Comparative Advantage and Optimal Trade Taxes

Transcription

1 Comparatve Advantage and Optmal Trade Taxes Arnaud Costnot (MIT), Dave Donaldson (MIT), Jonathan Vogel (Columba) and Iván Wernng (MIT) June 2014

2 Motvaton Two central questons Why do natons trade? 2. How should they conduct trade polcy? Theory of comparatve advantage Influental answer to #1 v Vrtually no mpact on #2

3 Ths Paper Take canoncal Rcardan model smplest and oldest theory of CA new workhorse model for theoretcal and quanttatve work Explore relatonshp... CA Optmal Trade Taxes

4 Man Result Optmal trade taxes: 1. unform across mported goods 2. monotone n CA across exported goods

5 Man Result Examples: zero mport tarff + export taxes ncreasng n CA Postve mport tarff + export subsdes decreasng n CA

6 Smple Economcs

7 Smple Economcs More room to manpulate prces n comparatve advantage sectors

8 Smple Economcs More room to manpulate prces n comparatve advantage sectors New perspectve on targeted ndustral polcy

9 Smple Economcs More room to manpulate prces n comparatve advantage sectors New perspectve on targeted ndustral polcy larger subsdes for less compettve sectors not from desre to expand output...

10 Smple Economcs More room to manpulate prces n comparatve advantage sectors New perspectve on targeted ndustral polcy larger subsdes for less compettve sectors not from desre to expand output but greater constrants to contract exports to explot monopoly power

11 Two Applcatons Agrculture and Manufacturng examples GT under optmal trade taxes are 20% and 33% larger than under no taxes GT under under optmal unform tarff are only 9% larger than under no taxes Mcro-level heterogenety matters for desgn and gans from optmal trade polcy

12 Related Lterature Optmal Taxes n an Open Economy: Lagrangan Methods: General results: Dxt (85), Bond (90) Rcardo: Itoh Kyono (87), Opp (09) Lagrangan methods n nfnte dmensonal space: AWA (06), Amador Bagwell (13) Cell-problems: Everett (63), CLW (13)

13 Roadmap Basc Envronment Optmal Allocaton Optmal Trade Taxes Applcatons

14 Basc Envronment

15 A Rcardan Economy Two countres: Home and Foregn Labor endowments: L and L CES utlty over contnuum of goods: u (c ) U c 1 1/ u (c )d 1. (1 1/ ) Constant unt labor requrements: a and a Home sets trade taxes t (t ) and lump-sum transfer Foregn s passve T

16 Compettve Equlbrum

17 Compettve Equlbrum c 2 argmax c 0 u ( c )d p (1 + t ) c d apple wl + T

18 Compettve Equlbrum c 2 argmax c 0 u ( c )d q 2 argmax q 0 {p (1 + t ) q wa q } p (1 + t ) c d apple wl + T

19 Compettve Equlbrum c 2 argmax c 0 u ( c )d q 2 argmax q 0 {p (1 + t ) q wa q } T = p t (c q ) d p (1 + t ) c d apple wl + T

20 Compettve Equlbrum c 2 argmax c 0 u ( c )d q 2 argmax q 0 {p (1 + t ) q wa q } T = p t (c q ) d c 2 argmax c 0 u ( c )d p (1 + t ) c d apple wl + T p c d apple w L

21 Compettve Equlbrum c 2 argmax c 0 u ( c )d q 2 argmax q 0 {p (1 + t ) q wa q } T = p t (c q ) d c 2 argmax c 0 u ( c )d q 2 argmax q 0 {p q w a q } p (1 + t ) c d apple wl + T p c d apple w L

22 Compettve Equlbrum c 2 argmax c 0 u ( c )d q 2 argmax q 0 {p (1 + t ) q wa q } T = p t (c q ) d c 2 argmax c 0 u ( c )d q 2 argmax q 0 {p q w a q } c + c = q + q, p (1 + t ) c d apple wl + T p c d apple w L

