International Trade 31E00500

Transcription

1 International Trade 31E00500 Lecture 6: Intra-industry trade and Gravity modelling Saara Tamminen 1 1 VATT Institute of Economic Research, Finland Winter 2016 Tamminen (VATT) Lecture / 53

2 Table of contents 1 Increasing returns to scale and benets from trade 2 Krugman, 1981 Introduction and Autarky Open trade 3 Introduction to Gravity modelling 4 Eaton-Kortum model - with geographic barriers Model Gravity estimations Tamminen (VATT) Lecture / 53

3 Production processes Tamminen (VATT) Lecture / 53

4 Review - Flows of sugar trade Tamminen (VATT) Lecture / 53

5 Introduction 1 Largest share of trade between the developed countries is intra-industry trade (IIT): trade in similar but not identical goods. Share of IIT in international trade has grown, as incomes have increased, international trade has grown at a faster rate than income. Basic classical theories do not say anything of IIT How to explain IIT? The "dirty" way (Eaton and Kortum) with perfect competition: assume there are given number of varieties of dierent goods, each variety produced by competitive rms. Does not explain the number of varieties and the reason why there is product dierentiation. Tamminen (VATT) Lecture / 53

6 Introduction 2 The clean way: If product dierentiation is a decision taken by rms, then the markets must by imperfectly competitive (almost) by denition: there are very few producers for each variety. This means one has to assume increasing returns to scale internal to rms. How to combine the simplicity of the competitive model with increasing returns to scale? Monopolistic competition model In addition we need theories of demand for dierent varieties: Love-of-variety (Dixit-Stiglitz demand), Ideal variety (Lancaster), consumers heterogenous. Tamminen (VATT) Lecture / 53

7 Increasing returns to scale and benets from trade Table of Contents 1 Increasing returns to scale and benets from trade 2 Krugman, 1981 Introduction and Autarky Open trade 3 Introduction to Gravity modelling 4 Eaton-Kortum model - with geographic barriers Model Gravity estimations Tamminen (VATT) Lecture / 53

8 Increasing returns to scale and benets from trade External returns to scale Economies of scale are external to an individual rm Individual rms "small" and can still compete in a perfect competition Large sector level output and rm level average costs are a function of industry-wide output Decrease in rm level average costs through sector level technological improvements Example: Large agricultural sector Protable to make new agricultural machinery and fertilizers Decrease in average costs of rms Example: Information spillovers Tamminen (VATT) Lecture / 53

9 Increasing returns to scale and benets from trade Internal returns to scale Economies of scale are internal Example: large xed start-up costs Total costs: TC x = α + βx Average costs: AC x = β + α /x where α= xed costs and β= marginal costs Tamminen (VATT) Lecture / 53

10 Increasing returns to scale and benets from trade Pro-competitive eect of trade with IRS Two identical countries start trade and specialize completely, one will produce all X, the other all Y Tamminen (VATT) Lecture / 53

11 Krugman, 1981 Table of Contents 1 Increasing returns to scale and benets from trade 2 Krugman, 1981 Introduction and Autarky Open trade 3 Introduction to Gravity modelling 4 Eaton-Kortum model - with geographic barriers Model Gravity estimations Tamminen (VATT) Lecture / 53

12 Krugman, 1981 Paul Krugman, Nobel price in Economics in 2008 for his work on new trade and geographic economics Tamminen (VATT) Lecture / 53

13 Krugman, 1981 Introduction and Autarky Introduction Krugman provides a model explaining IIT with a monopolistic competition model and with Dixit-Stiglitz demand: each rm has some monopoly power, but free entry drives prots to zero Main outcomes of the model: Increasing returns lead to intra-industry trade between two countries even if tastes, technology and factor endowments are identical When the countries are relatively similar and trade in products that have a low substitution elasticity (are sucient dierentiated), everybody gains from trade Tamminen (VATT) Lecture / 53

14 Krugman, 1981 Introduction and Autarky Assumptions of the Model There are a large number of potential goods in two dierent product categories /industries, 1 and 2 All individuals have the same utility function: U = ln ( N1 1/ρ c1,i) ρ + ln i=1 ( N2 1/ρ c2,i) ρ, 0 < ρ < 1 (1) c 1,i is consumption of good i in product category 1. The actual number of produced varieties is n 1 + n 2 There are two factors of production, type 1 labor and type 2 labor (L 1 and L 2 ), both of then are sector specic and mobile within sectors but not between sectors i=1 Tamminen (VATT) Lecture / 53

