International Trade Lecture 1: Trade Facts and the Gravity Equation

International Trade Lecture 1: Trade Facts and the Equation Stefania Garetto September 3rd, 2009 1 / 20

Trade Facts After WWII, unprecedented growth of trade volumes, both in absolute terms and as % of GDP. Figure 1: Volumes of World Trade 2 / 20

Trade Facts Volumes of trade in the U.S. increased then-fold. In recent years, negative trade balance. Figure 2: Volumes of U.S. Trade. 3 / 20

Trade Facts Facts Theory Figure 3: Trade as a % of GDP, selected countries. 4 / 20

Trade Facts Facts Theory Figure 4: US Import by country of origin. 5 / 20

Trade Facts Facts Theory More than 50% of total trade flows happen between developed countries; about 15% between developing counties; about 30% between developed and developing countries. Rising importance of China: Chinese exports increased 30-fold from 1978 to 2008 (from 2 to 40% of GDP). More than 40% of U.S. trade flows happen between firms boundaries.... and so on. 6 / 20

Trade Theory Facts Theory Trade theory tries to answer the following questions: What explains the pattern of trade across countries? What goods do countries trade? Which kind of firms trade? What is the role of FDI and multinational production? How do they affect trade patterns? What can explain the growth in trade? Does trade affect GDP growth? What are the effects of trade on the labor markets? 7 / 20

Helpman JEP 1999: what happened in the field 1960-1990 Facts Theory Well, even before that... 1817: Ricardo s Principles of Political Economy and Taxation THEORY OF COMPARATIVE ADVANTAGE: a country exports products in which its labor productivity is high relative to its labor productivity in other products. 1920s: Heckscher-Ohlin FACTOR ENDOWMENTS DETERMINE THE PATTERN OF TRADE: a country should export the product that is relatively intensive in using the factor with which the country is relatively well-endowed. 8 / 20

Testing the Heckscher-Ohlin prediction Facts Theory 1954: LEONTIEF PARADOX Leontief found that the K/L ratio embodied in US imports exceeded the one in US exports (opposite to HO if we believe the US are more capital intensive than their trading partners). 1960s-1980s: other attempts to thest the theory obtained mixed results BUT: based on pure accounting relationships and unrealistic assumptions (FPE, common technologies and production structures across countries). Trefler (1995): attempt of taking into account productivity differences. BUT: one can always reconcile the theory with the data adding arbitrary differences in technologies/production structure across countries and sectors, but this is not progress. 9 / 20

The New Trade Theory Facts Theory Krugman (1979): new, complementary theory based on ECONOMIES OF SCALE and PRODUCT DIFFERENTIATION. Motivated by: 1. Large volumes of trade between countries with similar factor proportions. 2. Large volumes of intra-industry trade. (None of this seems motivated by factor endowment differences). Economies of scale favor countries specialization in different products and could explain different countries development and use of different technologies and production structures. Consumers taste for variety then leads to intra-industry trade. 10 / 20

The Equation Consider a world where: - every country is specialized in a distinct set of products; - each country s population has the same homothetic preferences; - trade is balanced. 11 / 20

The Equation Consider a world where: - every country is specialized in a distinct set of products; - each country s population has the same homothetic preferences; - trade is balanced. - spending levels in each goods are proportional to GDP levels import and export are also proportional to GDP levels. GRAVITY: VOLUMES OF TRADE are positively related to the GDP LEVELS of the trading countries and negatively related to the DISTANCE between the trading countries. [Notice: gravity needs a minimal set of assumptions to hold. It could be generated by a Ricardian model theory, by HO, or by the new trade theory models.] 11 / 20

The Equation: Free Trade - y i k : country i s output of good k; - Y i := - Y := N k=1 C i=1 y i k : country i s GDP; Y i : world GDP; - s i := Y i /Y : country i s share of world expenditure (GDP). Exports from i to j of good k: X ij k = sj y i k. Total exports from i to j: X ij = N k=1 X ij k = sj N yk i = s j Y i = Y j Y i k=1 Y = s j s i Y (= X ji ). Bilateral trade between i and j: X ij + X ji = 2Y j Y i Y = 2s j s i Y. (1) 12 / 20

The Equation: Trade Between Countries of Different Size Let A denote a region composed by several countries, indexed by i A. Let s A = Y A /Y, s ia = Y i /Y A. Helpman (1987): Volume of trade in A GDP in A ( = s A 1 ) (s ia ) 2 i A }{{} size dispersion index. Volumes of trade are higher between countries of similar size. Tests of this prediction resulted in mixed evidence (support for OECD countries, not for others, see Debaere (2002)). BUT: the result is based on the assumption of complete specialization, which might not hold after all. 13 / 20