23 Compettve Equlbrum c 2 argmax c 0 u ( c )d q 2 argmax q 0 {p (1 + t ) q wa q } T = p t (c q ) d c 2 argmax c 0 u ( c )d q 2 argmax q 0 {p q w a q } c + c = q + q, a q d = L, p (1 + t ) c d apple wl + T p c d apple w L

24 Compettve Equlbrum c 2 argmax c 0 u ( c )d q 2 argmax q 0 {p (1 + t ) q wa q } T = p t (c q ) d c 2 argmax c 0 u ( c )d q 2 argmax q 0 {p q w a q } c + c = q + q, a q d = L, a q d = L. p (1 + t ) c d apple wl + T p c d apple w L

25 Government Problem

26 Government Problem c 2 argmax c 0 u ( c )d q 2 argmax q 0 {p (1 + t ) q wa q } T = p t (c q ) d c 2 argmax c 0 u ( c )d q 2 argmax q 0 {p q w a q } c + c = q + q a q d = L, a q d = L. p (1 + t ) c d apple wl + T p c d apple w L

27 Government Problem max t, T, w,w,p,c,c,q,q U(c) s.t. c 2 argmax c 0 u ( c )d q 2 argmax q 0 {p (1 + t ) q wa q } T = p t (c q ) d c 2 argmax c 0 u ( c )d q 2 argmax q 0 {p q w a q } p (1 + t ) c d apple wl + T p c d apple w L c + c = q + q a q d = L, a q d = L.

28 Optmal Allocaton

29 Let us Relax Prmal approach (Baldwn 48, Dxt 85): No taxes, no compettve markets at home Domestc government drectly controls domestc consumpton,, and output, c q

30 Plannng Problem max t, T, w,w,p,c,c,q,q U(c) s.t. c 2 argmax c 0 u ( c )d q 2 argmax q 0 {p (1 + t ) q wa q } T = p t (c q ) d c 2 argmax c 0 u ( c )d q 2 argmax q 0 {p q w a q } p (1 + t ) c d apple wl + T p c d apple w L c + c = q + q a q d = L, a q d = L.

31 Plannng Problem max t, T, w,w,p,c,c,q,q U(c) s.t. c 2 argmax c 0 u ( c )d q 2 argmax q 0 {p q w a q } p c d apple w L c + c = q + q a q d = L, a q d = L.

32 Plannng Problem max w,p,c,c,q,q U(c) s.t. c 2 argmax c 0 u ( c )d q 2 argmax q 0 {p q w a q } p c d apple w L c + c = q + q a q d = L, a q d = L.

33 Plannng Problem Convenent to focus on 3 key controls: Equlbrum abroad requres... p (m,w ) mn {u 0 ( m ),w a }, q (m,w ) max {m + d (w a ), 0}

34 Plannng Problem s.t. c 2 argmax c max w,p,c,c,q,q 0 u ( c )d q 2 argmax q 0 {p q w a q } U(c) p c d apple w L c + c = q + q a q d = L, a q d = L.

35 Plannng Problem s.t. max w,p,c,c,q,q U(c)

36 Plannng Problem s.t. max w,p,c,c,q,q a q d applel, U(c)

37 Plannng Problem s.t. max w,p,c,c,q,q a q d applel, a q (m,w ) d applel, U(c)

38 Plannng Problem s.t. max w,p,c,c,q,q a q d applel, a q (m,w ) d applel, p (m,w )m d apple0 U(c)

39 Plannng Problem s.t. max a q d applel, a q (m,w ) d applel, p (m,w )m d apple0 w, m, q U(c)

40 Plannng Problem s.t. max a q d applel, a q (m,w ) d applel, p (m,w )m d apple0 w, m, q U(m + q)

41 Three Steps 1. Decompose () nner problem () outer problem w 2. Concavty of nner problem Lagrangan Theorems (Luenberger 69) 3. Addtve separablty mples... (Everett 63) one nfnte-dmensonal problem many low-dmensonal problems

42 Inner Problem s.t. max a q d applel, a q (m,w ) d applel, p (m,w )m d apple0 w,m, q U(m + q)

43 Inner Problem s.t. max a q d applel, a q (m,w ) d applel, p (m,w )m d apple0 m, q U(m + q)

44 Lagrangan

45 Lagrangan Theorem m 0,q 0 solves nner problem ff max m,q L (m, q,,,µ; w ) for some 0, 0, µ 0, (,,µ) and a q 0 d apple L, wth complementary slackness, a q m 0,w d apple L, wth complementary slackness, p (m,w )m 0 d apple 0, wth complementary slackness.

