CESSA WP 2019-01
Gains from Trade due to Increased Variety in Mongolia
Enkhmaa Battogtvor
Craig R. Parsons
Yokohama National University

February 2019

Center for Economic and Social Studies in Asia (CESSA) Working Paper
Downloadable from:http://www.econ.ynu.ac.jp/cessa/publication/workingpaper.html

Center for Economic and Social Studies in Asia, Department of Economics
Yokohama National University

Gains from Trade due to Increased Variety in Mongolia*

Enkhmaa Battogtvor
Department of Economics
Yokohama National University
battogtvor-enkhmaa-wg@ynu.jp

Craig Parsons
Department of Economics
Yokohama National University
parsons-craig-gj@ynu.ac.jp

Keywords: Gains from trade, Elasticity of substitution, Welfare effect of trade liberalization
Abstract:
Contributing to the vast literature of gains from variety (Broda and Weinstein, 2006), we
estimated the welfare impact of the enormous imported varieties growth in Mongolia and foundit to be considerably larger than that found in other country studies. Thus, our results show thatfrom 1988 to 2015, the gains from variety were equal to 22 percent of Mongolia’s GDP, or 0.8
percent annually. While estimating the gains from variety, we estimated 1390 elasticities ofsubstitution exclusive to Mongolia using the most disaggregated data available for Mongolia.

Word Count: 6948*

We would like to thank Kiyotaka Sato, Eiichi Tomiura, Minako Fujio and Tsunao Okumura for their usefulcomments and suggestions on earlier drafts. This paper is an extension of Battogtvor`s doctoral dissertation. We
also thank My Duong who served as a discussant for the paper which was presented at the East Asian Economic
Association in Taiwan, Oct 27-28, 2018. All errors are the authors’ alone. Parsons is the contact author.

1

I.

Introduction
The paper estimates the comprehensive gains from variety for Mongolian economy

during 1988-2015, following the seminal works by Feenstra (1994) and Broda and Weinstein(2006). Mongolia undertook serious economic reforms in 1990 after the collapse of the Soviet
Union and suffered a long and dramatic process of transformation into the free-market
economy, easing price controls, liberalizing domestic and foreign trade. The centrally planned
economy, state-owned industries and banking systems were transferred to the private sectors.
However, the economy is still in transition.
In this paper, the gains from increased variety for the more open Mongolian economy
were estimated, using six-digit harmonized system (HS) product data, the most disaggregateddata available for Mongolia. We estimated 1390 elasticities and with these elasticities, weconstructed an exact price index to measure the welfare gains from variety growth. This method
is consistent with the theory of monopolistic competition and is robust in empirical applications(Feenstra, 1994).
The results show that the welfare gain owing to newly imported varieties from 1988 to2015 amounts to 22 percent of GDP, or 0.8 percent annually. This is a significant result
considering the moderate annual gains from 0.1 percent (Broda and Weinstein, 2006) to 0.4
percent (Chen and Ma, 2012) that most studies show.
We contribute to the growing literature by providing a measure of Mongolia’s welfare
gain due to import variety from 1988 to 2015. This is the first such study to apply themethodology of Broda and Weinstein (2006) to calculate Mongolian gains from variety, thus
we had two motivations in mind. First, by measuring Mongolia’s gains from import varieties
after the liberalization in 1990s, we provided supporting evidence favoring trade liberalization2

for developing countries. Second, we estimated elasticities exclusive to Mongolia using ahighly disaggregated import data and these elasticities may be useful for other studies.
The rest of the paper is organized as follows. Section 2 reviews the gains from trade
literature. Section 3 describes the data and reviews Mongolia’s rapid import growth from 1988
to 2015. Section 4 reviews the model of Broda and Weinstein (2006). Section 5 explains theestimation strategy and gives a brief overview of the importance of elasticities of substitution.
Section 6 reports the results of the analysis and presents the welfare gains. Section 7 concludes.
1. Gains from Trade Literature
In the core of the monopolistic competition model with differentiated goods pioneered
by Dixit and Stiglitz (1977), consumers and producers benefit from having more varieties offinal goods and intermediate inputs, respectively. However, most studies focus on theconventional sources of gains, such as productivity improvement as a result of increasing
returns of scale, trade-induced innovation, technology spillovers, and improved market
efficiency because of import competition (Chen and Ma, 2012). These studies often assume aconstant set of products over time and this leads to systematically understated welfare gain
calculations.
The quantitative analysis of gains from variety starts with the seminal work of Feenstra(1994). Feenstra (1994) showed how to estimate the elasticities of substitution of individual
products, and to incorporate these elasticities into a formula for an exact price index which hederived that can account for entry and exit of varieties. By doing so, Feenstra (1994)
demonstrated that new product varieties lead to an increase in consumer utility. However, acomprehensive measure of the gains from import variety for an entire country puts tremendous
demands on data availability and was not realized until Broda and Weinstein (2006).

