Melitz Model: Heterogenous Firm Model of Trade

Transcription

1 Melitz Model: Heterogenous Firm Model of Trade Seyed Ali Madanizadeh Sharif U. of Tech. May 7, 2014 Seyed Ali Madanizadeh (Sharif U. of Tech.) Melitz Model: Heterogenous Firm Model of Trade May 7, / 37

2 Introduction Challenges to Krugman model: There is a lot of heterogeneity across firms, within any sector. Very few firms export (import, engage in FDI) Exporters are very different from non exporters. There is a lot of reallocation between firms within sectors. Seyed Ali Madanizadeh (Sharif U. of Tech.) Melitz Model: Heterogenous Firm Model of Trade May 7, / 37

3 Introduction Figure: Bernard, Eaton, Jensen and Kortum (2003) AER Seyed Ali Madanizadeh (Sharif U. of Tech.) Melitz Model: Heterogenous Firm Model of Trade May 7, / 37

4 Introduction Figure: Bernard, Jenson, Redding and Shot (2007) JEP Seyed Ali Madanizadeh (Sharif U. of Tech.) Melitz Model: Heterogenous Firm Model of Trade May 7, / 37

5 Introduction Figure: Bernard, Jenson, Redding and Shot (2007) JEP Seyed Ali Madanizadeh (Sharif U. of Tech.) Melitz Model: Heterogenous Firm Model of Trade May 7, / 37

6 Introduction Figure: Eaton, Kortum and Kramarz (2004) AER P&P Seyed Ali Madanizadeh (Sharif U. of Tech.) Melitz Model: Heterogenous Firm Model of Trade May 7, / 37

7 Introduction Melitz Model 2003 Extension of Krugman model 1980 and Hopenhayn 1992 Chaney 2006 (NBER) & 2008 (AER) Intesnive and Extensive margins of trade Seyed Ali Madanizadeh (Sharif U. of Tech.) Melitz Model: Heterogenous Firm Model of Trade May 7, / 37

8 Model Assumptions Heterogeneity assumptions Firms differ in labor productivity Productivity is random, unobserved before firm starts. Trade barrier assumptions Firms face iceberg (variable) trade costs. Firms face fixed export costs. Simplifying assumption Symmetric countries Seyed Ali Madanizadeh (Sharif U. of Tech.) Melitz Model: Heterogenous Firm Model of Trade May 7, / 37

9 Model No differences in factor intensities One factor of production: Call it labor L with wage w Labor moves across producers but not across countries Seyed Ali Madanizadeh (Sharif U. of Tech.) Melitz Model: Heterogenous Firm Model of Trade May 7, / 37

10 Model Effi ciencies are different across producers Firms productivities distribution: g (z) (An example) Pareto distribution G (z) = Pr [Z < z] = { ( ) θ 1 z for z > z z0 0 0 for z < z 0 The range of goods to be produced or export are endogenous It is determined by the free entry conditions Each producer makes a different good: so it sells it monopolistically. The space of goods is modeled as a continuum Index the goods by j Consider 2 similar countries with trade costs = d Seyed Ali Madanizadeh (Sharif U. of Tech.) Melitz Model: Heterogenous Firm Model of Trade May 7, / 37

11 Model Firms pay an entry sunk cost f E to draw a random productivity. Then they decide to enter or not Measure M of firms are potential entrants. Production setup requires an operational fixed cost (additional labor) f o Measure M o of firms actually produce. Export also requires a fixed cost (additional labor) f x Measure M x of firms export. The range of goods to be produced or exported are endogenous. It is determined by the free entry conditions Seyed Ali Madanizadeh (Sharif U. of Tech.) Melitz Model: Heterogenous Firm Model of Trade May 7, / 37

12 Household Preferences: Spence-Dixit-Stiglitz (SDS) A CES over the continuum of goods: ( ) σ U = y (j) (σ 1)/σ σ 1 dj σ > 1 Budget Constraint: p (j) y (j) dj = X = wl + Π X : Total Spending Seyed Ali Madanizadeh (Sharif U. of Tech.) Melitz Model: Heterogenous Firm Model of Trade May 7, / 37

