International Trade Elasticity Puzzle & Dynamic market penetrat

Transcription

1 International Trade Elasticity Puzzle & Dynamic market penetration April 2012

2 Question Motivation How can we explain the low short run trade elasticity and large long run elasticity.

3 Question Motivation How can we explain the low short run trade elasticity and large long run elasticity. Why do we see large unemployment after trade liberalizations or large currency devalutions?

4 Question Motivation Propose a dynamic Market Penetration model (Extended EKK type model)

5 Question Motivation Propose a dynamic Market Penetration model (Extended EKK type model) Firms need to pay convex adjustment cost to penetrate into market. So it takes time for them to get into a new market, especially the new rms.

6 Question Motivation Propose a dynamic Market Penetration model (Extended EKK type model) Firms need to pay convex adjustment cost to penetrate into market. So it takes time for them to get into a new market, especially the new rms. Due to the sluggish adjustment, we do not observe large changes in trade shares in the short run.

7 Question Motivation Propose a dynamic Market Penetration model (Extended EKK type model) Firms need to pay convex adjustment cost to penetrate into market. So it takes time for them to get into a new market, especially the new rms. Due to the sluggish adjustment, we do not observe large changes in trade shares in the short run. Most of the labor movements and changes in rm sizes happen in the long run.

8 Question Motivation introducing labor market frictions.

9 Question Motivation introducing labor market frictions. It takes time for the rms to adjust and worker to re-allocate.

10 Question Motivation introducing labor market frictions. It takes time for the rms to adjust and worker to re-allocate. We get large unemployment in the short run

11 Question Motivation Sticky Wages:

12 Question Motivation Sticky Wages: This would magnify the frictions in the labor market to prevent wages to adjust to its optimal level

13 Question Motivation Sticky Wages: This would magnify the frictions in the labor market to prevent wages to adjust to its optimal level This friciton prevents labor movement toward more productive rms.

14 Question Motivation Sticky Wages: This would magnify the frictions in the labor market to prevent wages to adjust to its optimal level This friciton prevents labor movement toward more productive rms. Unemployment magni es.

15 Consumers Producers Consumers:

16 Consumers Producers Consumers: Same as EKK: max C j =! σ Z σ 1 Mij x ij (ν) σ σ 1 dµ (ν) i 0 Z Mij s.t. p ij (v) x ij (ν) dµ (ν) = X j = w j L j + Π j i 0

17 Consumers Producers Consumers: Same as EKK: max C j =! σ Z σ 1 Mij x ij (ν) σ σ 1 dµ (ν) i 0 Z Mij s.t. p ij (v) x ij (ν) dµ (ν) = X j = w j L j + Π j i 0 Each buyer will be reached with probability f ij (v) by a producer.

18 Consumers Producers Consumers: Same as EKK: max C j =! σ Z σ 1 Mij x ij (ν) σ σ 1 dµ (ν) i 0 Z Mij s.t. p ij (v) x ij (ν) dµ (ν) = X j = w j L j + Π j i 0 Each buyer will be reached with probability f ij (v) by a producer. Demand function for good v is : pij (v) (σ 1) X ij (v) = p ij (v) x ij (ν) = f ij (v) X j P j

19 Consumers Producers Producer: with Cost c and market share f

20 Consumers Producers Producer: with Cost c and market share f invests C (f 0 ; f ) to increase its share to f 0. 0, Π (p; c, P V (f ; c, P, X ) = 0, X 0 ) f 0 C (f 0 ; f ) + max p,f r V (f 0 ; c 0, P 0, X 0 ) where: C Π f 0, p; c, P, X = f 0, f = max ( 1 c p (σ 1) X (1) p P!) 0, F γ + αf + f 0 f (1 f 0 ) β (2)

21 Consumers Producers Entry

22 Consumers Producers Entry Firms enter if V 0 ) c t c t

23 Consumers Producers Entry Firms enter if V 0 ) c t c t Free Entry: V i Me i f ei

24 Consumers Producers X ijt = Me i Z cj 0 X ijt (c t ) d Pr (c) ij

25 Consumers Producers P jt = Z cjt Me it i 0 f ijt (c) p 1 ijt σ (c) d Pr (c) ij! 1 1 σ

26 Consumers Producers Recursuve Competitive Equilibrium: f 0 = f f, c; P 0, X 0, F E 0 = Ẽ f, c; P 0, X 0, F Xj 0 = X (fpg k, fx g k, ff g k ) Pj 0 = P (fpg k, fx g k, ff g k )

27 Consumers Producers FOC : p = σ σ 1 c

28 Consumers Producers FOC : p = σ σ 1 c π (c) r V 0 f 0, c 0 ; P 0, X 0 = V 0 f, c; P 0, X 0 = F (1 f 0 ) β 1 + β f 0 f 1 f 0! 1 (1 f 0 ) β α F

29 Steady State Small Open Economy Dynamics Calibration Productivity Pr (c ij (v) c) = Φ ij c θ

30 Steady State Small Open Economy Dynamics Calibration Productivity Entry Pr (c ij (v) c) = Φ ij c θ 1 d ij w i 1 + r A i z (v) = c σ 1 ij (v) c ij = D ij r (3)

31 Steady State Small Open Economy Dynamics Calibration π (c) = XP σ 1 (σ 1) c σmσ 1 f rf 1/β (c) = 1 = 1 (1 + r) π (c) V = 1 + r π (c) f (c) r c c ij σ 1 β

