Globalization and the Gains from Variety Christian Broda David E.Weinstein

Introduction Krugman(1979):how countries could gain from trade through the import of new variety But no one has estimated the impact of increased variety on aggregate welfare This paper try to answer the question how much increases in traded varieties matter for United States: varieties arise threefold in the last 30 years

Method Step 1:estimate elasticities of substitution among goods at various levels of aggregation Step 2:use these estimated parameters to construct import price index Step 3:use the price to obtain an estimate of gains from new imported varieties

Prior work Hausman(1981) 试图计算新产品减价对福 利的影响，这种方法不适用于计算产品总 价格指数 研究总体层面的文章都利用数值模拟，这 些研究不关注多样化如何影响价格，而是 关注潜在福利的变化 所有以上研究没有提供如何从理论跨越到 实证的第一步，而且需要多种限制性假设

假设不同产品的所有品种替代弹性是相同的；假 设产品之间的替代弹性与同一产品不同种类之间 的替代弹性相同；假设所有种类所有产品的替代 弹性相同 另外使用数值模型需要小心选择参数和效用函数 形式，而本文中所有的参数都是通过回归得到的 Anderson(1979) 利用双边贸易流对贸易成本和控 制变量回归，贸易成本系数为替代弹性。这种方 法假设贸易成本全部转嫁给消费者，而且贸易成 本不随进口需求的变化而改变，该假设是不符合 美国实际情况的。

The definiton of variety Krugman(1980) adopted a definition of variety that is based on firm level exports This paper use the same definition of variety as in Feenstra(1994)-----a seven or ten digit good produced in a particular country. For example, a good “red wine”, a variety “French red wine”

The definition highlights an important difference between monopolistic competition models and comparative advantage model: In comparative advantage model, consumers are indifferent about where a good is produced as long as the price does not vary, the elasticity of substitution among varieties is infinite In monopolistic competition model, the elasticity of substitution among varieties is finite

If the elasticity of substitution is large,the gains from varieties is small; low elasticity of substitution across varieties are a necessary condition for potential gain In Krugman model there are two channels for the gains from trade arising from variety growth: trade costs fall ;the size of the foreign country rise In comparative advantage model, all gains from are achieved through price change

We choose Dixit and Stigiltz(1977) SDS framework CES utility function is easy to estimate Helpman and Krugman(1985) model is not easy to create aggregate price index

DATA A variety is defined as the import of a particular good from a particular country In 1972 the share of import of goods in GDP is 4.8%,in 2001 the share increased to 11.7% There has been a dramatic increase in the number of countries supplying each individual good （ table 1,table 2 & table 3 ）

提供产品的国家增多与全球化以及国家间 产品差异是相联系的 如果国家之间的产品存在差异，那一定是 因为多样化可以带来收益 高增长率的国家如韩国、中国提供给美国 的产品种类迅速上升，也说明自由化对发 展中国家的作用很大 Eaton 等 (2004) 利用引力模型研究了产品多 样化、经济增长和贸易之间的关系

Empirical Strategy The Feenstra price index Identification and estimation of the elasticity of substitution

The Feenstra price index Build an exact aggregate price index corresponding to CES utility function Three level utility function: (1)aggregate imported goods into composite imported goods (variety-category) (2)aggregate these imported good into a composite import good (category-imported good) (3)combine this imported good with the domestic good to produce utility

The upper level utility function(1) The composite imported good(2) The third level(3)

The minimum unit cost function of subutility function If,then increase will lead to unit cost falling The minimum unit cost function of(2) is

The overall price index is

Proposition 1:the exact price index for good g with change in varieties is Where

Where capture the role of the new and disappearing varieties. Is the conventional price index It implies that the higher the expenditure share of new varieties,the lower is and the smaller is the exact price index relative to the conventional price index It implies that an increase in the number of varieties lead to a fall in the exact price index relative to the conventional price index

Proposition 2:the exact aggregate import price index with variety change is Where is the conventional Import price index, is import bias

The overall index is 以前的指标直接用 代替 ，会导致很大的 偏差，如新产品的消费量只占消费量很小的一 部分，那么旧的指标会放大新产品的作用 该方法消除了对称性误差，不同产品的同幅度 价格调整对消费者而言是不同的，因为 是 可以变化的

Identification and estimation of the elasticity of substitution Using a simple model of import demand and supply equations to estimate this elasticity of substitution. Demand equation is derived from equation(3) Supply equation is

Using shares instead of quality,the demand and supply function are: After some calculation, we get equation(18) where

Result Estimate strategy involves four stages Step1:estimate using (20) Step2:calculate for every good g Step3:calculate the exact price index using(11) Step4:estimate the movement of the aggregate price of imports using equation(12)

Elasticity of substitution As we disaggregate, varieties are increasingly substitutable Goods with high elasticity of substitution to correspond to goods that we think of as less substitution Goods traded on organized exchanges have higher elasticity than those that are not (see table IV & V)

The reasonableness of the estimates Rauch (1999) divided goods into three categories: commodities,reference priced goods and differentiated goods Commodities are probably correlated with more substitutable goods Estimate at the four digit level to make them directly comparable with Rauch (1999),see table VI

Growth in varieties 计算 中的一个困难：在 时 没有定义，解决方法是， 7 位代码或 10 位代 码中新增加的一个种类的替代率为，在同 一个 5 位代码类型中其他商品和种类的替代 率的加权平均 计算结果见表 VII

Import prices and welfare Aggregate exact price index 估计结果 (tabel VII) 价格在 年下降了 19.7 ％，在 年下降了 8.3 ％ 后期价格下降速度减慢说明从东南亚贸易中得到 的收益是在 90 年代之前得到的 由于之前没有类似的文献以证明结论的正确性， 利用一个 CPI 指数的研究从侧面类比。该研究指 出 CPI 价格指数高估了生活成本 1.2 ％，这种误差 来源于产品数量的变化。因此，如果采用传统的 unaccounted variety growth 得到的误差会很大

福利效应的计算采用 Krugman(1980) 框架， 结果显示消费者愿意利用他们收入的 2.6 ％ 去得到 2001 比 1972 年多的产品种类

Robustness 和之前的研究不同，本文允许不同种类产 品的消费份额是不同的，另外不同产品的 替代弹性不同，各个市场的供给弹性也不 同 消费份额相同、替代弹性相同都会高估多 样化带来的福利效应 放松 CES 效用函数假设，利用二次方程效 用函数仍然可以得到类似的结论

文中假设所有产品都是最终消费品，但是 实际情况不是如此，特别是资本品在长期 是会扩大产品多样化带来的收益，因此将 资本品当作最终产品计算会低估福利效应 在 Krugman 的生产函数中，国内产品种类 的变化不会影响国外产品，利用 Helpman and Krugman(1985) 模型，外国产品进入会 导致国内部门萎缩转向非贸易部门。在一 定的参数假设下，从国外引入一个品种会 取代 0.16 个国内品种，因此会把福利降低 16 ％