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)

1)1()1( )( ttt MDU

1)1( )(

Gggtt MM

• 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

)1(11 ))),(((

Gg

gtgtMgt

Mt dI

• The overall price index is

1111 )()( M

tDtt pp

• 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

MgP

• Proposition 2:the exact aggregate import price index with variety change is

• Where is the conventional

Import price index , is import bias

1

1

1111

)(

),(

),(),,,,(

ggtw

gt

gt

Gg

tMt

tMt

ttttM

ICIPI

dI

dIIxxPP

gtwgg

GgIPICIPI )()(

• 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

Mt

Dt

wM

w

Dt

Dt

p

p

1

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

gctgctg

ggtgct sp

ln1

ln

gctgctk

gctk

gctk

gctk uspsp )lnln()ln()ln( 2

21

2

)1)(1(1

gg

g

)1)(1(

)2(12

gg

gg

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 1972-1988 年下降了 19.7 ％，在 1990-20

01 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 ％