ManagementQualityandFirmOrganizationinthe AggregateEconomyccfour/MQFOGESlides.pdf ·...

Management Quality and Firm Organization in theAggregate Economy

Cheng Chen

School of Economics and FinanceThe University of Hong Kong

(Cheng Chen) Firms in the Global Economy 1 / 60

Introduction

Management Quality

Recent empirical research has developed new measures ofmanagement quality (Bloom and Van Reenen, 2007).Evidence of substantial cross-country differences in measuredmanagement quality (Bloom and Van Reenen, 2010). Categories

Details

I modern manufacturing techniques (Toyota lean production);I performance check and review;I performance clarity;I removing poor performers.


Introduction

Management Quality (cont.)

Management quality is strongly correlated with firm performance andhas causal effect on it (Bloom et al., 2013).

Exogenous variation (from the perspective of firms) in managementquality:

I information barriers;I rigid labor markets;I weak enforcement of laws.


Introduction

Management Quality (cont.)

Management quality is strongly correlated with firm performance andhas causal effect on it (Bloom et al., 2013).Exogenous variation (from the perspective of firms) in managementquality:

I information barriers;I rigid labor markets;I weak enforcement of laws.


Introduction

Monitoring-based IncentivesMonitoring-based incentives (M&I): one part of overall managementtechnology. Details

I performance check and review;I performance clarity;I removing poor performers.

Quality of M&I (management quality) differs across firms andcountries.

0.5

11.

52

Den

sity

.5 1 1.5 2Average Score on Monitoring and Incentives

IndiaU.S.

kernel = epanechnikov, bandwidth = 0.0699

Comparison between India and the U.S.


Introduction

This Paper

Provide a framework for analyzing the implications of differences inM&I for firm-level and aggregate-level economic outcomes in generalequilibrium. (existing evidence: U.S. and India)

I Internal firm organization and endogenous firm productivity (matter forintra-firm wage structures and firm profitability)

I Firm size distribution (matters for resource allocation)I Aggregate productivity (matters for the overall efficiency of an

economy)

How do improvements in management quality interact with tradeliberalization?

I Does M&I affect trade volume?I Does M&I affect the welfare gains from trade.

Quantitative effect.


Introduction

This Paper

Provide a framework for analyzing the implications of differences inM&I for firm-level and aggregate-level economic outcomes in generalequilibrium. (existing evidence: U.S. and India)

I Internal firm organization and endogenous firm productivity (matter forintra-firm wage structures and firm profitability)

I Firm size distribution (matters for resource allocation)I Aggregate productivity (matters for the overall efficiency of an

economy)How do improvements in management quality interact with tradeliberalization?

I Does M&I affect trade volume?I Does M&I affect the welfare gains from trade.

Quantitative effect.


Introduction

Related Literature

Hierarchies: Williamson (1967), Beckmann (1977), and Keren andLevhari (1979) etc.Monitoring-based hierarchy models: Calvo and Wellisz (1978, 1979),Qian (1994), and Meagher (2003) etc.Knowledge-based hierarchy models: Garicano (2000), Garicano andRossi-Hansberg (2004, 2006, 2012), Caliendo and Rossi-Hansberg(2012)

I Different mechanisms and different aggregate implications.

Heterogenous firms: BEKJ (2003), Melitz (2003), Yeaple (2005), andMelitz and Ottaviano (2007) etc.


Introduction

Preview of Results

Improvements in M&I for all firms have heterogenous impact on firms(selection effect: favor firms using organizations more intensively).

I firm size distribution;I aggregate productivity;I internal firm structure.

Better M&I increases trade share.Better M&I amplifies the welfare gains from trade.Firms’ organizational choice (i.e., the number of layers) is the key togenerating the heterogenous impact.


Introduction

Preview of Results



Better M&I increases trade share.

Better M&I amplifies the welfare gains from trade.Firms’ organizational choice (i.e., the number of layers) is the key togenerating the heterogenous impact.


Introduction

Preview of Results



Better M&I increases trade share.Better M&I amplifies the welfare gains from trade.

