Distribution Costs & The Size of Indian Manufacturing ...stanford.edu/~cruane/DistSlides.pdf · What We Do 1. New nding: distribution costs / sales "in plant size I Unique measurement

Distribution Costs &The Size of Indian Manufacturing

Establishments

Alessandra Peter, Cian Ruane

Stanford University

November 3, 2017

Question

Selling manufactured goods involves costs of distribution:

I Variable: Freight/shipping, insurance, commissions

I Fixed: Finding and contracting with distributors

1. How does low productivity in distribution sectors affectmanufacturing firms in developing countries?

I 2005 India-US TFP gap in Distribution sectors ≈ 8×I 2005 India-US TFP gap in Manufacturing sectors ≈ 4×

2. Can low productivity in distribution sectors explainsurvival of small plants in India?

I Median manufacturing employment in India ≈ 1 (47 in US)

I Constrain larger plants ⇒ enable inefficient plants to survive

Indian Distribution

I Poor infrastructure qualityI But large investments in recent years (GQ)

I Indian distribution sector highly fragmentedI Wholesalers & retailers tend to be small and local

I Large firms work with hundreds of distributors

I Tim Cook (July 24, 2012):

“I love India, but I believe Apple has some higher potential ... insome other countries. ... The multi-layered distributionreally adds to the cost of getting products to market.”

Recent Trends

Figure: Sectoral TFP (1995 = 1)Figure: (Distribution Costs /Sales) in Manufacturing

I Rapid productivity growth in distribution sectors

I Declining as share of sales in manufacturing

What We Do

1. New finding: distribution costs / sales ↑ in plant sizeI Unique measurement of plant-level distribution expenses in India

2. 2-Sector GE Model with Heterogeneous FirmsI Manufacturing firms ‘ship’ goods to consumers across spaceI Shipping further requires more distribution services

I Increasing relationship between size and distribution shareI Distribution costs ‘constrain’ larger plants more

I In GE, small plants survive

3. Preliminary Quantitative ExercisesI TFP increase in distribution → manufacturing

Literature

I Firm-size distribution and developmentI Hsieh & Klenow (2009, 2014), Hsieh & Olken (2014),

Bento & Restuccia (2015), Akcigit et al (2016)

I Intranational Trade CostsI Holmes & Stevens (2012), Atkin & Donaldson (2015)

I Model:I Melitz (2003), Arkolakis (2010)

Table of Contents

Data and Empirical Results

Model

Simple Quantitative Exercise

Data: Indian Annual Survey of Industries

I Survey of formal Indian manufacturing plants (1993-2011)I Representative sample > 10 workers Cleaning

I Unique measurement of outward distribution costs:

‘i.e. outward freight, rebate, commission, transit insurance ofgoods sold, packing fees etc’

I Includes variable costs

I Excludes fixed costs: finding distributors, advertising, etc...

I Distribution share (ds) = distribution expensessales (net of taxes)

I Average share = 2.2%

Distribution Share vs Size (Log-Scale)

Labor Cost, Materials + Fuels Output Robustness

Interpretation

I Rationalize this finding with 2 observations

1. Larger plants ship further (Holmes & Stevens (2012))2. Marginal distribution costs increasing in distance

I Larger plants use distribution services more extensively.

→ particularly affected by productivity in distribution sector.

I Key features we incorporate in our model.

Table of Contents

Data and Empirical Results

Model

Simple Quantitative Exercise

Model Preview

I Continuum of consumers & heterogeneous firmsI Firms differentiated by quality

I Firms choose set of consumers (and sales per consumer):I Selling to consumer ⇒ fixed cost & variable distribution costI Distribution cost ↑ in distance from consumerI ⇒ high quality firms:

I ↑ sales, ↑ consumers, ↑ distribution costs / sales

I ↑ rate at which distribution costs increase:I PE: firms sell to smaller set of consumersI GE: low-quality firms can survive

Environment

I Two sectors: Distribution (D) & Production (Q)I D: perfect competition, technology: D = ADL, price: pD

I Q: monopolistic competition, heterogeneous firms

I Continuum of consumers & firms uniformly distributed on circle:I Circumference = 1

I At each point on the circle:I Mass L of identical consumers (exogenous)I Mass J of heterogeneous firms (endogenous)I Consumers and firms symmetric at every point

I Free entry condition at each point

Consumer’s Problem

I Consumer (l) has CES preferences over available varieties Ωl

maxc(ω)

(∫ω∈Ωl

ψ(ω)c(ω)σ−1σ dω

) σσ−1

s.t

∫ω∈Ωl

p(ω)c(ω)dω ≤ w + π

I ψ(ω) = quality of variety (firm) ω

I Ωl determined in equilibrium

Demand: c(ω) = Pσ−1(w + π) ψ(ω)σ p(ω)−σ

Details

Active Firm’s Problem

I 2 steps

1. Maximize profits in each market N ∈ [0, N∗]2. Choose N∗ ∈ [0, 1/2]

1. In each market N

π∗(ψ,N) = maxq,l,d

p(q(ψ,N))q(ψ,N)− wl(ψ,N)− pDd(ψ,N)− wf(N)

s.t. l(ψ,N) = q(ψ,N)

d(ψ,N) = (1 + εN)q(ψ,N)

f(N) = f (1− 2N)−β

2. N∗(ψ) solves π∗(ψ) = maxN∗(ψ)

∫ N∗(ψ)

