第六讲 静态优化应用：引力方程.pdf

18ù · `zA^µÚ啧 •% E ŒÆ²LÆ •% (E ŒÆ²LÆ ) êþ²LÆ£18ù¤ 1 / 15 ù̇SN 1. Ú啧 1.1 ISn´ A ¯¢ 1.2 Úå .ÚÚ啧 1.3 Anderson and van Wincoop(2003) 1.4 ë•©z 2. ©z Ö •% (E ŒÆ²LÆ ) êþ²LÆ£18ù¤ 2 / 15 1. Ú啧 1.1 ISn´ A ¯¢ A ¯¢µISn´ •% (E ŒÆ²LÆ ) êþ²LÆ£18ù¤ 3 / 15 1. Ú啧 A ¯¢µn´þ†²L5 1.1 ISn´ A ¯¢ ƒ' Source: Head and Mayer(2014). •% (E ŒÆ²LÆ ) êþ²LÆ£18ù¤ 4 / 15 1. Ú啧 1.1 ISn´ A ¯¢ A ¯¢µn´þ†ålKƒ' Source: Head and Mayer(2014). •% (E ŒÆ²LÆ ) êþ²LÆ£18ù¤ 5 / 15 1. Ú啧 1.1 ISn´ A ¯¢ ƒ'A^µIS£¬ •% (E ŒÆ²LÆ ) êþ²LÆ£18ù¤ 6 / 15 1. Ú啧 ƒ'A^µIS† •% (E ŒÆ²LÆ ) 1.1 ISn´ A ¯¢ Ý] êþ²LÆ£18ù¤ 7 / 15 1. Ú啧 Úå 1.2 Úå .ÚÚ啧 .ÚÚ啧 I Newton’s law of universal gravitation I 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. I Head and Mayer(2014): three definitions of the gravity equation •% I General gravity xij = GSi Mj φij I yi j Strutural gravity xij = Ω φij i Φj I Naive gravity equation xij = Gyia yjb φij x (E ŒÆ²LÆ ) êþ²LÆ£18ù¤ 8 / 15 1. Ú啧 McCallum(1995) 1.2 Úå .ÚÚ啧 ¢yïÄ ln xij = α1 + α2 ln yi + α3 ln yj + α4 ln dij + α5 δij + α6 REMi + α7 REMj + εij I xij •/« i •/« j Ñ•¶ I yi , yj •ü‡/« IS ) oŠ¶ I dij •ü‡/« ål¶ I δij L«ü‡/«´ÄÓ áu˜‡I[£½,«² Lé† ¤ åCþ§> ¸ A ue δij I REMi = P m6=j •% ¶ dim " ym (E ŒÆ²LÆ ) êþ²LÆ£18ù¤ 9 / 15 1. Ú啧 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 20-50 percent. •% (E ŒÆ²LÆ ) êþ²LÆ£18ù¤ 10 / 15 1. Ú啧 1.3 Anderson and van Wincoop(2003) Ú啧 nØÄ:  σ  σ−1 σ−1 P M ax uj = (cij /βi ) σ i P P s.t. pij cij = yj = xji i d˜ ^‡ÚýŽ i å^‡Œ•/« i Ñ•  xij = pij cij = /« j βi pij Pj n´þ•£ 1−σ yj b½ pij = pi tij!tij = bij dρij §¿Pθi = yi /y W §²Lí 啧£structural gravity equation§ Œ e¡ ( 5Ú ©9 ª¤ µ yi yj xij = W y  tij Π i Pj  1    1−σ P tij 1−σ θ !Πi = Ù¥µPj = i Πi •% ©6ª¤ µ 1−σ P  tij 1−σ i j (E ŒÆ²LÆ ) êþ²LÆ£18ù¤ Pj ! 1 1−σ θj 11 / 15 1. Ú啧 1.3 Anderson and van Wincoop(2003) O(J Šâ( 5Ú啧§ü‡/«ƒm n´þÉ šål Ù¦{å£resistance terms¤ Rij 5 σ Sij!ålσ Dij Ú K•µ ln xij = ln yi + ln yj − ln y W + α1 ln dij + α2 (δij − ln Πi − ln Pj ) {z } | {z } | | {z } Sij Dij ©¥£25¤Ú£26¤ªr>¸ n´ Rij A£border effects¤½Â•Ñ•I >¸éüI K•µ  δij σ−1 e Pi Borderi = exp (Rii − Rij ) = Pj •% (E ŒÆ²LÆ ) êþ²LÆ£18ù¤ 12 / 15 1. Ú啧 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 1. Ú啧 1.4 ë•©z ë•©z I Anderson, J.E. and E. van Wincoop 2003: Gravity and gravitas: a solution to the border puzzle, American Economic Review, Vol.93, No.1, P170-192 I 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 2. ©z Ö žlÆ EBSCO Õe1e¡ ?¿˜Ÿ©Ù§± |•ü Ö wµ I Karabarbounis, L. and B. Neiman 2013: The global decline of the labor share, Quarterly Journal of Economics, Vol.129(1), P61-103 I Herrendorf B., R. Rogerson and A. Valentinyi 2013: Two perspectives on preferences and structural transformation, American Economic Review, Vol.103(7), P2752-89 I Desmet K. and E. Rossi-Hansberg 2013: Urban accounting and welfare, American Economic Review, Vol.103(6), P2296-2327 •% (E ŒÆ²LÆ ) êþ²LÆ£18ù¤ 15 / 15