The Gravity Model
基于新型引力模型的国际贸易量实证研究分析
２０１９年第 １期·总第 ２９５期
作为虚拟变量。由于中国于 ２００１年正式加入 ＷＴＯ，其他 四个国家在 １９９５年就已加入，所以 １９９９—２０１８年这 ２０ 年能够跨越中国加入 ＷＴＯ前后两个阶段，因此笔者可以 用这组数据研究虚拟变量。
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（ＢｕｓｉｎｅｓｓＳｃｈｏｏｌ，ＥａｓｔＣｈｉｎａＵｎｉｖｅｒｓｉｔｙｏｆＰｏｌｉｔｉｃａｌＳｃｉｅｎｃｅａｎｄＬａｗ，Ｓｈａｎｇｈａｉ２０１６２０） Ａｂｓｔｒａｃｔ：Ｂａｓｅｄｏｎｔｈｅｔｒａｄｉｔｉｏｎａｌｇｒａｖｉｔｙｍｏｄｅｌ，ｔｈｉｓｐａｐｅｒｃｏｎｓｔｒｕｃｔｓａｎｅｗｇｒａｖｉｔｙｍｏｄｅｌｂｙｉｎｔｒｏｄｕｃｉｎｇｎｅｗｖａｒｉａ ｂｌｅｓｓｕｃｈａｓｐｅｒｃａｐｉｔａＧＤＰ．Ａｔｔｈｅｓａｍｅｔｉｍｅ，ｔｈｉｓｐａｐｅｒｕｓｅｓｔｈｅｒｅｌｅｖａｎｔｄａｔａｏｆＣｈｉｎａ，ｔｈｅＵｎｉｔｅｄＳｔａｔｅｓ，Ｊａ ｐａｎ，ＳｏｕｔｈＫｏｒｅａａｎｄＧｅｒｍａｎｙｔｏｃｏｎｄｕｃｔａｑｕａｎｔｉｔａｔｉｖｅｒｅｇｒｅｓｓｉｏｎａｎａｌｙｓｉｓｔｏｔｈｅｎｅｗｇｒａｖｉｔｙｍｏｄｅｌ．Ｔｈｒｏｕｇｈｄａｔａ ｒｅｖｉｅｗ，ｄａｔａｓｅｌｅｃｔｉｏｎ，ｍｏｄｅｌｃｏｎｓｔｒｕｃｔｉｏｎａｎｄｒｅｓｕｌｔｓａｎａｌｙｓｉｓ，ｔｈｅａｕｔｈｏｒｈａｓａｒｅｌａｔｉｖｅｌｙｎｅｗｕｎｄｅｒｓｔａｎｄｉｎｇｏｆｔｈｅ ｇｒａｖｉｔｙｍｏｄｅｌ，ｅｘｐｌｏｒｅｄｏｔｈｅｒｒｅｌｅｖａｎｔｆａｃｔｏｒｓａｆｆｅｃｔｉｎｇｂｉｌａｔｅｒａｌｔｒａｄｅｖｏｌｕｍｅ，ａｎｄｐｒｏｖｉｄｅｄｃｏｒｒｅｓｐｏｎｄｉｎｇｓｕｇｇｅｓｔｉｏｎｓ ｆｏｒＣｈｉｎａ’ｓｉｎｔｅｒｎａｔｉｏｎａｌｔｒａｄｅ．Ｉｔｈａｓｃｅｒｔａｉｎｔｈｅｏｒｅｔｉｃａｌｒｅｓｅａｒｃｈｓｉｇｎｉｆｉｃａｎｃｅｆｏｒｔｈｅｆｏｌｌｏｗ－ｕｐｒｅｓｅａｒｃｈｉｎｒｅｌａｔｅｄ ｆｉｅｌｄｓ． Ｋｅｙｗｏｒｄｓ：ＮｅｗＧｒａｖｉｔｙＭｏｄｅｌ；ＥｍｐｉｒｉｃａｌＡｎａｌｙｓｉｓ；ＩｎｔｅｒｎａｔｉｏｎａｌＴｒａｄｅＶｏｌｕｍｅ
引力模型
•
My=KYiYj/Dij
• 式中，K为常数（通常也称为引力系 数）；Yi和Yj为内生变量，由模型要求通过 的特定条件“平衡”出来；Dij为空间距离。
二、引力模型及其应用
• 尽管早在19世纪中叶的学术研究中，就已出现对引 力模型公式模糊的应用，但真正的引力模型公式的 出现，还得从J.Q斯图尔特（Stewart，1948）和G.K. 齐夫（Zipf，1946）算起，他们两人独立同时提出 了这一公式。齐夫致力于对两个城市之间，空间相 互作用（运算上用铁路运输量、电话通话量，以及 相似的社会或经济交流形式的数量来定义）水平的 研究。他提出的特别有用的公式是（P1P2）/D，即 两个城市人口的积，除以其间的距离。他研究了研 究区内所有“城市对”的该比率，在双对数纸上画 出两个城市间的相互作用水平随着距离的变化，发 现了一种线性关系。
引力模型
• 引力模型(Gravity Model)是应用广泛的空间 相互作用模型，它是用来分析和预测空间 相互作用形式的数学方程，已被不断拓展， 运用于许多研究领域，如研究空间布局、 旅游、贸易和人口迁移等方面取得了很多 有益的研究成果。
牛顿万有引力定律
• • 17世纪牛顿提出了著名的万有引力定律，
由此牛顿物理学问世。万有引力定律给物 理学及许多自然科学学科的发展以划时代 的推动。根据这定律，任何两个物体之间 的作用（引力）的大小与它的质量成正比， 与它们之间的距离平方成反比。
高精度惯性导航系统对重力场模型的要求
个 高通滤波器 ,随着时间的增加 ,其值也在增加 ,
1 INS 误差分析方程
IN S 的基本原理是牛顿第二定律 ,它在惯性
系中的方程为[1 ] :
¨r = a + g ( r)
(1)
式中 , ¨r 是载体加速度 ; a 是加速度计所测的比力 ;
g ( r) 为引力 ,它与载体位置 r 有关 。
为了便于分析 ,不考虑惯性传感器自身误差
另外在短时间内重力误差引起的水平位置误差很小采用不同重力场模型的差别不是很大这间接反映了图1中所表对于使用球谐函数模型进行重力补偿则对应的残余重力扰动水平分量的功率谱等于在式6的低频部分乘以球谐函数模型相应的误差阶510武汉大学学报
第 31 卷 第 6 期 2006 年 6 月
武 汉 大 学 学 报 ·信 息 科 学 版 Geo matics and Info rmation Science of Wuhan University
[ 2 ] J eleli C. Gravity o n Precise Sho rt2Term ,32D Free2 Inertial Navigatio n [J ] . Navigatio n , 1997 , 44 (3) : 3472357
(6)
i =
式中 , K0 是变形贝塞耳函数 ;ωs 是空间角频率 , 而
式 (3) 中的 ω是时间角频率 , 它们之间可通过载
体速度 v 联系起来[2 ] :
n
∑ PS Dδgx (ω) = 2ω2 / v3 βσi 2i K0 (βωi / v) (7) i =1
对于使用球谐函数模型进行重力补偿 ,则对
李 斐等 :高精度惯性导航系统对重力场模型的要求
509
贸易引力模型实用教程
AGRODEP Technical Note TN-05April 2013Hands-on gravity estimation with STATAVersion 2Maria Cipollina and Luca SalvaticiHands-on gravity estimation with STATAIn this document we give several examples of hands-on estimation to familiarize yourself with the gravity equation methodological choices highlighted in the literature review. This guide provides an illustrative dataset with alternative Stata codes presenting the different possible estimation strategies.Part 1 describes how estimations are carried out with panel data and are directed to show the relevance of the multilateral resistance term as well as the modeling of the (trade) policy variables. In Part 2, cross-sections estimations show the importance of working with disaggregated data. Finally, Part 3 shows how you can solve the ‘zero (trade flows) problem’ using either Heckman or Poisson estimators.As you read this guide, you will use STATA to carry out estimations designed to familiarize you with the software and, more importantly, the gravity model. STATA is a statistical software program and we assume that you have a recent version of STATA (version 11.2 or later). The instructions in this guide are quite detailed. Our aim is to give sufficient detail to enable a new user of this software to follow the examples relying solely on this guide. On the other hand, the guide is strictly related to the literature review that highlights the main theoretical and methodological issues illustrated in the regressions.Data filesThere are two Data files:∙dataset_def.dta: it contains all the essential variables used in the regressions using panel data (Part 1). The dataset covers the period from 1996 to 2006 and includes 154 developed and developing countries.∙us_agr.dta: it contains all the essential variables used in the regressions using cross-section data (Part 2 and Part 3). It refers to year 2004 US agricultural imports from 226 countries. Data are disaggregated at the most detailed level allowed by the international Harmonized System (HS) classification (6 digits) and include 689 products.The variable names are largely self-explanatory and are described when the labels are created: their generation and construction can thus be directly inspected. The data sources are described in the Appendix.Do filesThere are three Do files:∙regressions aggregated data.do: it runs regressions using panel, aggregated data (Part1).∙regressions disaggregated data.do: it runs regressions using cross-section, disaggregated as well as aggregated data (Part 2).∙regressions zeroes treatment.do: it runs regressions using non-linear estimators (Heckman or Poisson) dealing with ‘zero’ trade flows (Part 3).Part 1: Aggregated dataA.Variable Generation.Part A brings in the data and generates the variables used in the analysis:(a)We use the data file dataset_defuse dataset_def.dta(b)We take the logs of all continuous variables included in the regressions:g limports=ln(imports)g lgdp_o=ln(gdp_o)g lgdp_d=ln(gdp_d)g ldist= ln(distw)g ltariff=ln(1+s_average)(c)We label the variables to be included in the tables.l a var limports “Ln(Imports)”la var colony “Colonial link”la var comlang_off “Common language”la var contig “Border”la var ldist “Ln(distance)”la var lgdp_d “Ln(GDP_importer)”la var lgdp_o “Ln(GDP_exporter)”la var rta “Regional Trade Agreement”la var ltariff “Ln(1+Tariff)”(d)Finally, we generate the different fixed effects.qui tab imp, g(dimp)qui tab exp, g(dexp)qui tab pair, g(dpair)qui tab year, g(dyear)B. Regression SpecificationsPart B runs panel regressions with aggregated data, and the dummy RTA (i.e., Regional Trade Agreements) as (trade) policy variable. Regressions are based on equation (2) with time, importer, exporter and country-pair fixed effects.We start by declaring data to be panel.tsset pair yearIn order to show the consequences of ignoring the multilateral resistance term, we firstly estimate equation (2) without fixed effectseststo: reg limports lgdp_d lgdp_o ldist contig colony comlang_off rta, robust Then, we introduce the different types of fixed effects:eststo: reg limports lgdp_d lgdp_o ldist contig colony comlang_off rta dyear*, robust eststo: reg limports lgdp_d lgdp_o ldist contig colony comlang_off rta dimp* dexp*, robusteststo: reg limports lgdp_d lgdp_o ldist contig colony comlang_off rta dimp* dexp* dyear*,robusteststo: reg limports lgdp_d lgdp_o ldist contig colony comlang_off rta dpair* dyear*, robustThe dummy for pair effects is equal to 1 for all observations of trade occurring between a given pair of countries, for all pairs. Country dummies remove cross-section, but not time-series biases. The latter is a serious shortcoming since omitted factors affecting bilateral trade costs often vary over time. Pair dummies cannot be used in cross-section data since the number of dummies would be equal to the number of observations.The command “esttab” creates the regression table in a file regressions1.docesttab using regressions1.doc, title (aggregate-dummy policy) se ar2 label replace rtf b(2) star (* 0.10 ** 0.05 *** 0.01) se(2) mti drop (dexp* dimp* dyear* dpair*)TABLE: Panel results with different fixed effectsModel 1and 2 report the base regression. Column (1.1) reports results without fixed effects. Column (2.1) reports results where time dummies are added to the regression, to account forthe changing nature of the relationship over time. Column (2.2) and (2.3) show results for time invariant importer and exporter fixed effects and for time varying exporter and importer fixed effects, respectively. Finally, column (2.4) presents a specification where pair effects are also added.