Food Processing Firms, Input Quality Upgrading and Trade

Eric Tseng and Ian Sheldon

Virginia Tech AAEC Seminar, April 17th, 2015

Motivation - Quality Matters❖ Quality an important determinant of trade flows (Linder 1961)

❖ Schott (2004) and Hummels & Klenow (2005) link exporter GDP per capita and product quality

❖ Hallack (2006) links product quality to importer GDP per capita

❖ Manova & Zhang (2012) show successful exporting firms in China use higher-quality intermediate inputs to produce higher-quality goods and firms vary quality of produces across destination markets

❖ Vertical product differentiation matters and should be modeled

Motivation - Food Markets❖ Food markets no longer characterized by homogenous products (Sexton 2013)

❖ Food quality matters, and firms in food industry use vertical product differentiation strategies

❖ Sunk costs related to production capacity and product quality matter

❖ Curzi, Raimondi & Olper (2014) investigate impact of trade liberalization on food product-quality

❖ Trade liberalization in exporting countries leads to faster upgrading of product quality for products closer to technology frontier

❖ On average, EU voluntary food-quality standards have positive effect on rate of quality upgrading

Goals of Analysis❖ Use modified heterogenous-firms framework allowing

for intermediate input markets (Kugler & Verhoogen, 2012)

❖ Extend to focus on food quality and quality of agricultural inputs (Sexton, 2013), the impact of trade liberalization on food product-quality (Curzi et al, 2014)

❖ Examine closely relationship between food product-quality, trade liberalization, and ability of firms to upgrade quality of final goods

Model - Consumers

❖ Consumers:

❖ Utility

❖ Demand

(1) U = q(ω )x(ω )( )σ −1σ dω

ω∈Ω∫⎡⎣⎢⎤⎦⎥

σσ −1

(2) x(ω ) = Xq(ω )σ −1 pO (ω )P

⎛⎝⎜

⎞⎠⎟−σ

Model - Firms

❖ Firms

❖ Intermediate agricultural good produced via production function:

❖ Since intermediate input market is perfectly competitive, then

I

(3) FI (A,c) = Ac

pI (c) = c

Model - Firms

❖ Food processors (final good producers) require fixed investment cost to obtain capability , where is drawn from Pareto distribution with ,

❖ Firms must pay fixed costs to enter market, , and also incur fixed cost of exporting in all periods

fe λ λ

G(λ) = 1− λm

λ⎛⎝⎜

⎞⎠⎟k

0 < λm ≤ λ

ffx

Model - Firms❖ Firms use inputs of capability, intermediate agricultural input and

composite input of specific quality

❖ : additional tangible input that affects firm quality choice, i.e., capital equipment required to ensure quality control

❖ Production function for final good is:

φ

φ

F(n) = nλa

φ

(4) MC = φpI (c)λ a

MCX =τφpI (c)

λ a

Model - Firms

❖ Food processors constrained by quality choice

❖ Inputs as complements in determining quality of good (Kremer, 1993; Kugler & Verhoogen, 2012)

(5) q = 13λ b( )β + 1

3φ 3( )β + 1

3c3( )β⎡

⎣⎢⎤⎦⎥

Model - Firms❖ The importance of

❖ is the scope of product-quality differentiation, approximating fixed costs of investment required to translate capability into product quality

❖ Additional channel impacting firms’ quality choices, where lower restricts available quality choices, while higher has higher available quality choices

b

b

bb

Equilibrium❖ Profit maximization yields following:

(7a) c*(λ) = pI*(λ) = λ

b3

(7b) φ*(λ) = λb3

(7c) q*(λ) = λ b

(7d) pO* (λ) = σ

σ −1⎛⎝⎜

⎞⎠⎟ λ

2b3−a

pO,X* (λ) = σ

σ −1⎛⎝⎜

⎞⎠⎟ τλ

2b3−a

(7e) r*(λ) = 1+ Zτ 1−σ( ) σ −1σ

⎛⎝⎜

⎞⎠⎟σ −1

ληXPσ , η ≡ σ −1( ) b3+ a⎡

⎣⎢⎤⎦⎥

Comparative Statics❖ Comparative statics regarding effects of parameters on firm

size and final good quality choice

(8a) ∂ln r*

∂τ=

1−σ( )Zτ −σ

1+ Zτ 1−σ( )2 < 0, and ∂lnq*

∂τ=b 1−σ( )Zτ −σ

η 1+ Zτ 1−σ( )2 < 0

(8c) c*(λ) = φ*(λ) = λb3

(8b) ∂ln r*

∂b=

σ −1( )3

lnλ > 0, and ∂lnq*

∂b= lnλ > 0

Comparative Statics

❖ Comparative statics imply:

❖ Firms’ size (i.e., revenue) and the quality choice of final good increase with falling trade costs

❖ A firm that is better able to translate capability into quality produces higher-quality goods and is larger