13 Household Demand for good j : ( ) p (j) (σ 1) x (j) = X P where ( ) 1/(σ 1) P = p (j) (σ 1) dj Seyed Ali Madanizadeh (Sharif U. of Tech.) Melitz Model: Heterogenous Firm Model of Trade May 7, / 37

14 Producer The market structure is monopolistic competition. Each good is produced by a separate monopolist who takes total spending X and the price index P in each market as given. Markets are segmented so that producers can set a different price in each national market. Producers draw their random productivity from a cumulatative distribution function F (z). For analytical tractabality, We assume G (z) = Pr (Z > z) is pareto distributed. Seyed Ali Madanizadeh (Sharif U. of Tech.) Melitz Model: Heterogenous Firm Model of Trade May 7, / 37

15 Producer Profit maximization of a firm with productivity z Constant Markup m = over price: σ σ 1 p (z) = m w in local market z p (z) = m wd in export market z is the price of a producer with effi ciency z Seyed Ali Madanizadeh (Sharif U. of Tech.) Melitz Model: Heterogenous Firm Model of Trade May 7, / 37

16 Firm s Revenue Consider 2 similar countries and trade costs d HF = d FH = d Revenue of a local producer: r (z) = z σ 1 ( mw) (σ 1) P σ 1 X Seyed Ali Madanizadeh (Sharif U. of Tech.) Melitz Model: Heterogenous Firm Model of Trade May 7, / 37

17 Firm s Profit Profit of a local producer π o (z) = r (z) σ wf o Seyed Ali Madanizadeh (Sharif U. of Tech.) Melitz Model: Heterogenous Firm Model of Trade May 7, / 37

18 Closed Economy Let s consider the close economy case first. So, there is not export. Seyed Ali Madanizadeh (Sharif U. of Tech.) Melitz Model: Heterogenous Firm Model of Trade May 7, / 37

19 Aggregation Define convenient aggregate productivity: ( ) 1 z = z σ 1 σ 1 µ (z) dz Aggregate variables: R = Mr ( z) Π = Mπ ( z) P = M 1 σ 1 p ( z) Seyed Ali Madanizadeh (Sharif U. of Tech.) Melitz Model: Heterogenous Firm Model of Trade May 7, / 37

20 Local Entry Who enters the local market? π o (z) 0 r (z) σwf o So there is a threshold z o such that firms enter if and only if: z z o = mw P ( σwfo X ) 1/(σ 1) It means that only firms more productive than z o would produce in the local market. Seyed Ali Madanizadeh (Sharif U. of Tech.) Melitz Model: Heterogenous Firm Model of Trade May 7, / 37

21 Local Entry There is an endogenous distribution of productivities: µ (z) dz µ (z) = { g (z) 1 G ( z o ) z z o 0 O.W Seyed Ali Madanizadeh (Sharif U. of Tech.) Melitz Model: Heterogenous Firm Model of Trade May 7, / 37

22 "Zero Cutoff Profits" condition Aggregate productivity: ( 1 z ( z o ) == 1 G ( z o ) z o ) 1 z σ 1 σ 1 g (z) dz Average profits are profits of the "average" firm π = π ( z ( z)) Profits of the marginal firm directly related to average profits: ] π ( z o ) = 0 π = wf o [ ( z z o ) σ 1 1 (ZCP) Seyed Ali Madanizadeh (Sharif U. of Tech.) Melitz Model: Heterogenous Firm Model of Trade May 7, / 37

23 Endogenous Entry Value of entering is the expected profits minus sunk entry cost: V E = E [π (z) wf E ] = (1 G ( φ)) π wf E Free entry drives down the expected profits to zero: V E 0 π = wf E 1 G (z) (FE) Seyed Ali Madanizadeh (Sharif U. of Tech.) Melitz Model: Heterogenous Firm Model of Trade May 7, / 37

24 Labor Market Equilibrium Total Revenue = Total income R = wl (LMC) Mσ ( π + wf o ) = wl (1) M = wl σ ( π + wf o ) (2) Seyed Ali Madanizadeh (Sharif U. of Tech.) Melitz Model: Heterogenous Firm Model of Trade May 7, / 37