* p < 0.10, ** p < 0.05, *** p < 0.01All coefficients have the expected signs, the only exception is the coefficient of the colonial links that seem to have a negative impact if we do not consider country fixed effects (columns 1.1 and 2.1). Focusing on the most widely used specification (column 2.3), the estimated coefficients should be interpreted as follows: size of importer country has a positive and significant impact with an elasticity of 0.91, so that an increase in GDP of 10% increase trade by 9.1%; an increase in distance of 10% reduce trade by around 15%; the existence of border and language links imply an increase in trade of 72% and 118% (e0.54-1=0.72; e0.78-1= 1.18), respectively; the estimated coefficient of dummy for RTA of 0.62 implies that regional trade agreements increase trade of 86% (e0.62-1=0.86).Finally, in order to show the relevance of an actual measure we estimate equation (3) using a continuous variable for trade policyreg limports lgdp_d lgdp_o ldist contig colony comlang_off ltariff dimp* dexp* dyear*, robustThen we create the results tableesttab using regressions1.doc, title (aggregate-tariff) se ar2 label replac rtf b(2) star (* 0.10 ** 0.05 *** 0.01) se(2) mti drop (dexp* dimp* dyear*) appendTABLE: Panel results with continuous policy variable* p < 0.10, ** p < 0.05, *** p < 0.01All coefficients have the expected signs. Trade policies have a negative and significant impact on trade, a tariff factor increase by 10% leads to a 6% reduction of trade.Part 2: Disaggregated dataA.Variable Generation.(a)We use the data file us_agruse us_agr.dta(b)We take the logs of all continuous variables included in the regressionsg limports=ln(trade)g lgdp_o=ln(gdp_o)g lgdp_d=ln(gdp_d)g ldist= ln(distw)g ltariff=ln(1+tariff)(c)We label the variables to be included in the tables.la var limports "Ln(Imports)"la var colony "Colonial link"la var comlang_off "Common language"la var contig “Border”la var ldist "Ln(distance)"la var lgdp_d "Ln(GDP_importer)"la var lgdp_o "Ln(GDP_exporter)"la var ltariff "Ln(1+Tariff)"(d)We generate the exporter and product fixed effectsqui tab exp, g(dexp)qui tab hs6, g(dhs6)B. Regression Specifications(a)As in Part 1, we firstly estimate equation (2) using the OLS estimator without fixedeffectseststo: reg limports lgdp_o ldist contig colony comlang_off ltariff, robust(b)Then, we introduce the different types of fixed effects:eststo: reg limports lgdp_o ldist contig colony comlang_off ltariff dhs6*, robusteststo: reg limports contig colony comlang_off ltariff dexp* dhs6*, robust(c)Finally, we collapse the dataset in order to obtain aggregated data for a robustnessanalysis.collapse (sum) trade (mean) tariff gdp_o distw contig colony comlang_off, by(exp)g limports=ln(trade)g lgdp_o=ln(gdp_o)g ldist= ln(distw)g ltariff=ln(1+tariff)(d)and we run again the regression to highlight the relevance of the aggregation issueeststo: reg limports lgdp_o ldist contig colony comlang_off ltariff, robust(e)The command “esttab” creates the regression table in a file regressions2.docesttab using regressions2.doc, title (dati_us_agr) se ar2 label replac rtf b(2) star (*0.10 ** 0.05 *** 0.01) se(2) mti drop (dexp* dhs6*) appendeststo clearTABLE: Cross-section results with different fixed effects and different levels of aggregation Cross-sectional model covering imports in 689 agricultural commodities from 227 countries to US in 2004.Columns (1) to (3) show results with disaggregated data using different fixed-effects specifications. Column (4) reports result of aggregated data.* p < 0.10, ** p < 0.05, *** p < 0.01Most empirical analyses use gravity models with aggregated data, but using aggregate trade flows to analyze the effects of trade policies applied at product level seems misleading. As a matter of fact, the estimated coefficient related to trade policy, namely Ln(1+tariff), is not significant in column (4).Part 3: Zeroes treatmentA.Variable Generation(a)We use the data file us_agruse us_agr.dtaWe take the logs of all continuous variables included in the regressionsg limports=ln(trade)g lgdp_o=ln(gdp_o)g lgdp_d=ln(gdp_d)g ldist= ln(distw)g ltariff=ln(1+tariff)(c)We label the variables to be included in the tables.la var limports "Ln(Imports)"la var colony "Colonial link"la var comlang_off "Common language"la var ldist "Ln(distance)"la var lgdp_d "Ln(GDP_importer)"la var lgdp_o "Ln(GDP_exporter)"la var ltariff "Ln(1+Tariff)"(d)We generate the exporter and product fixed effectsqui tab exp, g(dexp)qui tab hs6, g(dhs6)B. Regression Specifications(a)We firstly run the regression using the Heckman estimatoreststo: heckman limports contig colony comlang_off ltariff , select(contig colony ltariff) mills(lambda)(b)Then we run the regression using the Poisson Pseudo-Maximum Likelihood estimatoreststo: ppml trade contig colony comlang_off ltariff(c)The command “esttab” creates the regression table in a file regressions3.docesttab using regressions3.doc, title (treatment of zeros) se ar2 label replace rtf b(2) star (* 0.10 ** 0.05 *** 0.01) se(2) mtiTABLE: Results with different estimators: Heckman and PoissonModel (1) reports results obtained using the Heckman two-step procedure. The first column shows the second stage estimates of the trade flow, whereas the second column reports the first-stage Probit selection equation. Model (2) shows results obtained using Poisson Pseudo-Maximum Likelihood estimator.The use of disaggregated data raises the “zero trade flows” issue, which introduces obvious problems in the log-linear form of the gravity equation. Several authors consider the Heckman two-step estimator as the best procedure, others argue that gravity type models should be estimated in multiplicative form, and recommend the Poisson Pseudo-Maximum Likelihood (PPML) estimator to deal with the problem of zeros in the trade matrix, in order to achieve unbiased and consistent estimates. The significant coefficient of the Mills ratio confirms that correcting for sample selection bias is justified, however, because of the presence of heteroskedasticity, estimates of the log-linear form of the gravity equation are biased and inconsistent, and this may lead to prefer the Poisson specification of the trade gravity model.APPENDIX: Data SourceDataset_def.dta: Dataset is building on extraction from WITS (/wits/index.html) and on information provided by the CEPII dataset (http://www.cepii.fr/).The WITS application gives access to international trade statistics of UN COMTRADE (The United Nations Commodity Trade Statistics database) and tariff database of UNCTAD-TRAINS (Trade Analysis and Information System).The Cepii dataset includes data on GDP and distances between countries and dummies for contiguity, common language, and former colonial links.Us_agr.dta: Data on trade and tariffs at the HS6 level of detail are taken from the MAcMapHS6-V2 database (/publication/picture-tariff-protection-across-world-2004). MAcMapHS6 provides a consistent worldwide assessment of protection, including ad valorem equivalent rates of specific duties and tariff rate quotas (including those introduced at the end of the Uruguay Round), for 2004. Data for the remaining explanatory variables are from the Cepii dataset.。