Firms’ organizational choice (i.e., the number of layers) is the key togenerating the heterogenous impact.


Introduction

Preview of Results



Better M&I increases trade share.Better M&I amplifies the welfare gains from trade.Firms’ organizational choice (i.e., the number of layers) is the key togenerating the heterogenous impact.


The Model

1 Introduction

2 The ModelFirm-Level AnalysisEquilibrium Analysis

3 Management Quality and Economic Outcomes

4 Trade Liberalization and Management Quality

5 Quantitative Analysis

6 Appendix


The Model

Factors, Sectors and Firms

Two sectors: CES sector and homogeneous sector.I CES (Constant Elasticity of Substitution) sector: firm makes demand

draw θ after paying an entry cost.F Entry cost f1 and fixed production cost f0. (paid in form of final

composite good: defined below)F Firms need to monitor and incentivize workers to work using a

management hierarchy.

I Homogeneous sector: CRS production technology and no incentivesproblems (for simplification).

Two factors: Homogeneous workers (fixed endowment: L) and a largepool of potential entrepreneurs.

I Workers: choose one type of job to apply for. (Harris and Todaro)I Potential entrepreneurs: enter the CES sector or not. (outside option is

f2)


The Model





management hierarchy.I Homogeneous sector: CRS production technology and no incentives

problems (for simplification).

Two factors: Homogeneous workers (fixed endowment: L) and a largepool of potential entrepreneurs.


f2)


The Model






problems (for simplification).Two factors: Homogeneous workers (fixed endowment: L) and a largepool of potential entrepreneurs.

I Workers: choose one type of job to apply for. (Harris and Todaro)

I Potential entrepreneurs: enter the CES sector or not. (outside option isf2)


The Model






problems (for simplification).Two factors: Homogeneous workers (fixed endowment: L) and a largepool of potential entrepreneurs.


f2)


The Model

PreferenceUtility function of all agents:

U =(Cc

γ

)γ( Ch

1− γ

)1−γ− Iψ. (1)

I Ch: consumption of the homogenous good.

Cc =

( ∫Ω

θ1σ y(θ)

σ−1σ Mµ(θ)dθ

) σσ−1

. (2)

I I and ψ: an indicator function and the disutility to exert effort.

Normalize the price index of the (final) composite good to one.

PγCp

1−γh ≡ 1, (3)

PC : the ideal price index of CES goods; ph: price of the homogenousgood.


The Model Firm-Level Analysis

A Management Hierarchy

Layer 0

Layer 1

Layer 2

Etrepreneur

Non-production Worker

Production Worker

E

MM

Monitor

W

Monitor

W WW

Monitor

WW



A Management Hierarchy (cont.)

One entrepreneur at layer 0. She monitors her direct subordinates.The firm may hire mi non-production workers at layer i whereT > i > 0. Non-production workers monitor their direct subordinatesand don’t produce output.mT production workers at the bottom layer T (≥ 1) produce output∫ mT

j=0ajdj ,

where aj ∈ 0, 1: work or shirk.Monitors also need to be monitored.



Firm’s Problem (part one)

The firm’s optimization problem if it decides to stay in the market:

maxmi ,aii=1,...,T ,T Aθ1σ

( ∫ mT

j=0ajdj

) σ−1σ −

T

∑i=1

wi (θ)mi (θ)

s.t. m0 = 1.

A ≡(

γEP1−σ

C

)1/σ: the adjusted market size.

wi (θ): wage offered at layer i in firm with demand draw θ.Key ingredient: endogenous determination of wage schedules.



The Determination of Wage Schedules in the CES Sector

The worker at layer i is induced to exert effort for wage wi (θ), iff

wi (θ)− ψ ≥ (1− qi )wi (θ). (4)

qi ≡ q(b, xi (θ)): the prob. of catching and firing a shirking worker.

q(b, xi (θ)) =1

bxi (θ).

I xi (θ): the span of control adjusted by effort (endogenous).I 1

b : the quality of M&I (exogenous).