3

Applying Feenstra’s estimation technique Broda and Weinstein (2006) estimated thewelfare gain that the US enjoyed through trade liberalization over the past 30 years bycomputing the elasticities of substitutions of more than 30,000 products. Using these elasticities,
they created the import price index adjusted for new and disappearing varieties and measured
the value that consumers attached to these new product varieties. They found that the total gainfrom the introduction of new varieties in the U.S. was 2.6 percent of GDP between 1972 and2001. Strictly speaking, this means that in order to obtain the new set of varieties imported
each year, consumers would be willing to pay on average 0.1 percent of their income.
Following Broda and Weinstein (2006), a body of country studies emerged, using thesame methodology.1 Chen and Ma (2012) found that the welfare gain in the Chinese economy
as a result of new import variety amounts to 4.9 percent of GDP, or 0.4 percent annually
between 1997 and 2008. Minondo and Requena (2010) investigated the welfare gains due toSpanish imports of new varieties over the period 1988-2006. They found that the total welfare
gains were equal to 1.2 percent of GDP in 2006. In a comparative study of Switzerland and the
U.S., Mohler (2009) estimated a lower and an upper bound of the gains from variety. He foundthat during the period from 1990 to 2006, the gains from variety in Switzerland were between
0.3 and 4.98 percent of GDP and that in the U.S. the gains from variety were between 0.5 and4.7 percent of GDP. Mohler and Seitz (2012) applied the methodology to the 27 countries of
the European Union for the period of 1999 to 2008. Their results show that within the European
Union, especially “newer” and smaller member states exhibit high gains from newly imported
varieties. For instance, Estonia gained 2.74 percent of its GDP, Slovakia 2.37 percent, Latvia
1.65 percent, Bulgaria 1.59 percent, and so on. They also found that interestingly, two of the1
Only a few of the many papers are mentioned here. In addition to its welfare gain estimation, Broda andWeinstein (2006) paper is often cited for its import demand elasticity estimates. Elasticity estimates of 73
countries (which does not include Mongolia) are available at Columbia University`s webpage:
http://www.columbia.edu/~dew35/TradeElasticities/TradeElasticities.html

4largest economies in the group, France and Germany, both had negative gains from variety.
They argue that the reason for this is that these larger economies were already heavily
integrated in the European economy and did therefore not experience the increase in productvarieties as did the “new”, smaller economies.
We contribute to the growing literature by providing a measure of Mongolia’s welfare
gain due to import variety from 1988 to 2015. This is the first study that pursues this measure
for Mongolia, thus we have two motivations in mind as briefly stated in the introduction. First,
as a small open economy, Mongolia underwent a drastic liberalization after the dissolution of
the Soviet Union. The economy is now in transition. Thus, measuring Mongolia’s gains fromimport varieties provides additional supporting evidence favoring trade liberalization fordeveloping countries. Our findings may also provide informative implications for Mongolia’s
policymakers. Second, we obtain estimates for hundreds of elasticities of substitution using
highly disaggregated import data of Mongolia, which may be useful for other future studies.
For example, different elasticities may imply different responsiveness of imported products todemand shocks or exchange rate movements suggested by Chen and Ma (2012).
The definition of variety used in this paper is same as the variety defined in Broda andWeinstein (2006), which is an Armington (1969) definition of a product variety. By thisdefinition, a variety is a particular good produced in a particular country. To be more specific,
a product in this paper is defined as a six-digit HS good. To give an example, sparkling wine(with HS-6 product code 220410) was imported from only one country, Germany, in 1989. In
sharp contrast to this, in 2015 wine was imported from 13 different countries such as France,
Spain, Italy, Chile etc. As in Broda and Weinstein, we follow the Armington (1969) assumption,
where an HS-6 product supplied by one country is regarded as a different variety as the same
product supplied by another country.

5Gains from increased import varieties are not limited to consumers. Access to more
imported varieties may enhance productivity growth, leading domestic firms to gain
substantially. In fact, with the widely used constant elasticity of substitution (CES) structure,
new varieties could be modeled either as consumption goods or as intermediate inputs (Romer,1994). We follow Broda and Weinstein (2006) and treat all imported goods as intended forfinal consumption.
2. Data and Descriptive Analysis
We used the United Nations Comtrade - International Trade Statistics database for the
trade data. The import data of Mongolia was not sufficient, lacking the years 2002, 2008-2012,2015- 2016. Therefore, due to this data availability problem, we used the export data of rest of
the world to Mongolia from 1988 to 2015, covering 28 continuous years. The data contains
information on the total value, quantities and trading partner of registered product imports to
Mongolia. When Comtrade had import data but reported the country of origin as ‘Unspecified’,that data point was dropped. Likewise, if there was ‘Value’ but no ‘Quantity’ of imports, thatdata point was also dropped. Furthermore, due to the insufficient numbers of varieties, HS-6
products with less than 37 observations were dropped.2 This is due to the problem that many
products were not imported to Mongolia constantly throughout the period. This left us with158 thousand observations over 1628 products. Gross domestic product (GDP) data were takenfrom the World Bank Database.
To study the welfare implications of the drastic increase in imports of Mongolia, weshould consider the increase in value of each product imported (i.e. the intensive margin) andthe increase in the number of products and varieties for each product (i.e. the extensive margin).

37 is, of course, arbitrary. There were some HS-6 products with only a handful of observations which were
dropped. 37 was a sort of natural cutoff where after that observations picked up rapidly.
26Figure 1 Exports and Imports (Billions of US Dollars)
8
7
6
5
4
3
2
1
0
1988

1992

1996

2000

2004

Exports

2008

2012

2016

Imports

Source: The authors. Based on UN Comtrade data.