克鲁格曼《国际经济学》第八版课后答案(英文)-Ch02.doc
Chapter 2World Trade: An Overview⏹Chapter OrganizationWho Trades with Whom?Size Matters: the Gravity ModelThe Logic of the Gravity ModelUsing the Gravity Model: Looking for AnomaliesImpediments to Trade: Distance, Barriers, and BordersThe Changing Pattern of World TradeHas the World Gotten SmallerWhat Do We Trade?Service OutsourcingDo Old Rules Still Apply?Summary⏹Key ThemesBefore entering into a series of theoretical models that explain why countries trade across borders and the benefits of this trade (Chapters 3–11), Chapter 2 considers the pattern of world trade which we observe today. The core idea of the chapter is the empirical model known as the gravity model. The gravity model is based on the observations that: (1) countries tend to trade with other nearby economies and (2) countries’ trade is proportional to their size. The model is called the gravity model as it is similar in form to the physics equation that describes the pull of one body on another as proportional to their size and distance.The basic form of the gravity equation is T ij=A⨯Y i⨯Y j/D ij. The logic supporting this equation is that large countries have large incomes to spend on imports and produce a large quantity of goods to sell as exports. This means that the larger either trade partner, the larger the volume of trade between them. At the same time, the distance between two trade partners can substitute for the transport costs that they face as well as proxy for more intangible aspects of a trading relationship such as the ease of contact for firms. This model can be used to estimate the predicted trade between two countries and look for anomalies in trade patterns. The text shows an example where the gravity model can be used to demonstrate the importance of national borders in determining trade flows. According to many estimates, the border between the U.S. and Canada has the impact on trade equivalent to roughly 2000 miles of distance. Other factors, such as tariffs, trade agreements, and common language can all affect trade and can be incorporated into the gravity model.The chapter also considers the way trade has evolved over time. While people often feel that the modern era has seen unprecedented globalization, in fact, there is precedent. From the end of the 19th century to World War I, the economies of different countries were quite connected. Trade as a share of GDP was higher in 1910 than 1960, and only recently have trade levels surpassed the pre World War trade. The nature of trade has change though. The majority of trade is in manufactured goods with agriculture and mineral products (and oil) making up less than 20% of world trade. Even developing countries now export primarily manufactures. In contrast, a century ago, more trade was in primary products as nations tended to trade for things that literally could not be grown or found at home. Today, the reasons for trade are more varied and the products we trade are ever changing (for example, the rise in trade of things like call centers). Th e chapter concludes by focusing on one particular expansion of what is “tradable”—the increase in services trade. Modern information technology has greatly expanded what can be traded as the person staffing a call center, doing your accounting, or reading your X-ray can literally be half-way around the world. While still relatively rare, the potential for a large increase in service outsourcing is an important part of how trade will evolve in the coming decades. The next few chapters will explain the theory of why nations trade.Answers to Textbook Problems1. We saw that not only is GDP important in explaining how much two countries trade, but also,distance is crucial. Given its remoteness, Australia faces relatively high costs of transporting imports and exports, thereby reducing the attractiveness of trade. Since Canada has a border with a largeeconomy (the U.S.) and Australia is not near any other major economy, it makes sense that Canada would be more open and Australia more self-reliant.2. Mexico is quite close to the U.S., but it is far from the European Union (EU). So it makes sense thatit trades largely with the U.S. Brazil is far from both, so its trade is split between the two. Mexico trades more than Brazil in part because it is so close to a major economy (the U.S.) and in partbecause it is a member of a free trade agreement with a large economy (NAFTA). Brazil is farther away from any large economy and is in a free trade agreement with relatively small countries.3. No, if every country’s GDP were to double, world trade would not quadruple. One way to see thisusing the example from Table 2-2 would simply be to quadruple all the trade flows in 2-2 and also double the GDP in 2-1. We would see that the first line of Table 2-2 would be—, 6.4, 1.6, 1.6. If that were true, Country A would have exported $8 trillion which is equal to its entire GDP. Likewise, it would have imported $8 trillion, meaning it had zero spending on its own goods (highly unlikely). If instead we filled in Table 2-2 as before, by multiplying the appropriate shares of the world economy times a country’s GDP, we would see the first line of Table 2-2 reads—, 3.2, 0.8, 0.8. In this case, 60% of Country A’s GDP is exported, the same as before. The logic is that while the world G DP has doubled, increasing the likelihood of international trade, the local economy has doubled, increasing the likelihood of domestic trade. The gravity equation still holds. If you fill in the entire table, you will see that where before the equation was 0.1 ⨯ GDP i⨯ GDP j, it now is 0.05 ⨯ GDP i⨯ GDP j. The coefficient on each GDP is still one, but the overall constant has changed.4. As the share of world GDP which belongs to East Asian economies grows, then in every traderelationship which involves an East Asian economy, the size of the East Asian economy has grown.This makes the trade relationships with East Asian countries larger over time. The logic is similar for why the countries trade more with one another. Previously, they were quite small economies, meaning that their markets were too small to import a substantial amount. As they became morewealthy and the consumption demands of their populace rose, they were each able to importmore. Thus, while they previously had focused their exports to other rich nations, over time, they became part of the rich nation club and thus were targets for one another’s exports. Again, using the gravity model, when South Korea and Taiwan were both small, the product of their GDPs was quite small, meaning despite their proximity, there was little trade between them. Now that they have both grown considerably, their GDPs predict a considerable amount of trade.5. As the chapter discusses, a century ago, much of world trade was in commodities that in many wayswere climate or geography determined. Thus, the UK imported goods that it could not make itself.This meant importing things like cotton or rubber from countries in the Western Hemisphere or Asia.As the UK’s climate and natural resource endowments were fairly similar to those in the rest of Europe, it had less of a need to import from other European countries. In the aftermath of the IndustrialRevolution, where manufacturing trade accelerated and has continued to expand with improvements in transportation and communications, it is not surprising that the UK would turn more to the nearby and large economies in Europe for much of its trade. This is a direct prediction of the gravity model.。
