more stable for small firms hindered by too coarse
data binning ? (minor point)
Distinguish between finite number of draws from a stable (stationary)
distribution (e.g. measurement error)
and fluctuation of the underlying distribution
Impulse response functions
Clarify what dynamics ? (convergence to the stationary equilibrium ?)
Minor point : why “average” marginal productivity of labor ? (p.34)
Tail indices and dispersion of FSD
More loosely connected to your model
Variance of sales very similar to herfindahl index
Distributional dynamics over the business cycle
More like a test of specification (production function) ?

6. Measurement Aspects :
What definition (“theory”) of a firm ?
Census data:
domestic,
public and private
Compustat data:
international?
public

7. Measurement Issues (1) : Double counts ?
Headquarter Listed units Simple public affiliates Complex public affiliates Private affiliates

8. Measurement Issues (2) : What concept of firm ?
(What shocks ?)
Headquarter Listed units Simple public affiliates Complex public affiliates Private affiliates

9. Quantification exercises
Measurement aspects : what definition of firms ?
Analysis of the firm size distribution
You seem to predict too few large firms, and too high FSD fluctuation ?
Argument that FSD is more stable for small firms hindered by too coarse
data binning ? (minor point)
Distinguish between finite number of draws from a stable (stationary)
distribution (e.g. measurement error)
and fluctuation of the underlying distribution
Impulse response functions
Clarify what dynamics ? (convergence to the stationary equilibrium ?)
Minor point : why “average” marginal productivity of labor ? (p.34)
Tail indices and dispersion of FSD
More loosely connected to your model
Variance of sales very similar to herfindahl index
Distributional dynamics over the business cycle
More like a test of specification (production function) ?

10. Discussion of
“Large Firm Dynamics and the Business Cycle”
by Vasco Carvalho and Basile Grassi
Claire Lelarge
RITM and CREST