02π∗(ψ,N)dN

Active Firm’s Problem

I 2 steps

1. Maximize profits in each market N ∈ [0, N∗]2. Choose N∗ ∈ [0, 1/2]

1. In each market N

π∗(ψ,N) = maxq,l,d

p(q(ψ,N))q(ψ,N)− wl(ψ,N)− pDd(ψ,N)− wf(N)

s.t. l(ψ,N) = q(ψ,N)

d(ψ,N) = (1 + εN)q(ψ,N)

f(N) = f (1− 2N)−β

2. N∗(ψ) solves π∗(ψ) = maxN∗(ψ)

∫ N∗(ψ)

02π∗(ψ,N)dN

Active Firm’s Problem

I 2 steps

1. Maximize profits in each market N ∈ [0, N∗]2. Choose N∗ ∈ [0, 1/2]

1. In each market N

π∗(ψ,N) = maxq,l,d

p(q(ψ,N))q(ψ,N)− wl(ψ,N)− pDd(ψ,N)− wf(N)

s.t. l(ψ,N) = q(ψ,N)

d(ψ,N) = (1 + εN)q(ψ,N)

f(N) = f (1− 2N)−β

2. N∗(ψ) solves π∗(ψ) = maxN∗(ψ)

∫ N∗(ψ)

02π∗(ψ,N)dN

Entry & Exit

I Entry & Exit:

1. Entrant pays sunk cost wfE2. Draw ψ from distribution g(ψ)3. If π∗(ψ) ≥ 0 produce, otherwise endogenously exit (defines ψ)4. Active firms exit with exogenous probability δ

I Focus on stationary equilibria in whichI Mass of successful entrants = mass of exiting firms

I Free entry condition: expected profits from entry = wfE

Sketching model solution Market Clearing Equilibrium

Productive firms sell to more markets

Set β = 0 for closed-form solutions.

I Constant fixed cost of accessing new markets

N(ψ)∗ =1

ε

(ADw

(σ − 1

σ

)(L

fσ

) 1σ−1

ψσσ−1 − (AD + 1)

)

→ Higher ψ firms reach more consumers.

Low ε drives out low TFP firms

N(ψ)∗ =1

ε

(ADw

(σ − 1

σ

)(L

fσ

) 1σ−1

ψσσ−1 − (AD + 1)

)

I Lower εI All active firms sell a further distanceI w ↑ to restore labor market clearing

ψ = w

(1 +

1

AD

)σ−1σ(σf

L

) 1σ(

σ

σ − 1

)σ−1σ

I ψ ↑: low quality firms driven out of the market

Table of Contents

Data and Empirical Results

Model

Simple Quantitative Exercise

Outline

1. Calibrate ε, β and AD to match:I Aggregate and average distribution share of sales

I Elasticity of distribution expenses wrt size

2. Effect of ↓ ε within the modelI Reduction in cost of shipping longer distances

I Improving highway network

3. Improvements in productivity of distribution sector (AD):I Model predictions for distribution share

I ε = 0 vs ε > 0

Calibration

Calibrate 3 main parameters (11 total) to match 3 key moments.All parameters

Parameter Value

Rate Distribution Costs ↑ With Distance ε 20Productivity of Distribution Sector AD 70Rate Fixed Costs ↑ With Distance β 2

Moment Data Model

Elasticity of distribution costs wrt size 1.20 1.21Aggregate distribution share 3.5% 3.5%Average distribution share 2.2% 2.0%

Impact of ε

Increase in AD: model and data

1995-2009: “AD” increased by ≈ 51%

1. Compare predicted effects on distribution share in baseline model.

Data Baseline ε = 0

AD +51% +51%Aggr. distr share −35% −31%Elasticity of distr costs ≈ 0% +0.5%

Median EmploymentAverage EmploymentWelfare (TFP)

Increase in AD: model and data

1995-2009: “AD” increased by ≈ 51%

1. Compare predicted effects on distribution share in baseline model.

2. Compare to model withI ε = 0I AD recalibrated to match aggregate distribution share

Data Baseline ε = 0

AD +51% +51% +51%Aggr. distr share −35% −31% −35%Elasticity of distr costs ≈ 0% +0.5% -

Median Employment +5.2% +1.8%Average Employment +5.7% +1.8%Welfare (TFP) +1.80% +1.79%

Conclusion

1. Stylized FactI Distribution costs non-trivial

I Distribution costs / sales increasing in plant size

2. 2-Sector ModelI Firms sell to consumers & incur distribution costsI Higher quality firms: profitably sell to more distant consumers