GravityModel
The Gravity Model∗James E.AndersonBoston College and NBERJanuary18,2011AbstractGravity has long been one of the most successful empirical models in economics.In-corporating deeper theoretical foundations of gravity into recent practice has led toa richer and more accurate estimation and interpretation of the spatial relations de-scribed by gravity.Wider acceptance has followed.Recent developments are reviewedhere and suggestions are made for promising future research.JEL Classification:F10,R1.Contact information:James E.Anderson,Department of Economics,Boston Col-lege,Chestnut Hill,MA02467,USA.Keywords:Incidence,multilateral resistance,trade costs,migration.∗This review was prepared for Annual Review of Economics,vol.3.I thank Jeffrey H.Bergstrand,Keith Head,J.Peter Neary and Yoto V.Yotov for helpful comments.The gravity model in economics was until relatively recently an intellectual orphan,un-connected to the rich family of economic theory.This review is a tale of the orphan’s reunion with its heritage and the benefits that continue toflow from connections to more distant relatives.Gravity has long been one of the most successful empirical models in economics,order-ing remarkably well the enormous observed variation in economic interaction across space in both trade and factor movements.The goodfit and relatively tight clustering of coeffi-cient estimates in the vast empirical literature suggested that some underlying economic law must be at work,but in the absence of an accepted connection to economic theory,most economists ignored gravity.The authoritative survey of Leamer and Levinsohn(1995)cap-tures the mid-90’s state of professional thinking:“These estimates of gravity have been both singularly successful and singularly unsuccessful.They have produced some of the clearest and most robust empiricalfindings in economics.But,paradoxically,they have had virtually no effect on the subject of international economics.Textbooks continue to be written and courses designed without any explicit references to distance,but with the very strange im-plicit assumption that countries are both infinitely far apart and infinitely close,the former referring to factors and the latter to commodities.”Subsequently,gravityfirst appeared in textbooks in2004(Feenstra,2004),following on success in connecting gravity to economic theory,the subject of Section3.Reviews are not intended to be surveys.My take on the gravity model,thus licensed to be idiosyncratic,scants or omits some topics that others have found important while it emphasizes some topics that others have scanted.My emphases and omissions are intended to guide the orphan to maturity.An adoptive parent’s biases may have contaminated my judgment,caveat emptor.My focus is on theory.Incorporating the theoretical foundations of gravity into recent practice has led to richer and more accurate estimation and interpretation of the spatial relations described by gravity,so where appropriate I will point out this benefit.The har-vest reaped from empirical work applying the gravity model is recently surveyed elsewhere (Anderson and van Wincoop,2004;Bergstrand and Egger,2011).From a modeling standpoint,gravity is distinguished by its parsimonious and tractable representation of economic interaction in a many country world.Most international economic theory is concentrated on two country cases,occasionally extended to three country cases with special features.The tractability of gravity in the many country case is due to its modularity:the distribution of goods or factors across space is determined by gravity forces conditional on the size of economic activities at each location.Modularity readily allows for disaggregation by goods or regions at any scale and permits inference about trade costs not dependent on any particular model of production and market structure in full general equilibrium.The modularity theme recurs often below,but is missing from some other prominent treatments of gravity in the literature.1Traditional GravityThe story begins by setting out the traditional gravity model and noting clues to its union with economic theory.The traditional gravity model drew on analogy with Newton’s Law of Gravitation.A mass of goods or labor or other factors of production supplied at origin i,Y i, is attracted to a mass of demand for goods or labor at destination j,E j,but the potential flow is reduced by the distance between them,d ij.Strictly applying the analogy,X ij=Y i E j/d2ijgives the predicted movement of goods or labor between i and j,X ij.Ravenstein(1889) pioneered the use of gravity for migration patterns in the19th century UK.Tinbergen(1962) was thefirst to use gravity to explain tradeflows.Departing from strict analogy,traditional gravity allowed the exponents of1applied to the mass variables and of−2applied to bilateral distance to be generated by data tofit a statistically inferred log-linear relationship betweendata onflows and the mass variables and distance.Generally,across many applications,the estimated coefficients on the mass variables cluster close to1and the distance coefficients cluster close to−1while the estimated equationfits the data well:most data points cluster close to thefitted line in the sense that80−90%of the variation in theflows is captured by thefitted relationship.Thefit of traditional gravity improved when supplemented with other proxies for trade frictions,such as the effect of political borders and common language.Notice that bilateral frictions alone would appear to be inadequate to fully explain the effects of trade frictions on bilateral trade,because the sale from i to j is influenced by the resistance to movement on i’s other alternative destinations and by the resistance on move-ment to j from j’s alternative sources of supply.Prodded by this intuition the traditional gravity literature recently developed remoteness indexes of each country’s‘average’effectivedistance to or from its partners(id ij/Y i was commonly defined as the remoteness of coun-try j)and used them as further explanatory variables in the traditional gravity model,with some statistical success.The general problem posed by the intuition behind remoteness indexes is analogous to the N-body problem in Newtonian gravitation.An economic theory of gravity is required for an adequate solution.Because there are many origins and many destinations in any application,a theory of the bilateralflows must account for the relative attractiveness of origin-destination pairs.Each sale has multiple possible destinations and each purchase has multiple possible origins:any bilateral sale interacts with all others