外文翻译
原文
The Gravity Equation in International Trade
Material Source: KELLY SCHOOL OF BUSINESS INDIANA UNIVERSITY Department of Business Economics and Public Policy Author: Michele Fratianni
Abstract
This chapter offers a selective survey of the gravity equation (GE) in international trade. This equation started in the Sixties as a purely empirical proposition to explain bilateral trade flows, without little or no theoretical underpinnings. At the end of the Seventies, the GE was “legitimized” by a series of theoretical articles that demonstrated that the basic GE form was consistent with various models of trade flows. Empirical applications of GE expanded to cover a variety of issues, such as the impact of regional trade agreements, national borders and currency unions on trade, as well as the use of the equation to sort out the relative merit of alternative trade theories. A new wave of studies is now concentrating on the general equilibrium properties of the GE and finer econometrics points. The renewed interest of the academic profession in the development of the GE is undoubtedly driven by the equation’s empirical success.
Keywords: gravity equation, trade theories, borders, regional trade agreement, currency unions.
JEL Classification: E58, F15, F33, G15 Draft date: August, 2007
I. INTRODUCTION
International economics and international business have common interests but somewhat different research agendas. The former emphasizes cross-border trade and capital flows, whereas the latter looks predominantly at foreign direct investment. Part of this difference results from the emphasis that scholars in international business place on the study of the multinational firm and part is due to intellectual
specialization. It is worth recalling that the yearly flows of international trade are a large multiple of the yearly flows of foreign direct investment, while the stock of foreign direct investment has only recently approached annual trade flows (see Figure 1). Furthermore, total real exports have grown faster, on average, than the world real GDP since the mid-1980s (see Figure 2). Finally, it is widely believed that exports are an engine of economic growth; see Krueger (2006). For all these reasons, international trade economists spend a great deal of time and resources understanding and explaining trade flows.
With this brief background, I can state the objectives and outline of the chapter. The objective is to explain trade flows in terms of the gravity equation (GE). The reason for focusing on GE is two fold. The first is that GE, unlike other frameworks, has had great empirical success in explaining bilateral trade flows. For a long time, however, GE was a child without a father in the sense that it was thought to have no theoretical support. Since the late 1970s, this state of affairs has changed radically. Now, the gravity equation has strong theoretical support and can be derived from a variety of models of international trade. The second is that GE can be used to sort out alternative hypotheses of international trade.
In its simplest form, the gravity equation (GE) explains flows of a good between pairs of countries in terms of the countries’ incomes, distance and a host of idiosyncratic factors--such as common border, common language, and common money-- that enhance or reduce bilateral trade flows:
（1） Mijk?A0kYik?1kYjk?2kdij?3kUijk， where exported
by
country
i
and
denotes that the k good is
imported
by
country
j, and
are expenditures on the k good by the
two countries, and d is distance; A and αs are coefficients, and U is a well behaved error term. The vector of idiosyncratic factors has been omitted in (1) because these factors are more control variables than theoretically derived variables. Aggregating over all k goods, the GE of a given product can be transformed into a GE of total exports of country i:
（2） Mijk?A0Yi?1Yj?2dij?3Uij，
where the k subscript has been suppressed and Y is the country’s income (for
example, nominal gross domestic product or GDP). The implications of GE –which we develop and discuss below-- are such that α1 and α2 are positive and in some instances equal to one and that α3 is negative. Typically, equation (2) is specified in log linear form and estimated either with cross-section or panel data. In the latter case, a time subscript τ is added, except for the time-invariant physical distance:
（3） ln(Mijt)??0??ln(Yjt)??3ln(dij)??4Fij?uijt，
Where in stands for the natural logarithm, ln(A0)??0 and uijt?ln(Uijt). The vector of idiosyncratic factors,
, has also
been added to equation (3). These factors are typically measured as dummy variables that acquire the value of one for the existence of the phenomenon and zero for its absence. The coefficients α1 through α3 are interpreted as elasticity’s or as percentage changes in bilateral trade for one percentage change in income and distance. The coefficient α4 is positive if the factor is trade enhancing (e.g., common language) and negative if trade reducing (e.g., terrorism).
In the following section I will explore different models of international trade from which GE can be derived, ranging from models of complete specialization and identical consumers’ preferences (Anderson 1979; Bergstrand 1985; Deardorff 1998) to models of product differentiation in a regime of monopolistic competition (Helpman 1987) to hybrid models of different factor proportions and product differentiation (Bergstrand 1989; Evenett and Keller 2002) to models of incomplete specialization and trading costs (Haveman and Hummels 2004).
