Melitz (2003) model - firm heterogeneity

1990 firm level data revolution findings

Only a small fraction of firms export

Exporters sell most of their output domestically

Exporters are bigger than non-exporters

• increasing RtS means larger firms can divide fixed costs over more units

Exporters are more productive than non-exporters

• Increasing RtS + size leads to increased productivity

Trade liberalisation reduces a firm’s probability of surviving

• pushing less productive firms out as competition increases

• Trade costs fall

Trade liberalisation increases share of exporting firms

• Surviving firms take up left over share from pushed out firms

• More firms export as TC reduced → more productive firms select into the export market

Selection → trade liberalisation increases aggregate productivity as least productive firms ‘die’

• K, L reallocated to surviving firms (less consensus)

• Learning by exporting

Who exports

2002 US firm census

• Under 35% of firms in an industry

• Of exporting firms, only 10-20% of shipments are exports

How Melitz (2003) built on Krugman (1980)

Within-sector firm level heterogeneity

• in size and productivity

Included fixed / sunk costs → leads to only most productive firms exporting

Kept Monopolistic competition framework

Preferences under Melitz

Constant elasticity of substitution (CES) over a continuum of varieties

ω ε (0, M)

Utility function

0 < ρ < 1 & σ = 1 / (1 - ρ) > 1

Technology function

Each variety will now have a different productivity

Trade costs and extensive margin of export

As TC increase → reduces prob of firm entering X market

• effect weaker for more productive firms

Low barriers to trade = more firms exporting

Household problem - Melitz (2003)

Household problem solved for variety

Price index function

Firm problem - Melitz (2003)

Firm problem - markup / optimal pricing

More productive firms can set lower prices

use w as the numeraire (set = 1)

L = 1 by assumption

Optimal profit function

B is exogenous - depends on economy so B is the same for all firms

Mono C - each variety produced by 1 firm so can replace variety (ω) with productivity (φ)

Survival cutoff

firms pay a fixed cost of entry (f_e)

• to draw productivity from a given distribution and earn profits

If profits > 0 then firm produces, otherwise exit

Zero Profit Condition (ZPC)

φ* - minimum productivity firm that is indifferent between producing & exiting

profits solution

Free entry (FE)

Firms enter up to point they expect to stop making profits

To find out firm type is costly but reveals their productivity

Firms know the distribution of productivities and so join based on expectations

Expected productivity drop (of paying Fixed C) > cutoff productivity OR cost of learning firm productivity -> join market

EQ in autarky - profits & productivity

EQ in autarky - B & productivity

Selection in autarky

Firms only enter if expected profit > f_E

Firms below φ* do not produce

w = 1 as numeraire but show for generality

Open to trade assumptions

2 identical countries

GFT from variety + selection

Fixed cost of exporting and dom sales

• only most productive / largest can pay to export

Exporting has iceberg TC

Firm problem - trade

Symmetrical apart from iceberg cost

w = w* , B = B*, L = L^F (=1), P = P^F as symmetric countries

Solve dom & X markets separately

Firm problem solved for markup pricing - trade

Markup depends on elasticity of substitution

Cutoffs with trade

Cutoff ratio

Selection in open economy

π = π_D + π_X

ZPC in open economy

Free entry with trade

Profit in open economy

EQ in open economy - graph

Cutoff shifts upward when opening up to free trade

• leads to fewer but more productive firms

Trade liberalisation & cutoff ratio graph

Conditional on surviving, TC fall makes X easier BUT dom cutoff higher

Trade lib & selection effects on productivity

Reduction in TC makes F firms more competitive

• Dom market D falls so non-exporters lose market share

• Least productive dom firms exit → Min dom productivity rises

Trade lib makes X cheaper

• Most productive non-exporters start exporting

• Min productivity to X falls

Raises industry avg productivity

Avg productivity at entry

Pareto distribution with k > 1

low k = few very productive firms and many small low productivity firms

High k means productivity more evenly distributed

Welfare and Price index

Welfare is proportional to price index (P)

P is a negative function of avg productivity

Increasing avg productivity generates new GFT - selection

Price index, Demand and trade

Dom market D changes when opening to trade: B → B^A

• B < B^A

Due to GFT, P must be lower under trade

• Therefore profit (trade vs autarky) curves must intersect

Winners and losers - graph

Winners and losers from trade

Compared to autarky

• All non-exporters lose profits → some lose all and exit

• Least productive exporters lose profits & Only most productive exporters gain

• Since productivity distribution highly skewed, there are only few firms at the top → gains highly concentrated

Unequal gains

• All Consumers gain - trade leads to lower P + love for variety

• Small firm owners / entrepreneurs lose → may shut down

• A few large firm owners gain → concentrates market share / profits even more

Extending model to account for unemployment

Allowing for unemployment shows workers in ‘losing firms’ either lose their jobs or have to take a pay cut

Even though unemployment may be reduced, workers still worse off in smaller firms FROM TRADE