The Border Effect Mc Callum (1995): compare within-canada and US-Canada trade. lnx ij = α + β 1 ln(y i ) + β 2 ln(y j ) + ρln(d ij ) + γδ ij + ε ij where d ij = distance and δ ij = 1 if within-canada trade, zero otherwise. Results: ˆβ 1, ˆβ 2 1 ˆρ < 0 negative effect of distance ˆγ 3 BORDER EFFECT: intranational trade is about 22 times larger than international trade!!! Need of introducing TRADE BARRIERS into the analysis! BUT: This implies that prices may differ across countries: need for more microfoundation, including prices in the equation. 14 / 20

A Simple Model - X ij k : exports from i to j of good k ; - c ij k : consumption in j of good k (produced in i), X ij k = pij k cij k ; - N i : number of products produced in country i; - p i : F.O.B. price of goods produced in country i; - p ij = T ij p i : C.I.F. price of goods prod. in i and sold in j, T ij 1, T ii = 1. Assume p ij k = pij, k c ij Consumers problem: k = cij, k. [ C max U j = c ij s.t. i=1 N i (c ij ) σ 1 σ ] σ σ 1 C N i p ij c ij = Y j i=1 (where σ > 1). The solution takes the form: X ij = N i ( p ij P j ) 1 σ Y j = Y i Y j (p i ) σ ȳ ( T ij P j ) 1 σ (2) where P j = [ C i=1 Ni (p ij ) 1 σ ] 1 1 σ. 15 / 20

Estimating Price Indexes Equation: X ij = Y i Y j (p i ) σ ȳ ( T ij P j ) 1 σ Estimating equation: lnx ij = ln(y i Y j )+(1 σ) lnt ij σ lnp i +(σ 1) ln(p j )+ε ij 16 / 20

Estimating Price Indexes Equation: X ij = Y i Y j (p i ) σ ȳ ( T ij P j ) 1 σ Estimating equation: lnx ij = ln(y i Y j )+(1 σ) lnt ij σ lnp i +(σ 1) ln(p j )+ε ij BUT: Ideal price indexes are not observable! 3 approaches: 1. directly measure them as GDP deflators; 2. estimate them using the model market clearing conditions: Anderson and van Wincoop (2003); 3. proxy for them using country fixed effects. 16 / 20

Anderson and van Wincoop (2003) Market clearing: p i y i = C T ij p i c ij. j=1 Theorem 1 Assume trade costs are symmetric: T ij = T ji. Then an implicit solution to the market clearing condition is: p i = 1 P i ( s i N i ) 1 1 σ (3) which implies: (P j ) 1 σ = C j=1 s i ( T ij P i ) 1 σ. (4) Why this is progress? Substituting (3) into the gravity equation, we obtain: X ij = Y i Y j Y ( T ij P i P j ) 1 σ. 17 / 20

Anderson and van Wincoop (2003) (contd.) Assume the following form for T ij : The gravity equation X ij = Y i Y j Y estimation equation: T ij = τ ij + ρln(d ij ) + ε ij. (5) ( T ij P i P j ) 1 σ leads to the following ln(x ij /(Y i Y j )) = ρ(1 σ)ln(d ij ) + (1 σ)τ ij +... Estimation strategy: 1. Use (5) to obtain predicted values for T ij. +ln(p i ) σ 1 + ln(p j ) σ 1 + (1 σ)ε ij. 2. Use (4) to compute the multilateral resistance terms (P i ) σ 1, (P j ) σ 1 ). 3. Run the estimation equation. 18 / 20

Anderson and van Wincoop (2003) (contd.) Results: 1. Size (+) and trade barriers (-) matter in determining volumes of trade. 19 / 20

Anderson and van Wincoop (2003) (contd.) Results: 1. Size (+) and trade barriers (-) matter in determining volumes of trade. 2. The multilateral resistance terms P j describe how remote a county is from the rest of the world: for given trade barriers, the more isolated a country is, the higher the price index, the lower is the volume of trade. 3. Estimates of τ ij (the border effect on prices) depend on the value of σ and range between 10-50% ; 4. Downsizing of McCallum estimates of the border effect for Canada: intranational trade is about 10 times higher than international trade for Canada Mc Callum larger number is due to the omitted variables P i. 19 / 20

Anderson and van Wincoop (2004) : Trade Costs Exhaustive survey of the literature on measurement of trade costs. Look at different types of trade costs: 1. Transportation costs 2. Policy barriers (tariff and non-tariff barriers) 3. Wholesale and distribution costs and at sources of data on trade costs: direct measures indirect measures from evidence on quantities from evidence on prices. Use gravity theory to infer trade costs from trade volumes and other observable variables. 20 / 20