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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
Leandro Freylejer Firm Heterogeneity, Directed Search and Trade
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)
Leandro Freylejer Firm Heterogeneity, Directed Search and Trade
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
Leandro Freylejer Firm Heterogeneity, Directed Search and Trade
Heterogeneous Firm Models-Exporting Decisions
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))
Leandro Freylejer Firm Heterogeneity, Directed Search and Trade
Heterogeneous Firm Models-Exporting Decisions
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)
Leandro Freylejer Firm Heterogeneity, Directed Search and Trade
Heterogeneous Firm Models-Exporting Decisions
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
Leandro Freylejer Firm Heterogeneity, Directed Search and Trade
Heterogeneous Firm Models-Exporting Decisions
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
Leandro Freylejer Firm Heterogeneity, Directed Search and Trade
Heterogeneous Firm Models-Exporting Decisions
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
Leandro Freylejer Firm Heterogeneity, Directed Search and Trade
Heterogeneous Firm Models-Exporting Decisions
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
Leandro Freylejer Firm Heterogeneity, Directed Search and Trade
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
Leandro Freylejer Firm Heterogeneity, Directed Search and Trade
Data: Does the ranking order of exporting markets hold?
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
Leandro Freylejer Firm Heterogeneity, Directed Search and Trade
Data: Does the ranking order of exporting markets hold?
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
Leandro Freylejer Firm Heterogeneity, Directed Search and Trade
Data: Does the ranking order of exporting markets hold?
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
Leandro Freylejer Firm Heterogeneity, Directed Search and Trade
Data: Does the ranking order of exporting markets hold?
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)
Leandro Freylejer Firm Heterogeneity, Directed Search and Trade
A Directed Search Model
Why would a firm sell in a non-optimal market?
Leandro Freylejer Firm Heterogeneity, Directed Search and Trade
A Directed Search Model
Why would a firm sell in a non-optimal market?
Leandro Freylejer Firm Heterogeneity, Directed Search and Trade
A Directed Search Model
Why would a firm sell in a non-optimal market?
Leandro Freylejer Firm Heterogeneity, Directed Search and Trade
A Directed Search Model
Why would a firm sell in a non-optimal market?
Leandro Freylejer Firm Heterogeneity, Directed Search and Trade
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
Leandro Freylejer Firm Heterogeneity, Directed Search and Trade
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
Leandro Freylejer Firm Heterogeneity, Directed Search and Trade
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’
Leandro Freylejer Firm Heterogeneity, Directed Search and Trade
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
Leandro Freylejer Firm Heterogeneity, Directed Search and Trade