I More customers, ↑ total sales, ↑ distribution share of sales

3. Preliminary Quantitative ResultsI ↓ in rate at which distribution costs increase with distance

I ↑ in welfare

I ↑ in median plant size

Next Steps

Focus explicitly on wholesale / retail sector

I Fragmentation ⇒ ↑ fixed costs: related to β graph

I How do we get discipline on this?I NSS Traders Survey (1991 & 1997)

Use variation across time and geography

I Infrastructure improvements (GQ)

I ‘Fragmentation of distribution sector’

I FDI liberalization in distribution sector 2011

THANK YOU

Robustness

I Robust to measure of size & geographic aggregation

I Not driven by exporters ⇒ intranational distribution costsI Exporters by Decile Distribution Share non-exporters

I Not driven by reporting of 0’s (≈ 21.5% of plants)I Zeros by Decile Distribution Share vs Size

I All components of distribution expenses increase with sizeI Distribution Subcomponents

I Opposite relationship on inward freight costsI Inward Freight Share vs Size

I Different from other inputs (labor, materials):I Labor share decreasing with plant size

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Other Quotes

I In India, Distribution is God (Harvard Business Review,2012):

“In India, because of fragmented distribution networks, it’sdifficult for a new venture to get its products to a large audience.In the US, innovative companies can bypass delivery problems by

working directly with large consumer-facing hubs such asWal-Mart (old), Amazon (new), or iTunes (new, new), which

allows them to quickly and efficiently reach early adopters”

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Aggregate Labor

Π = J

∫ψ∈Ψ

π(ψ)µ(ψ)dψ

LD =J

AD

∫ψ∈Ψ

d(ψ)µ(ψ)dψ

LP = J

∫ψ∈Ψ

(l(ψ) + fN∗(ψ))µ(ψ)dψ

LE = fEδME

I µ(ψ) = equilibrium quality distribution

I ME = mass of potential firms

I N∗(ψ) = optimal N for firm of productivity ψ

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Distribution Share vs Size

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Distribution Share vs Size

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Distribution Share vs Size (Exports I)

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Distribution Share vs Size (Exports II)

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Distribution Share vs Size(Sub-Components)

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Distribution Share vs Size (Zeros I)

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Distribution Share vs Size (Zeros II)

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Inward Freight Share vs Size

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Indian ASI: Data Cleaning Steps

Step Cleaning # of Dropped Obs Remaining Obs

1 Open plants (1993-2007) – 547,1542 Missing key variables 110,035 437,1193 Missing distribution 17,179 419,9404 Trimming Extreme Values 3,351 416,5895 Consistent Sectoral Definitions 7,216 409,373

I Key variables are:I Output, employment, labor cost, intermediates, capital.

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Sketching solution

I Free entryI average profits = π = 0I consumer’s income = w = GDP per capita

I Demand for good of quality ψ:

c(ψ,N) = w ψσ p(ψ,N)−σ

I Each level of w determinesI Cut-off productivity ψI Total sales (and hence labor demand) of firms with ψ > ψ

I In equilibrium, w is such thatI L = Le + Lp + Ld

I Expected operating profits P (ψ > ψ) πo = wfe

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Market Clearing Conditions

1. Aggregate Labor Constraint:

LD + LP + LE = L

I LD = labor in distribution sectorI LP = labor in production sector (variable & fixed)I LE = labor for entry

2. Aggregate Budget Constraint:

wL+ Π =

∫l∈[0,1]

∫ω∈Ωl

pl(ω)cl(ω)dω

I Π = aggregate profits (net of entry costs)

Expressions back

Equilibrium

Given a quality distribution g(ψ), an equilibrium is set of:

1. prices pD, w, P, p(ψ,N)2. quantities LD, LE , LP , c(ω), q(ψ), l(ψ), d(ψ), J,ME

such that

1. Consumers optimize subject to their budget constraint

2. Active firms optimize subject to constraints

3. Production = consumption ∀ω4. Aggregate constraints hold

5. Free entry condition holds

Focus on stationary distribution of firms:

I Net Entry = 0

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————————————————————————————

Solution to Consumer’s Problem

Demand:

c(ψ,N) = Pσ−1yψσp(ψ,N)−σ

Price Index:

P ≡ 1 =

[2J

∫N∈[0, 12 ]

∫ψ∈Ψ

ψσp(ψ,N)1−σf(ψ,N)dψdN

] 11−σ

I Symmetry across all points on the circle → price index identical

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Productivity Improvements inDistribution Sector

Impact of β

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Calibration

I Distribution of ψ = truncated Pareto (η, ψmin, ψmax)

Parameter Value

Rate Distribution Costs ↑ With Distance ε 20Productivity of Distribution Sector AD 70Rate Fixed Costs ↑ With Distance β 2

ψmin .5ψmax 3

Aggregate Labor L 1Fixed Cost f .01Fixed Entry Cost fE .05Exit Rate δ .05Pareto Shape Parameter η 4.2Elasticity of Substitution σ 3

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