Mongolia undertook serious economic reforms in 1990 after the collapse of the Soviet
Union and suffered a long and dramatic process of transformation into the free-market
economy, liberalizing domestic and foreign trade. Figure 1 shows Mongolian foreign trade
between 1988 and 2016. We can see that there was dramatic growth in the value of imports.
According to our data, the value of imports was nearly zero in 1988 and gradually increased
until peaking at seven ($7) billion dollars in 2012.
Figure 2 shows Mongolia’s imports share of GDP between 1988 and 2016. The importshare was almost zero in 1988. It gradually rose after the liberalization in 1990, and reached
45 percent when Mongolia became a World Trade Organization (WTO) member in 1997. By
2012, the share was 61 percent of GDP.3 We can see an obvious rising demand for imports
from Figures 1 and 2, and it demonstrates the importance of imports to Mongolian economy.

However, as a result of the downturn in the economy and falling commodity prices, the share of imports
of GDP in Figure 2.2, as well as its absolute volume in Figure 2.1, has dropped after 2012.
37

Figure 2 Imports Share of GDP (%)
70.0%
61%

60.0%

54%

50.0%

51%

45%

43%

40.0%
38%

30.0%

48%
33%

19%

20.0%

15%
10.0%
3%
1988
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
2007
2008
2009
2010
2011
2012
2013
2014
2015

0.0%

Import/GDP

Source: Authors’ calculation based on import data from UN Comtrade and GDP datafrom the World Bank.

Table 1 summarizes the count measure of imported varieties of Mongolia between 1988
and 2015. The count measure is simply the number of varieties imported in each year, where
the count of varieties, of wine, for example, was 15 in 2015. We can see that behind the rapid
growth in import value was dramatic growth in import varieties (i.e. the extensive margin).
Column (2) reports the number of HS-6 products for the related years. We can see that the
number of these products increased by seven-fold during the period, from only 226 in 1988 to1610 in 2015. Moreover, column (5) shows the total number of imported product varieties.

8

Table 1 Variety in Mongolian Imports (1988-2015)

All 1988 goods

Year
(1)
1988

Number of
HS-6
products(2)
226

Mediannumber ofexportingcountries(3)
1

Averagenumber ofexportingcountries
(4)
1.1

Total
number ofvarieties(5)
255

All 2001 goods

2001

1512

3

3.5

5304

All 2015 goods

2015

1610

5

6.2

10052

Common, 1988-2015

1988

219

1

1.1

247

Common, 1988-2015

2015

219

3

8.0

1746

1988 not in 2015

1988

7

1

1.1

8

2015 not in 1988

2015

1391

3

6.0

8306

Source: Authors’ calculation based on UN Comtrade data.

It can be seen from column (5) that the total number of varieties increased 40 times,
from 255 to 10052. This is a remarkable increase that no other country study has ever shown.
Columns (3) and (4) show the median and average number of source countries exporting to
Mongolia, i.e. the number of varieties. We can observe that the number of exporting countries
increased over time. In 1988 only one variety or source country was available per good, but in2015 on average six varieties were available. The middle part of the Table 1 reports statisticsof the common goods which were available in both the beginning and the end of the period. It
is notable that, on average, these common products were imported from only one source
country in 1988, however in 2015 the number of source countries rose to eight. The last two
rows of the table show that there are 1391 new goods which were not available in 1988,
imported from six different countries on average. These dramatic changes in goods andvarieties suggest that conventional measures using a fixed basket of goods or varieties could
be largely biased. Consequently, these facts demonstrate that the gains from variety are notnegligible.
93. Methodology: the Broda and Weinstein Method
Following Feenstra (1994) and Broda and Weinstein (2006), we start by deriving anexact price index for a constant elasticity of substitution (CES) utility function of a single goodwith a constant number of varieties. This index is then extended by allowing for new anddisappearing varieties. Finally, we show how to construct an aggregate import price index andgains from variety formula. Let us start with a simple CES utility function with the following
functional form for a single imported good. Assume that varieties of a good 𝑔 are treated as
differentiated across countries of supply, c:

𝑀

𝒹

;𝜎

𝑚

1

(1)

∈

where C denotes the set of all countries and hence of all potentially available varieties. In theequation, 𝑚is the subutility derived from the consumption of imported variety c of good 𝑔in period t; 𝒹is the corresponding taste or quality parameter. The elasticity of substitution

among varieties of good 𝑔 is given by 𝜎 and is assumed to be larger than one.
Let 𝐼

⊂ 𝐶 be the subset of all varieties of good 𝑔 imported in period t. Using standard

cost minimization for the sub-utility function (1) gives us the minimum unit-cost function:𝜙𝐼 , 𝑑⃗

𝑑

𝑝

(2)

∈

where 𝑝is the price of variety c of good 𝑔 in period t and 𝑑⃗parameters for each country.
10

is the vector of taste or quality

Suppose the set of varieties 𝐼 in period 𝑡 and 𝑡𝑑⃗ are also constant over time and 𝑥⃗

and 𝑥⃗

1 are identical, the taste parameters

are the cost-minimizing consumption bundle

vectors for the varieties of good 𝑔 for given the price vectors. In this case Diewert (1976)
defines an exact price index as a ratio of the minimum cost functions:𝑃 𝑝⃗ , 𝑝⃗, 𝑥⃗ , 𝑥⃗,𝐼𝜙𝐼 , 𝑑⃗𝜙𝐼 , 𝑑⃗(3)

where the price index does not depend on the unknown taste or quality parameters 𝑑 . Sato
(1976) and Vartia (1976) have derived the exact price index for the case of the CES unit-costfunction. It can be written as the geometric mean of the individual variety price changes:

𝑃 𝑝⃗ , 𝑝⃗, 𝑥⃗ , 𝑥⃗

,𝐼
∈

𝑝
𝑝

where the weights are calculated using the expenditure shares 𝑠

𝑤

𝑠
ln 𝑠
∑∈

𝑠

𝑠
ln 𝑠
𝑝
∑∈

𝑠
ln 𝑠
𝑠
ln 𝑠
𝑥
𝑝 𝑥

(4)

:

(4.1)

(4.2)

So far, it was assumed that all varieties of good 𝑔 were available in both periods tocalculate the exact price index. To include new and disappearing varieties into account,
Feenstra (1994) showed how to modify this exact price index for the case of different, but
overlapping, sets of varieties in the two periods. This contribution of Feenstra is given by thefollowing proposition.

11

Proposition: For every good 𝑔, if 𝑑𝑑for 𝑐 ∈ 𝐼

𝐼 ∩𝐼

,𝐼

∅, then theexact price index for good 𝑔 with change in varieties is given by𝜋 𝑝⃗ , 𝑝⃗, 𝑥⃗ , 𝑥⃗

𝐼 , 𝑑⃗

𝜙

,𝐼

𝜙

(5)

, 𝑑⃗

𝐼

𝑃 𝑝⃗ , 𝑝⃗

,𝐼

𝜆
𝜆

∑∈ 𝑝

𝑥

∑∈

𝑥

, 𝑥⃗ , 𝑥⃗

(6)

where

𝜆

∑∈ 𝑝

𝑥

∑∈

𝑥

𝑝

and

𝜆

𝑝

(7)

Feenstra’s theoretical contribution is correcting the conventional price index 𝑃 𝐼

bymultiplying it with an additional term which captures the influence of new and disappearing
varieties. This additional term is called the lambda ratio. The numerator of this term, 𝜆 ,captures the impact of newly available varieties. 𝜆available in both periods (i.e., 𝑐 ∈ 𝐼available in period t (i.e., 𝑐 ∈ 𝐼

𝐼 ∩𝐼. Hence, 𝜆is the ratio of expenditures on varieties) relative to the entire set of varieties

decreases when expenditure share of newvarieties increases and therefore, the exact price index decreases relative to the conventional
price index. On the other hand, the denominator of the lambda ratio, 𝜆of disappearing varieties. 𝜆, captures the impact

increases when there are only few disappearing varieties, andtherefore the exact price index is relatively low when compared to the conventional price index.
The exact price index also depends on the elasticity of substitution between varieties,
𝜎 . If 𝜎 is high,is close to zero and the additional term

12

is close to unity.

Hence the variety change has small influence on the price index. This is intuitive, when 𝜎 ishigh since new and disappearing products are close substitutes to existing varieties, they only
have a minor influence on the price index.
The exact price index with variety change for good 𝑔 was derived in equation (6).
Aggregating it for all imported goods G gives us the aggregate exact import price index:

Π 𝑝⃗ , 𝑝⃗, 𝑥⃗ , 𝑥⃗,𝐼

𝜙 𝐼 , 𝑑⃗𝜙

𝐼

𝐶𝐼𝑃𝐼 𝐼∈

where 𝐶𝐼𝑃𝐼 𝐼∏ ∈ 𝑃 𝐼(8), 𝑑⃗and the weights 𝑤

𝜆
𝜆

(9)

are defined in equation (4.1). Equation(9) shows that the aggregate exact import price index is the product of the aggregate
conventional import price index, CIPI(I), and the aggregated lambda ratios which is referred
as an “aggregate bias” of the import price in Broda and Weinstein (2006).
The aggregate import bias, or simply the bias measure, is thus an indicator of an upwardbias of the aggregate conventional import price index compared to the aggregate exact importprice index. The ratio between aggregate exact price index including variety and the aggregate
conventional price is as follows.

𝐵𝑖𝑎𝑠

∏ 𝐼
𝐶𝐼𝑃𝐼 𝐼

∈

𝜆
𝜆

(10)

Using a simple Krugman (1980) structure of the economy, the inverse of the bias canbe weighted by the import expenditure share to get the gains from variety:

13

1
𝐵𝑖𝑎𝑠

𝐺𝐹𝑉

𝜆
𝜆

1
∈

(11)

1

is the import expenditure share in t. 4

where 𝑤

4. Estimation Strategy
Equation (9) implies that in order to compute the exact import price index we have toestimate the elasticity of substitution between varieties of each good. Therefore, in this section,
we briefly review the estimator developed by Feenstra (1994) and improved by Broda andWeinstein (2006). After the review, using examples we explain the importance of theelasticities of substitution.
The estimation procedure allows for random changes in the taste parameters forimported varieties and is robust to measurement errors produced by using unit values. Given
the utility function (1), the import demand equation for a specific variety using expenditure
shares is as follows:∆ ln 𝑠where 𝜑∆ ln 𝑑

𝜎

1 ln

𝜑

𝜎

1 ∆ ln 𝑝𝜀(12)

is a random effect since 𝑑 is random and 𝜀. The export supply equation is specified by:∆ ln 𝑝𝜓𝜔1𝜔

∆ ln 𝑠𝛿(13)

4
The import expenditure share 𝑤 is calculated as the share of imports in GDP in t. This is the separation
point of our work from Broda and Weinstein (2006). To estimate the overall welfare gain, they used theideal import share for their whole sample period, however they do not provide an estimation annually. In
contrast to that, we estimate the welfare gain for each year in our sample period and as an overall gain, we
simply take the summation. Refer to section 2.5.3 for details.

