1.3 Anderson and van Wincoop(2003) 1.4 ë z

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1 18ù `za^µúå % E ŒÆ²LÆ % (E ŒÆ²LÆ) êþ²læ 18ù 1 / 15

2 ùì SN 1. Úå 1.1 ISn A 1.2 Úå.ÚÚå 1.3 Anderson and van Wincoop(2003) 1.4 ë z 2. zö % (E ŒÆ²LÆ) êþ²læ 18ù 2 / 15

3 1. Úå 1.1 ISn A A µisn % (E ŒÆ²LÆ) êþ²læ 18ù 3 / 15

4 1. Úå 1.1 ISn A A µn þ ²L5ƒ' Source: Head and Mayer(2014). % (E ŒÆ²LÆ) êþ²læ 18ù 4 / 15

5 1. Úå 1.1 ISn A A µn þ ålkƒ' Source: Head and Mayer(2014). % (E ŒÆ²LÆ) êþ²læ 18ù 5 / 15

6 1. Úå 1.1 ISn A ƒ'a^µis % (E ŒÆ²LÆ) êþ²læ 18ù 6 / 15

7 1. Úå 1.1 ISn A ƒ'a^µis Ý] % (E ŒÆ²LÆ) êþ²læ 18ù 7 / 15

8 1. Úå 1.2 Úå.ÚÚå Úå.ÚÚå Newton s law of universal gravitation Gravity Model: Basic gravity models state that economic interactions between two geographically defined entities are proportional to the size of these entities and inversely related to the distance between them. They have great empirical explanatory power. Head and Mayer(2014): three definitions of the gravity equation General gravity x ij = GS im jφ ij Strutural gravity x ij = y i x j Ω i Φ j φ ij Naive gravity equation x ij = Gyi a yjφ b ij % (E ŒÆ²LÆ) êþ²læ 18ù 8 / 15

9 1. Úå 1.2 Úå.ÚÚå McCallum(1995) yïä ln x ij = α 1 + α 2 ln y i + α 3 ln y j + α 4 ln d ij + α 5 δ ij + α 6 REM i + α 7 REM j + ε ij x ij /«i /«j Ñ y i, y j ü /«IS )oš d ij ü /«ål δ ij L«ü /«ÄÓ áu I[ ½,«² Lé åcþ > Au e δ ij REM i = m j d im ym " % (E ŒÆ²LÆ) êþ²læ 18ù 9 / 15

10 1. Úå 1.3 Anderson and van Wincoop(2003) Anderson and van Wincoop(2003)Ÿ Ú z Gravity equations have been widely used to infer trade flow effects of various institutional arrangements. We show that estimated gravity equations do not have a theoretical foundation. This implies both that estimation suffers from omitted variables bias and that comparative statics analysis is unfounded. We develop a method that (i) consistently and efficiently estimates a theoretical gravity equation and (ii) correctly calculates the comparative statics of trade frictions. We apply the method to solve the famous McCallum border puzzle. Applying our method, we find that national borders reduce trade between industrialized countries by moderate amounts of percent. % (E ŒÆ²LÆ) êþ²læ 18ù 10 / 15

11 1. Úå 1.3 Anderson and van Wincoop(2003) Úå nøä: ( ) σ Max u j = (c ij/β i) σ 1 σ 1 σ s.t. i i p ijc ij = y j = i d ^ ÚýŽå^ Œ/«i Ñ /«j n þ 6ª µ x ji ( ) 1 σ βip ij x ij = p ijc ij = y j b½ p ij = p it ij!t ij = b ijd ρ ij Pθi = yi/yw ²LíŒe (5Ú å structural gravity equation 9 ª µ ( ( ) ) 1 tij 1 σθi Ù µp j = Π i i P j ( ) 1 σ x ij = yiyj tij y W Π ip j 1 σ!πi = ( j ) 1 ( ) tij 1 σθj 1 σ P j % (E ŒÆ²LÆ) êþ²læ 18ù 11 / 15

12 1. Úå 1.3 Anderson and van Wincoop(2003) O(J Šâ(5Úå ü /«ƒmn þé5ïƒ S ij!ålïƒ D ij Ú šålù {å resistance terms R ijk µ ln x ij = ln y i + ln y j ln y W + α 1 ln d ij + α 2 (δ ij ln Π i ln P j) }{{}}{{}}{{} S ij D ij 25 Ú 26 ªr> A border effects ½Â Ñ I> éüi n K µ ( e δ ij P i Border i = exp (R ii R ij) = P j R ij ) σ 1 % (E ŒÆ²LÆ) êþ²læ 18ù 12 / 15

13 1. Úå 1.3 Anderson and van Wincoop(2003) Head and Mayer(2014)µn«O {' Notes: Top value in each cell is the mean estimate (based on 1000 repetitions). The true parameters are -1 for distance and.5 for RTA. Average standard error in /( )0 and standard deviation of estimate in/[ ]0. % (E ŒÆ²LÆ) êþ²læ 18ù 13 / 15

14 1. Úå 1.4 ë z ë z Anderson, J.E. and E. van Wincoop 2003: Gravity and gravitas: a solution to the border puzzle, American Economic Review, Vol.93, No.1, P Head, K. and T. Mayer 2014: Gravity equations: workhorse, toolkit, and cookbook, Chapter 3 in G. Gopinath, E. Helpman and K. Rogoff (eds), Handbook of International Economics(Vol.4), Elsevier % (E ŒÆ²LÆ) êþ²læ 18ù 14 / 15

15 2. zö žlæ EBSCO Õe1e? Ÿ Ù ± Öwµ ü Karabarbounis, L. and B. Neiman 2013: The global decline of the labor share, Quarterly Journal of Economics, Vol.129(1), P Herrendorf B., R. Rogerson and A. Valentinyi 2013: Two perspectives on preferences and structural transformation, American Economic Review, Vol.103(7), P Desmet K. and E. Rossi-Hansberg 2013: Urban accounting and welfare, American Economic Review, Vol.103(6), P % (E ŒÆ²LÆ) êþ²læ 18ù 15 / 15

Gravity Models and the Armington Assumption

Gravity Models and the Armington Assumption Background Economists love the elegance and completeness of physics, and what could be more elegant than Newton s Law of Universal Gravity? To recap: The gravitational