The incentive-compatible wage at layer i : Evidence

wi (θ) = bxi (θ)ψ. (5)



The Firm’s Problem (part two)

The firm’s optimization problem can be restated as

maxmii=1,...,T ,T Aθ1σ m

σ−1σ

T −T

∑i=1

bxi ψmi

s.t. xi =mi

mi−1;

m0 = 1.

I have used that in equilibrium the continuous case

I ai = 1 for all T ≥ i ≥ 0.I Every worker in the same layer receives the same monitoring intensity.



Why do Firms Choose to Add Multiple layers? (part one)

When demand draw θ is small...

E

Firm A

0

1 W

Monitor

W



Why do Firms Choose to Add Multiple layers? (part two)

When demand draw θ is big...

E

Firm B

0

1

2

W

Monitor

WWWWW

E

MM

Monitor

W

Monitor

W WW

Monitor

WW



Why do Firms Choose to Add Multiple layers? (part three)

Adding layer: like efficiency-enhancing investment with a “fixed cost”.

E

Firm A

0

1

2

W

Monitor

W

E

Firm B

MM

Monitor

W

Monitor

W WW

Monitor

WW



Optimal Number of Layers (Contribution)Drops for the MC curves. Kinks for the AVC curves.

Differences from CRH (2012)

1 2 3 4 5 6 7 8100

200

300

400

500

600

700

800AVC, MC for firms with 2-4 layers

Quantity Produced

AVC,

MC

AVC for T=1AVC for T=2AVC for T=3MCthe final AVC



Firm-Level Outcomes

Proposition 1Firms that receive better demand draws produce more and have morelayers.

Proposition 2

Given the number of layers, both wages and wage ratios (i.e., wi (θ)wi+1(θ)

)

increase with firm’s demand draw. When the firm adds a layer due to amarginal improvement in the demand draw, both wages and wage ratiosfall at existing layers.

Key: changes in the span of control.Predictions: consistent with evidence (Caliendo, Monte, andRossi-Hansberg (2012)).



Firm ProductivityProductivity: inverse of unit cost.

Prod(q) =q

TC (q, b).

Assume that 1b > 4ψ

f0(i.e., M&I is efficient enough) → generally

increasing function of output. AC the other cont. labor productivity

2 3 4 5 6 7 8

0.57

0.58

0.59

0.6

0.61

0.62

0.63

0.64

0.65

Firm Productivity

Quantity produced

Pro

duct

ivity

b=1.5,ψ=0.25,f0=1.8


The Model Equilibrium Analysis

EquilibriumCES sector:

I Zero cutoff payoff (ZCP) condition: Π(θ,A) ≡ π(θ,A)− f = 0.I Free entry (FE) condition:

∫ ∞θ (π(θ,T (θ),A)− f )g(θ)dθ = fe .

Indifference condition à la Harris and Todaro (1970): labor submarkets(i , θ) and (i

′, θ′).

mi (θ)

Q(θ, i)(wi (θ)− ψ) =

mi ′ (θ′)

Q(θ ′ , i ′)(wi ′ (θ

′)− ψ) = ph.

Labor and product market clearing conditions. Details

Proposition 3Under restrictions on parameter values, there exists a unique equilibriumthat has unemployment in every labor submarket.

Conditions


Management Quality and Economic Outcomes

1 Introduction





6 Appendix



Selection Effect of Better Management (Main Contribution)Consider M&I improves for all firms. Details

I Institutional reforms or spread of good management rules.I Cost reduction effect for all firms.I Uneven effect: firms with more layers (i.e., bigger firms) benefit more.

Proposition 4b ↓: the smallest firms exit, and profit and revenue of the biggest firms ↑.For all surviving firms: the spans of control ↑ or the number of layers ↑.

Proposition 5b ↓: both the firm size distribution and the distribution of the number oflayers move to the right in the first order stochastic dominance (FOSD)sense, if the distribution of θ is a Pareto distribution.