and involves all other bilateral frictions.This general equilibrium problem is neatly solved with structural gravity models.For expositional ease,the discussion focuses below on goods movements except when migration or investment is specifically treated.2Frictionless Gravity LessonsTaking a step toward structure,an intuitively appealing starting point is the description of a completely smooth homogeneous world in which all frictions disappear.Developing the implications of this structure yields a number of useful insights about the pattern of world trade.A frictionless world implies that each good has the same price everywhere.In a homoge-neous world,economic agents everywhere might be predicted to purchase goods in the same proportions when faced with the same prices.In the next section the assumptions on pref-erences and/or technology that justify this plausible prediction are the focus,but here the focus is on the implications for trade patterns.In a completely frictionless and homogeneous world,the natural benchmark prediction is that X ij/E j=Y i/Y,the proportion of spending by j on goods from i is equal to the global proportion of spending on goods from i,where Y denotes world spending.Any theory must impose adding up constraints,which for goods requires that the sum of sales to all destinations must equal Y i,the total sales by origin i,and the sum of purchases from all origins must equal E j,the total expenditure for each destination j.Total sales andexpenditures must be equal:i.e.,iY i=jE j=Y.One immediate payoffis an implication for inferring trade frictions.Multiplying both sides of the frictionless benchmark prediction X ij/E j=Y i/Y by E j yields predicted friction-less trade Y i E j/Y.The ratio of observed trade X ij to predicted frictionless trade Y i E j/Y represents the effect of frictions along with random influences.(Bilateral trade data are notoriously rife with measurement error.)Fitting the statistical relationship between the ratio of observed to frictionless trade and various proxies for trade costs is justified by this simple theoretical structure as a proper focus of empirical gravity models.Thus far,the treatment of tradeflows has been of a generic good that most of the literature has implemented as an aggregate:the value of aggregate bilateral trade in goods for example.But the model applies more naturally to disaggregated goods(and factors)becausethe frictions to be analyzed below are likely to differ markedly by product characteristics. The extension to disaggregated goods,indexed by k,is straightforward.X kij =Y kiE kjY k=s kib kjY k.(1)Here s ki =Y ki/Y k is country i’s share of the world’s sales of goods class k and b kj=E kj/Y kis country j’s share of the world spending on k,equal to the world’s sales of k,Y k.The notation and logic also readily apply to the disaggregation of countries into regions, and indeed a prominent portion of the empirical literature has examined bilateralflows between city pairs or regions,motivated by the observation that much economic interaction is concentrated at very short distances.The model can interpreted to reflect individual decisions aggregated with a probability model;see section5.1below.In aggregate gravity applications(i.e.,most applications),it has been common to use origin and destination mass variables equal to Gross Domestic Product(GDP).This is con-ceptually inappropriate and leads to inaccurate modeling unless the ratio of gross shipments to GDP is constant(in which case the ratio goes into a constant term).A possible direction for aggregate modeling is to convert trade to the same value-added basis as GDP,but this seems more problematic than using disaggregated gravity to explain the pattern of gross shipments and then uniting estimated gravity models within a superstructure to connect to GDP.That is the strategy of the structural gravity model research program reviewed here.Equation(1)generates a number of useful implications.1.Big producers have big market shares everywhere,2.small sellers are more open in the sense of trading more with the rest of the world,3.the world is more open the more similar in size and the more specialized the countriesare,4.the world is more open the greater the number of countries,and5.world openness rises with convergence under the simplifying assumption of balancedtrade.Implication1,that big producers have big market shares everywhere,follows because, reverting to the generic notation and omitting the k superscript,the frictionless gravity prediction is that:X ij/E j=s i.Implication2,that small sellers are more open in the sense of trading more with the rest of the world follows fromi=jX ij/E j=1−Y j/Y=1−s jusingjE j=iY i,which implies balanced trade for the world.Implication3is that the world is more open the more similar in size and the more special-ized the countries are.It is convenient to define world openness as the ratio of internationalshipments to total shipments,ji=jX ij/Y.Dividing(1)through by Y k and suppressingthe goods index k,world openness is given byji=jX ij/Y=jb j(1−s j)=1−jb j s j.Using standard statistical propertiesj b j s j=Nr bsV ar(s)V ar(b)+1/N,where N is the number of countries or regions,V ar denotes variance,r bs is the correlationcoefficient between b and s and1/N=is i/N=jb j/N,the average share.This equationfollows from the shares summing to one and using standard properties of covariance.Here, V ar(s)and V ar(b)measures size dis-similarity and the correlation of s and b,r bs,is aninverse measure of specialization.Substituting into the expression for world openness:ji=jX ij/Y=1−1/N−Nr bsV ar(s)V ar(b)(2)Implication3follows from equation(2)because on the right-hand side the similarity of country size shrinks the variances while specialization shrinks the correlation r bs.The country-size similarity property has been prominently stressed in the monopolistic competition and trade literature.(It is sometimes taken as evidence for monopolistic com-petition in a sector rather than as a consequence of gravity no matter what explains the pattern of the b’s and s’s.)The specialization property has also been noted in that liter-ature as reflecting forces that make for greater net international trade,the absolute value of s j−b j.Making comparisons across goods classes,variation in the right-hand side of(2) results from variation in specialization and in the dispersion of the shipment and expenditure shares.Notice again that the cross-commodity variation in world openness arises here in a frictionless world,a reminder that measures of world home bias in a world with frictions must be evaluated relative to the frictionless world benchmark.Country-size similarity also tends to increase bilateral trade between any pair of countries, all else equal.This point(Bergstrand and Egger,2007)is seen most clearly with aggregate trade that is also balanced,hence s j=b j.Equation(1)can be rewritten asX ij=s iji s ijj(Y i+Y j)2Y,where s iji ≡Y i/(Y i+Y j),the share of i in the joint GDP of i and j.The product s ijis ijjis maximized at s iji =s ijj=1/2,so for given joint GDP size,bilateral trade is increasingin country similarity.