eco364 - international trade - chapter 7 - heterogenous firms

ECO364 - International TradeChapter 7 - Heterogenous Firms

Christian Dippel

University of Toronto

Summer 2009

Christian Dippel (University of Toronto) ECO364 - International Trade Summer 2009 1 / 42

Firm Heterogeneity Introduction

I In the chapter on Monopolistic Competition we developed a model ofintra-industry trade.

I In that model, we allowed for product differentiation but assumedthat all firms are homogenous and symmetric.

I This meant that all firms are exporters and each firm sells the sameshare in each country regardless of the firm’s location.

I Because of better firm-level data, we now know that this is far fromtrue and that firm-heterogeneity is very important.



Some facts

I In most OECD-countries across most industries, only about 20% offirms export

I These exporters typically sell only about 20 % of their output abroad

I Exporters are bigger and more productive than non-exporters andMultinational Enterprises (MNE) with foreign affiliates are evenbigger and more productive yet.

I Fixed/sunk organizational costs of being an exporter seem to beimportant

I Trade Liberalization leads to within-industry restructuring with morefirms becoming exporters, some non-exporters going bankrupt andaverage productivity increasing.



I We need to have a model that rationalizes these patterns and let’s usask:

I What kinds of firms export or become MNEs?

I What role do Fixed/Sunk costs of different organization forms play?

I How does trade liberalization affect firms of differing size?I Why does aggregate sector-productivity increase after

trade-liberalization?



Exporters tend to “outperform” firms that only service the domesticmarket.

Table: Trade by Commodities (1995)

Export PremiumVariable Canada United States

(%) (%)

Wage — 9.3Wage (skilled workers) — 5.4

Wage (unskilled workers) — 7.4Value Added per Worker 48.2 15.8Total Factor Productivity 12.4 11.0Capital per Worker (K/L) 34.0 9.3

Source: Baldwin and Gu (2003) and Bernard and Jensen (1995, 1999) for U.S. Data.



Model Idea

I Basic idea: there are high and low productivity types of firms.

I There are fixed costs of (a) producing and (b) of exporting or settingup a plant in a different country and becoming a MNE.


The “Melitz Model” Selecting into Types

Timing

I Let’s sketch out a version of the model without exporting to get thebasic elements.

I Timing:I Firms enter an industryI After they enter, they learn their productivity level αI Once they know their productivity, they decide if they stay in the

market and produce and whether they serve only the domestic or boththe domestic and foreign market



I One factor of production: labor.

I All firms face the same cost of labor (w).

I Each firm produces a different and imperfectly substitutable variety.

I Demand for a variety j is xj = Sp−εj where ε > 1 is the demand

elasticity.I Each firm produces at most one variety so varieties and firms are

synonymous.I Generally, this model can be viewed as an extension of the

Monopolistic Competition Model to firm heterogeneity.



Cost-Structure

I There are fixed and variable costs.

I To produce at all firms must incur a fixed cost wLD , where LD is afixed amount of labor that must be employed for any production tooccur multiplied by the wage rate w .

I If a firm wants to export it needs to incur additional organizationalfixed costs of setting up a distribution network. These are wLE

I A firm’s variable costs per unit depend on the productivity draw andcan be written as w/α



Decision to produce at all

I Firm j maximizes π(α) = (pj − w/αj)xj − wLD with respect to pj

I where xj = Sp−εj

I The optimal solution is pj = 1−εε w/α (the optimal price is a markup

over marginal cost)

I Plugging this back into π gives us π(j) = αε−1j B − wLD , where B is a

constant term (depending on ε and w) that does not vary by firms.



I Let us for simplicity write αε−1j = a so that we can write profits as

π(a) = aB − wLD

I With ε > 1, profits are strictly increasing in a so that there is a cutoffpoint aD below which a domestic producer cannot earn positive profits

I Only firms with a above that cutoff will produce, the others drop out.



Model: No Exporting



Exporting

I Now suppose that firms can export to a foreign market with demandx∗j = S∗((1 + τ)pj)

−ε

I The demand level S∗ can be different in Foreign but moreimportantly, trading costs τ drive a wedge in between the producerand consumer prices.

I To export, firms must incur a fixed cost wLE to set up a distributionnetwork

I We assume that it is more costly to serve the foreign than the domesticmarket: LE > LD

I The same maximization as before gives us πE (a) = aB∗ − wLE

I We assume B∗ < B. This might be true because the foreign market issmaller but more importantly it is caused by trading costs τ .

I B∗ < B and LE > LD imply that πE (a) lies everywhere below π(a) sothat the productivity cutoff for exporters is above the productivitycutoff for firms that sell only domestically

I This is because productivity pertains only to variable costs and B∗ putsa lower weight on this variable cost-productivity than B.



I Note that every every exporting firm also sells domestically

I We can therefore write the profits of an exporter asπx(a) = πE (a) + π(a)

I πx(a) is “shifted down” relative to the “domestic” profit functionπ(a).

I It is also steeper because the returns to having a higher productivitylevel are greater due to being able to access foreign markets.



I Now we have an industry structure where firms sell domestically onlyif π(a) = max{0, π(a), πx(a)}

I Firms sell domestically and internationally ifπx(a) = max{0, π(a), πx(a)}

I The model-structure generates a partition of firms into domestic andinternational producers.



Upper Envelope of Profit-Functions



MNE and Horizontal FDI

I It is easy to incorporate Multinational Corporations (MNE) into thisframework.

I Here is the intuition:I A firm that wants to serve foreign markets can do so by exporting or by

opening a plant in the foreign market through a Foreign DirectInvestment (FDI) and serving from there.