Sketch of proof for Prop. 4 Sketch of proof for Prop. 5

Selection effect and resource reallocation effect would disappear, if allfirms were forced to have the same number of layers.



Average Firm Size (Source: Hsieh and Klenow (2012))

We observe difference in average firm size across countries.



Firm Size Distribution (Source: Hsieh and Klenow (2012))



Management Quality and Resource Allocation

Bloom, Sadun, and Van Reenen (2012a) and Bloom et al. (2013)argue that in India

I Weak rules of law and low quality of M&I → efficient firms areconstrained more → impede inter-firm reallocation.

The FOSD result: consistent with the evidence in Poschke (2014).Bloom, Sadun, and Van Reenen (2012b): one unit of increase inmanagement score has biggest impact on firms size in the U.S.

I θ: quality of management technology that is not related to M&I(operations or targets).

Positive impact of ICT of the number of layers (unique prediction):consistent with the evidence in Guadalupe and Wulf (2010).Welfare may increase or decrease depend on σ. Welfare






The FOSD result: consistent with the evidence in Poschke (2014).

Bloom, Sadun, and Van Reenen (2012b): one unit of increase inmanagement score has biggest impact on firms size in the U.S.








The FOSD result: consistent with the evidence in Poschke (2014).Bloom, Sadun, and Van Reenen (2012b): one unit of increase inmanagement score has biggest impact on firms size in the U.S.





Gains in Aggregate ProductivityWithin-firm: cost-reductions for all firms.Between-firm: exit of least productive firms and expansion of mostproductive firms.


Trade Liberalization and Management Quality

1 Introduction





6 Appendix



Symmetric Countries

I extend the baseline model into the open economy.I Two symmetric countries.I No international trade of the homogenous good.I A fixed trade cost fx and the iceberg trade cost τ for firms in CES

sector to trade.

When the economy moves from autarky to open economy...I Non-exporters flatten their hierarchies by decreasing the number of

layers and increasing the span of control.I Non-exporters use more incentive-based pay because of the increasing

span of control.

Above results are consistent with the findings from Cunat and MariaGuadalupe (2005, 2009) and Guadalupe and Wulf (2010).



Symmetric Countries

I extend the baseline model into the open economy.I Two symmetric countries.I No international trade of the homogenous good.I A fixed trade cost fx and the iceberg trade cost τ for firms in CES

sector to trade.When the economy moves from autarky to open economy...

I Non-exporters flatten their hierarchies by decreasing the number oflayers and increasing the span of control.

I Non-exporters use more incentive-based pay because of the increasingspan of control.

Above results are consistent with the findings from Cunat and MariaGuadalupe (2005, 2009) and Guadalupe and Wulf (2010).



Aggregate Trade Statistics and Management Quality

Better M&I increases trade share.I Intuition: firms are bigger in economies with better M&I (in autarky).

Better M&I amplifies the welfare gains from trade under certainconditions.

I Intuition: variety effect and productivity effect.



The Complementarily Result

M&I and the welfare gains from trade.

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.90.35

0.4

0.45

0.5

0.55Welfare Gains from Trade and Management Quality

Management Quality (1/b)

Wel

fare

Gai

ns fr

om T

rade

ψ=0.2, f=5, fx=5, τ=1.3, σ=3.8, k=1.1, γ=0.6

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.90.03

0.04

0.05

0.06

0.07

0.08

0.09Welfare Gains from Trade and Management Quality

Management Quality (1/b)

Wel

fare

Gai

ns fr

om T

rade

ψ=0.2, f=5, fx=5, τ=1.6, σ=5, k=1.1, γ=0.6


Quantitative Analysis

1 Introduction





6 Appendix



Simple Quantitative Exercise

Calibrate the model to match six moments obtained form the US data.Quantitatively assess impact of improvements in M&I on firm size,aggregate productivity, and welfare. (counterfactual experiments)



Moments

Table: Moments from the Data and the Model

Data ModelPareto Shape Parameter 1.095 1.097Employment per firm 46.57 46.57

Fraction of small firms (< 10 employees) 55.04% 55.14%Fraction of big firms (> 500 employees) 1.03% 0.76%

Fraction of exporting firms 18% 17.84%Trade Share (relative to GDP) 14% 14.00%

Pareto shape parameter: obtained from the regression of log rank on log firm size.