(With unbalanced trade or specialization,an analogous similarity property holds for the bilateral similarity of income and expenditure shares.Letγj=E j/Y j. Then the same equation as before holds with the right-hand side multiplied byγj.)A more novel implication of equation(2)is implication4,that world openness is ordinarilyincreasing in the number of countries.Increasing world openness due to a rise in the number of countries reflects the property that smaller countries are more naturally open and division makes for more and smaller countries.This effect is seen by differentiating the left-hand side ofji=jX ij/Y=1−jb j s j,yielding−j(b j ds j+s j db j).Increasing the number of countries tends to imply reducingthe share of each existing country while increasing the share(from zero)of the new country. The preceding differential expression should thus ordinarily be positive.The qualification‘ordinarily’is needed because the pattern of share changes will depend on the underlying structure as revealed by the left-hand side of equation(2).On the one hand,the average share1/N decreases as N rises,raising world openness.On the otherhand,the change in the number of countries will usually change r bsin waysthat depend on the type of country division(or confederation)as well as indirect effects on shares as prices change.(The apparent direct effect of N in thefirst term on the right-handside of equation(2)vanishes because1/N scalesV ar(b)V ar(s).)A practical implication of this discussion is that inter-temporal comparisons of ratios of world international trade to world income,to be economically meaningful,should be con-trolled for changes in the size distribution and the number of countries,a correction of large practical importance in the past50to100years.Alternatively,measures of openness meant to reflect the effects of trade frictions should be constructed in relation to the frictionless benchmark.Applied to aggregate trade data,gravity yields implication5,that world openness rises with convergence under the simplifying assumption of balanced trade for each country,b j= s j,∀j.The right-hand side of equation(2)becomes NV ar(s)+1/N under balanced trade, and per-capita income convergence lowers V ar(s)toward the variance of population.Baier and Bergstrand(2001)use the convergence property to partially explain postwar growth in world trade/income,finding relatively little action,although presumably more recent data influenced by the rise of China and India might give more action.Pointing toward a connection with economic theory,the shares s i and b j and the plau-sible hypothesis of the frictionless model must originate from an underlying structure of preferences and technology.Also,the deviation of observed X ij from the frictionless pre-diction reflects frictions as they act on the pattern of purchase decisions of buyers and the sales decisions of sellers,which originate from an underlying structure of preferences and technology.3Structural GravityModeling economies with trade costs works best if it moves backward from the end user. Start by evaluating all goods at user prices,applying demand-side structure to determine the allocation of demand at those prices.Treat all costs incurred between production and end use as being incurred by the supply side of the market,even though there are often significant costs directly paid by the user.What matters economically in the end is the full cost between production and end use,and the incidence of that cost on the producer and the end user.Many of these costs are not directly observable,and the empirical gravity literature indicates the total is well in excess of the transportation and insurance costs that are observable(see Anderson and van Wincoop,2004,for a survey of trade costs).The supply side of the market under this approach both produces and distributes the delivered goods,incurring resource costs that are paid by end users.The factor markets for those resources must clear at equilibrium factor prices,determining costs that link to end-user prices.Budget constraints require national factor incomes to pay for national expenditures plus net lending or transfers including remittances.Below the national accounts,individual economic agents also meet budget constraints.Goods markets clear when prices are found such that demand is equal to supply for each good.The full general equilibrium requires a set of bilateral factor prices and bilateral goods prices such that all markets clear and all budget constraints are met.This standard description of general economic equilibrium is too complex to yield some-thing like gravity.A hugely useful simplification is modularity,subordinating the economic determination of equilibrium distribution of goods within a class under the superstructure determination of the distribution of production and expenditure between classes of goods. Anderson and van Wincoop(2004)call this property trade separability.Observing that goods are typically supplied from multiple locations,even withinfine census commodity classes,it is natural to look for a theoretical structure that justifies grouping in this way. The structural gravity model literature has uncovered two structures that work,one on the demand side and one on the supply side,detailed in sections3.1and3.2.Modularity(trade separability)permits the analyst to focus exclusively on inference about distribution costs from the pattern of distribution of goods(or factors)without having to explain at the same time what determines the total supplies of goods to all destinations or the total demand for goods from all origins.This is a great advantage for two reasons.First, it simplifies the inference task enormously.Second,the inferences about the distribution of goods or factors is consistent with a great many plausible general equilibrium models of national(or regional)production and consumption.Modularity also requires a restriction on trade costs,so that only the national aggregate burden of trade costs within a goods class matters for allocation between classes.The most popular way to meet this requirement is to restrict the trade costs so that the distribution of goods uses resources in the same proportion as the production of those same goods.Samuel-son(1952)invented iceberg melting trade costs in which the trade costs were proportional to the volume shipped,as the amount melted from the iceberg is proportional to its volume. The iceberg metaphor still applies when allowing for afixed cost,as if a chunk of the ice-berg breaks offas it parts from the mother glacier.Mathematically,the generalized iceberg trade cost is linear in the volume shipped.Economically,distribution continues to require resources to be used in the same proportion as in production.Fixed costs are realistic and potentially play an important role in explaining why many potential bilateralflows are equalto zero.More general nonlinear trade cost functions continue to satisfy the production propor-tionality restriction and thus meet the requirements of modularity,but depart from the iceberg metaphor.Bergstrand(1985)derived a joint cost function that is homogeneous of degree one with Constant Elasticity of Transformation(CET).This setup allows for substi-tution effects in costs between destinations rather than the cost independence due tofixed coefficients in the iceberg model.Bilateral costs have a natural aggregator that is an iceberg cost facing monopolistically competitivefirms.A nice feature of the joint cost model is its