14

Where 𝜓

𝜔

∆

∑∈

, 𝐸

𝑝

𝑥

and 𝜔

0 is the good specific∆inverse supply elasticity5 (assumed to be constant across countries) and 𝛿
error term that captures any random changes in a technology factor 𝑣

is an

.

To identify the elasticity of substitution we can assume that the error terms between the
demand and supply curve (𝜀,𝛿) are uncorrelated after controlling for good and time

specific effects. This means, demand and supply errors at the variety level are assumed to be
uncorrelated, once good-time specific effects are controlled for. To take advantage of thisassumption, we first eliminate the random terms 𝜑and 𝜓from equations (12) and (13) bytaking differences relative to a reference country k:∆ ln 𝑠𝜎𝜔∆ ln 𝑝where ∆ 𝑥

∆𝑥

∆𝑥

,𝜀

1 ∆ ln 𝑝

1
𝜀

𝜔
𝜀

𝜀

∆ ln 𝑠

𝛿

and 𝛿

𝛿

(14)

(15)

𝛿

. Next, we multiply(14) and (15) and use the assumption of the independent error terms, i.e. 𝐸 𝜀

𝛿

0. As

a result, we obtain the following:∆ ln 𝑝𝜃 ∆ ln 𝑠𝜃 ∆ ln 𝑝

and 𝑢∆ ln 𝑠

𝜀

𝛿

𝑢

(16)

where 𝜃, 𝜃

correlation between 𝑢

and the explanatory variables. To make the error term 𝑢. However, there is a𝜔
0 is a special case of the export supply equation (13), where it is horizontal and there is no simultaneitybias, which is used for most of the empirical studies with gravity model to estimate the elasticity of substitution.
However, stating 𝜔
0, this study allows the export supply equation of variety c to vary with the amount ofexports.
515

independent of the explanatory variables, the average of all variables over t are taken anddenoted by upper bar:∆ ln 𝑝𝜃 ∆ ln 𝑠𝜃 ∆ ln 𝑝∆ ln 𝑠𝑢(17)

Using weighted least squares estimation, the estimates of 𝜃 and 𝜃 can be now consistent.
For each good 𝑔, the following objective function is used to obtain Hansen’s (1982)
estimator:𝛽

where 𝐺 ∗ 𝛽𝜎1 and 𝜔arg min 𝐺 ∗ 𝛽∈

𝑊𝐺 ∗ 𝛽(18)

is the sample analog of 𝐺 𝛽 , B is the set of economically feasible 𝛽 such that
1 , and 𝑊 is a positive definite weighting matrix. The optimal weights

depend on the time span and import quantities (Broda and Weinstein, 2006). We estimate 𝜃and 𝜃 and subsequently solve for 𝜎 . If the estimated 𝜎 is not economically reasonable, we
use a grid search over the space defined by B. In this case, we follow Broda and Weinstein(2006) to compute the minimized GMM objective function over 𝜎 ∈ [1.05, 131.5] at intervals
which are 5 percent apart.6
Why Elasticities are Important?
An elasticity of substitution is a responsiveness (of the buyers) of a good to the pricechanges in its substitutes. Basically, it shows what happens to the relative demand whenrelative price changes between two goods. It is measured as the ratio of proportionate change
in the relative demand for two goods to the proportionate change in their relative prices. In
order to obtain estimates, we make several simplifying assumptions. Similarly, in order to value

6

For a more detailed explanation refer to the working paper version Broda and Weinstein (2004).

16

varieties, we assume that we have only one or at most two elasticities of substitution, an
assumption often made when using a utility function. This will implicitly assume the following(Broda and Weinstein, 2006). First, elasticities of substitution among varieties of different
goods are the same. However, the same amount of increase in price of a variety of two different
goods may be valued differently by consumers. For example, presumably consumers care more
about varieties of computers than crude oil. So, in reality, all increases in imports do not givethe same gains. Second, elasticities of substitution across goods equals that across varieties ofa given good. However, it is likely that we care more about the different varieties of vegetables
available than about the varieties of potatoes. Third, the largest problem arises from assumingthat all varieties enter into the utility function with a common elasticity. For example, let’s say
Saudi Arabian oil prices went up. Then what will happen to our imports of Mexican oil? What
will happen to our imports of automobiles? One should rise and the other should fall. The
reason is that Mexican oil is an almost perfect substitute of the Saudi Arabian oil and cars are
the complements. However, if we assume that the elasticities are equal, then it is very hard tointerpret the meaning of the elasticity and there will be no intuition to its magnitude.
5. Results
In this section we discuss the results of our estimation of Mongolian welfare gains froman increased import product variety from 1988 to 2015. The estimation has four steps. First,
following the estimation strategy in section 5, elasticities of substitution 𝜎 for each productare estimated. Second, we use equation (7) to calculate the lambda ratios 𝜆 for each imported
product category. Third, with 𝜎 and 𝜆 , we obtain an estimate of the exact price index for eachproduct after import variety change. Finally, using equation (9), we apply the log-change ideal
weights to the price movements of each good in order to estimate the impact of variety growthon the aggregate import price index. Then with the knowledge of each year’s aggregate import17