15 Krugman, 1981 Introduction and Autarky Equilibrium in a Closed Economy Analysis proceeds in three steps: 1 Analyze consumer behavior to derive demand functions (last lecture!) 2 Derive prot maximizing behavior by rms (last lecture!) 3 Impose free entry to determine equilibrium number of rms 4 Include labour market restraints The Chamberlinian approach generates an important advantage: We can rule out strategic interdependence among rms: if the number of goods is large, the eect of the price of any good on the demand for any other good is negligible Tamminen (VATT) Lecture / 53

16 Krugman, 1981 Introduction and Autarky Dixit-Stiglitz Monopolistic competition Dixit-Stiglitz Monopolistic competition Each product variety produced by a single producer, who has signicant monopoly power in the production of that variety. However, each producer will: 1 Take the price-setting behaviour of other rms as given; and 2 Ignore the eect of changing its own price on the general price index. Both assumptions reasonable when the number of varieties N is large. Demand for variety j equals:, where ε denotes the price elasticity of demand c j = p ε j P ε 1 I (2) Tamminen (VATT) Lecture / 53

17 Krugman, 1981 Introduction and Autarky How large N is large enough? Tamminen (VATT) Lecture / 53

18 Krugman, 1981 Introduction and Autarky Monopolistic competition With increasing returns to scale the amount of labor, l, required depends on production level x, and xed f and marginal m labor inputs requirements: l i = f + mx i ; i = 1,..., n 1 Notice that all varieties are assumed to have the same production technique (implying the same cost function). Maximization of prots requires that MR=MC With mark-up pricing and marginal cost mw, the price equals then:, where W equals the general wage level p(1 1/ε) = mw (3) Tamminen (VATT) Lecture / 53

19 Krugman, 1981 Introduction and Autarky Prot maximization and free entry The prots of a rm are π = px (f + mx) W With free entry all prots are competed away, π = 0. By using the pricing rule, this determines the rm size: π = 0 px = fw + mwx ( ) ε ε 1 mw x = fw + mwx ( ) ε ε 1 1 mwx = fw x i = f (ε 1) m Tamminen (VATT) Lecture / 53

20 Krugman, 1981 Introduction and Autarky Labour markets 1 With a determinate rm size only a nite number of varieties can be produced. How many? The size of the market and economy determines this. With labor supply xed to L 1 and L 2, the labor market is in equilibrium when the number of varieties is such that n 1 l 1 = L 1 Full employment implies that the total labor force at home, which is xed arbitrarily at 2 now, is just exhausted by sector specic labor used in production: { n1 l i=1 1,i = L 1 = 2 z n2 l, 0 < z < 1 i=1 2,i = L 2 = z z measures the factor proportions Tamminen (VATT) Lecture / 53

21 Krugman, 1981 Introduction and Autarky Labour markets 2 Amount of labor l 1,i used to produce the dierent goods under each product category: l 1,i = f 1 +m 1 x 1,i = f 1 +m 1 f 1 (ε 1 1) m 1 = f 1 +f 1 (ε 1 1) = f 1 ε 1 ; i = 1,..., n 1 l 2,j = f 2 + m 2 x 2,j = f 2 ε 2 ; j = 1,..., n 2 Note: n 1 l 1 = L 1 and n 2 l 2 = L 2 So, number of rms: n 1 = (2 z)/f 1 ε 1 n 2 = z/f 2 ε 2 Tamminen (VATT) Lecture / 53

22 Krugman, 1981 Open trade Open trade 1 Trading patterns: Assume rst there are two otherwise identical countries (except for the total labor force and labor division), Home and Foreign, beginning to trade with each other. There closed economy equilibria are the same except for the number of varieties: larger country has a larger number of varieties. Why? In the free trade equilibrium, all the prices are the same as in the closed economy. Each variety consumed by all consumers the same amount c H = c F = x L H + L F Equilibrium consumption of each good falls. Individuals are spreading their income over more product varieties. Tamminen (VATT) Lecture / 53

23 Krugman, 1981 Open trade Open trade 2 The relative sizes of the two countries labor forces will be now equal, but reversed: L 1 = 2 z L 2 = z L = z 1 L = 2 2 z Let's have a look on how much intra-industry trade there will be then. We will measure intra-industry trade with index I (Grubel-Lloyd index): ( ) [ ] I = 1 X k M k / (X k + M k ) (4) k where X refers to exports and M to imports of industries k If I is close to 1, lots of intra-industry trade, when I = 0 only inter-industry trade k Tamminen (VATT) Lecture / 53