Parameter Value

Table: Parameter Values

Value Sourcesσ 4 Bernard et al. (2003)L 16.48 Caliendo and Rossi-Hansberg (2012)τ 1.3 Ghironi and Melitz (2005)f 4.98fe 3.00fx 4.84k 1.188bψ 0.649γ 0.545



A Check

Table: Moments Related to Internal Firm Organization

Data ModelThe number of managerial layers 3.1-3.2 3.44Wage share of production workers 57.7% 52.1%



Counterfactual Experiments

Score on M&I : 22% higher for U.S. firms than for Indian firms.Consider similar percentage change in management quality in themodel.

Table: Firm Size, Aggregate Productivity and Welfare

Prodw Employment Sales WelfareM&I ↑ 22% 22.2% 72.2% 36.9% 47.1%

Table: Trade Share and the Welfare Gains from Trade

b=2.141 b=1.755 ComplementarityWGT 16.42% 17.63% 1.21%

Share of exporting firms 12.53% 17.84% 5.31%



Conclusions

Better management quality for all firms: heterogeneous impact andselection effect.

I Favors firms with more layers.I Exit of smallest firms and expansion of biggest firms.

M&I plays a role in shaping firm-level and aggregate-level outcomes.I Internal firm organization and firm size distribution.I Aggregate productivity.I Welfare gains from trade.

Future work:I How does management quality affect exporting behavior of firms?I How is management quality affected by firms’ exporting behavior and

trade liberalization?I Other types of management technology: promotion, quality control etc.I Firm boundaries and management quality.


Appendix

1 Introduction





6 Appendix


Appendix

Management Practices

I use the data from Bloom and Van Reenen (2010).18 management practices in total.

I Operations: Toyota lean production (2 practices).I Targets: “how companies set the right targets, track the right

outcomes, and take appropriate action if the two are inconsistent” (5practices).

I Monitoring: “how companies monitor what goes on inside their firmsand use this for continuous improvement” (5 practices).

I Incentives: “how companies promote and reward employees based onperformance, and whether or not companies try to hire and keep theirbest employees” (6 practices).

Management scores are strongly correlated with independent measuresof firm performance. Go back Evidence


Appendix

Survey Questions (Bloom and Van Reenen, 2010)

Performance tracking: Is tracking ad hoc and incomplete, or isperformance continually tracked and communicated to all staff?Performance review: Is performance reviewed infrequently?Performance clarity: Are performance measures ill-defined, poorlyunderstood, and private, or are they well-defined, clearlycommunicated, and made public?Consequence management: To what extent does failure to achieveagreed objectives carry consequences, which can include retraining orreassignment to other jobs?Removing poor performers: Are poor performers rarely removed, or arethey retrained and/or moved into different roles or out of the companyas soon as the weakness is identified? Go back


Appendix

Monitoring and Incentives

7 items are related to monitoring and incentives practice discussed inthis paper.Finding and catching the shirking employees:

I performance tracking;I performance review;I performance dialogue;I performance clarity.

Punishing and firing the shirking employees:I consequence management;I rewarding high performance;I remove poor performers.Go back


Appendix

Relationship with CRH (2012)Caliendo and Rossi-Hansberg (2012) model hierarchies based oninformation processing.

I Changes in the ICT affects internal firm organization. No role forincentives and monitoring.

This paper models hierarchies based on monitoring and incentives.I Changes in laws and institutions affect monitoring, incentives, and

internal firm organization. No role for the ICT.

Differences in micro-level predictions:I Decreasing average variable cost in Caliendo and Rossi-Hansberg

(2012) v.s. increasing average variable cost in this paper.Focus on different aggregate questions:

I Implications of improvement in M&I for the firm size distribution,internal firm organization, aggregate productivity (this paper).