price index, using equation (11), we quantify the variety gains from trade with respect to GDP.
5.1 Elasticities of Substitution
We estimated equation (17) for each HS-6 product and obtained 1390 elasticities ofsubstitution (henceforth, the ‘sigmas’). Although it is impossible to report all sigmas, Table 2
presents the descriptive statistics of sigmas and Table 3 reports sigmas for the 20 products withthe largest import share. By examining these tables, we can obtain a sense of the degree ofsubstitutability among varieties. If sigma is high, say above 10 or 20, then this suggests thatthe potential for gains from variety, are small. When 𝜎 is high, since new and disappearing
products are close substitutes to existing varieties, they will only have a minor influence on theprice index and hence the gains from variety.7 On the other hand, if sigma is low, then thissuggests that goods are highly differentiated by country, meaning the potential for gains is high.
Table 2 Estimated Elasticities of Substitution
StatisticHS-6 level

Percentile 90

12.1

Percentile 50 (Median)

3.6

Percentile 10

1.8

Mean

8.4

No of HS products

1390

Median variety per product14

Note: Authors’ calculation. See text for explanation.

Table 2 shows that the average elasticity of substitution is 8.4. and median is7

If we look at equation (6) and (9), it is clear that if 𝜎 is high,is close to zero and the additional termis closer to unity. Hence the variety change has small influence on the price index, when 𝜎 is
high.

18

3.6. 8 Table 3 shows that products with the largest import share, save for one, have lower
elasticities of substitution, which implies larger gains from variety.
Table 3 Sigmas for the 20 Products with the Largest Import ShareHS-6
products
271000

2.39

Importshare (%)
22.95

870323

1.44

2.33

8429521.20

1.33870410

24.63

1.33

8703227.33

1.118704232.43

1.06

1101002.21

1.05

Motor vehicles for the transport of goods Dumpers designed for offhighway use
Other Vehicles, Spark-ignition Engine Of a cylinder capacity
exceeding 1,000 cc but not exceeding 1,500 cc
Motor vehicles for the transport of goods GVW exceeding 20 metric
tons
Wheat Flour, Meslin Flour

7308908.69

1.02

Other Structures and Parts of Structures, of Iron or Steel

2523295.04

1.01

Other Portland Cement2402202.90

0.94

Cigarettes (Containing Tobacco)

8431493.39

0.81

Parts of Derricks, Cranes, Graders, Levelers, Scrapers or Pile-drivers

1806905.06

0.788474902.26

0.753004902.07

0.73

Cocoa Preparations (In Containers, Packings, in Liquid, Powder,
Granular Form)
Parts of Machinery for Sorting, Crushing, Mixing, Molding or
Shaping
Other Medicaments (Put up in Packings for Retail Sale)

721420

17.22

0.72

6104625.78

0.70

630221

3.71

0.66

Concrete reinforcing bars and rods, Hot-rolled, Hot-drawn, Hotextruded
Women's or Girls' Trousers, Breeches, of Cotton, Knitted or
Crocheted
Bed Linen, Printed, of Cotton

732611

4.11

0.59

Grinding Balls and Similar Forged or Stamped Articles for Mills

2713203.26

0.58

Petroleum Bitumen

1704903.12

0.55

Other Sugar Confectionery, Not Containing Cocoa

Sigma

Descriptions
Petroleum Oils, Oils Obtained from Bituminous Minerals,
Preparations Thereof
Other Vehicles, Spark-ignition Engine Of a cylinder capacity
exceeding 1,500 cc but not exceeding 3,000 cc
Machinery With a 360degrees Revolving Superstructure

Source: Authors’ calculation.

8

As a reference results of Broda and Weinstein (2006) are as follows, mean is 17.3 in HS9, 7.5 in SITC-5
and median is 3.7 in HS9, 2.8 in SITC-5 in period 1972-1988 in US.

19

5.2 Change in Varieties
The second step is to calculate the changes in variety over time (i.e. the lambda ratio).
The calculation of lambdas requires the existence of common varieties in the beginning and at
the end of the period.9 This is one of the major obstacles we face when implementing thetechnique. As a result, there are fewer lambda ratios than product groups or sigmas. Somelambda ratios cannot be defined at the HS-6 level since there is no common variety. We thenfollow Broda and Weinstein (2006) and define the lambda ratio at the HS-4 level.
Table 4 shows the summary statistics for the lambda ratios. The median lambda ratio
is 0.96, expressing that the typical imported product category in Mongolia experienced apositive variety growth of about 4 percent10. Using the lambda ratios as a measure of variety
growth is more sophisticated than just counting new and disappearing varieties. Due to thelarge number of new varieties with small market shares, just counting the new varieties can bemisleading. This underscores the importance of carefully measuring variety growth when
making price and welfare calculations. The measure also accounts for the importance ofdifferent varieties to the consumer budget decision by using expenditure shares as weights. The
lower the lambdas the greater the varieties, and the more we spend on new varieties.

9

The reason why we need common varieties is that we cannot value the creation and destruction of a variety
without knowing something about how this affects the consumption of other varieties (Broda and Weinstein,2006).
10
Calculated as 1/0.96=4.2%.

20

Table 4 Descriptive Statistics of Lambda Ratios
StatisticHS-6 level

Percentile 5

0.14

Percentile 50 (Median)

0.96

Percentile 95

4.78

Note: In here, due to the existence of outliers
reaching high absolute values, the median ispreferred to the mean.