24 Krugman, 1981 Open trade Open trade 3 Pricing rules and the rm size remain unchanged x 1 = f 1(ε 1 1) m 1 The total number of varieties per category increases to n 1 + n 1, where n 1 = n 2 = (2 z)/f 1 ε 1 n 2 = n 1 = z/f 2 ε 2 The possibility to trade increases the number of varieties available to consumers and consumer's utility. Tamminen (VATT) Lecture / 53

25 Krugman, 1981 Open trade Open trade 4 Everyone will spend an equal amount on the products of both industries. When the total income in both countries (when they have identical size and production technologies) equals Y: X 1 = 1 [ ] 2 Y n 1 n 1 + n = 1 [ ] 2 z 1 2 Y = 1 [ ] 2 z 2 z + z 2 Y 2 X 2 = 1 [ z ] 2 Y 2 M 1 = 1 [ z ] 2 Y 2 M 2 = 1 [ ] 2 z 2 Y 2 X refers to exports to the industry, M to imports Here z can be considered to measure the similarity of factor proportions Tamminen (VATT) Lecture / 53

26 Krugman, 1981 Open trade Open trade 5 When we insert the previous denitions to 4, we get: I = z Result: The index in intra-industry trade = the index of similarity in factor proportions Tamminen (VATT) Lecture / 53

27 Krugman, 1981 Open trade Gains and losses from trade 1 Krugman analyses also changes in utility between autarky and open trade for workers in sectors 1 and 2 He concludes that the relative gains and losses depend critically of only two parameters: ρ and z If ρ < 0.5 both worker groups gain If ρ > 0.5, gains depend on z If z is sucient high and countries have relatively similar factor endowments, both factors gain If z is low, workers which are scarce, will loose from open trade And the same graphically: Tamminen (VATT) Lecture / 53

28 Krugman, 1981 Open trade Gains and losses from trade 2 Tamminen (VATT) Lecture / 53

29 Krugman, 1981 Open trade Export products demand elasticities, factor intensities and trade partners Intra-industry trade by region (Grubel-Lloyd index, 2008), Source: IMF World Economic Outlook Database Tamminen (VATT) Lecture / 53

30 Introduction to Gravity modelling Table of Contents 1 Increasing returns to scale and benets from trade 2 Krugman, 1981 Introduction and Autarky Open trade 3 Introduction to Gravity modelling 4 Eaton-Kortum model - with geographic barriers Model Gravity estimations Tamminen (VATT) Lecture / 53

31 Introduction to Gravity modelling Main trading partners of Finland, 2013 Source: Statistics Finland Tamminen (VATT) Lecture / 53

32 Introduction to Gravity modelling Main trading partners of US & China Tamminen (VATT) Lecture / 53

33 Introduction to Gravity modelling Gravity equation in trade 1 In general, many theories still do not explain the following trade patterns: 1 Trade diminishes dramatically with distance 2 Prices vary across locations, with greater dierences between places far apart 3 Factor rewards are not equal across countries 4 Countries relative productivity levels vary across industries. In addition, economic activity in general is signicantly unequally spread geographically (see Geographic economics for better answers) Tamminen (VATT) Lecture / 53

34 Introduction to Gravity modelling Global trade ows Source: European logistic hub (website) Tamminen (VATT) Lecture / 53

35 Introduction to Gravity modelling Gravity equation in trade 2 These trade pattern can be described by "the gravity equation of trade", which predicts trade extremely well in general In simplest form: the bilateral trade between countries is directly proportional to the product of the countries' GDPs. However, also trade barriers and transport costs aect the ows Eaton & Kortum with transport costs Countries trade most with large countries, with geographically close countries and with countries which have low trade barriers Tamminen (VATT) Lecture / 53

36 Introduction to Gravity modelling Newton's law of universal gravitation Isaac Newton, 1687: F = G m 1m 2 r 2 (5) where F = gravitation force, m 1 and m 2 = masses of objects 1 and 2, G = gravitational constant and r = distance between the objects Take the logarithm of function 5: lnf = lng + lnm 1 + lnm 2 2ln(r) (6) This law used in dierent elds: trade economics, trac ows, water otations and contamination management, etc. Tamminen (VATT) Lecture / 53