II. TRADE THEORY AND THE GE Complete specialization
Specialization is at the heart of trade theory; it is complete or deepest when each country specializes in the production of its own output and consumers purchase the output of each country according to identical and homothetic preferences. Furthermore, trade occurs without friction, meaning that it is not impeded either by transport costs, tariffs or tariff-equivalent border obstacles. This idealized set-up serves the purpose of creating a benchmark of maximum trade flows. Each country imports and consumes a share of the goods produced by all other countries, as well as a share of its own output. These shares are the same for all countries. Consider, for example, two countries, country 1 and country 2, producing differentiated
products by country of origin. Country 1 will export its own good to country 2 in the amount of M12?b1Y2, where b1=marginal propensity to import good 1 in country 2. Country 1 will also sell b1Y2 amount of the good it produces to domestic consumers. Note that the propensity to consume good 1 is the same across all consumers regardless of location. Income of country 1 is the sum of purchases by consumers located in country 1 and consumers located in country 2, i.e., Y1?bY11?bY12?bY1w, where Yw= world income = Y1?Y2. Thus, identical and homothetic preferences imply that the propensity to import and consume good 1 is equal to country 1’s share of world income. Replacing b1 with Y1/Yw, M12?YY12/Yw. This is the simple GE derived by Anderson (1979, p. 108):
译文
国际贸易中的引力方程
资料来源：印地安那大学凯莱商学院校刊 作者：米歇尔·弗拉蒂安尼
摘要
本文章精心选择并调查了在国际贸易中的重力方程（简称GE）。这个等式最早出现于六十年代，最初仅作为一个纯粹的实证命题来解释两国间的贸易流量，总体缺乏理论基础。七十年代末，引力方程终于由一系列理论研究论文而“正名”，且文章同时表明，引力方程的基本形式与贸易流动的各种模型一致。对于引力方程的实证研究范围扩展至诸如区域贸易协定的影响、国家边界问题、贸易货币联盟，以及利用该公式梳理出非传统贸易理论的相对优点。目前新一轮的研究集中在引力方程的一般均衡性质和更深入的计量经济观点。引力模型在发展过程中于学术界重新被关注，无疑是因为该方程在实证方面的成功所带来的。
关键词：引力模型，贸易理论，边境，区域贸易协定，货币联盟。 JEL分类：E58，F15，F33，G15。 草拟日：2007年8月。 I.引言
国际经济与国际商务存在共同利益，但其研究在某种程度上却有着不同的工作事项。前者强调跨国界的贸易和资金流，而后者主要表现在对外直接投资。
这些差异有一部分来源于国际商务研究者对跨国公司的过分注重，一部分由于知识产权专业化。值得一提的是，国际贸易每年的资金流动量占对外直接投资量的流量的部分，而外国直接投资存量仅在最近的年度接近贸易流量（见图1）。此外，实际总出口增长加快，自80年代中期以来均高于世界生产总值平均水平（见图2）。最后，人们普遍认为，出口是经济增长的引擎，见于克鲁格（2006）。由于所有这些原因，国际贸易经济学家投入大量的时间和资源来了解和解释的贸易流动。
有了这个简短的背景，我就能简要阐述目标和大致的章节。 目的在于就引力方程角度解释贸易流动。着重强调引力方程的原因在于两方面：首先，引力方程不像其他的理论模型，它已经在解释双边贸易流量研究中取得了巨大的成功经验。然而在过去的很长一段时间内，引力方程一直不够完善，而且缺乏理论的支持。20世纪70年代末以来，这种状况发生了根本性的转变。现在，引力方程已经具有了充分的理论支持，可从各种国际贸易模型中推导总结得出。其次，引力方程可以用来整理归纳各种非传统国际贸易理论与假说。在这种最简单的形式下，引力方程（GE）就国家收入、距离等一系列因素出发考虑，很好地解释了两国之间的贸易与资金流动——如共同边界，共同语言，共同的货币——即增强或减少双边贸易流量：
（1） Mijk?A0kYik?1kYjk?2kdij?3kUijk， 其中，j
国
，
表示i国将k商品出口给
和
表示i国生产k商品的成本和j国进
口该商品的价格，d表示两国之间的距离。A与α为系数，U为良性误差项。在（1）式中忽略向量特质，因为这些因素比理论中推导出的变量更难以控制。归总所有的k货物，在给定一种产品的情况下，引力方程可以转化为一个关于i国出口总额的方程式：
（2） Mijk?A0Yi?1Yj?2dij?3Uij，
在此方程右侧，下标的k已经被取消，Y是国家的收入（例如，名义国内生产总值或国内生产总值。关于引力方程的内在涵义——我们将在下面展开讨论——通常，α1和α2是正的，在某些情况下等于之一，α3为负。一般情况下，方程（2）被指定用在对数或线性形式下以横截面或面板数据估计。在后一种情况下，添加了一个时间下标t，时间恒定的物理距离情况除外：
（3） ln(Mijt)??0??ln(Yjt)??3ln(dij)??4Fij?uijt，
其中，ln表示自然对数，ln(A0)??0，uijt?ln(Uijt)。向量本身的特质因素
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