I Impact of trade liberalization on firm organization and productivity(CRH, 2012).

Go back


Appendix

Relationship with CRH (2012)Caliendo and Rossi-Hansberg (2012) model hierarchies based oninformation processing.

I Changes in the ICT affects internal firm organization. No role forincentives and monitoring.

This paper models hierarchies based on monitoring and incentives.I Changes in laws and institutions affect monitoring, incentives, and

internal firm organization. No role for the ICT.Differences in micro-level predictions:

I Decreasing average variable cost in Caliendo and Rossi-Hansberg(2012) v.s. increasing average variable cost in this paper.

Focus on different aggregate questions:I Implications of improvement in M&I for the firm size distribution,

internal firm organization, aggregate productivity (this paper).I Impact of trade liberalization on firm organization and productivity

(CRH, 2012).Go back


Appendix

Empirical Support

Empirical support for the specification:I Rebitzer (1995) finds evidence on the trade-off between supervision

intensity and wage payment.I Groshen and Krueger (1990) and Ewing and Payne (1999) find

evidence on the negative relationship between the span of control andwages paid to subordinates.

Go back


Appendix

A Continuous Number of Layers

I treat the number of layers as a continuous variable as in Keren andLevhari (1979) and Qian (1994).

maxmt ,T Aθ1σ m

σ−1σ

T −∫ T

t=0bψstmtdt

s.t. mt = mt log(st)m0 = 1,

I The span of control (constant): st(θ,A) = e.I The number of layers: T (θ,A) = log(mT (θ,A)).I Output: mT (θ,A) = θ

(Aβbψe

)σ.

I Operating profit: π(θ,A) = (1− β)Aσθ(

βbψe

)σ−1+ bψe.

Go back


Appendix

Firm Productivity: Average Cost Curve

2 3 4 5 6 7 81.5

1.55

1.6

1.65

1.7

1.75

1.8Average Cost

Quantity Produced

Ave

rage

Cos

t

b=1.5,ψ=0.25,f0=1.8

Go back


Appendix

The Other Case

2 3 4 5 6 7 80.46

0.465

0.47

0.475

0.48

0.485

0.49

0.495

0.5

0.505

0.51Firm Productivity

Quantity produced

Pro

duct

ivity

b=2.2,ψ=0.25,f0=1.8

Go back


Appendix

Firm Productivity: continuous number of layers

2 3 4 5 6 7 80.5

0.55

0.6

0.65

0.7

0.75

0.8

0.85

0.9

0.95

1Firm Productivity

Quantity produced

Pro

duct

ivity

b=1.5,ψ=0.25,f0=1.8

Go back


Appendix

Labor Productivity

Go back


Appendix

Restrictions on L: the discrete case (cont.)

Restrictions:I If σ−1

σ > γ and L is small → ph is small in equilibrium.I If σ−1

σ < γ and L is large → ph is small in equilibrium.I Ex-post check: solve equilibrium and check whether or not

wmin − ψ ≥ ph, where wmin is the lowest wage offered in the CESsector.

Go back


Appendix

Restrictions on L: the continuous case

I treat the number of layers as a continuous variable. θ: a Paretodistribution with a coefficient k .A necessary and sufficient condition for the existence of unemploymentin every labor submarket is

[ (fe(k − 1))1k B(b)

βσ−1θminL

] γγ−(1−γ)(σ−1) ≤ ψ(be − 1),

where

B(b) =tσ−1

(f − t)1k

[(f − t)

(σ− γ

γ− ψ(σ− 1)

t)− k − 1

k(t − ψ)

]and

t ≡ bψe.

Go back


Appendix

Equilibrium ConditionsMarket-clearing of homogeneous good:

phLh = (1− γ)E ,

where E is the aggregate income.Market-clearing of final composite good:

E =∫ ∞

θLC (θ)

Mg(θ)1− G (θ)

dθ + phLh +(f + fe

( θ

θmin

)k)M.