37 Introduction to Gravity modelling Empirical gravity analyses of trade E.g. Baier and Bergstrand (2001) derive from CES utility function a gravity equation that accounts for prices, taris and transport costs. Their gravity equation explains nearly half of the 150% in global trade between and for the OECD countries. They nd that GDP growth explains two-third of the total growth (100%), reductions in taris another one quarter (38% increase in trade) and reduction in transport costs one-twelfth (12% ) of total. Conclusion? Tari reductions and other border eects more important than reductions in transportation costs. Next, we will study border eects, technology dierences and gravity with Eaton & Kortum, 2002, model Tamminen (VATT) Lecture / 53

38 Eaton-Kortum model - with geographic barriers Table of Contents 1 Increasing returns to scale and benets from trade 2 Krugman, 1981 Introduction and Autarky Open trade 3 Introduction to Gravity modelling 4 Eaton-Kortum model - with geographic barriers Model Gravity estimations Tamminen (VATT) Lecture / 53

39 Eaton-Kortum model - with geographic barriers Introduction Original Ricardian model features two countries, two goods and one factor of production Extension to multiple goods: Dornbusch, Fischer and Samuelson (1977) Extension to multiple goods and multiple countries: Eaton and Kortum (2002), Econometrica EK develop model with continuum of goods and probabilistic formulation of productivity: each country draws productivity of each good on the continuum and cheapest country (most productive corrected for trade costs) supplies certain good EK maintain one factor of production as in original Ricardian model, but include trade in intermediates and trade costs Tamminen (VATT) Lecture / 53

40 Eaton-Kortum model - with geographic barriers Introduction Model can be characterized by three parameters: each country's state of technology, governing absolute advantage the heterogeneity of productivity, governing comparative advantage geographic barriers Only the most important features and equations of the model included here (for more detailed explanations on their derivations, see original article) EK derive gravity equation from model and estimate it with data from 19 OECD countries EK also regress trade shares on price dierences to identify trade elasticity (trade values with respect to trade costs) separately from distance elasticity (trade costs with respect to distance) Tamminen (VATT) Lecture / 53

41 Eaton-Kortum model - with geographic barriers Introduction Use structural model to examine number of counterfactuals (More during the next lecture!): Gains from trade: small countries gain more How do technology and geography determine patterns of specialization: with falling barriers from autarky level, manufactures move to large countries with cheaper intermediate inputs. With further fall in barriers, manufactures moves to small countries Role of trade in spreading benets from technology: all countries benet from technology improvement in certain country. Magnitude of gains depends on proximity and ability to downsize manufacturing sector Consequences of tari reductions: every country benets, unless they do unilateral liberalization. EU integration might harm members through trade diversion or non-members through worsened terms of trade. Tamminen (VATT) Lecture / 53

42 Eaton-Kortum model - with geographic barriers Model Model Setup N countries and continuum of goods ranging from 0 to 1 Productivity varies across countries and across goods Country i's eciency in producing good j [0, 1] is denoted as z i (j) Input cost in country i is denoted as c i (equal across sectors) With constant returns to scale, cost of producing good j in country i is thus c i /z i (j) Geographic barriers introduced with iceberg trade costs: delivering a unit from country i to country n requires producing d ni > 1 units in i Tamminen (VATT) Lecture / 53

43 Eaton-Kortum model - with geographic barriers Model Model Setup Delivering a good j from country i to country n costs: ( ) ci p ni (j) = d ni (7) z i (j) Under perfect competition p ni (j) is also the price for consumers in country n. Consumers in country n buy the cheapest good (no search costs). So the price of good j in country n, p n (j), is the minimum across all sources: p n (j) = min {p ni (j) ; i = 1,..., N} (8) Utility across continuum of goods is CES with substitution elasticity σ: U = ˆ1 0 Q (j) σ 1 σ dj σ σ 1 (9) Tamminen (VATT) Lecture / 53