46 Cell Structure m 0,q 0 solves nner problem ff m 0 solves,q 0 max L (m,q,, m,q,µ; w ) for some 0, 0, µ 0, (,,µ) and a q 0 d apple L, wth complementary slackness, a q m 0,w d apple L, wth complementary slackness, p (m,w )m 0 d apple 0, wth complementary slackness.

47 Hgh-School Math: Optmal Output

48 Hgh-School Math: Optmal Output q, q M I 0 M II m

49 Hgh-School Math: Optmal Net Imports

50 Hgh-School Math: Optmal Net Imports L L m I MI 0 M II m M I 0 M II m (a) a /a < A I. (b) a /a 2 [A I, A II ). L L M I 0 M II m M I 0 M II m III m (c) a /a = A II. (d) a /a > A II.

51 Optmal Trade Taxes

52 Wedges Wedges at plannng problem s soluton: 0 u0 c 0 p 0 1 Prevous analyss mples: 0 = 8 >< >: 0 1 µ 0 1, f a 0 a w 0 a a 1, f A I < a a <A I 1 µ 0 w 0 0 ; apple A II µ0 w ; w 0 + µ 0 1, f a a >A II.

53 Optmal Trade Taxes Any soluton to Home's plannng problem can be mplemented by t 0 = 0 Conversely, f t 0 solves the domestc's government problem, then the assocated allocaton and prces must solve Home s plannng problem and satsfy: t 0 = u0 c 0 p 0 1

54 Optmal Trade Taxes

55 Optmal Trade Taxes

56 Intuton When a /a <A I, Home has ncentves to charge constant monopoly markup When a /a 2 A I,A II, there s lmt prcng: foregn frms are exactly ndfferent between producng and not producng those goods When a /a >A II, unform tarff s optmal: Home cannot manpulate relatve prces

57 Industral Polcy Revsted

58 Industral Polcy Revsted At the optmal polcy, governments protects a subset of less compettve ndustres but targeted/non-unform subsdes do not stem from a greater desre to expand producton they reflect tghter constrants on ablty to explot monopoly power by contractng exports

59 Industral Polcy Revsted At the optmal polcy, governments protects a subset of less compettve ndustres but targeted/non-unform subsdes do not stem from a greater desre to expand producton they reflect tghter constrants on ablty to explot monopoly power by contractng exports Countres have more room to manpulate world prces n ther comparatve-advantage sectors

60 Robustness Smlar qualtatve results hold n more general envronments: Iceberg trade costs Separable, but non-ces utlty Addtonal consderatons: Trade costs mply that zero mports are optmal for some goods at soluton of Home s plannng problem Non-CES utlty leads to varable markups for goods wth strongest CA

61 Applcatons

62 Agrcultural Example Home = U.S. Foregn = R.O.W. Each good corresponds to 1 of 39 crops Land s the only factor of producton Productvty from FAO s GAE project Land endowments match acreage devoted to 39 crops n U.S. and R.O.W. Symmetrc CES utlty wth σ=2.9 as n BW (06)

63 Optmal Trade Taxes

64 Optmal Trade Taxes % -20% t 0 t 0-40% -40% -60% a /a -60% a /a

65 Gans from Trade

66 Gans from Trade No Trade Costs Trade Costs U.S. R.O.W. U.S. R.O.W. Lassez-Fare 39.15% 3.02% 5.02% 0.25% Unform Tarff 42.60% 1.41% 5.44% 0.16% Optmal Taxes 46.92% 0.12% 5.71% 0.04%