❖ Trade costs negatively impact quality choice

Comparative Statics

Comparative Statics❖ Comparative statics examining impact of trade liberalization and ability to

translate capability on export entry cutoff point

❖ (11) states falling trade costs induce most productive non-exporting firms to enter export market, and least productive firms forced out of market, as exporting firms now capture larger market share

❖ Classic heterogenous-firms result (see Melitz, 2003)

(11a) ∂lnλ*

∂lnτ=k 1−σ( )

ηλm

fηδ fe k −η( )

ffx

⎛⎝⎜

⎞⎠⎟

k−ηητk 1−σ( )−η

η < 0

(11b) ∂lnλx*

∂lnτ= σ −1

ηλ* fx

f⎛⎝⎜

⎞⎠⎟

1ητ

σ −η−1η > 0

Comparative Statics❖ Comparative statics examining impact of trade liberalization

and ability to translate capability on market entry cutoff point

❖ These results are ambiguous in sign, due to other parameters

(12a) ∂λ*

∂b= 3kτ

−kb3+a λm f

δ fe

⎛⎝⎜

⎞⎠⎟

ln ffX

⎛⎝⎜

⎞⎠⎟− σ −1( )lnτ⎛

⎝⎜⎞⎠⎟

ffX

⎛⎝⎜

⎞⎠⎟

kηΛ− ρ f

fX

⎛⎝⎜

⎞⎠⎟

k−ηη+τ

−k3a+b

⎛

⎝⎜⎜

⎞

⎠⎟⎟

⎡

⎣

⎢⎢⎢

⎤

⎦

⎥⎥⎥

ρΛ2

(12b) ∂λx*

∂b= −λ* σ −1

3η2ffX

⎛⎝⎜

⎞⎠⎟

1ητ

σ −1η ln f

fX

⎛⎝⎜

⎞⎠⎟+ σ −1( )lnτ⎛

⎝⎜⎞

⎠⎟

⎡

⎣

⎢⎢

⎤

⎦

⎥⎥

ρ = ffX

⎛⎝⎜

⎞⎠⎟

3a + b( ), Λ = 3 η − k( )

Comparative Statics❖ (12a) is dependent on this condition:

❖ The impact of depends on shape of the distribution of firms, , i.e., market structure

(13a) ∂λ*

∂b< 0 when k <η + γ , and vice versa

γ = − ησ −1

1+ ffX

⎛⎝⎜

⎞⎠⎟

η−kητ

−k3a+b

⎛

⎝⎜⎜

⎞

⎠⎟⎟

ln ffX

⎛⎝⎜

⎞⎠⎟− σ −1( )lnτ⎛

⎝⎜⎞⎠⎟

⎛

⎝

⎜⎜

⎞

⎠

⎟⎟> 0

kb

Comparative Statics

Comparative Statics❖ (12b) is dependent on this condition:

❖ The impact of depends on extent that . If , then export rents outweigh fixed costs of exporting given an increased . If , then fixed costs of exporting outweigh export rents, leading to export exit.

(13b) ∂λX*

∂b< 0 when ln f

fX

⎛⎝⎜

⎞⎠⎟+ σ −1( )lnτ > 0, and vice versa

b fX > f f → fX

fX >> fb

Data

❖ Source: Chile’s Encuesta Nacional Industrial Anual (ENIA), an unbalanced panel data set. Industry-level tariff rates from TRAINS database (WITS).

❖ Sample years: 2001-2007.

❖ Sample size: 11,196 observations, approximately 1,600 food-processing firms per year in the sample.

Data

Data

Empirical Specifications❖ Export Entry:

❖ Market Exit:

❖ Specification forthcoming: depends on how ENIA tracks firm exit

❖ Quality Choice:

❖ Changes in Size:

(14) Pr Exporti,t = 1 Exporti,t−1 = 0( ) =α + β1 ⋅c + β2 ⋅φ + γ ⋅b +δ ⋅ Δτ + µ ⋅λ +κ ⋅X + ε

(15) q =α + β1 ⋅c + β2 ⋅φ + γ ⋅b +δ ⋅ Δτ + µ ⋅λ +κ ⋅X + ε

(16) ΔSize =α + β1 ⋅c + β2 ⋅φ + γ ⋅b +δ ⋅ Δτ + µ ⋅λ +κ ⋅X + ε

Results

Conclusion❖ Theoretical model adapts heterogenous-firms framework to food industry

context

❖ Firms that remain in the market select higher quality and are larger given falling trade costs and increased ability to upgrade quality, and use concurrently higher-quality inputs

❖ Trade liberalization forces the least productive firms out of the market while most productive non-exporters enter the export market

❖ Impact of ability to upgrade quality dependent on the market structure: distribution of firms in the market and structure of fixed costs matter

❖ Empirical analysis currently provides mixed evidence: results cast doubt on quality constraint, but generally support the impact of on firm characteristics and market structure

b