LC (θ): total wage payment of firms with demand draw θ.Labor market clearing:

L = Lh + Lc ,

where Lc : number of total job applicants in the CES sector.

Lc =∫ ∞

θ=θ

T (θ,A)

∑i=1

Q(θ, i)Mg(θ)

1− G (θ)dθ.

Go back


Appendix

Resource Reallocation and M&I

Consider a case in which b decreases for all firms. (i.e., M&Iimproves)

I Deregulating labor markets or improving efficiency of judicial systems→ prob. of firing shirking workers ↑.

Labor costs decrease for all firms. And this effect favors firms withmore layers (a multiplying effect).

I Consider two firms: θ2 > θ1 and T2 > T1. Operating profit of firmswith more layers is more sensitive to a change in 1

b . Graphical illustration

π(θ2,T2 = 2) = (1− 3β

4)(Aθ

1σ )

4σσ+3( β

243 bψ

) 3(σ−1)σ+3

π(θ1,T2 = 1) = (1− β

2)(Aθ

1σ )

2σσ+1( β

2bψ

) σ−1σ+1

Go back


Appendix

Uneven Effect

Go back


Appendix

Proof of Proposition 4

For θ: proof by contradiction.

For the number of layers and the span of control:I What matters is A

b .I Prove that

1 >A2A1

>b2b1

,

1b2: the quality of M&I after the improvements.

1b1: the quality of M&I before the improvements. Go back


Appendix


For θ: proof by contradiction.For the number of layers and the span of control:

I What matters is Ab .

I Prove that1 >

A2A1

>b2b1

,

1b2: the quality of M&I after the improvements.

1b1: the quality of M&I before the improvements. Go back


Appendix


For the distribution of the number of layers:I Prove that T (t θ2,A2, b2) ≥ T (t θ1,A1, b1) where t ≥ 1.I T (θ,A, b): the optimal number of layers.I θ2: the exit cutoff after the improvements.I θ1: the exit cutoff before the improvements.

For the firm size distribution:I Prove that S(t θ2,A2, b2) ≥ S(t θ1,A1, b1) where t ≥ 1.I S(θ,A, b): revenue or employment or output. Go back


Appendix

Welfare

Welfare: the expected payoff from entering the CES sector.The expected payoff depends on average wage and average prob. ofbeing employed.

Welfare can either go up or go down depending on the value of σ

σ governs the sensitivity of firm’s expansion w.r.t. an improvement inM&I.σ is bigger → firm’s expansion is substantial → market size increases(i.e., E ) → the mass of firms increases → the prob. of beingemployed increases → the expected payoff increases.When σ is small: both wages and the prob. of being employed godown.


Appendix

Welfare

Welfare: the expected payoff from entering the CES sector.The expected payoff depends on average wage and average prob. ofbeing employed.Welfare can either go up or go down depending on the value of σ



Appendix

Welfare


σ governs the sensitivity of firm’s expansion w.r.t. an improvement inM&I.σ is bigger → firm’s expansion is substantial → market size increases(i.e., E ) → the mass of firms increases → the prob. of beingemployed increases → the expected payoff increases.

When σ is small: both wages and the prob. of being employed godown.


Appendix

Welfare




Appendix

ExamplesWhen σ is high:

Welfare Ave(wage) Ave(ur) M Eb=1.6 0.2873 0.9582 0.5644 1.0235 25.6156b=1.5 0.3492 0.8988 0.4178 1.1471 31.3347ur: unemployment rate; M: the mass of firms; E: total incomeσ = 3.8, γ = 0.6, ψ = 0.3

When σ is low:Welfare Ave(wage) Ave(ur) M E

b=1.6 0.3819 0.9530 0.4145 2.6066 53.4884b=1.5 0.2910 0.8956 0.5119 1.9007 41.0722σ = 2.8, γ = 0.75, ψ = 0.3

When I treat the number of layers as a continuous variable, welfareincreases i.f.f. Go back

σ− 1σ

> γ.


Appendix

Firm Size Distribution

Go back


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