5.3 Welfare Gain
Using the estimated elasticities of substitution and the lambda ratios, now we are readyto calculate the variety change effects on price. Following equation (9) by aggregating thelambda ratios gives the estimates of the impact of variety growth on the aggregate exact importprice index. Table 5 reports the results of this exercise.
In column (4) of Table 5, the ratio of the aggregate exact price index including variety
and the aggregate conventional price index is reported as the bias measure as in equation (10).
It is worth explaining the intuition behind this bias. If this fraction is lower than one, it meansthat the changing set of imported varieties has lowered the import price index. In that case, theconsumers benefit from lower unit costs of imports. Thus, these lower costs are the source of
the welfare gains. On the other hand, if the bias is larger than one, this means that the importprice index is increased by the changing variety set. Thus, the disappearing varieties are morevaluable to the consumers than the new varieties and it results in welfare loss. Column (4)shows that in most years, the bias is lower than one, meaning the variety change resulted inlower import price index. On average, the bias measure is 0.978 which means that ignoring
new and disappearing product varieties in the conventional price index had led to an upward21

bias of 2.25 percent.11 This is the same thing as saying that import price inflation is overstatedby 2.25 percent per year.
It is now time to calculate the welfare effect of the fall in the Mongolian exact importprice. It should be noted that the welfare gain from this price fall is based on the functional
forms assuming the Dixit-Stiglitz structure and cannot be general. Although our estimate of
the impact of imported varieties on import prices is correct for any domestic production
structure (Broda and Weinstein, 2006), it is not possible to translate this into a welfare gain
without making explicit assumptions about the structure of domestic production. Following
Broda and Weinstein (2006), our choice is to assume the same structure of the Mongolian
economy as in Krugman (1980). There are two reasons for this. First, since Krugman’s modelis the dominant model of varieties, to understand the potential welfare gains, it provides a usefulbenchmark. Second reason is the lack of the necessary data and model of the economy’s inputoutput linkages to estimate variants of the monopolistic competition model with more complex
interactions between imported and domestic varieties.
Column (5) of Table 5 presents the gains from variety for every year between 1988 and2015. The results show that in yearly basis, the welfare gain due to the increase in imported
product varieties in Mongolia, accounted for average 0.8 percent of GDP. This means that a
representative Mongolian consumer would be willing to give up 0.8 percent of her income toaccess the new import varieties every year. The welfare gains for the whole sample period from1988 to 2015 is approximately 22 percent of the GDP and it is a remarkable result considering
the moderate gains the most studies show.

11

Calculated as

1

100.

22

Considering the relatively high results of the welfare gain, we consider the following
two reasons among many, to be important. First, as presented in section 3, the Mongolian
import share of GDP is extremely high. In Table 5, Column (3) shows the import shares from1988 to 2015. The import share rose significantly after 1996 and the average was 36 percent
during the period. This is rather high compared to other studies. For instance, Broda andWeinstein (2006) found the ideal import share of the U.S.to be 6.7 percent for 1972-1988 and10.3 percent for 1990-2001, respectively and Chen and Ma (2012) found the log-change ideal
weight of China’s import in GDP to be 11.5 percent during 1997-2008. Since we used the shareof imports in GDP as a weight 𝑤

in equation (11), and the Mongolian import share of GDP

is relatively high, the variety gain is consequently high.12 Second and the main reason is that
not only the growth in number of varieties was drastic, but also the growth in number of
products was significant. Column (1) and (2) of Table 5 present the average number of varieties
and number of HS-6 products, respectively. We can see that during the period, the number ofvarieties rose 6 times, from one to six, and on the other hand, the number of products rose 7
times, from 226 to 1610. This means that the numerator of the lambda ratios, 𝜆 , which
captures the impact of newly available varieties is low. Since 𝜆is the ratio of expenditures

on varieties available in both periods (i.e., 𝑐 ∈ 𝐼) relative to the entire set ofvarieties available in period t (i.e., 𝑐 ∈ 𝐼

𝐼 ∩𝐼, evolving of the new variety decreases 𝜆 . Hence,the exact price index is relatively low and the welfare gain is relatively high.

12

Recall the results mentioned in section 2 (Mohler and Seitz, 2012) which found the gains from variety for
Estonia to be 2.7%, followed by Slovakia (2.3%) and Bulgaria (1.57%). These transitional economies pale incomparison to Mongolia’s experience.

23

Table 5 Import Price Bias and the Gains from Variety

Year

1988
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
2007
2008
2009
2010
2011
2012
2013
2014
2015
Total (1988-2015)
Average per-annum

Averagenumber ofvarieties
(1)
1.1
1.2
1.3
1.2
1.4
1.6
2.1
2.5
2.9
2.9
3.0
2.8
3.3
3.5
3.5
4.1
4.3
4.4
4.6
4.9
5.1
4.9
5.7
6.6
7.1
7.7
7.4
6.2

Number of
HS-6
products
(2)
226
275
342
485
783
791
1114
1216
1408
1382
1398
1410
1521
1512
1542
1579
1592
1573
1601
1587
1599
1601
1608
1611
1613
1614
1616
1610