67 Gans from Trade No Trade Costs Trade Costs U.S. R.O.W. U.S. R.O.W. Lassez-Fare 39.15% 3.02% 5.02% 0.25% Unform Tarff 42.60% 1.41% 5.44% 0.16% Optmal Taxes 46.92% 0.12% 5.71% 0.04%

68 Gans from Trade No Trade Costs Trade Costs U.S. R.O.W. U.S. R.O.W. Lassez-Fare 39.15% 3.02% 5.02% 0.25% Unform Tarff 42.60% 1.41% 5.44% 0.16% Optmal Taxes 46.92% 0.12% 5.71% 0.04%

69 Gans from Trade No Trade Costs Trade Costs U.S. R.O.W. U.S. R.O.W. Lassez-Fare 39.15% 3.02% 5.02% 0.25% Unform Tarff 42.60% 1.41% 5.44% 0.16% Optmal Taxes 46.92% 0.12% 5.71% 0.04%

70 Gans from Trade No Trade Costs Trade Costs U.S. R.O.W. U.S. R.O.W. Lassez-Fare 39.15% 3.02% 5.02% 0.25% Unform Tarff 42.60% 1.41% 5.44% 0.16% Optmal Taxes 46.92% 0.12% 5.71% 0.04%

71 Manufacturng Example Home=U.S. and Foregn=R.O.W. 400 goods. Labor s the only factor of producton Labor endowments set to match populaton n U.S. and R.O.W Productvty s dstrbuted Fréchet: a = T 1 and a = 1 T 1 θ=5 set to match average trade elastcty n HM (13). T and T* set to match U.S. share of world GDP. Symmetrc CES utlty wth σ=2.5 as n BW (06)

72 Optmal Trade Taxes

73 Optmal Trade Taxes % -20% t 0-40% t 0-40% -60% -60% a /a a /a

74 Gans from Trade

75 Gans from Trade No Trade Costs Trade Costs U.S. R.O.W. U.S. R.O.W. Lassez-Fare 27.70% 6.59% 6.18% 2.02% Unform Tarff 30.09% 4.87% 7.31% 1.31% Optmal Taxes 36.85% 0.93% 9.21% 0.36%

76 Gans from Trade No Trade Costs Trade Costs U.S. R.O.W. U.S. R.O.W. Lassez-Fare 27.70% 6.59% 6.18% 2.02% Unform Tarff 30.09% 4.87% 7.31% 1.31% Optmal Taxes 36.85% 0.93% 9.21% 0.36%

77 Gans from Trade No Trade Costs Trade Costs U.S. R.O.W. U.S. R.O.W. Lassez-Fare 27.70% 6.59% 6.18% 2.02% Unform Tarff 30.09% 4.87% 7.31% 1.31% Optmal Taxes 36.85% 0.93% 9.21% 0.36%

78 Gans from Trade No Trade Costs Trade Costs U.S. R.O.W. U.S. R.O.W. Lassez-Fare 27.70% 6.59% 6.18% 2.02% Unform Tarff 30.09% 4.87% 7.31% 1.31% Optmal Taxes 36.85% 0.93% 9.21% 0.36%

79 Gans from Trade No Trade Costs Trade Costs U.S. R.O.W. U.S. R.O.W. Lassez-Fare 27.70% 6.59% 6.18% 2.02% Unform Tarff 30.09% 4.87% 7.31% 1.31% Optmal Taxes 36.85% 0.93% 9.21% 0.36%

80 Concludng Remarks Frst stab at how CA affects optmal trade polcy Smple economcs: countres have more room to manpulate prces n ther CA sectors New perspectve on targeted ndustral polcy Larger subsdes are not about desre to expand, but constrant on ablty to contract

81 Concludng Remarks More applcatons of our technques market structures (e.g. BEJK, 2003; Meltz, 2003) Results suggest desgn and gans from trade polcy depends on mcro-level heterogenety