32 Steady State Small Open Economy Dynamics Calibration Γ (D ij ) = 1 + r ζ r Ξ (D ij ) = 0 D ij θ σ 1 1 F ij = 0 X ij = 1 + r ζθσ r P j = r X θ σ 1 j m r σ ζ = 1 θ σ + 1 θ σ 1 1 Me i Φ ij F ij D θ σ 1 ij i 1 σ 1 β + θ σ + 1 θζme i Φ ij F 1 ij θ σ 1! 1 θ

33 Steady State Small Open Economy Dynamics Calibration Trade Balance Equation: Free Entry: X i = j X i = 0 σ Me i Φ ij F 1 θ ij n Me n Φ nj F 1 nj σ σ 1 w i L i θ σ 1 1 A X j 1 + r X ij M ei f ei V i = V ij = j j r σ = 1 + r X i r σ

34 Steady State Small Open Economy Dynamics Calibration Equilirium w i L i = j 0 1 dij w θ i φ i A i n 1 φ n dnj w n A n θ 1 C A w j L j where: φ i = f ei w i L i

35 Steady State Small Open Economy Dynamics Calibration Entry Decision: E 0 1 if c c (P (c, f ) = 0, X 0, F ) 0 OW

36 Steady State Small Open Economy Dynamics Calibration Entry Decision: E 0 1 if c c (P (c, f ) = 0, X 0, F ) 0 OW f 00 = f 0 = f = 0 ) c ij Pj 0, Xj r X 0 P 0σ 1 1 σ 1, F ij = α + r σm σ 1 F ij

37 Steady State Small Open Economy Dynamics Calibration Productivity Structure: Pr (Z z) = z θ Following EKK de ne c ij = d ijw i A i z c ij Φ ij = Ai d ij w i θ Pr (c ij c) = Φ ij c θ

38 Steady State Small Open Economy Dynamics Calibration Equivalence theorem: W (g; A) = max g 0 ( where the policy function is 0, Ag 0 γ + αg + g 0 g (1 g 0 ) β g 0 = g (g, A)! r W g 0 ; A ) (4) V (f ; c, P, X ) = FW f (f ; c, P, X ) = g f ; f ; XP σ 1 σm σ 1 F c1 σ XP σ 1 σm σ 1 F c1 σ

39 Steady State Small Open Economy Dynamics Calibration De ne D ij = X jpj σ 1 σm σ 1 F ij 1 + r c ij = α + r D ij 1 σ 1 f t (c) = f f t 1 (c), D ij c 1 σ Γ t (D ij ) = Ξ t (D ij ) = Z c(dij ) 0 Z c(dij ) 0 f t (c) c θ σ dc γ + αf t 1 (c) + f t (c) f t 1 (c) (1 f t (c)) β! c θ 1 dc

40 Steady State Small Open Economy Dynamics Calibration Agreagte Sale of i in j : X 0 ij,t (D ij ) = θσme i Φ ij F ij D ij Γ t (D ij ) F ij = X ij Ξ t (D ij ) σ D ij Γ t (D ij ) Π ij = X ij Ξ t (D ij ) 1 σ D ij Γ t (D ij )

41 Steady State Small Open Economy Dynamics Calibration Based on EKK we calibrate the parameters as below: β = 1 λ = 1 = θ σ 1 = 2.46 σ = 2.98 θ = 4.87

42 Numerical Tricks Use the sum of the value functions Solve for an interval of f instead of just one point or the whole interval. Provide the Jacobian and Hessian functions (patterns) Using a compact set instead of (0, 1) : There s discontinuity Solve for A 0 s rst, and then do the iterations and integrations. Writing the costs in terms of destination.

43 Convergence of policy and value functions

44 Values Functions/Policy Functions

45 Evolution of f over time for each c.

46 f over c for each time t.

47 Evolution of Agregate sale/pro t/ xed costs over time.

48 Evolution of sale/pro t/ xed costs over time for each c.

49 Distribution of pro t over c

50 Half time for each c

51 Value and policy functions vs β

52 Evolution of Agregate sale/pro t/ xed costs over time vs β

53 Distribution of pro t over c vs β

54 Half time vs β

55 Value and policy functions vs r

56 Evolution of Agregate sale/pro t/ xed costs over time vs r

57 Distribution of pro t over c vs r

58 Half time vs r

59 Evolution of Agregate sale/pro t/ xed costs over time vs F or X, P

60 Distribution of pro t over c vs F or X, P

61 Half time vs F

62 Show Stedy states for c Aggregate SS vs β, r, F, X (, P)

63 of going from Autarki to (free) trade

64 of reducing trade costs by 10% and show the long run and short run elasticities.

65 Show fraction of exporters

66 show graphically what happens in GE (show things are monotone)

67 Estimate trade elasticity.

68 Agreagte Sale of i in j : X 0 ij,t (D ij ) = θσme i Φ ij F ij D ij Γ t (D ij ) π ni = Me i Φ ij Γ t (D ij ) n Me n Φ nj Γ t (D nj ) Pj 0 = m θ Me i Φ ij Γ t (D ij ) i Ξ t (D ij ) F ij = X ij σ Π ij = X ij σ Π i = X i σ D ij Γ t (D ij ) Ξ t (D ij ) 1 D ij Γ t (D ij ) X ij Ξ t (D ij ) σ D ij Γ t (D ij ) j! 1 1 σ

69 Trade Balance Equation: X i = j Me i Φ ij Γ t (D ij ) n Me n Φ nj Γ t (D nj ) X j Income and Expenditure X i = σ σ 1 w i L i! Me i θφ ij F ij Ξ t (D ij ) j