Firm Heterogeneity, Directed Search and Tradehomes.chass.utoronto.ca/~pitchik/4060/10LeandroFPapProp.pdf · Leandro Freylejer Firm Heterogeneity, Directed Search and Trade. Heterogeneous

Firm Heterogeneity, Directed Search and Trade

Leandro Freylejer

March 16th, 2011

Leandro Freylejer Firm Heterogeneity, Directed Search and Trade

Quick roadmap

Export decisions in heterogeneous firm models

Data patterns

A directed search model

Modeling issues

Conclusion


Heterogenous Firm Models

Exogenous source of heterogeneity −→ firm specificproductivity

Product differentiation −→ monopolistic competitive models

Continuum of firms −→ no interaction of firms

Two sources of exporting costs:

Market penetration costs (fixed costs)

Iceberg costs (variable costs)


Heterogeneous Firm Models-Exporting Decisions

Firm j’s profit from selling in market i is:

Maxpi (j)

{πi (j) =

[pi (j)−

c

ϕ(j)(1 + di (j))

]q(pi (j))− fi (j)

}Solution to this problem:

pi (j) =ηq,pc(1 + di (j))

(ηq,p − 1)ϕ(j)

pi (j) ≥ 0 iff ηq,p ≥ 1



The profit function is then:

πi (j) =

[ηq,pc(1 + di (j))

(ηq,p − 1)ϕ(j)− c(1 + di (j))

ϕ(j)

]q(pi (j))− fi (j)

Two possibilities:

ηq,p = σ → CES (Krugman(1980), Melitz(2003))

ηq,p varies with q (Krugman(1979), Melitz & Ottaviano(2008))



Intensive Margin of Trade:

Under CES the demand is:

qi (j) = QiPσi

[σc(1 + di (j))

(σ − 1)ϕ(j)

]−σ︸︷︷︸

pi (j)

Increasing in total expenditure of country i, Qi

Decreasing in competition −→ varieties↑ → Pi ↓ → qi (j) ↓

Decreasing in price, pi (j)



Extensive Margin of Trade:

A firm j in n will export to market i if:

πi (j) ≥ 0⇒

[(σ − 1)(σ−1)

c(σ−1)

]ϕ(j)(σ−1) ≥ fi (j)(1 + di (j))(σ−1)

QiPσi

Lefthand side is origin-destination specific:

rn,i =fn,i (1 + dn,i )

(σ−1)

QiPσi

Assume i = 1, ..., I and for a given n order markets as follows:

r1 < r2 < r3 < ... < rI



From the previous analysis note the following

1 If the j th firm in n export to rI , it will also export to rI−1, ..., r1

2 Conditional on exporting, firm j :

exports more to market ri than to market ri+1

makes more profit in market ri than in market ri+1

3 If for j = z and j = t, where z 6= t, ϕ(z) > ϕ(t), then z

export to at least the same markets than t and possibly more

∴ r1 < r2 < r3 < ... < rI ⇒ r1 � r2 � r3 � ... � rI



From the previous analysis note the following

1 If the j th firm in n export to rI , it will also export to rI−1, ..., r1

2 Conditional on exporting, firm j :

exports more to market ri than to market ri+1

makes more profit in market ri than in market ri+1

3 If for j = z and j = t, where z 6= t, ϕ(z) > ϕ(t), then z

export to at least the same markets than t and possibly more

∴ r1 < r2 < r3 < ... < rI ⇒ r1 � r2 � r3 � ... � rI



Extensions:

Melitz & Ottaviano (2008) → no CES

Arkolakis (forthcoming) → consumer margin

Leleeva & Trefler (2010) → exporting raises productivity

Heterogeneous firm models with domestic frictions

Manova (2010) → financial constraints

Fajgelbaum (2010) → labor market constraints


Data: Does the ranking order of exporting markets hold?

Table: French Firms Exporting to the Seven Most Popular Destinationsa

Country Number of Exporters Fraction of Exporters

Belgium (BE) 17,699 52%Germany (DE) 14,579 42.8%Switzerland (CH) 14,173 41.6%Italy (IT) 10,643 31.3%United Kingdom (UK) 9,752 28.7%Netherlands (NL) 8,294 24.4%United States (US) 7,608 22.4%

Total Exporters 34,035

aSource:EKK(2008),p.63



Table: French Firms Selling to Strings of Top Seven Countriesa

Number of French ExportersCountry Data Under IndependenceModel

BE 3,988 1,700BE-DE 863 1,274BE-DE-CH 579 909BE-DE-CH-IT 330 414BE-DE-CH-IT-UK 313 166BE-DE-CH-IT-UK-NL 781 54BE-DE-CH-IT-UK-NL-US 2,406 15

Total 9,260 4,532

aSource:EKK(2008),p.63



From French firm level data

27% of firms adhere to the hierarchy

73% of firms do not adhere to the hierarchy

In aggregate → better ranked markets attract more firms

Model should include both: hierarchy and possible deviations



EKK (2008) −→ add producer-destination shocks:

αi (j) (demand shock)

εi (j) (fixed cost shock)

Previous Expression is now:

(σ − 1)(σ−1)σ

c(σ−1)ϕ(j)(σ−1) ≥ εi (j)fin(1 + din)(σ−1)

αi (j)QiPσi

Ranking is now firm specific



Intuition

Firm uncertain about demand levels (e.g. experimentation

problem)

Firm uncertain about exporting fixed costs (e.g. product

requirements)

Matching model to data −→ calibrate αn(j), εn(j) joint dist.

Ad-hoc solution to the problem (no micro-foundations)


A Directed Search Model

Why would a firm sell in a non-optimal market?











A Directed Search Model: Model Description

Intermediaries post ‘vacancies’

Heterogeneous firms search for intermediaries in international

markets

Directed Search is costly and outcome is uncertain

Better ranked markets −→ higher tightness

On the match search −→ higher matching probability(Networking effect)

Remark:

Demand uncertainty is endogeneous

Selling in sub-optimal markets → maximizing life-time profit


A Directed Search Model: Note on Model’s Interpretation

Two alternative interpretations

Networking Effect (Chaney 2011)

Quality of products, demand uncertainty and experimentation

Modified version of networking effect:

Easier to model

Empirical evidence


A Directed Search Model:Modeling Issues

Tractability of distribution:

On the match search&

Directed Search

→ block recursive equilibrium(Shi 2008, 2009, 2010)

Two sources of heterogeneity:

1 productivity

2 destination

Competitive market for intermediation

Separate ‘trade’ analysis from ‘search’


Conclusion

In models of trade entry decisions are static andover-simplified

Empirics differ from this simplified extensive patterns of trade

Recent models that try to reconcile data with theory eitheronly improve on the intensive trade or they add ad-hoc firmspecific shocks

I propose a directed search model based on network effectswhich are empirically relevant (see Chaney 2011)

Not the first research to propose search in trade, but first oneto propose an analysis where firms search for internationalmarkets


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Firm Heterogeneity, Directed Search and Tradehomes.chass.utoronto.ca/~pitchik/4060/10LeandroFPapProp.pdf · Leandro Freylejer Firm Heterogeneity, Directed Search and Trade. Heterogeneous