25 General Equilibrium Firms below z o exit (ZCP). Free entry drives down (expected) profits to zero (FE). Labor markets clear (LMC) [ ( ) ] σ 1 π = wf o 1 z z o π = M = wf E 1 G (z) wl σ ( π + wf o ) (ZCP) and (FE) solves for z o and π. (LMC) and π solves for M. Seyed Ali Madanizadeh (Sharif U. of Tech.) Melitz Model: Heterogenous Firm Model of Trade May 7, / 37

26 Survival threshold Seyed Ali Madanizadeh (Sharif U. of Tech.) Melitz Model: Heterogenous Firm Model of Trade May 7, / 37

27 Ownership structure Stationary equilibrium: exit mass = entry mass: M E = M 1 G ( z o ) Expected profits of firm owners cover the financing of entrants: Π = M E wf E All firms owned by a continuum of competitive mutual funds that hold diversified portfolios of firms. Note: no financing frictions. Seyed Ali Madanizadeh (Sharif U. of Tech.) Melitz Model: Heterogenous Firm Model of Trade May 7, / 37

28 Trade Two similar economies Iceberg trade cost: d Fixed export cost: f X Seyed Ali Madanizadeh (Sharif U. of Tech.) Melitz Model: Heterogenous Firm Model of Trade May 7, / 37

29 Exporters s Revenue and Profit Revenue of an exporter: r x (z) = = ( ) mw (σ 1) ( ) mwd (σ 1) X + X zp zp [z σ 1 ( mw) (σ 1)] [ P σ 1 X ] [ 1 + d (σ 1)] Profit of an exporter π x (z) = x (z) σ (wf o + wf x ) Seyed Ali Madanizadeh (Sharif U. of Tech.) Melitz Model: Heterogenous Firm Model of Trade May 7, / 37

30 Export Entry Who enters the export market? π x (z) 0 r (z) σ (wf o + wf x ) z z x = mw ( ) σw (fo + f x ) 1/(σ 1) d P X where d = (1 + d (σ 1)) 1/(σ 1) So, only firms with productivity greater than z x would export. Seyed Ali Madanizadeh (Sharif U. of Tech.) Melitz Model: Heterogenous Firm Model of Trade May 7, / 37

31 Selecting into Export π x ( z x ) = 0 z x = d Empirically motivated restriction: d So not all firms export. ( fx f o ( fx f o ) 1/(σ 1) > 1 z x > z o ) 1/(σ 1) z o (ZCP X ) Seyed Ali Madanizadeh (Sharif U. of Tech.) Melitz Model: Heterogenous Firm Model of Trade May 7, / 37

32 Trade Equilibrium Profits derived from domestic and export sales: with prob X = 1 G ( z X ) 1 G ( z o ) π = π D ( z ( z o )) + prob X π X ( z x ) Seyed Ali Madanizadeh (Sharif U. of Tech.) Melitz Model: Heterogenous Firm Model of Trade May 7, / 37

33 Equilibrium Conditions z x = d ( fx f o π = wf o [ ( z ( zo ) z o ) 1/(σ 1) z o ) σ 1 1] [ ( ) z ( zx ) σ 1 + prob x wf x 1] z o π = M = wf E 1 G (z) wl σ ( π + wf o + prob x wf x ) Seyed Ali Madanizadeh (Sharif U. of Tech.) Melitz Model: Heterogenous Firm Model of Trade May 7, / 37

34 Selection under trade Seyed Ali Madanizadeh (Sharif U. of Tech.) Melitz Model: Heterogenous Firm Model of Trade May 7, / 37

35 Seyed Ali Madanizadeh (Sharif U. of Tech.) Melitz Model: Heterogenous Firm Model of Trade May 7, / 37

36 Trade and Aggregate productivity Opening up to trade induces reallocation towards more productive firms. Aggregate productivity goes up. Seyed Ali Madanizadeh (Sharif U. of Tech.) Melitz Model: Heterogenous Firm Model of Trade May 7, / 37

37 References Melitz 2003 Chaney 2006(NBER), 2008(AER) Eaton Kortum Kramarz (2012) Seyed Ali Madanizadeh (Sharif U. of Tech.) Melitz Model: Heterogenous Firm Model of Trade May 7, / 37