44 Eaton-Kortum model - with geographic barriers Model Technology Technology is stochastic: country i's eciency in producing good j is the realization of a random variable Z i (independent across j) with distribution function F i (z) = Pr (Z i z) Using a continuum of sectors, by the law of large numbers F i (z) is also the fraction of goods for which country i's eciency is smaller than z Working with a Frechet distribution for eciency generates a simple expression for the probability π ni that country i is cheapest: F i (z) = e T i z θ = 1 e T i z θ i (10) Country specic T i > 0 governs the location of the distribution: a bigger T i implies that a high eciency draw for any good j is more likely. Measure of absolute advantage. Common θ measures the variation of the eciency distribution and the comparative advantage. A bigger θ implies less variability. With a very large θ, probabilities for all goods become equal. Tamminen (VATT) Lecture / 53

45 Eaton-Kortum model - with geographic barriers Model Price Levels Production combines labor and intermediates, with labor having a constant share β. The cost of an input bundle in country i is: c i = w β i p 1 β i (11) With the information on costs, trade shares can be expressed as a function of price levels and wage levels (see EK 4.2): X ni X n = π ni = T i ( ) γd ni w β i p 1 β θ i (12) p n Exports X ni from country i to country n (relative to country n's total spending X n ) depend on foreign technology level T i, on relative prices, wage level in source country i and trade barriers between the countries Tamminen (VATT) Lecture / 53

46 Eaton-Kortum model - with geographic barriers Gravity estimations Estimation To solve the model numerically, we need values for the technology parameters T i, trade costs d ni and the heterogeneity parameter θ. β is taken from real data. Estimates based on bilateral trade ows of 19 OECD countries from year To determine the other parameters a gravity type equation is estimated. Dividing the import share of country n from country i from equation (12) by the domestic spending share of country n gives: X ni = T ( ) βθ ( ) (1 β)θ i wi pi d θ ni (13) X nn T n w n p n p i p n can be expressed as follows, using again equation (12): p i = w ( ) 1 i Ti p n w n T n ( Xnn βθ X n X ii X i ) 1 βθ (14) Tamminen (VATT) Lecture / 53

47 Eaton-Kortum model - with geographic barriers Gravity estimations Estimation Substituting equation (14) into equation (13) and rearranging leads to: With ln X ni = θ X nn ln d ni + 1 β ln T i θ ln w i (15) T n w n X ni = X ni 1 β β ln X ii X i Dening S i as S i = 1 β ln T i θ ln w i leads to the following empirical gravity equation: ln X ni = θ X nn ln d ni + S i S n (16) S i can be interpreted as a measure of country's i competitiveness, its state of technology adjusted for labor costs. Tamminen (VATT) Lecture / 53

48 Eaton-Kortum model - with geographic barriers Gravity estimations Estimation Trade costs can be written as a function of distance, language and treaties as follows: ln d ni = d k + b + l + e h + m n + δ ni (17) d k (k = 1,..., 6) is the eect of distance between n and i lying in the kth interval, b is the eect of n and i sharing a border, l is the eect of n and i sharing a language, e h is the eect of n and i both belonging to trading area h and m n is an overall destination eect. δ ni is the error term. Substituting equation (17) into equation (16) generates the following estimating equation: ln X ni = S X nn i S n θd k θb θl θe h θm n θδ ni (18) Equation (18) can be estimated with xed eects (including two sets of dummies for importers and exporters). The xed eects represent a country's competitiveness, technology adjusted for labor costs. Table III reports the results. Tamminen (VATT) Lecture / 53

49 Eaton-Kortum model - with geographic barriers Gravity estimations Tamminen (VATT) Lecture / 53

50 Eaton-Kortum model - with geographic barriers Gravity estimations Estimation Estimates of S i in table III indicate that Japan is the most competitive country in 1990, followed by the US, whereas Belgium and Greece are the least competitive. The US, Japan and Belgium are the most open countries, while Greece is the least open (identied from the overall destination eect m n). Technology T i can be calculated from the estimates of S i using data on wages (adjusted for education) and the estimate of θ. Table VI displays the results. Estimates show that Japan is more competitive than the US mainly because of lower wage levels rather than a higher state of technology. Belgium's uncompetitiveness follows mainly from the high wage levels. The geographic barriers can also be identied with the estimate of θ from the price data Tamminen (VATT) Lecture / 53

51 Eaton-Kortum model - with geographic barriers Gravity estimations Estimation Tamminen (VATT) Lecture / 53

52 Eaton-Kortum model - with geographic barriers Gravity estimations Estimation Tamminen (VATT) Lecture / 53

53 Eaton-Kortum model - with geographic barriers Gravity estimations Next lecture Tuesday 26.1, 10-12, on Strategic and applied trade policy Tamminen (VATT) Lecture / 53