3.8

1293

Import
share

Bias

(3)
0.01
0.01
0.01
0.03
0.17
0.19
0.15
0.18
0.37
0.45
0.43
0.38
0.44
0.46
0.49
0.50
0.51
0.47
0.43
0.49
0.54
0.53
0.48
0.61
0.57
0.50
0.43
0.33

(4)
1.000
0.992
0.993
1.017
0.911
0.888
1.041
0.903
0.811
0.998
1.011
0.973
0.978
0.942
0.959
0.966
0.991
1.009
1.036
0.957
0.983
0.993
0.993
0.981
1.049
0.937
1.027
1.058

0.36

0.978

Gains from
Variety
(%)
(5)
0.00%
0.01%
0.01%
-0.06%
1.56%
2.32%-0.60%
1.84%
8.14%
0.07%
-0.46%
1.06%
1.01%
2.79%
2.10%
1.75%
0.45%
-0.40%-1.53%
2.17%
0.95%
0.36%
0.32%
1.18%
-2.68%
3.27%-1.15%-1.84%
22.63%
0.81%

Note: Authors’ calculation based on six-digit disaggregated data from UN Comtrade. See text for
detailed explanation.

24

6. Conclusion
There is a considerable amount of literature attempting to quantify the welfare gain of
growing import variety. Thus, the importance of importing new varieties has been longestablished. Moreover, the literature confirms that gains from trade varieties are in generalmuch higher in developing countries than in developed countries. Mongolia is a small country
that opened up in 1990s and has been in transition since. Compared to its size, the economy
imports a great deal, spending on average 36 percent of the total expenditure in a year from1988 to 2015. The economy has been gaining greatly from international trade. However, nocomprehensive study exists on how much Mongolia gained from import variety growth.
We use highly disaggregated import data from 1988 to 2015 to estimate the elasticities
of substitution for 1390 imported goods. These elasticities allow us to construct acomprehensive measure of the welfare gain using the seminal works by Feenstra (1994) and
Broda and Weinstein (2006). The welfare gain due to growth in import varieties over the entire
period amounts to 22.6% of GDP (or 0.8% annually). The welfare impact of import variety
growth is remarkable are is much larger that studies of other countries.
The evidence from this chapter suggests that, especially for small and transitioning
economies, the creation and extension of trade linkages can be an important source of increased
welfare, a fact often neglected in the discussion about the positive effects of globalization andeconomic integration.
References
Armington, P. (1969) "A Theory of Demand for Products Distinguished by Place ofProduction" International Monetary Fund Staff Papers XVI, 159-78.
Broda, C. and D. E. Weinstein (2004) “Globalization and the Gains from Variety” NBER
Working Paper 10314.
25

Broda, C. and D. E. Weinstein (2006) “Globalization and the Gains from Variety” Quarterly
Journal of Economics 121, 541–85.
Chen, B and H. Ma (2012) “Import Variety and Welfare Gain in China” Review of International
Economics 20, 807-20.
Diewert, W. E. (1976) “Exact and Superlative Index Numbers” Journal of Econometrics 4,
115–45.
Dixit, A. K. and J. E. Stiglitz (1977) "Monopolistic Competition and Optimum Product
Diversity" American Economic Review 67, 297–308.
Eaton, J. and S. Kortum (2002) “Technology, Geography, and Trade” Econometrica 70, 174179.
Feenstra, R. C. (1994) “New Product Varieties and the Measurement of International Prices”
American Economic Review 84, 157-77.
Hansen, L. P. (1982) “Large Sample Properties of Generalized Method of Moments Estimators”
Econometrica 50, 1029–54.
Helpman, E. (1981) “International Trade in the Presence of Product Differentiation, Economics
of Scale and Monopolistic Competition: A Chamberlin-Heckscher-Ohlin Approach”
Journal of International Economics 11, 305-40.
Helpman, E. and P. Krugman (1985) Market Structure and Foreign Trade: Increasing Returns,
Imperfect Competition and the International Economy. Cambridge, Massachusetts: MIT
Press.
Klenow, P. J. and A. Rodriguez-Clare. (1997) “Quantifying Variety Gains from Trade
Liberalization” Unpublished manuscript, University of Chicago, Berkeley.
Krugman, P. (1979) “Increasing Returns, Monopolistic Competition and International Trade”
Journal of International Economics 10, 469-79.

26

Krugman, P. (1980) “Scale Economies, Product Differentiation, and the Pattern of Trade”
American Economic Review 70, 950-59.
Krugman, P. (1981) “Intra-industry Specialization and the Gains from Trade” Journal of
Political Economy 89, 959-73.
Minondo, A. and F. Requena (2012) “Welfare Gains from Imported Varieties in Spain, 1988–
2006” Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie) Working Paper
WP-EC2010-12.
Mohler, L. (2009) “Globalization and the Gains from Variety: Size and Openness of Countries
and the Extensive Margin” University Library of Munich MPRA Paper.
Mohler, L and M. Seitz (2012) “The Gains from Variety in the European Union” Review ofWorld Economics, 148 (3) 475-500.
Sato, K. (1976) “The Ideal Log-Change Index Number” Review of Economics and Statistics
58, 223–28.
Stock, J. H., and M. W. Watson (2011) Introduction to Econometrics, Boston: Addison-Wesley.
Vartia, Y. O. (1976) “Ideal Log-Change Index Numbers” Scandinavian Journal of Economics
3, 121–26.
Web page:
Columbia University
http://www.columbia.edu/~dew35/TradeElasticities/TradeElasticities.html

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