I The trade-off is that having a plant in the foreign market reducestransportation costs (variable costs) but incurs a higher fixed cost thanexporting

I This can be easily incorporated in the above model with a B∗FDI > B∗

and LFDI > LE

I The result is a partition where the most productive exporters becomeMNEs.



Horizontal and Vertical FDI

I The FDI described above is of the horizontal type.

I Horizontal means that a firm chooses where to locate the entireproduction process (KO Ch.7).

I The trade-off is one between higher fixed costs of operating in aforeign country and lower variable costs of serving the foreign country

I This is in contrast to vertical FDI, where firms locate in low-wagecountries to reduce production costs and not to be closer to foreignmarkets

I Most North-North and South-North FDI are of the horizontal type.North-South FDI is of the vertical type.

I We re-visit vertical FDI in the next chapter on the fragmentation ofthe production process.


The “Melitz Model” Trade Liberalization

Trade Liberalization

I How does trade liberalization affect the industry equilibrium in thismodel?

I Suppose trade liberalization means that trading costs fall in bothcountries.

I Lower tariffs in Foreign open new profit-making opportunities fordomestic exporters.

I This is easy to see as a reduction in τ

I Lower tariffs in Home lead to increased competition from aborad indomestic markets.

I This actually does not show up in the domestic demand function wewrote down. To keep things simple, let’s simply assume that there is asome term denoting foreign competition that enters the demandfunction negatively.



I With access to foreign markets, large firms are able to move downtheir average cost curves and increase production.

I This causes two specific changes to the above system:I Increases competition at home from both larger domestic exporting

firms and increased competition from abroad.I This causes profits to fall for each level of productivity (a shift down).I The marginal return to productivity (B∗) increases as tariffs are less

restrictive.

I Let’s examine the effects of trade liberalization in two parts: theeffects of increased competition (i.e. lower domestic tariffs) and theeffects of lower foreign tariffs.



The Effect of Increased Competition



I Because of increased competition, the minimum levels of productivityneeded to produce profitably increases.

I The minimum level of productivity needed to export profitably alsoincreases.

I Let us compare this to the effect of the lower foreign tariffs:



The Effect of Lower Tariffs



With lower tariffs, the minimum level of productivity needed to export falls.



I Trade increases the minimum level of productivity necessary toproduce domestically.

I Increased competition diminishes profitability.I Firms that produce domestically do not benefit from increased market

access.

I There are conflicting effects on firms that export.I Increased competition lowers profitability.I Increased market access abroad increases profitability.I In sum, the level of productivity necessary to export falls.



Upper Envelope before Trade Opening



Upper Envelope after Trade Opening



Trade Liberalization changes the selection process



Marginal producers close down or move into exporting



I Key points that you should concentrate on...

1. The least productive firms go out of business or stay out of business.2. Intermediate productivity firms’ profits fall due to increased

competition.3. Most productive firms’ profits rise due to increased market access

abroad.

I This model creates a new way of thinking about the winners andlosers’ from trade liberalization.



Embedding Melitz in Heckscher-Ohlin

I Let’s briefly think about a two-factor version of Melitz

I Sectors vary in factor-intensity and there is Heckscher-Ohlin typeComparative Advantage

I Trade opening of the form discussed above will lead sectors to expandthat use intensively the abundant good.

I This implies that Heckscher-Ohlin type CA in this model causesRicardian CA!

I Because it improves productivity



I We have created a Ricardian model.

I because trade depends on technology differences

I However, unlike the basic Ricardian model, there are winners andlosers from trade.

I because firms vary in their productivity.

I In addition, it provides a framework where increased “openness”causes higher levels of income through reallocation of output to themost productive firms.

I Also provides a rationale for why exporters are more productive: the“selection effect.”



Application: The Effect of NAFTA on Canadian Firms

I Read the New York Times’ write-up of Daniel Trefler’s work onNAFTA.

I While NAFTA went into force in 1993, the Canadian-American FreeTrade Agreement (FTA) was enacted in 1989.

I Involved tariff concessions by both Canada and the United States.

I Prior to this one in four Canadian industries were protected byaverage stated tariffs of at least 10%.

I Canadian firms were protected by average tariffs of 8.1%



I Partially due to a lower tariffs against American goods, Canadianmanufacturing fell by 5% (100,000 jobs!)

I What is the counterfactual? Unclear.

I However, within ten years, employment rates had recovered.

I “..the employment gains by more productive firms more than offsetthe employment losses in less productive firms.”



I In formerly sheltered industries, labor productivity (value added perworker) grew by 15%.

I Approximately half of this productivity gain came from reallocationacross firms

I Firm heterogeneity model explains this first half.I Note that the remainder came from within firm improvements, which

we have not modeled here.

I Interestingly, in the sectors that benefited most from tariff cuts, theleast productive firms contracted/suffered.

I Explicitly predicted by the above model as the most productive firmsenhance their productive scale.



Intensive and Extensive Margins of Trade

I Note that increased trade will come from some incumbent exportersexporting more and some firms that did not previously exportbeginning to export.

I The increase in trade that occurs in firms that were previouslyexporting is referred to as the intensive margin of trade.

I The increase in trade that occurs from new exporters is referred to asthe extensive margin of trade.

I This way, can decompose the total increase in trade into intensivemargin and extensive margin.

I For example, if exports increase by 10% then 8% can be due to theintensive margin and 2% can be due to the extensive margin.

I Different studies examining different countries find mixed evidenceregarding which margin dominates.


eco364 - international trade - chapter 7 - heterogenous firms

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