econometric tractability under the hypothesis of profit maximizing choice of destinations. Although potentially more realistic,the joint cost refinement turns out to make relatively little difference empirically.Arkolakis(2008)develops a nonlinear(in volume)trade cost function in which hetero-geneous customers are obtained byfirms with a marketing technology featuring afixed-cost component(running a national advertisement)and a variable-cost component(leafletting or telemarketing)subject to diminishing returns as the less likely customers are encountered. Because of the Ricardian production and distribution technology,resource requirements in distribution remain proportional to production resource requirements.Arkolakis shows that the marketing technology model can rationalize features of thefirm-level bilateral shipments data that cannot be explained with the linearfixed-costs model.His setup is not economet-rically tractable but is readily applicable as a simulation model.In all applications based on the preceding cost functions,proxies for costs are entered in some convenient functional form,usually loglinear in variables such as bilateral distance,con-tiguity,membership of a country,continent or regional trade agreement,common language and common legal traditions.See Anderson and van Wincoop(2004)for more discussion.More generality in trade costs that violates the production proportionality restriction comes at the price of losing modularity.See Matsuyama(2007)for recent exploration of the implications of non-iceberg trade costs in a2country Ricardian model.See Deardorff(1980)for a very general treatment of the resource requirements of trade costs as a setting for his demonstration that the law of comparative advantage holds quite generally.3.1Demand-Side StructureThe second requirement for modularity can be met by restricting the preferences and/or technology such that the cross effects in demand between classes of goods(either interme-diate orfinal)flow only through aggregate price indexes.This demand property is satisfied when preferences or technology are homothetic and weakly separable with respect to a par-tition into classes whose members are defined by location,a partition structure called the Armington assumption.Thus for example steel products from all countries are members of the steel class.Notice that the assumption implies that goods are purchased from multiple sources because they are evaluated differently by end users,and goods are differentiated by place of origin.It is usual to impose identical preferences across countries.Differences in demand across countries,such as a home bias in favor of locally produced goods,can be accommodated, understanding that‘trade costs’now include the effect of a demand side home bias.In practice it is very difficult to distinguish demand-side home bias from the effect of trade costs, since the proxies used in the literature(common language,former colonial ties,or internal trade dummies,etc.)plausibly pick up both demand and cost differences.Henceforth trade cost is used without qualification but is understood to potentially reflect demand-side home bias.Declines in trade costs can be understood as reflecting homogenization of tastes.Separability implies that each goods class has a natural quantity aggregate and a nat-ural price aggregate,with substitution between goods classes occurring as if the quantity aggregates were goods in the standard treatment.The separability assumption implies that national origin expenditure shares within the steel class are not altered by changes in the prices of non-steel products,though of course the aggregate purchase of steel is affected by the aggregate cross effect.Homotheticity ensures that relative demands are functions onlyof relative aggregate prices.Thefirst economic foundation for the gravity model was based on specifying the expendi-ture function to be a Constant Elasticity of Substitution(CES)function(Anderson,1979). Expenditure shares in the CES case are given byX ij E j =βi p i t ijP j1−σ(3)where P j is the CES price index,σis the elasticity of substitution parameter,βi is the ‘distribution parameter’for varieties shipped from i,p i is their factory gate price and t ij>1 is the trade cost factor between origin i and destination j.The CES price index is given byP j=i(βi p i t ij)1−σ1/(1−σ).(4)Notice that the same parameters characterize expenditure behavior in all locations;prefer-ences are common across the world by assumption.Notice also that the shares are invariant to income,preferences are homothetic.With frictionless trade,t ij=1,∀(i,j)and therefore all the buyers’shares of good i must equal the sellers share of world sales(at destination prices),Y i/Y.Thus the frictionless benchmark is justified by assuming identical homothetic preferences.For intermediate goods,the same logic works replacing expenditure shares with cost shares.The‘distribution parameters’βi bear several interpretations.They could be exogenous taste parameters.Alternatively,in applications to monopolistically competitive products,βi is proportional to the number offirms from i offering distinct varieties(Bergstrand,1989). Countries with more activefirms get bigger weights.In long run monopolistic competition the number offirms is endogenous.Due tofixed entry costs,bigger countries have more active firms in equilibrium,all else equal.The number of activefirms contributes to determining the Y i’s that are given in the gravity module.The other building block in the structural gravity model is market clearance:at deliveredprices Y i=jX ij.Multiplying both sides of(3)by E j and summing over j yields a solutionforβi p1−σi,βi p1−σi =Y ij(t ij/P j)1−σE j.Define the denominator asΠ1−σi.Substituting into(3)and(4)yields the structural gravity model:Xij =EjYiYtijPjΠi1−σ(5)(Πi )1−σ=jtijPj1−σEjY(6)(Pj )1−σ=itijΠi.1−σYiY.(7)The second ratio on the right-hand side of(5)is a decreasing function(under the empirically valid restrictionσ>1)of direct bilateral trade costs relative to the product of two indexes of all bilateral trade costs in the system.Anderson and van Wincoop(2003)called the terms P j andΠi inward and outwardmultilateral resistance respectively.Note that{P1−σj ,Π1−σi}can be solved from(6)-(7)forgiven t1−σij’s,E j’s and Y i’s combined with a normalization.1Under the assumption of bilateral trade cost symmetry t ij=t ji,∀i,j and balanced trade E j=Y j,∀j,the natural normalization isΠi=P i.Anderson and van Wincoop estimated their gravity equation for Canada’s provinces and US states with a full information estimator that utilized(7)withΠi=P i. Subsequent research has focused mostly on estimating(5)with directional countryfixedeffects to control for E j/P1−σj and Y i/Π1−σi.Multilateral resistance is on the face of it an index of inward and outward bilateral trade costs,but because of the simultaneity of the system(6)-(7),all bilateral trade costs in the world contribute to the solution values.This somewhat mysterious structure has a simple1For any solution to the system{P0j ,Π0i},{λP0j,Π0i/λ}is also a solution.Thus a normalization is needed.Anderson and Yotov(2010a)find that the system(6)-(7)solves quite quickly,not surprisingly because it is quadratic in the1−σpower transforms of the P’s andΠ’s.。
克鲁格曼国际经济学第十版英文版
Copyright © 2012 Pearson Education. All rights reserved.
