在用引力模型估计某项因素对双边贸易的影响时，一般需要控制的变量有：地理距离，是否具有相同语言，是否接壤，历史上是否具有殖民关系或具有共同宗主国；其他经常控制的变量还有：双边关税、是否签署自贸协定。这些都是贸易成本的代理。

另外还有其他估计贸易成本的方法，这里介绍两种我觉得比较有意思的：

1、Head-Ries指数

由Head and Ries (2001)提出，假设从i国到j国双边贸易流符合引力模型 ，其中 为来源国特征变量， 为目的国特征变量， 为双边贸易成本， 为贸易弹性，则 ，假设双边贸易成本对称 ，本国贸易成本 ，则有 ，贸易弹性可以用以往文献估计出的，双边贸易流和本国份额可以观测到，即可算出贸易成本，这就是大名鼎鼎的Head-Ries指数

2、Donaldson (2018)

去年克拉克奖得主Donaldson的JMP的方法，用来测度印度殖民地时期两地之间的贸易成本。太牛逼以至于我第一次看时瞬间跪了，原理很简单：如果价格是与边际成本成正比，则对同一种产品 ，来源地i的价格与目的地j的价格之比 即为i到j的贸易成本。但用这种方法估计的关键，也是难点在于找一种同质的产品，比较两地的价格。大神选择的产品是：盐。直接上原文：

Throughout Northern India, several different types of salt were consumed, each of which was regarded as homogeneous and each of which was only capable of being made at one unique location. For example, traders and consumers would speak of ‘Kohat salt’ (which could only be produced at the salt mine in the Kohat region) or of ‘Sambhar salt’ (which could only be produced at the Sambhar Salt Lake).24 And official price statistics would report a distinct price for each different type of salt. I have collected data on salt prices in Northern India, in which the prices of eight regionally-differentiated types of salt are reported in 124 districts annually from 1861-1930. Crucially, because salt is an essential commodity, it was consumed (and therefore sold at markets where its price could be easily recorded) throughout India both before and after the construction of railroads. I use these salt price data, ……， to estimate how Indian railroads reduced trade costs.

盐是大体上是一种同质产品，而且就在印度某几个地方生产，而各地又保存了历史上的盐价数据，于是天然地成为估计贸易成本的工具。不得不承认，这个idea实在是精彩之至，不愧是克拉克得主的成名作。

参考文献：

Head K, Ries J. Increasing returns versus national product differentiation as an explanation for the pattern of US-Canada trade[J]. American Economic Review, 2001, 91(4): 858-876.

Donaldson D. Railroads of the Raj: Estimating the impact of transportation infrastructure[J]. American Economic Review, 2018, 108(4-5): 899-934.

Head K, Mayer T. Gravity equations: Workhorse, toolkit, and cookbook[M]//Handbook of international economics. Elsevier, 2014, 4: 131-195.

来源：知乎 www.zhihu.com

作者：冯路

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