2-9
– influence of an economy’s size on trade – distance and other factors that influence trade
• Borders and trade agreements • Globalization: then and now • Changing composition of trade • Service outsourcing
Copyright © 2012 Pearson Education. All rights reserved.
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Distance and Borders
• Estimates of the effect of distance from the gravity model predict that a 1% increase in the distance between countries is associated with a decrease in the volume of trade of 0.7% to 1%.
5. Borders: crosห้องสมุดไป่ตู้ing borders involves formalities that take time and perhaps monetary costs like tariffs.
– These implicit and explicit costs reduce trade. – The existence of borders may also indicate the existence of
国际贸易引力模型
国际贸易引力模型1.什么是国际贸易引力模型？国际贸易引力模型（Gravity Model）是一种用于描述贸易量之间的关系的经济模型，基本思想是：根据经济理论中因素互相作用的规律，可以用一个数学方程来估算国家之间的贸易量。
国际贸易引力模型涉及到两个实体之间的主观和客观因素，它们影响两个国家或地区之间的贸易。
通俗地讲，就是根据两国的距离和经济发展水平，估算两国之间的贸易量。
2. 国际贸易引力模型的构成(1) 双方的经济规模：这是描述双方贸易量大小的最重要因素。
我们常用国民生产总值（GDP）来作为代表国家经济规模的指标，因为GDP 可以反映一个国家或地区的实力，能力以及有能力生产的商品和服务种类的多少。
(2) 交通距离：这是描述两个国家贸易关系的重要因素之一，主要是反映货物的运输成本以及货物的流动性。
根据经济学的理论，贸易成本随着距离的增加而增加，而距离的递增会减少两国之间的贸易。
(3) 两国的相似性：从文化角度看，语言和宗教有可能影响两国之间的贸易关系，所以把这种相似性也作为一个重要因素。
(4) 贸易条件：贸易条件指的是两个国家之间有关贸易的政策、协议、许可证等等，这也可能影响两国之间的贸易量。
3. 国际贸易引力模型的优点(1) 它提供了一种统一的框架，可以客观准确地衡量两个国家贸易关系的状态，可以从宏观上了解国际贸易的发展情况，看出全球经济的大致态势。
(2) 通过该模型，对于促进国际贸易合作与发展也具有很好的策略指导意义，可以通过调整政策组合，从而有效地控制双方的贸易量的大小。
(3) 模型具有良好的可预测性、模型简洁，可以快速拟合和计算，可以预测和分析国际贸易水平运动趋势。
4. 国际贸易引力模型的局限性(1) 双方的经济规模不等：每个国家的经济规模和货物的需求量大小不同，通过国际贸易引力模型可能会忽略到这一点的影响。
(2) 单一货币条件：国际贸易引力模型假定货币是单一的，没有货币差异或汇率重估等，实际情况中现实是复杂合共性，国际贸易涉及到多种影响因素，可能破坏模型的正确性。
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Who Trades with Whom?
In fact, the size of an economy is directly related to the volume of imports and exports.
-Larger economies: produce more goods and services, more to sell in the export market. -Larger economies: more income from the goods and services sold, so people are able to buy more imports.
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Who Trades with Whom?
Why does US trade most with Germany, UK and France and not other European countries?
- Germany, UK and France, 3 of top 10 trading partners with US in 2015 were also the 3 largest European economics.
Tasks and exercises
The gravity model
Influence of size and distance as well as other factors on trade
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Who Trades with Whom?
Size Matters: The Gravity Model
General form of the gravity model: Tij = A Yia Yjb /Dijc Linearise by taking natural logs
ln Tij = ß0 + ß1 ln Yi + ß2 ln Yj – ß3 ln Dij
Run multiple regression where ß0, ß1, ß2 and ß3, and are the point estimates corresponding to ln A, a, b and c.
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Gravity Model
The gravity model can also assess the effect of trade agreements on trade: does a trade agreement lead to significantly more trade among its partners than one would otherwise predict given their GDPs and distances from one another? In general, the literature finds the positive trade volume effects of FTA and CU while it finds the diverging and conflicting results for GATT/WTO.
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Who Trades with Whom?
Another US major trade partners are Canada, and Mexico.
-The total value of imports from and exports to Canada in 2015 was about $659 billion dollars.
2. Cultural affinity: if two countries have cultural ties, it is likely that they also have strong economic ties. 3. Geography: harbours and lack of mountain barriers make transportation and trade easier.
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Who Trades with Whom?
The U.S. signed a free trade agreement with Mexico and Canada in 1994, the North American Free Trade Agreement (NAFTA).
Because of NAFTA and because Mexico and Canada are close to the U.S., the amount of trade between the U.S. and its northern and southern neighbours as a fraction of GDP is larger than between the U.S. and European countries.
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The gravity model: evidence
Border effects
• Borders increase cost and time needed to trade.
• Trade agreements between countries are intended to reduce the formalities and tariffs needed to cross borders, and therefore to increase trade.
0
20
40
60
80
100
120
140
160
Two-way trade (AUD bil)
Source: Department of Foreign Affairs and Trade, Australia
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Who Trades with Whom?
Fig. 2-2: The Size of European Economies, and the Value of Their Trade with the United States
• • These implicit and explicit costs reduce trade. The existence of borders may also indicate the existence of different languages (see 2) or different currencies.
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The gravity model Other things besides size matter for trade
4. Multinational corporations: corporations spread across different nations import and export many goods between their divisions. 5. Trade Agreements such as WTO, FTA, Customs Unions (CU) 6. Borders: crossing borders involves formalities that take and costs.
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Who Trades with Whom?
US does markedly more trade with is neighbours than it does with European economics of the same size.
Fig. 2-3: Economic Size and Trade with the United States
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The gravity model formalised
Basic form of the gravity model: Tij = A Yi Yj /Dij where
Tij is the value of trade between country i and country j A is a constant Yi the GDP of country i Yj is the GDP of country j Dij is the distance between country i and country j
More general form of the model (commonly estimated): Tij = A Yia Yjb /Dijc
where a, b, and c are allowed to differ from 1.
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The gravity model: estimation
• The US signed a free trade agreement with Mexico and Canada in 1994, the North American Free Trade Agreement (NAFTA).
Yet even with a free trade agreement between the US and Canada, which use a common language, the border between these countries still reduces trade.
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Total US trade with major partners, 2012
Source: US Department of Commerce 5
Total Australia trade with major partners, 2014
10 Germany Thailand Malaysia United Kingdom New Zealand Singapore Republic of Korea United States Japan China 9 1 2 3 4 5 6 7 8